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is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Hou%2C+B&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Hou%2C+B&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Hou%2C+B&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.09960">arXiv:2411.09960</a> <span> [<a href="https://arxiv.org/pdf/2411.09960">pdf</a>, <a href="https://arxiv.org/format/2411.09960">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> Stable Similarity Comparison of Persistent Homology Groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=He%2C+J">Jiaxing He</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Wu%2C+T">Tieru Wu</a>, <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.09960v1-abstract-short" style="display: inline;"> Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by persistent homology groups of topological spaces, and we provide that our pseudometric $d_{S}^{(2)}$ is a similarity invariant. Thereby, we establish a connection… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.09960v1-abstract-full').style.display = 'inline'; document.getElementById('2411.09960v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.09960v1-abstract-full" style="display: none;"> Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by persistent homology groups of topological spaces, and we provide that our pseudometric $d_{S}^{(2)}$ is a similarity invariant. Thereby, we establish a connection between Operator Theory and Topological Data Analysis. We give the calculation formula of the pseudometric $d_{S}^{(2)}$ $(d_{S}^{(1)})$ by arranging all eigenvalues of matrices determined by barcodes in descending order to get the infimum over all matchings. Since conformal linear transformation is one representative type of similarity transformations, we construct comparative experiments on both synthetic datasets and waves from an online platform to demonstrate that our pseudometric $d_{S}^{(2)}$ $(d_{S}^{(1)})$ is stable under conformal linear transformations, whereas the bottleneck and Wasserstein distances are not. In particular, our pseudometric on waves is only related to the waveform but is independent on the frequency and amplitude. Furthermore, the computation time for $d_{S}^{(2)}$ $(d_{S}^{(1)})$ is significantly less than the computation time for bottleneck distance and is comparable to the computation time for accelerated Wasserstein distance between barcodes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.09960v1-abstract-full').style.display = 'none'; document.getElementById('2411.09960v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 7 figures, 6 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 55N31; 68T09; Secondary 15A18; 47B15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.14484">arXiv:2405.14484</a> <span> [<a href="https://arxiv.org/pdf/2405.14484">pdf</a>, <a href="https://arxiv.org/ps/2405.14484">ps</a>, <a href="https://arxiv.org/format/2405.14484">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Novel semi-explicit symplectic schemes for nonseparable stochastic Hamiltonian systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hong%2C+J">Jialin Hong</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Baohui Hou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+L">Liying Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.14484v1-abstract-short" style="display: inline;"> In this manuscript, we propose efficient stochastic semi-explicit symplectic schemes tailored for nonseparable stochastic Hamiltonian systems (SHSs). These semi-explicit symplectic schemes are constructed by introducing augmented Hamiltonians and using symmetric projection. In the case of the artificial restraint in augmented Hamiltonians being zero, the proposed schemes also preserve quadratic in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.14484v1-abstract-full').style.display = 'inline'; document.getElementById('2405.14484v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.14484v1-abstract-full" style="display: none;"> In this manuscript, we propose efficient stochastic semi-explicit symplectic schemes tailored for nonseparable stochastic Hamiltonian systems (SHSs). These semi-explicit symplectic schemes are constructed by introducing augmented Hamiltonians and using symmetric projection. In the case of the artificial restraint in augmented Hamiltonians being zero, the proposed schemes also preserve quadratic invariants, making them suitable for developing semi-explicit charge-preserved multi-symplectic schemes for stochastic cubic Schr枚dinger equations with multiplicative noise. Through numerical experiments that validate theoretical results, we demonstrate that the proposed stochastic semi-explicit symplectic scheme, which features a straightforward Newton iteration solver, outperforms the traditional stochastic midpoint scheme in terms of effectiveness and accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.14484v1-abstract-full').style.display = 'none'; document.getElementById('2405.14484v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.04332">arXiv:2401.04332</a> <span> [<a href="https://arxiv.org/pdf/2401.04332">pdf</a>, <a href="https://arxiv.org/format/2401.04332">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> Flexible filtrations for multiparameter persistent homology detect digital images </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=He%2C+J">Jiaxing He</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Wu%2C+T">Tieru Wu</a>, <a href="/search/math?searchtype=author&query=Xin%2C+Y">Yue Xin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.04332v2-abstract-short" style="display: inline;"> Two important problems in the field of Topological Data Analysis are defining practical multifiltrations on objects and showing ability of TDA to detect the geometry. Motivated by the problems, we constuct three multifiltrations named multi-GENEO, multi-DGENEO and mix-GENEO, and prove the stability of both the interleaving distance and multiparameter persistence landscape of multi-GENEO with respe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.04332v2-abstract-full').style.display = 'inline'; document.getElementById('2401.04332v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.04332v2-abstract-full" style="display: none;"> Two important problems in the field of Topological Data Analysis are defining practical multifiltrations on objects and showing ability of TDA to detect the geometry. Motivated by the problems, we constuct three multifiltrations named multi-GENEO, multi-DGENEO and mix-GENEO, and prove the stability of both the interleaving distance and multiparameter persistence landscape of multi-GENEO with respect to the pseudometric of the subspace of bounded functions. We also give the estimations of upper bound for multi-DGENEO and mix-GENEO. Finally, we provide experiment results on MNIST dataset to demonstrate our bifiltrations have ability to detect geometric and topological differences of digital images. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.04332v2-abstract-full').style.display = 'none'; document.getElementById('2401.04332v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.04913">arXiv:2309.04913</a> <span> [<a href="https://arxiv.org/pdf/2309.04913">pdf</a>, <a href="https://arxiv.org/ps/2309.04913">ps</a>, <a href="https://arxiv.org/format/2309.04913">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Extending structures for perm algebras and perm bialgebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.04913v1-abstract-short" style="display: inline;"> We investigate the theory of extending structures by the unified product for perm algebras, and the factorization problem as well as the classifying complements problem in the setting of perm algebras. For a special extending structure, non-abelian extension, we study the inducibility of a pair of automorphisms associated to a non-abelian extension of perm algebras, and give the fundamental sequen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.04913v1-abstract-full').style.display = 'inline'; document.getElementById('2309.04913v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.04913v1-abstract-full" style="display: none;"> We investigate the theory of extending structures by the unified product for perm algebras, and the factorization problem as well as the classifying complements problem in the setting of perm algebras. For a special extending structure, non-abelian extension, we study the inducibility of a pair of automorphisms associated to a non-abelian extension of perm algebras, and give the fundamental sequence of Wells in the context of perm algebras. For a special extending structure, bicrossed product, we introduce the concept of perm bialgebras, equivalently characterized by Manin triples of perm algebras and certain matched pairs of perm algebras. We introduce and study coboundary perm bialgebras, and our study leads to the ''$\mathcal{S}$-equation" in perm algebras, which is an analogue of the classical Yang-Baxter equation. A symmetric solution of $\mathcal{S}$-equation gives a perm bialgebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.04913v1-abstract-full').style.display = 'none'; document.getElementById('2309.04913v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Comments are welcome. arXiv admin note: text overlap with arXiv:1511.08571 by other authors</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.12052">arXiv:2306.12052</a> <span> [<a href="https://arxiv.org/pdf/2306.12052">pdf</a>, <a href="https://arxiv.org/ps/2306.12052">ps</a>, <a href="https://arxiv.org/format/2306.12052">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</span> </div> </div> <p class="title is-5 mathjax"> Some invariants of $U(1,1;\mathbb{H})$ and diagonalization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Yao%2C+C">Cailing Yao</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Feng%2C+X">Xiaoqi Feng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.12052v1-abstract-short" style="display: inline;"> Denote by $\mathbb{H}$ the set of all quaternions. We are interested in the group $U(1,1;\mathbb{H})$, which is a subgroup of $2\times 2$ quaternionic matrix group and is sometimes called $Sp(1,1)$. As well known, $U(1,1;\mathbb{H})$ corresponds to the quaternionic M枚bius transformations on the unit ball in $\mathbb{H}$. In this article, some similar invariants on $U(1,1;\mathbb{H})$ are discussed… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.12052v1-abstract-full').style.display = 'inline'; document.getElementById('2306.12052v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.12052v1-abstract-full" style="display: none;"> Denote by $\mathbb{H}$ the set of all quaternions. We are interested in the group $U(1,1;\mathbb{H})$, which is a subgroup of $2\times 2$ quaternionic matrix group and is sometimes called $Sp(1,1)$. As well known, $U(1,1;\mathbb{H})$ corresponds to the quaternionic M枚bius transformations on the unit ball in $\mathbb{H}$. In this article, some similar invariants on $U(1,1;\mathbb{H})$ are discussed. Our main result shows that each matrix $T\in U(1,1;\mathbb{H})$, which corresponds to an elliptic quaternionic M枚bius transformation $g_T(z)$, could be $U(1,1;\mathbb{H})$-similar to a diagonal matrix. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.12052v1-abstract-full').style.display = 'none'; document.getElementById('2306.12052v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 15A20; 15B33; 30G35 (Primary); 15A18; 16R30 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.10261">arXiv:2306.10261</a> <span> [<a href="https://arxiv.org/pdf/2306.10261">pdf</a>, <a href="https://arxiv.org/ps/2306.10261">ps</a>, <a href="https://arxiv.org/format/2306.10261">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Xin%2C+Y">Yue Xin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.10261v1-abstract-short" style="display: inline;"> Let $H^{\infty}$ be the Banach algebra of bounded analytic functions on the unit open disc $\mathbb{D}$ equipped with the supremum norm. As well known, inner functions play an important role of in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define $Q_{inn}$ and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.10261v1-abstract-full').style.display = 'inline'; document.getElementById('2306.10261v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.10261v1-abstract-full" style="display: none;"> Let $H^{\infty}$ be the Banach algebra of bounded analytic functions on the unit open disc $\mathbb{D}$ equipped with the supremum norm. As well known, inner functions play an important role of in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define $Q_{inn}$ and $Q_{out}$ the maps from $H^{\infty}$ to $\mathfrak{I}$ the set of inner functions and $\mathfrak{F}$ the set of outer functions, respectively. In this paper, we study the $H^{2}$-norm continuity and $H^{\infty}$-norm discontinuity of $Q_{inn}$ and $Q_{out}$ on some subsets of $H^{\infty}$. On the other hand, the Beurling theorem connects invariant subspaces of the multiplication operator $M_z$ and inner functions. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of $Q_{inn}$ and $Q_{out}$ on $\textrm{Hol}(\overline{\mathbb{D}})$, the set of all analytic functions in the closed unit disk, are also considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.10261v1-abstract-full').style.display = 'none'; document.getElementById('2306.10261v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 30J05; 30J10; Secondary 15A60; 15B05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.05910">arXiv:2305.05910</a> <span>  </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Novel structure-preserving schemes for stochastic Klein--Gordon--Schr枚dinger equations with additive noise </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hong%2C+J">Jialin Hong</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Baohui Hou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+L">Liying Sun</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+X">Xiaojing Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.05910v2-abstract-short" style="display: inline;"> Stochastic Klein--Gordon--Schr枚dinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution la… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.05910v2-abstract-full').style.display = 'inline'; document.getElementById('2305.05910v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.05910v2-abstract-full" style="display: none;"> Stochastic Klein--Gordon--Schr枚dinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fully-discrete scheme for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.05910v2-abstract-full').style.display = 'none'; document.getElementById('2305.05910v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This is a duplicate submission and has been withdrawn. Please see arXiv:2305.05117</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.05117">arXiv:2305.05117</a> <span> [<a href="https://arxiv.org/pdf/2305.05117">pdf</a>, <a href="https://arxiv.org/ps/2305.05117">ps</a>, <a href="https://arxiv.org/format/2305.05117">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Novel structure-preserving schemes for stochastic Klein--Gordon--Schr枚dinger equations with additive noise </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hong%2C+J">Jialin Hong</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Baohui Hou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+L">Liying Sun</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+X">Xiaojing Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.05117v2-abstract-short" style="display: inline;"> Stochastic Klein--Gordon--Schr枚dinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution la… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.05117v2-abstract-full').style.display = 'inline'; document.getElementById('2305.05117v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.05117v2-abstract-full" style="display: none;"> Stochastic Klein--Gordon--Schr枚dinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fully-discrete scheme for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.05117v2-abstract-full').style.display = 'none'; document.getElementById('2305.05117v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.12663">arXiv:2304.12663</a> <span> [<a href="https://arxiv.org/pdf/2304.12663">pdf</a>, <a href="https://arxiv.org/ps/2304.12663">ps</a>, <a href="https://arxiv.org/format/2304.12663">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> A new version of the Gelfand-Hille theorem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fang%2C+J">Junsheng Fang</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Jiang%2C+C">Chunlan Jiang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.12663v1-abstract-short" style="display: inline;"> Let $\mathcal{X}$ be a complex Banach space and $A\in\mathcal{L}(\mathcal{X})$ with $蟽(A)=\{1\}$. We prove that for a vector $x\in \mathcal{X}$, if $\|(A^{k}+A^{-k})x\|=O(k^N)$ as $k \rightarrow +\infty$ for some positive integer $N$, then $(A-\mathbf{I})^{N+1}x=0$ when $N$ is even and $(A-\mathbf{I})^{N+2}x=0$ when $N$ is odd. This could be seemed as a new version of the Gelfand-Hille theorem. As… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.12663v1-abstract-full').style.display = 'inline'; document.getElementById('2304.12663v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.12663v1-abstract-full" style="display: none;"> Let $\mathcal{X}$ be a complex Banach space and $A\in\mathcal{L}(\mathcal{X})$ with $蟽(A)=\{1\}$. We prove that for a vector $x\in \mathcal{X}$, if $\|(A^{k}+A^{-k})x\|=O(k^N)$ as $k \rightarrow +\infty$ for some positive integer $N$, then $(A-\mathbf{I})^{N+1}x=0$ when $N$ is even and $(A-\mathbf{I})^{N+2}x=0$ when $N$ is odd. This could be seemed as a new version of the Gelfand-Hille theorem. As a corollary, we also obtain that for a quasinilpotent operator $Q\in\mathcal{L}(\mathcal{X})$ and a vector $x\in\mathcal{X}$, if $\|\cos(kQ)x\|=O(k^N)$ as $k \rightarrow +\infty$ for some positive integer $N$, then $Q^{N+1}x=0$ when $N$ is even and $Q^{N+2}x=0$ when $N$ is odd. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.12663v1-abstract-full').style.display = 'none'; document.getElementById('2304.12663v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 47B10; 47B15; 47B40; Secondary 47A10; 47D03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.12807">arXiv:2303.12807</a> <span> [<a href="https://arxiv.org/pdf/2303.12807">pdf</a>, <a href="https://arxiv.org/format/2303.12807">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Neural and Evolutionary Computing">cs.NE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Granular-ball Optimization Algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Xia%2C+S">Shuyin Xia</a>, <a href="/search/math?searchtype=author&query=Chen%2C+J">Jiancu Chen</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bin Hou</a>, <a href="/search/math?searchtype=author&query=Wang%2C+G">Guoyin Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.12807v1-abstract-short" style="display: inline;"> The existing intelligent optimization algorithms are designed based on the finest granularity, i.e., a point. This leads to weak global search ability and inefficiency. To address this problem, we proposed a novel multi-granularity optimization algorithm, namely granular-ball optimization algorithm (GBO), by introducing granular-ball computing. GBO uses many granular-balls to cover the solution sp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.12807v1-abstract-full').style.display = 'inline'; document.getElementById('2303.12807v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.12807v1-abstract-full" style="display: none;"> The existing intelligent optimization algorithms are designed based on the finest granularity, i.e., a point. This leads to weak global search ability and inefficiency. To address this problem, we proposed a novel multi-granularity optimization algorithm, namely granular-ball optimization algorithm (GBO), by introducing granular-ball computing. GBO uses many granular-balls to cover the solution space. Quite a lot of small and fine-grained granular-balls are used to depict the important parts, and a little number of large and coarse-grained granular-balls are used to depict the inessential parts. Fine multi-granularity data description ability results in a higher global search capability and faster convergence speed. In comparison with the most popular and state-of-the-art algorithms, the experiments on twenty benchmark functions demonstrate its better performance. The faster speed, higher approximation ability of optimal solution, no hyper-parameters, and simpler design of GBO make it an all-around replacement of most of the existing popular intelligent optimization algorithms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.12807v1-abstract-full').style.display = 'none'; document.getElementById('2303.12807v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 22 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.08233">arXiv:2302.08233</a> <span> [<a href="https://arxiv.org/pdf/2302.08233">pdf</a>, <a href="https://arxiv.org/ps/2302.08233">ps</a>, <a href="https://arxiv.org/format/2302.08233">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Composition operators on weighted Hardy spaces of polynomial growth </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Jiang%2C+C">Chunlan Jiang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.08233v1-abstract-short" style="display: inline;"> In the present paper, we study the composition operators acting on weighted Hardy spaces of polynomial growth, which are concerned with norms, spectra and (semi-)Fredholmness. Firstly, we estimate the norms of the composition operators with symbols of disk automorphisms. Secondly, we discuss the spectra of the composition operators with symbols of disk automorphisms. In particular, it is proven of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.08233v1-abstract-full').style.display = 'inline'; document.getElementById('2302.08233v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.08233v1-abstract-full" style="display: none;"> In the present paper, we study the composition operators acting on weighted Hardy spaces of polynomial growth, which are concerned with norms, spectra and (semi-)Fredholmness. Firstly, we estimate the norms of the composition operators with symbols of disk automorphisms. Secondly, we discuss the spectra of the composition operators with symbols of disk automorphisms. In particular, it is proven of that the spectrum of a composition operator with symbol of any parabolic disk automorphism is always the unit circle. Thirdly, we consider the Fredholmness of the composition operator $C_{\varphi}$ with symbol $\varphi$ which is an analytic self-map on the closed unit disk. We prove that $C_{\varphi}$ acting on a weighted Hardy space of polynomial growth has closed range (semi-Fredholmness) if and only if $\varphi$ is a finite Blaschke product. Furthermore, it is obtained that $C_{\varphi}$ is Fredholm if and only if $\varphi$ is a disk automorphism. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.08233v1-abstract-full').style.display = 'none'; document.getElementById('2302.08233v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B33; 47A30; 47A25; 47A53 (Primary); 47B38; 46E20 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.00830">arXiv:2302.00830</a> <span> [<a href="https://arxiv.org/pdf/2302.00830">pdf</a>, <a href="https://arxiv.org/ps/2302.00830">ps</a>, <a href="https://arxiv.org/format/2302.00830">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> A note on connectedness of Blaschke products </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Xin%2C+Y">Yue Xin</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.00830v1-abstract-short" style="display: inline;"> Consider the space $\mathcal{F}$ of all inner functions on the unit open disk under the uniform topology, which is a metric topology induced by the $H^{\infty}$-norm. In the present paper, a class of Blaschke products, denoted by $\mathcal{H}_{SC}$, is introduced. We prove that for each $B\in\mathcal{H}_{SC}$, $B$ and $zB$ belong to the same path-connected component of $\mathcal{F}$. It plays an i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.00830v1-abstract-full').style.display = 'inline'; document.getElementById('2302.00830v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.00830v1-abstract-full" style="display: none;"> Consider the space $\mathcal{F}$ of all inner functions on the unit open disk under the uniform topology, which is a metric topology induced by the $H^{\infty}$-norm. In the present paper, a class of Blaschke products, denoted by $\mathcal{H}_{SC}$, is introduced. We prove that for each $B\in\mathcal{H}_{SC}$, $B$ and $zB$ belong to the same path-connected component of $\mathcal{F}$. It plays an important role of a method to select a fine subsequence of zeros. As a byproduct, we obtain that each Blaschke product in $\mathcal{H}_{SC}$ has an interpolating and one-component factor. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.00830v1-abstract-full').style.display = 'none'; document.getElementById('2302.00830v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 30J05; 30J10 (Primary); 54C35 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2211.10842">arXiv:2211.10842</a> <span> [<a href="https://arxiv.org/pdf/2211.10842">pdf</a>, <a href="https://arxiv.org/ps/2211.10842">ps</a>, <a href="https://arxiv.org/format/2211.10842">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="K-Theory and Homology">math.KT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> </div> </div> <p class="title is-5 mathjax"> Crossed modules, non-abelian extensions of associative conformal algebras and Wells exact sequences </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Zhao%2C+J">Jun Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2211.10842v1-abstract-short" style="display: inline;"> In this paper, we introduce the notions of crossed module of associative conformal algebras, 2-term strongly homotopy associative conformal algebras, and discuss the relationship between them and the 3-th Hochschild cohomology of associative conformal algebras. We classify the non-abelian extensions by introducing the non-abelian cohomology. We show that non-abelian extensions of an associative co… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.10842v1-abstract-full').style.display = 'inline'; document.getElementById('2211.10842v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2211.10842v1-abstract-full" style="display: none;"> In this paper, we introduce the notions of crossed module of associative conformal algebras, 2-term strongly homotopy associative conformal algebras, and discuss the relationship between them and the 3-th Hochschild cohomology of associative conformal algebras. We classify the non-abelian extensions by introducing the non-abelian cohomology. We show that non-abelian extensions of an associative conformal algebra can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra, and prove that the Deligne groupoid of this differential graded Lie algebra corresponds one to one with the non-abelian cohomology. Based on this classification, we study the inducibility of a pair of automorphisms about a non-abelian extension of associative conformal algebras, and give the fundamental sequence of Wells in the context of associative conformal algebras. Finally, we consider the extensibility of a pair of derivations about an abelian extension of associative conformal algebras, and give an exact sequence of Wells type. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2211.10842v1-abstract-full').style.display = 'none'; document.getElementById('2211.10842v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages, comments are welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.00466">arXiv:2210.00466</a> <span> [<a href="https://arxiv.org/pdf/2210.00466">pdf</a>, <a href="https://arxiv.org/ps/2210.00466">ps</a>, <a href="https://arxiv.org/format/2210.00466">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> </div> </div> <p class="title is-5 mathjax"> The cohomology of left-symmetric conformal algebra and its applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhao%2C+J">Jun Zhao</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.00466v2-abstract-short" style="display: inline;"> In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces of the left-symmetric conformal algebra and its sub-adjacent Lie conformal algebra. As applications of the cohomology theory, we study linear deformations, form… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.00466v2-abstract-full').style.display = 'inline'; document.getElementById('2210.00466v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.00466v2-abstract-full" style="display: none;"> In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces of the left-symmetric conformal algebra and its sub-adjacent Lie conformal algebra. As applications of the cohomology theory, we study linear deformations, formal $1$-parameter deformations, $T^*$-extensions of a left-symmetric conformal algebra respectively and obtain some properties. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.00466v2-abstract-full').style.display = 'none'; document.getElementById('2210.00466v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.08715">arXiv:2209.08715</a> <span> [<a href="https://arxiv.org/pdf/2209.08715">pdf</a>, <a href="https://arxiv.org/ps/2209.08715">ps</a>, <a href="https://arxiv.org/format/2209.08715">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="K-Theory and Homology">math.KT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Gerstenhaber algebra of an associative conformal algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Shen%2C+Z">Zhongxi Shen</a>, <a href="/search/math?searchtype=author&query=Zhao%2C+J">Jun Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.08715v2-abstract-short" style="display: inline;"> We define a cup product on the Hochschild cohomology of an associative conformal algebra $A$, and show the cup product is graded commutative. We define a graded Lie bracket with the degree $-1$ on the Hochschild cohomology $\HH^{\ast}(A)$ of an associative conformal algebra $A$, and show that the Lie bracket together with the cup product is a Gerstenhaber algebra on the Hochschild cohomology of an… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08715v2-abstract-full').style.display = 'inline'; document.getElementById('2209.08715v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.08715v2-abstract-full" style="display: none;"> We define a cup product on the Hochschild cohomology of an associative conformal algebra $A$, and show the cup product is graded commutative. We define a graded Lie bracket with the degree $-1$ on the Hochschild cohomology $\HH^{\ast}(A)$ of an associative conformal algebra $A$, and show that the Lie bracket together with the cup product is a Gerstenhaber algebra on the Hochschild cohomology of an associative conformal algebra. Moreover, we consider the Hochschild cohomology of split extension conformal algebra $A\hat{\oplus}M$ of $A$ with a conformal bimodule $M$, and show that there exist an algebra homomorphism from $\HH^{\ast}(A\hat{\oplus}M)$ to $\HH^{\ast}(A)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.08715v2-abstract-full').style.display = 'none'; document.getElementById('2209.08715v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.03852">arXiv:2209.03852</a> <span> [<a href="https://arxiv.org/pdf/2209.03852">pdf</a>, <a href="https://arxiv.org/ps/2209.03852">ps</a>, <a href="https://arxiv.org/format/2209.03852">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Operator Algebras">math.OA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Analytic automorphism group and similar representation of analytic functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Jiang%2C+C">Chunlan Jiang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.03852v4-abstract-short" style="display: inline;"> In geometry group theory, one of the milestones is M. Gromov's polynomial growth theorem: Finitely generated groups have polynomial growth if and only if they are virtually nilpotent. Inspired by M. Gromov's work, we introduce the growth types of weighted Hardy spaces. In this paper, we focus on the weighted Hardy spaces of polynomial growth, which cover the classical Hardy space, weighted Bergman… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.03852v4-abstract-full').style.display = 'inline'; document.getElementById('2209.03852v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.03852v4-abstract-full" style="display: none;"> In geometry group theory, one of the milestones is M. Gromov's polynomial growth theorem: Finitely generated groups have polynomial growth if and only if they are virtually nilpotent. Inspired by M. Gromov's work, we introduce the growth types of weighted Hardy spaces. In this paper, we focus on the weighted Hardy spaces of polynomial growth, which cover the classical Hardy space, weighted Bergman spaces, weighted Dirichlet spaces and much broader. Our main results are as follows. $(1)$ We obtain the boundedness of the composition operators with symbols of analytic automorphisms of unit open disk acting on weighted Hardy spaces of polynomial growth, which implies the multiplication operator $M_z$ is similar to $M_{\varphi}$ for any analytic automorphism $\varphi$ on the unit open disk. Moreover, we obtain the boundedness of composition operators induced by analytic functions on the unit closed disk on weighted Hardy spaces of polynomial growth. $(2)$ For any Blaschke product $B$ of order $m$, $M_B$ is similar to $\bigoplus_{1}^m M_z$, which is an affirmative answer to a generalized version of a question proposed by R. Douglas in 2007. $(3)$ We also give counterexamples to show that the composition operators with symbols of analytic automorphisms of unit open disk acting on a weighted Hardy space of intermediate growth could be unbounded, which indicates the necessity of the setting of polynomial growth condition. Then, the collection of weighted Hardy spaces of polynomial growth is almost the largest class such that Douglas's question has an affirmative answer. $(4)$ Finally, we give the Jordan representation theorem and similarity classification for the analytic functions on the unit closed disk as multiplication operators on a weighted Hardy space of polynomial growth. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.03852v4-abstract-full').style.display = 'none'; document.getElementById('2209.03852v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 46J40; 46J25; 46E20; Secondary 47B35; 47B33; 30J10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.02829">arXiv:2207.02829</a> <span> [<a href="https://arxiv.org/pdf/2207.02829">pdf</a>, <a href="https://arxiv.org/format/2207.02829">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Data Structures and Algorithms">cs.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Tarzanagh%2C+D+A">Davoud Ataee Tarzanagh</a>, <a href="/search/math?searchtype=author&query=Nazari%2C+P">Parvin Nazari</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bojian Hou</a>, <a href="/search/math?searchtype=author&query=Shen%2C+L">Li Shen</a>, <a href="/search/math?searchtype=author&query=Balzano%2C+L">Laura Balzano</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.02829v7-abstract-short" style="display: inline;"> This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting. Specifically, we provide new notions of \textit{bilevel regret}, develop an online alternating time-averaged gradient method that is capable of leveraging smoothn… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.02829v7-abstract-full').style.display = 'inline'; document.getElementById('2207.02829v7-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.02829v7-abstract-full" style="display: none;"> This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting. Specifically, we provide new notions of \textit{bilevel regret}, develop an online alternating time-averaged gradient method that is capable of leveraging smoothness, and give regret bounds in terms of the path-length of the inner and outer minimizer sequences. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.02829v7-abstract-full').style.display = 'none'; document.getElementById('2207.02829v7-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published at AISTATS 2024. V7: minor edits to the statement of Lemma 18 and Assumption A</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.03588">arXiv:2205.03588</a> <span> [<a href="https://arxiv.org/pdf/2205.03588">pdf</a>, <a href="https://arxiv.org/ps/2205.03588">ps</a>, <a href="https://arxiv.org/format/2205.03588">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> Topologically Conjugate Classifications of the Translation Actions on Compact Connected Lie Groups ${\rm SU}(2) \times T^n$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Pan%2C+X">Xiaotian Pan</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.03588v1-abstract-short" style="display: inline;"> In this article, we focus on the left (translation) actions on noncommutative compact connected Lie groups ${\rm SU}(2) \times T^n$. We define the rotation vectors of the left actions induced by the elements in the maximal tori of ${\rm SU}(2) \times T^n$, and utilize rotation vectors to give the complete topologically conjugate classifications of left actions. Algebraic conjugacy and smooth conju… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.03588v1-abstract-full').style.display = 'inline'; document.getElementById('2205.03588v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.03588v1-abstract-full" style="display: none;"> In this article, we focus on the left (translation) actions on noncommutative compact connected Lie groups ${\rm SU}(2) \times T^n$. We define the rotation vectors of the left actions induced by the elements in the maximal tori of ${\rm SU}(2) \times T^n$, and utilize rotation vectors to give the complete topologically conjugate classifications of left actions. Algebraic conjugacy and smooth conjugacy are also considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.03588v1-abstract-full').style.display = 'none'; document.getElementById('2205.03588v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">42 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 37C15; 37E45; 57N65; Secondary 22C05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.02306">arXiv:2203.02306</a> <span> [<a href="https://arxiv.org/pdf/2203.02306">pdf</a>, <a href="https://arxiv.org/ps/2203.02306">ps</a>, <a href="https://arxiv.org/format/2203.02306">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="K-Theory and Homology">math.KT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Gao%2C+J">Jin Gao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.02306v1-abstract-short" style="display: inline;"> In this paper, we study the Batalin-Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras $A_{q}$ of type $\widetilde{\mathbf{A}}_{1}$. We first calculate the dimensions of Hochschild homology groups and Hochschild cohomology groups of $A_{q}$. Based on these computations, we determine the Hochschild cohomology ring of $A_{q}$, and give the Batalin-Vilkovisky operator and th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.02306v1-abstract-full').style.display = 'inline'; document.getElementById('2203.02306v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.02306v1-abstract-full" style="display: none;"> In this paper, we study the Batalin-Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras $A_{q}$ of type $\widetilde{\mathbf{A}}_{1}$. We first calculate the dimensions of Hochschild homology groups and Hochschild cohomology groups of $A_{q}$. Based on these computations, we determine the Hochschild cohomology ring of $A_{q}$, and give the Batalin-Vilkovisky operator and the Gerstenhaber bracket on Hochschild cohomology ring of $A_{q}$ explicitly. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.02306v1-abstract-full').style.display = 'none'; document.getElementById('2203.02306v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.08191">arXiv:2201.08191</a> <span> [<a href="https://arxiv.org/pdf/2201.08191">pdf</a>, <a href="https://arxiv.org/ps/2201.08191">ps</a>, <a href="https://arxiv.org/format/2201.08191">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.jcp.2022.111453">10.1016/j.jcp.2022.111453 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hong%2C+J">Jialin Hong</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Baohui Hou</a>, <a href="/search/math?searchtype=author&query=Li%2C+Q">Qiang Li</a>, <a href="/search/math?searchtype=author&query=Sun%2C+L">Liying Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.08191v1-abstract-short" style="display: inline;"> Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide numerical approximations with better numerical stability, and are of vital significance for obtaining correct nu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.08191v1-abstract-full').style.display = 'inline'; document.getElementById('2201.08191v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.08191v1-abstract-full" style="display: none;"> Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide numerical approximations with better numerical stability, and are of vital significance for obtaining correct numerical results. In this paper, we propose three novel multi-symplectic methods for stochastic Hamiltonian partial differential equations based on the local radial basis function collocation method, the splitting technique, and the partitioned Runge-Kutta method. Concrete numerical methods are presented for nonlinear stochastic wave equations, stochastic nonlinear Schr枚dinger equations, stochastic Korteweg-de Vries equations and stochastic Maxwell equations. We take stochastic wave equations as examples to perform numerical experiments, which indicate the validity of the proposed methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.08191v1-abstract-full').style.display = 'none'; document.getElementById('2201.08191v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.01313">arXiv:2107.01313</a> <span> [<a href="https://arxiv.org/pdf/2107.01313">pdf</a>, <a href="https://arxiv.org/ps/2107.01313">ps</a>, <a href="https://arxiv.org/format/2107.01313">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> Scaled Homology and Topological Entropy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Igusa%2C+K">Kiyoshi Igusa</a>, <a href="/search/math?searchtype=author&query=Liu%2C+Z">Zihao Liu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.01313v3-abstract-short" style="display: inline;"> In this paper, we build up a scaled homology theory, $lc$-homology, for metric spaces such that every metric space can be visually regarded as "locally contractible" with this newly-built homology. We check that $lc$-homology satisfies all Eilenberg-Steenrod axioms except exactness axiom whereas its corresponding $lc$-cohomology satisfies all axioms for cohomology. This homology can relax the smoo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.01313v3-abstract-full').style.display = 'inline'; document.getElementById('2107.01313v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.01313v3-abstract-full" style="display: none;"> In this paper, we build up a scaled homology theory, $lc$-homology, for metric spaces such that every metric space can be visually regarded as "locally contractible" with this newly-built homology. We check that $lc$-homology satisfies all Eilenberg-Steenrod axioms except exactness axiom whereas its corresponding $lc$-cohomology satisfies all axioms for cohomology. This homology can relax the smooth manifold restrictions on the compact metric space such that the entropy conjecture will hold for the first $lc$-homology group. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.01313v3-abstract-full').style.display = 'none'; document.getElementById('2107.01313v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3: minor edits according to the referee's report. To appear in PAMS. 16 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2105.14720">arXiv:2105.14720</a> <span> [<a href="https://arxiv.org/pdf/2105.14720">pdf</a>, <a href="https://arxiv.org/ps/2105.14720">ps</a>, <a href="https://arxiv.org/format/2105.14720">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.jcp.2021.110829">10.1016/j.jcp.2021.110829 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hong%2C+J">Jialin Hong</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Baohui Hou</a>, <a href="/search/math?searchtype=author&query=Sun%2C+L">Liying Sun</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2105.14720v2-abstract-short" style="display: inline;"> In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the interior penalty discontinuous Galerkin finite element method to discretize space variable and present two semi-discrete schemes, respectively. Then we make use of t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.14720v2-abstract-full').style.display = 'inline'; document.getElementById('2105.14720v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2105.14720v2-abstract-full" style="display: none;"> In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the interior penalty discontinuous Galerkin finite element method to discretize space variable and present two semi-discrete schemes, respectively. Then we make use of the discrete gradient method and the Pad茅 approximation to propose efficient fully-discrete schemes. These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law. In particular, we also prove that the proposed fully-discrete schemes exactly inherit the averaged energy evolution law almost surely if the considered model is driven by additive noise. Numerical experiments are given to confirm theoretical findings. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.14720v2-abstract-full').style.display = 'none'; document.getElementById('2105.14720v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.07451">arXiv:1908.07451</a> <span> [<a href="https://arxiv.org/pdf/1908.07451">pdf</a>, <a href="https://arxiv.org/ps/1908.07451">ps</a>, <a href="https://arxiv.org/format/1908.07451">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="K-Theory and Homology">math.KT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> On the relative $L$-theory and the relative signature of PL manifolds with boundary </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Liu%2C+H">Hongzhi Liu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.07451v5-abstract-short" style="display: inline;"> In this paper, we give a new description of the group structure of the relative structure group of PL manifolds with boundary, and obtain a surgery exact sequence in the category of groups. Then we focus on the relative $L$-group of PL manifolds with boundary, and map it to the $K$-theory additively. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.07451v5-abstract-full" style="display: none;"> In this paper, we give a new description of the group structure of the relative structure group of PL manifolds with boundary, and obtain a surgery exact sequence in the category of groups. Then we focus on the relative $L$-group of PL manifolds with boundary, and map it to the $K$-theory additively. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.07451v5-abstract-full').style.display = 'none'; document.getElementById('1908.07451v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 19J25; 19K99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1806.07866">arXiv:1806.07866</a> <span> [<a href="https://arxiv.org/pdf/1806.07866">pdf</a>, <a href="https://arxiv.org/ps/1806.07866">ps</a>, <a href="https://arxiv.org/format/1806.07866">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Angles and Schauder basis in Hilbert spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a>, <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+X">Xinzhi Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1806.07866v2-abstract-short" style="display: inline;"> Let $\mathcal{H}$ be a complex separable Hilbert space. We prove that if $\{f_{n}\}_{n=1}^{\infty}$ is a Schauder basis of the Hilbert space $\mathcal{H}$, then the angles between any two vectors in this basis must have a positive lower bound. Furthermore, we investigate that $\{z^{蟽^{-1}(n)}\}_{n=1}^{\infty}$ can never be a Schauder basis of $L^{2}(\mathbb{T},谓)$, where $\mathbb{T}$ is the unit c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.07866v2-abstract-full').style.display = 'inline'; document.getElementById('1806.07866v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1806.07866v2-abstract-full" style="display: none;"> Let $\mathcal{H}$ be a complex separable Hilbert space. We prove that if $\{f_{n}\}_{n=1}^{\infty}$ is a Schauder basis of the Hilbert space $\mathcal{H}$, then the angles between any two vectors in this basis must have a positive lower bound. Furthermore, we investigate that $\{z^{蟽^{-1}(n)}\}_{n=1}^{\infty}$ can never be a Schauder basis of $L^{2}(\mathbb{T},谓)$, where $\mathbb{T}$ is the unit circle, $谓$ is a finite positive discrete measure, and $蟽: \mathbb{Z} \rightarrow \mathbb{N}$ is an arbitrary surjective and injective map. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.07866v2-abstract-full').style.display = 'none'; document.getElementById('1806.07866v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 46B15; Secondary 46B20; 47B37 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1803.08430">arXiv:1803.08430</a> <span> [<a href="https://arxiv.org/pdf/1803.08430">pdf</a>, <a href="https://arxiv.org/ps/1803.08430">ps</a>, <a href="https://arxiv.org/format/1803.08430">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Pan%2C+X">Xiaotian Pan</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1803.08430v2-abstract-short" style="display: inline;"> In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of ${\rm SU}(2),\,{\rm U}(2),\,{\rm SO}(3),\,{\rm SO}(3) \times S^1$ and ${\rm Spin}^{\mathbb{C}}(3)$. We define the rotation vectors (numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vec… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08430v2-abstract-full').style.display = 'inline'; document.getElementById('1803.08430v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1803.08430v2-abstract-full" style="display: none;"> In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of ${\rm SU}(2),\,{\rm U}(2),\,{\rm SO}(3),\,{\rm SO}(3) \times S^1$ and ${\rm Spin}^{\mathbb{C}}(3)$. We define the rotation vectors (numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors (numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism $f:L(p, -1)\times S^1\rightarrow L(p, -1)\times S^1$, the induced isomorphism $(蟺\circ f\circ i)_*$ maps each element in the fundamental group of $L(p, -1)$ to itself or its inverse, where $i:L(p,-1)\rightarrow L(p, -1)\times S^1$ is the natural inclusion and $蟺:L(p, -1)\times S^1\rightarrow L(p, -1)$ is the projection. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1803.08430v2-abstract-full').style.display = 'none'; document.getElementById('1803.08430v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 March, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">50 pages. Accepted for publication in SCIENCE CHINA Mathematics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37C15; 55S37; 22C05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1801.06971">arXiv:1801.06971</a> <span> [<a href="https://arxiv.org/pdf/1801.06971">pdf</a>, <a href="https://arxiv.org/ps/1801.06971">ps</a>, <a href="https://arxiv.org/format/1801.06971">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> </div> </div> <p class="title is-5 mathjax"> New code upper bounds for the folded n-cube </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+L">Lihang Hou</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Gao%2C+S">Suogang Gao</a>, <a href="/search/math?searchtype=author&query=Yu%2C+W">Wei-Hsuan Yu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1801.06971v1-abstract-short" style="display: inline;"> Let $螕$ denote a distance-regular graph. The maximum size of codewords with minimum distance at least $d$ is denoted by $A(螕,d)$. Let $\square_n$ denote the folded $n$-cube $H(n,2)$. We give an upper bound on $A(\square_n,d)$ based on block-diagonalizing the Terwilliger algebra of $\square_n$ and on semidefinite programming.The technique of this paper is an extension of the approach taken by A. Sc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1801.06971v1-abstract-full').style.display = 'inline'; document.getElementById('1801.06971v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1801.06971v1-abstract-full" style="display: none;"> Let $螕$ denote a distance-regular graph. The maximum size of codewords with minimum distance at least $d$ is denoted by $A(螕,d)$. Let $\square_n$ denote the folded $n$-cube $H(n,2)$. We give an upper bound on $A(\square_n,d)$ based on block-diagonalizing the Terwilliger algebra of $\square_n$ and on semidefinite programming.The technique of this paper is an extension of the approach taken by A. Schrijver \cite{s} on the study of $A(H(n,2),d)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1801.06971v1-abstract-full').style.display = 'none'; document.getElementById('1801.06971v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2018. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.02580">arXiv:1712.02580</a> <span> [<a href="https://arxiv.org/pdf/1712.02580">pdf</a>, <a href="https://arxiv.org/format/1712.02580">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Li-Yorke chaos translation set for linear operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Luo%2C+L">Lvlin Luo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.02580v1-abstract-short" style="display: inline;"> In order to study Li-Yorke chaos by the scalar perturbation for a given bounded linear operator $T$ on Banach spaces $X$, we introduce the Li-Yorke chaos translation set of $T$, which is defined by $S_{LY}(T)=\{位\in\mathbb{C};位+T \text{ is Li-Yorke chaotic}\}$. In this paper, some operator classes are considered, such as normal operator, compact operator, shift and so on. In particular, we show th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.02580v1-abstract-full').style.display = 'inline'; document.getElementById('1712.02580v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.02580v1-abstract-full" style="display: none;"> In order to study Li-Yorke chaos by the scalar perturbation for a given bounded linear operator $T$ on Banach spaces $X$, we introduce the Li-Yorke chaos translation set of $T$, which is defined by $S_{LY}(T)=\{位\in\mathbb{C};位+T \text{ is Li-Yorke chaotic}\}$. In this paper, some operator classes are considered, such as normal operator, compact operator, shift and so on. In particular, we show that the Li-Yorke chaos translation set of Kalisch operator on Hilbert space $\mathcal{L}^2[0,2蟺]$ is a simple point set $\{0\}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.02580v1-abstract-full').style.display = 'none'; document.getElementById('1712.02580v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages,1 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A16 (Primary); 37D45 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1605.07047">arXiv:1605.07047</a> <span> [<a href="https://arxiv.org/pdf/1605.07047">pdf</a>, <a href="https://arxiv.org/ps/1605.07047">ps</a>, <a href="https://arxiv.org/format/1605.07047">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Li-Yorke chaos for invertible mappings on compact metric spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Luo%2C+L">Lvlin Luo</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1605.07047v1-abstract-short" style="display: inline;"> In this paper, we construct a homeomorphism on the unit closed disk to show that an invertible mapping on a compact metric space is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1605.07047v1-abstract-full" style="display: none;"> In this paper, we construct a homeomorphism on the unit closed disk to show that an invertible mapping on a compact metric space is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.07047v1-abstract-full').style.display = 'none'; document.getElementById('1605.07047v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 37B99; 54H20; Secondary 37C15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.03294">arXiv:1601.03294</a> <span> [<a href="https://arxiv.org/pdf/1601.03294">pdf</a>, <a href="https://arxiv.org/ps/1601.03294">ps</a>, <a href="https://arxiv.org/format/1601.03294">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Entropy of a semigroup of maps from a set-valued view </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Wang%2C+X">Xu Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1601.03294v1-abstract-short" style="display: inline;"> In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bi艣. Some examples with positive or zero Hausdorff metric entropy are given. Moreover,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.03294v1-abstract-full').style.display = 'inline'; document.getElementById('1601.03294v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.03294v1-abstract-full" style="display: none;"> In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bi艣. Some examples with positive or zero Hausdorff metric entropy are given. Moreover, some notions of chaos are also well generalized for finitely generated semigroups from a set-valued view. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.03294v1-abstract-full').style.display = 'none'; document.getElementById('1601.03294v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 0 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37A35; 37B40; 54H20; 37C85 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.4232">arXiv:1204.4232</a> <span> [<a href="https://arxiv.org/pdf/1204.4232">pdf</a>, <a href="https://arxiv.org/ps/1204.4232">ps</a>, <a href="https://arxiv.org/format/1204.4232">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Schauder Bases and Operator Theory III: Schauder Spectrums </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a>, <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.4232v1-abstract-short" style="display: inline;"> In this paper, we study spectrums of Schauder operators. We show that we always can choose a Schauder operator in a given orbit such that the Schauder spectrum of it is empty. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.4232v1-abstract-full" style="display: none;"> In this paper, we study spectrums of Schauder operators. We show that we always can choose a Schauder operator in a given orbit such that the Schauder spectrum of it is empty. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.4232v1-abstract-full').style.display = 'none'; document.getElementById('1204.4232v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 47A10; 47A99; Secondary 40C05; 46A35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1203.3603">arXiv:1203.3603</a> <span> [<a href="https://arxiv.org/pdf/1203.3603">pdf</a>, <a href="https://arxiv.org/ps/1203.3603">ps</a>, <a href="https://arxiv.org/format/1203.3603">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Schauder Bases and Operator Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a>, <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1203.3603v1-abstract-short" style="display: inline;"> In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1203.3603v1-abstract-full" style="display: none;"> In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1203.3603v1-abstract-full').style.display = 'none'; document.getElementById('1203.3603v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 47B37; 47B99; Secondary 54H20; 37B99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.3951">arXiv:1102.3951</a> <span> [<a href="https://arxiv.org/pdf/1102.3951">pdf</a>, <a href="https://arxiv.org/ps/1102.3951">ps</a>, <a href="https://arxiv.org/format/1102.3951">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> </div> </div> <p class="title is-5 mathjax"> Generalized McKay Quivers, Root System and Kac-Moody Algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+S">Shilin Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1102.3951v1-abstract-short" style="display: inline;"> Let $Q$ be a finite quiver and $G\subseteq\Aut(\mathbbm{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and $螕$ is the generalized Mckay quiver and the valued graph corresponding to $(Q, G)$ respectively. In this paper we discuss the relationship between indecomposable $\hat{Q}$-representations and the root system of Kac-Moody algebra $\mathfrak{g}(螕)$. Moreover, we may lift $G$ to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.3951v1-abstract-full').style.display = 'inline'; document.getElementById('1102.3951v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.3951v1-abstract-full" style="display: none;"> Let $Q$ be a finite quiver and $G\subseteq\Aut(\mathbbm{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and $螕$ is the generalized Mckay quiver and the valued graph corresponding to $(Q, G)$ respectively. In this paper we discuss the relationship between indecomposable $\hat{Q}$-representations and the root system of Kac-Moody algebra $\mathfrak{g}(螕)$. Moreover, we may lift $G$ to $\bar{G}\subseteq\Aut(\mathfrak{g}(\hat{Q}))$ such that $\mathfrak{g}(螕)$ embeds into the fixed point algebra $\mathfrak{g}(\hat{Q})^{\bar{G}}$ and $\mathfrak{g}(\hat{Q})^{\bar{G}}$ as $\mathfrak{g}(螕)$-module is integrable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.3951v1-abstract-full').style.display = 'none'; document.getElementById('1102.3951v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">26 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 16G10; 16G20; 17B67 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1010.3386">arXiv:1010.3386</a> <span> [<a href="https://arxiv.org/pdf/1010.3386">pdf</a>, <a href="https://arxiv.org/ps/1010.3386">ps</a>, <a href="https://arxiv.org/format/1010.3386">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Limits of J-class operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1010.3386v1-abstract-short" style="display: inline;"> The purpose of the present work is to answer an open problem which is raised by G.Costakis and A.Manoussos in their paper "J-class operators and hypercyclicity " accepted by J. Operator Theory. More precisely, we give the spectral description of the closure of the set of J-class operators acting on a separable Hilbert space. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1010.3386v1-abstract-full" style="display: none;"> The purpose of the present work is to answer an open problem which is raised by G.Costakis and A.Manoussos in their paper "J-class operators and hypercyclicity " accepted by J. Operator Theory. More precisely, we give the spectral description of the closure of the set of J-class operators acting on a separable Hilbert space. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1010.3386v1-abstract-full').style.display = 'none'; document.getElementById('1010.3386v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 October, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 0 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A55 (Primary); 47A53; 47A16; 54H20 (Secondary); 37B99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1003.1797">arXiv:1003.1797</a> <span> [<a href="https://arxiv.org/pdf/1003.1797">pdf</a>, <a href="https://arxiv.org/ps/1003.1797">ps</a>, <a href="https://arxiv.org/format/1003.1797">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Skew group algebras of deformed preprojective algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+S">Shilin Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1003.1797v2-abstract-short" style="display: inline;"> Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite group, $k$ is an algebraic closed field whose characteristic does not divide the order of $G$. For any algebra $螞=kQ/{\mathcal {I}}$, $\mathcal {I}$ is an arbitrary ideal of path algebra $kQ$, we give all the indecomposable $螞G$-modules from indecomposable $螞$-modules when $G$ is abelian. In particular, we apply this result t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.1797v2-abstract-full').style.display = 'inline'; document.getElementById('1003.1797v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1003.1797v2-abstract-full" style="display: none;"> Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite group, $k$ is an algebraic closed field whose characteristic does not divide the order of $G$. For any algebra $螞=kQ/{\mathcal {I}}$, $\mathcal {I}$ is an arbitrary ideal of path algebra $kQ$, we give all the indecomposable $螞G$-modules from indecomposable $螞$-modules when $G$ is abelian. In particular, we apply this result to the deformed preprojective algebra $螤_{Q}^位$, and get a reflection functor for the module category of $螤_{Q}^位G$. Furthermore, we construct a new quiver $Q_{G}$ and prove that $螤_{Q}^位G$ is Morita equivalent to $螤_{Q_{G}}^畏$ for some $畏$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1003.1797v2-abstract-full').style.display = 'none'; document.getElementById('1003.1797v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 March, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 06B15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0905.4535">arXiv:0905.4535</a> <span> [<a href="https://arxiv.org/pdf/0905.4535">pdf</a>, <a href="https://arxiv.org/format/0905.4535">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Approximation of chaotic operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Shi%2C+L">Luoyi Shi</a>, <a href="/search/math?searchtype=author&query=Zhu%2C+S">Sen Zhu</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0905.4535v1-abstract-short" style="display: inline;"> As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we consider classes of operators with some kinds of chaotic properties in this article. First of all, the closures of the sets of all Li-Yorke chaotic operators o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0905.4535v1-abstract-full').style.display = 'inline'; document.getElementById('0905.4535v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0905.4535v1-abstract-full" style="display: none;"> As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we consider classes of operators with some kinds of chaotic properties in this article. First of all, the closures of the sets of all Li-Yorke chaotic operators or distributionally chaotic operators are discussed. We give a spectral description of them and prove that the two closures coincide with each other. Moreover, both the set of all Li-Yorke chaotic operators and the set of all distributionally chaotic operators have nonempty interiors which coincide with each other as well. The article also includes the containing relation between the closure of the set of all hypercyclic operators and the closure of the set of all distributionally chaotic operators. Finally, we get connectedness of the sets considered above. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0905.4535v1-abstract-full').style.display = 'none'; document.getElementById('0905.4535v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 May, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A55; 47A53; 54H20; 37B99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.4558">arXiv:0903.4558</a> <span> [<a href="https://arxiv.org/pdf/0903.4558">pdf</a>, <a href="https://arxiv.org/ps/0903.4558">ps</a>, <a href="https://arxiv.org/format/0903.4558">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Some dynamical properties for linear operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Tian%2C+G">Geng Tian</a>, <a href="/search/math?searchtype=author&query=Shi%2C+L">Luoyi Shi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0903.4558v1-abstract-short" style="display: inline;"> In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed that norm-unimodality is similar invariant and the spectra of norm-unimodal operator is referred to. As an application, in each nest algebra there exist distrib… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4558v1-abstract-full').style.display = 'inline'; document.getElementById('0903.4558v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.4558v1-abstract-full" style="display: none;"> In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed that norm-unimodality is similar invariant and the spectra of norm-unimodal operator is referred to. As an application, in each nest algebra there exist distributional chaotic operators. Moreover, normal operators and compact operators with regard to norm-unimodality and Li-Yorke chaos are also be considered. Specially, a small compact perturbation of the unit operator could be distributionally chaotic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4558v1-abstract-full').style.display = 'none'; document.getElementById('0903.4558v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B37; 47B99; 54H20; 37B99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.4555">arXiv:0903.4555</a> <span> [<a href="https://arxiv.org/pdf/0903.4555">pdf</a>, <a href="https://arxiv.org/ps/0903.4555">ps</a>, <a href="https://arxiv.org/format/0903.4555">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> $2B_{p}$ and $4B_{p}$ are topologically conjugate </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Liao%2C+G">Gongfu Liao</a>, <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0903.4555v1-abstract-short" style="display: inline;"> Let $位B_{p}$, where $位$ is a nonzero complex number, denote a constant-weighted backward shift operators on $l^{p}$ for $1\leq p<\infty$. In this article, we investigate, in topologically conjugacy, the complete classification for $位B_{p}$. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.4555v1-abstract-full" style="display: none;"> Let $位B_{p}$, where $位$ is a nonzero complex number, denote a constant-weighted backward shift operators on $l^{p}$ for $1\leq p<\infty$. In this article, we investigate, in topologically conjugacy, the complete classification for $位B_{p}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4555v1-abstract-full').style.display = 'none'; document.getElementById('0903.4555v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37C15; 47B37 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0903.4246">arXiv:0903.4246</a> <span> [<a href="https://arxiv.org/pdf/0903.4246">pdf</a>, <a href="https://arxiv.org/ps/0903.4246">ps</a>, <a href="https://arxiv.org/format/0903.4246">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Chaos for Cowen-Douglas operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Cui%2C+P">Puyu Cui</a>, <a href="/search/math?searchtype=author&query=Cao%2C+Y">Yang Cao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0903.4246v1-abstract-short" style="display: inline;"> In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0903.4246v1-abstract-full" style="display: none;"> In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0903.4246v1-abstract-full').style.display = 'none'; document.getElementById('0903.4246v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 March, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B37; 47B99; 54H20; 37B99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0902.0106">arXiv:0902.0106</a> <span> [<a href="https://arxiv.org/pdf/0902.0106">pdf</a>, <a href="https://arxiv.org/ps/0902.0106">ps</a>, <a href="https://arxiv.org/format/0902.0106">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Difference between Devaney chaos associated with two systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bingzhe Hou</a>, <a href="/search/math?searchtype=author&query=Ma%2C+X">Xianfeng Ma</a>, <a href="/search/math?searchtype=author&query=Liao%2C+G">Gongfu Liao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0902.0106v1-abstract-short" style="display: inline;"> We discuss the relation between Devaney chaos in the base system and Devaney chaos in its induced hyperspace system. We show that the latter need not imply the former. We also argue that this implication is not true even in the strengthened condition. Additionally we give an equivalent condition for the periodically density in the hyperspace system. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0902.0106v1-abstract-full" style="display: none;"> We discuss the relation between Devaney chaos in the base system and Devaney chaos in its induced hyperspace system. We show that the latter need not imply the former. We also argue that this implication is not true even in the strengthened condition. Additionally we give an equivalent condition for the periodically density in the hyperspace system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0902.0106v1-abstract-full').style.display = 'none'; document.getElementById('0902.0106v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 February, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37B10; 37D45; 54B20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0103128">arXiv:math/0103128</a> <span> [<a href="https://arxiv.org/pdf/math/0103128">pdf</a>, <a href="https://arxiv.org/ps/math/0103128">ps</a>, <a href="https://arxiv.org/format/math/0103128">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0253-6102/35/6/669">10.1088/0253-6102/35/6/669 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Free boson representation of $DY_{\hbar}(\hat{sl} (M+1|N+1)) $ at level one </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-yu Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W+-">W. -L. Yang</a>, <a href="/search/math?searchtype=author&query=Zhen%2C+Y">Y. Zhen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0103128v2-abstract-short" style="display: inline;"> We construct a realization of the central extension of super-Yangian double $DY_{\hbar}(\hat{sl}(M+1|N+1))$ at level-one in terms of free boson fields with a continuous parameter. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0103128v2-abstract-full" style="display: none;"> We construct a realization of the central extension of super-Yangian double $DY_{\hbar}(\hat{sl}(M+1|N+1))$ at level-one in terms of free boson fields with a continuous parameter. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0103128v2-abstract-full').style.display = 'none'; document.getElementById('math/0103128v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2001; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 March, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, latex, reference revised</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 17B37; 81R10; 81R50; 16W30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/nlin/0102025">arXiv:nlin/0102025</a> <span> [<a href="https://arxiv.org/pdf/nlin/0102025">pdf</a>, <a href="https://arxiv.org/ps/nlin/0102025">ps</a>, <a href="https://arxiv.org/format/nlin/0102025">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Condensed Matter">cond-mat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0305-4470/35/11/306">10.1088/0305-4470/35/11/306 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> q-deformed Supersymmetric t-J Model with a Boundary </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-Yu Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+Y">Yao-Zhong Zhang</a>, <a href="/search/math?searchtype=author&query=Zhen%2C+Y">Yi Zhen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="nlin/0102025v1-abstract-short" style="display: inline;"> The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. </span> <span class="abstract-full has-text-grey-dark mathjax" id="nlin/0102025v1-abstract-full" style="display: none;"> The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('nlin/0102025v1-abstract-full').style.display = 'none'; document.getElementById('nlin/0102025v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 February, 2001; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2001. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTex file 18 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. A35 (2002) 2593-2608 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0003041">arXiv:math/0003041</a> <span> [<a href="https://arxiv.org/pdf/math/0003041">pdf</a>, <a href="https://arxiv.org/ps/math/0003041">ps</a>, <a href="https://arxiv.org/format/math/0003041">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Quantum currents in the Coset Space SU(2)/U(1) </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ding%2C+X">Xiang-Mao Ding</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-Yu Hou</a>, <a href="/search/math?searchtype=author&query=Zhao%2C+L">Liu Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0003041v1-abstract-short" style="display: inline;"> We propose a rational quantum deformed nonlocal currents in the homogenous space $SU(2)_k/U(1)$, and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level $k=c$ is obtained. In the classical limit $\hbar \to 0$, the quantum nonlocal currents become $SU(2)_k$ parafermion, and the realization of Yangian double becomes the parafermion… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0003041v1-abstract-full').style.display = 'inline'; document.getElementById('math/0003041v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0003041v1-abstract-full" style="display: none;"> We propose a rational quantum deformed nonlocal currents in the homogenous space $SU(2)_k/U(1)$, and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level $k=c$ is obtained. In the classical limit $\hbar \to 0$, the quantum nonlocal currents become $SU(2)_k$ parafermion, and the realization of Yangian double becomes the parafermion realization of $SU(2)_k$ current algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0003041v1-abstract-full').style.display = 'none'; document.getElementById('math/0003041v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Latex, 9 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> AMSS-1999-020 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Commun.Theor.Phys. 37 (2002) 59-62 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9904018">arXiv:math/9904018</a> <span> [<a href="https://arxiv.org/pdf/math/9904018">pdf</a>, <a href="https://arxiv.org/ps/math/9904018">ps</a>, <a href="https://arxiv.org/format/math/9904018">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/S0550-3213(99)00348-X">10.1016/S0550-3213(99)00348-X <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-yu Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a>, <a href="/search/math?searchtype=author&query=Zhang%2C+Y">Yao-Zhong Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9904018v3-abstract-short" style="display: inline;"> We derive the exchange relations of the vertex operators of $U_q(A_2^{(2)})$ and show that these vertex operators give the bosonization of the Izergin-Korepin model. We give an integral expression of the correlation functions of the Izergin-Korepin model and derive the difference equations which they satisfy. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9904018v3-abstract-full" style="display: none;"> We derive the exchange relations of the vertex operators of $U_q(A_2^{(2)})$ and show that these vertex operators give the bosonization of the Izergin-Korepin model. We give an integral expression of the correlation functions of the Izergin-Korepin model and derive the difference equations which they satisfy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9904018v3-abstract-full').style.display = 'none'; document.getElementById('math/9904018v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 April, 1999; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 April, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 1999. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">RevTex 15 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B556(1999), 485-501. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9802104">arXiv:math/9802104</a> <span> [<a href="https://arxiv.org/pdf/math/9802104">pdf</a>, <a href="https://arxiv.org/ps/math/9802104">ps</a>, <a href="https://arxiv.org/format/math/9802104">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.533136">10.1063/1.533136 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-yu Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W">Wen-Li Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9802104v2-abstract-short" style="display: inline;"> From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars'). The corresponding r-matrix is shown to be the classical $Z_n$-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version---the $A_{n-1}$ Calogero-Moser model. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9802104v2-abstract-full" style="display: none;"> From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars'). The corresponding r-matrix is shown to be the classical $Z_n$-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version---the $A_{n-1}$ Calogero-Moser model. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9802104v2-abstract-full').style.display = 'none'; document.getElementById('math/9802104v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 September, 1999; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 February, 1998; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 1998. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Misprints are corrected; LaTex file 15 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Math.Phys. 41 (2000) 357-369 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9801062">arXiv:math/9801062</a> <span> [<a href="https://arxiv.org/pdf/math/9801062">pdf</a>, <a href="https://arxiv.org/ps/math/9801062">ps</a>, <a href="https://arxiv.org/format/math/9801062">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0305-4470/32/10/012">10.1088/0305-4470/32/10/012 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Infinite Hopf family of elliptic algebras and bosonization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-Yu Hou</a>, <a href="/search/math?searchtype=author&query=Zhao%2C+L">Liu Zhao</a>, <a href="/search/math?searchtype=author&query=Ding%2C+X">Xiang-Mao Ding</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9801062v4-abstract-short" style="display: inline;"> Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a struct… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9801062v4-abstract-full').style.display = 'inline'; document.getElementById('math/9801062v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9801062v4-abstract-full" style="display: none;"> Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9801062v4-abstract-full').style.display = 'none'; document.getElementById('math/9801062v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 April, 1998; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 January, 1998; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 1998. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX, 11 pages. This is the new and final version</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/q-alg/9711018">arXiv:q-alg/9711018</a> <span> [<a href="https://arxiv.org/pdf/q-alg/9711018">pdf</a>, <a href="https://arxiv.org/ps/q-alg/9711018">ps</a>, <a href="https://arxiv.org/format/q-alg/9711018">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.532533">10.1063/1.532533 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A one-dimensional many-body integrable model from $Z_n$ Belavin model with open boundary conditions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fan%2C+H">Heng Fan</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-Yu Hou</a>, <a href="/search/math?searchtype=author&query=Li%2C+G">Guang-Liang Li</a>, <a href="/search/math?searchtype=author&query=Shi%2C+K">Kang-Jie Shi</a>, <a href="/search/math?searchtype=author&query=Wang%2C+Y">Yan-Shen Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="q-alg/9711018v1-abstract-short" style="display: inline;"> We use factorized $L$ operator to construct an integrable model with open boundary conditions. By taking trigonometic limit($蟿\to \sqrt{-1}\infty$) and scaling limit($蠅\to 0$), we get a Hamiltonian of a classical integrable system. It shows that this integrable system is similar to those found by Calogero et al. </span> <span class="abstract-full has-text-grey-dark mathjax" id="q-alg/9711018v1-abstract-full" style="display: none;"> We use factorized $L$ operator to construct an integrable model with open boundary conditions. By taking trigonometic limit($蟿\to \sqrt{-1}\infty$) and scaling limit($蠅\to 0$), we get a Hamiltonian of a classical integrable system. It shows that this integrable system is similar to those found by Calogero et al. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('q-alg/9711018v1-abstract-full').style.display = 'none'; document.getElementById('q-alg/9711018v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Latex file, 17 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/q-alg/9711010">arXiv:q-alg/9711010</a> <span> [<a href="https://arxiv.org/pdf/q-alg/9711010">pdf</a>, <a href="https://arxiv.org/ps/q-alg/9711010">ps</a>, <a href="https://arxiv.org/format/q-alg/9711010">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> The nondynamical r-matrix structure for the elliptic $A_{n-1}$ Calogero-Moser model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-yu Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W">Wen-li Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="q-alg/9711010v1-abstract-short" style="display: inline;"> In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$ Calogero-Moser model with general $n(2\leq n$) from the classical dynamical twisting,in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic $Z_n$-symmetric r-matrix. </span> <span class="abstract-full has-text-grey-dark mathjax" id="q-alg/9711010v1-abstract-full" style="display: none;"> In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$ Calogero-Moser model with general $n(2\leq n$) from the classical dynamical twisting,in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic $Z_n$-symmetric r-matrix. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('q-alg/9711010v1-abstract-full').style.display = 'none'; document.getElementById('q-alg/9711010v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 November, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, Latex file 38k</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IMPNWU-971109 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/q-alg/9709024">arXiv:q-alg/9709024</a> <span> [<a href="https://arxiv.org/pdf/q-alg/9709024">pdf</a>, <a href="https://arxiv.org/ps/q-alg/9709024">ps</a>, <a href="https://arxiv.org/format/q-alg/9709024">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0305-4470/31/23/016">10.1088/0305-4470/31/23/016 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Dynamically twisted algebra $A_{q,p;\hat蟺}(\hat{gl_2})$ as current algebra generalizing screening currents of q-deformed Virasoro algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hou%2C+B+Y">B. Y. Hou</a>, <a href="/search/math?searchtype=author&query=Yang%2C+W+L">W. L. Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="q-alg/9709024v2-abstract-short" style="display: inline;"> In this paper, we propose an elliptic algebra $A_{q,p;\hat蟺}(\hat{gl_2})$ which is based on the relations $RLL=LLR^{*}$, where $R$ and $R^{*}$ are the dynamical R-maxtrices of $A^{(1)}_{1}$ type face model with the elliptic moduli shifted by the center of the algebra. From the Ding-Frenkel correspondence, we find that its corresponding (Drinfeld) current algebra at level one is the algebra of sc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('q-alg/9709024v2-abstract-full').style.display = 'inline'; document.getElementById('q-alg/9709024v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="q-alg/9709024v2-abstract-full" style="display: none;"> In this paper, we propose an elliptic algebra $A_{q,p;\hat蟺}(\hat{gl_2})$ which is based on the relations $RLL=LLR^{*}$, where $R$ and $R^{*}$ are the dynamical R-maxtrices of $A^{(1)}_{1}$ type face model with the elliptic moduli shifted by the center of the algebra. From the Ding-Frenkel correspondence, we find that its corresponding (Drinfeld) current algebra at level one is the algebra of screening currents for q-deformed Virasoro algebra.We realize the elliptic algebra at level one by Miki's construction from the bosonization for the type I and type II vertex operators.We also show that the algebra $A_{q,p;\hat蟺}(\hat{gl_2})$ is related with the algebra $A_{q,p}(\hat{gl_2})$ by a dynamically twisting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('q-alg/9709024v2-abstract-full').style.display = 'none'; document.getElementById('q-alg/9709024v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 1997; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 September, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, Latex file 66K</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> IMPNWU-970911 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-th/9709016">arXiv:hep-th/9709016</a> <span> [<a href="https://arxiv.org/pdf/hep-th/9709016">pdf</a>, <a href="https://arxiv.org/ps/hep-th/9709016">ps</a>, <a href="https://arxiv.org/format/hep-th/9709016">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.532288">10.1063/1.532288 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Free boson representation of DY_{\hbar}(gl_N)_k </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ding%2C+X+M">X. M. Ding</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B+Y">B. Y. Hou</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B+Y">B. Yuan Hou</a>, <a href="/search/math?searchtype=author&query=Zhao%2C+L">L. Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-th/9709016v1-abstract-short" style="display: inline;"> We construct a realization of the Yangian double DY_\hbar(gl_N) and DY_\hbar(sl_N) of an arbitrary level k in terms of free boson fields with a continuous parameter. In the \hbar \to 0 limit this realization becomes the Wakimoto realization of kac-Moody algebra gl_N and sl_N, respectively. The vertex operators and the screening currents are also constructed with the same spirits; the screening c… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-th/9709016v1-abstract-full').style.display = 'inline'; document.getElementById('hep-th/9709016v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-th/9709016v1-abstract-full" style="display: none;"> We construct a realization of the Yangian double DY_\hbar(gl_N) and DY_\hbar(sl_N) of an arbitrary level k in terms of free boson fields with a continuous parameter. In the \hbar \to 0 limit this realization becomes the Wakimoto realization of kac-Moody algebra gl_N and sl_N, respectively. The vertex operators and the screening currents are also constructed with the same spirits; the screening currents commute with DY_\hbar(sl_N) modulo total difference. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-th/9709016v1-abstract-full').style.display = 'none'; document.getElementById('hep-th/9709016v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 September, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19pages, Latex, no figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J.Math.Phys.39:2273-2289,1998 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/q-alg/9704018">arXiv:q-alg/9704018</a> <span> [<a href="https://arxiv.org/pdf/q-alg/9704018">pdf</a>, <a href="https://arxiv.org/ps/q-alg/9704018">ps</a>, <a href="https://arxiv.org/format/q-alg/9704018">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/0305-4470/30/21/032">10.1088/0305-4470/30/21/032 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhao%2C+L">Liu Zhao</a>, <a href="/search/math?searchtype=author&query=Hou%2C+B">Bo-Yu Hou</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="q-alg/9704018v2-abstract-short" style="display: inline;"> With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra. </span> <span class="abstract-full has-text-grey-dark mathjax" id="q-alg/9704018v2-abstract-full" style="display: none;"> With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('q-alg/9704018v2-abstract-full').style.display = 'none'; document.getElementById('q-alg/9704018v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 April, 1997; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 April, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">LaTeX file, 9 pages. Errors in Serre relation corrected. Two references to Awata,H. et al added</span> </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Hou%2C+B&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Hou%2C+B&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Hou%2C+B&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div 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