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CQ*-algebras</title> <meta name="description" content="Search results for: CQ*-algebras"> <meta name="keywords" content="CQ*-algebras"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler 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id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="CQ*-algebras"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 18</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: CQ*-algebras</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">18</span> Introducing Quantum-Weijsberg Algebras by Redefining Quantum-MV Algebras: Characterization, Properties, and Other Important Results</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lavinia%20Ciungu">Lavinia Ciungu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the last decades, developing algebras related to the logical foundations of quantum mechanics became a central topic of research. Generally known as quantum structures, these algebras serve as models for the formalism of quantum mechanics. In this work, we introduce the notion of quantum-Wajsberg algebras by redefining the quantum-MV algebras starting from involutive BE algebras. We give a characterization of quantum-Wajsberg algebras, investigate their properties, and show that, in general, quantum-Wajsberg algebras are not (commutative) quantum-B algebras. We also define the ∨-commutative quantum-Wajsberg algebras and study their properties. Furthermore, we prove that any Wajsberg algebra (bounded ∨-commutative BCK algebra) is a quantum-Wajsberg algebra, and we give a condition for a quantum-Wajsberg algebra to be a Wajsberg algebra. We prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. We establish the connection between quantum-Wajsberg algebras and quantum-MV algebras, proving that the quantum-Wajsberg algebras are term equivalent to quantum-MV algebras. We show that, in general, the quantum-Wajsberg algebras are not commutative quantum-B algebras and if a quantum-Wajsberg algebra is self-distributive, then the corresponding quantum-MV algebra is an MV algebra. Our study could be a starting point for the development of other implicative counterparts of certain existing algebraic quantum structures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=quantum-Wajsberg%20algebra" title="quantum-Wajsberg algebra">quantum-Wajsberg algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum-MV%20algebra" title=" quantum-MV algebra"> quantum-MV algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=MV%20algebra" title=" MV algebra"> MV algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=Wajsberg%20algebra" title=" Wajsberg algebra"> Wajsberg algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=BE%20algebra" title=" BE algebra"> BE algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum-B%20algebra" title=" quantum-B algebra"> quantum-B algebra</a> </p> <a href="https://publications.waset.org/abstracts/192449/introducing-quantum-weijsberg-algebras-by-redefining-quantum-mv-algebras-characterization-properties-and-other-important-results" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192449.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">15</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17</span> Inner Derivations of Low-Dimensional Diassociative Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Fiidow">M. A. Fiidow</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20M.%20Alenezi"> Ahmad M. Alenezi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we study the inner derivations of diassociative algebras in dimension two and three, an algorithmic approach is adopted for the computation of inner derivation, using some results from the derivation of finite dimensional diassociative algebras. Some basic properties of inner derivation of finite dimensional diassociative algebras are also provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diassociative%20algebras" title="diassociative algebras">diassociative algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=inner%20derivations" title=" inner derivations"> inner derivations</a>, <a href="https://publications.waset.org/abstracts/search?q=derivations" title=" derivations"> derivations</a>, <a href="https://publications.waset.org/abstracts/search?q=left%20and%20right%20operator" title=" left and right operator"> left and right operator</a> </p> <a href="https://publications.waset.org/abstracts/54133/inner-derivations-of-low-dimensional-diassociative-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">270</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">16</span> Derivation of BCK\BCI-Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tumadhir%20Fahim%20M%20Alsulami">Tumadhir Fahim M Alsulami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=BCK" title="BCK">BCK</a>, <a href="https://publications.waset.org/abstracts/search?q=BCI" title=" BCI"> BCI</a>, <a href="https://publications.waset.org/abstracts/search?q=algebras" title=" algebras"> algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=derivation" title=" derivation"> derivation</a> </p> <a href="https://publications.waset.org/abstracts/148017/derivation-of-bckbci-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148017.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">124</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">15</span> Quantum Algebra from Generalized Q-Algebra</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muna%20Tabuni">Muna Tabuni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Q-algebras" title="Q-algebras">Q-algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=BCI" title=" BCI"> BCI</a>, <a href="https://publications.waset.org/abstracts/search?q=BCK" title=" BCK"> BCK</a>, <a href="https://publications.waset.org/abstracts/search?q=BCH-algebra" title=" BCH-algebra"> BCH-algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20mechanics" title=" quantum mechanics"> quantum mechanics</a> </p> <a href="https://publications.waset.org/abstracts/138379/quantum-algebra-from-generalized-q-algebra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138379.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">199</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14</span> Stem Covers of Leibniz n-Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nat%C3%A1lia%20Maria%20Rego">Natália Maria Rego</a> </p> <p class="card-text"><strong>Abstract:</strong></p> ALeibnizn-algebraGis aK-vector space endowed whit a n-linearbracket operation [-,…-] : GG … G→ Gsatisfying the fundamental identity, which can be expressed saying that the right multiplication map Ry2, …, ᵧₙ: Gn→ G, Rᵧ₂, …, ᵧₙn(ˣ¹, …, ₓₙ) = [[ˣ¹, …, ₓₙ], ᵧ₂, …, ᵧₙ], is a derivation. This structure, together with its skew-symmetric version, named as Lie n-algebra or Filippov algebra, arose in the setting of Nambumechanics, an n-ary generalization of the Hamiltonian mechanics. Thefirst goal of this work is to provide a characterization of various classes of central extensions of Leibniz n-algebras in terms of homological properties. Namely, Commutator extension, Quasi-commutator extension, Stem extension, and Stem cover. These kind of central extensions are characterized by means of the character of the map *(E): nHL1(G) → M provided by the five-term exact sequence in homology with trivial coefficients of Leibniz n-algebras associated to an extension E : 0 → M → K → G → 0. For a free presentation 0 →R→ F →G→ 0of a Leibniz n-algebra G,the term M(G) = (R[F,…n.., F])/[R, F,..n-1..,F] is called the Schur multiplier of G, which is a Baer invariant, i.e., it does not depend on the chosen free presentation, and it is isomorphic to the first Leibniz n-algebras homology with trivial coefficients of G. A central extension of Leibniz n-algebras is a short exact sequenceE : 0 →M→K→G→ 0such that [M, K,.. ⁿ⁻¹.., K]=0. It is said to be a stem extension if M⊆[G, .. n.., G]. Additionally, if the induced map M(K) → M(G) is the zero map, then the stem extension Eis said to be a stem cover. The second aim of this work is to analyze the interplay between stem covers of Leibniz n-algebras and the Schur multiplier. Concretely, in the case of finite-dimensional Leibniz n-algebras, we show the existence of coverings, and we prove that all stem covers with finite-dimensional Schur multiplier are isoclinic. Additionally, we characterize stem covers of perfect Leibniz n-algebras. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=leibniz%20n-algebras" title="leibniz n-algebras">leibniz n-algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=central%20extensions" title=" central extensions"> central extensions</a>, <a href="https://publications.waset.org/abstracts/search?q=Schur%20multiplier" title=" Schur multiplier"> Schur multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=stem%20cover" title=" stem cover"> stem cover</a> </p> <a href="https://publications.waset.org/abstracts/140090/stem-covers-of-leibniz-n-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140090.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">157</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">13</span> On Lie-Central Derivations and Almost Inner Lie-Derivations of Leibniz Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Natalia%20Pacheco%20Rego">Natalia Pacheco Rego</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=almost%20inner%20Lie-derivation" title="almost inner Lie-derivation">almost inner Lie-derivation</a>, <a href="https://publications.waset.org/abstracts/search?q=Lie-center" title=" Lie-center"> Lie-center</a>, <a href="https://publications.waset.org/abstracts/search?q=Lie-central%20derivation" title=" Lie-central derivation"> Lie-central derivation</a>, <a href="https://publications.waset.org/abstracts/search?q=Lie-derivation" title=" Lie-derivation"> Lie-derivation</a> </p> <a href="https://publications.waset.org/abstracts/127473/on-lie-central-derivations-and-almost-inner-lie-derivations-of-leibniz-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127473.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12</span> A Fundamental Functional Equation for Lie Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ih-Ching%20Hsu">Ih-Ching Hsu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied? <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fundamental%20functional%20equation" title="fundamental functional equation">fundamental functional equation</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20functional%20equations" title=" generalized functional equations"> generalized functional equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lie%20algebras" title=" Lie algebras"> Lie algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=quaternions" title=" quaternions"> quaternions</a> </p> <a href="https://publications.waset.org/abstracts/76600/a-fundamental-functional-equation-for-lie-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76600.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">223</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">11</span> Non Commutative Lᵖ Spaces as Hilbert Modules</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salvatore%20Triolo">Salvatore Triolo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We discuss the possibility of extending the well-known Gelfand-Naimark-Segal representation to modules over a C*algebra. We focus our attention on the case of Hilbert modules. We consider, in particular, the problem of the existence of a faithful representation. Non-commutative Lᵖ-spaces are shown to constitute examples of a class of CQ*-algebras. Finally, we have shown that any semisimple proper CQ*-algebra (X, A#), with A# a W*-algebra can be represented as a CQ*-algebra of measurable operators in Segal’s sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gelfand-Naimark-Segal%20representation" title="Gelfand-Naimark-Segal representation">Gelfand-Naimark-Segal representation</a>, <a href="https://publications.waset.org/abstracts/search?q=CQ%2A-algebras" title=" CQ*-algebras"> CQ*-algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=faithful%20representation" title=" faithful representation"> faithful representation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-commutative%20L%E1%B5%96-spaces" title=" non-commutative Lᵖ-spaces"> non-commutative Lᵖ-spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20in%20Hilbert%20spaces" title=" operator in Hilbert spaces"> operator in Hilbert spaces</a> </p> <a href="https://publications.waset.org/abstracts/142662/non-commutative-l-spaces-as-hilbert-modules" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142662.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">248</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10</span> Fuzzy Implicative Pseudo-Ideals of Pesudo-BCK Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Gilani">Alireza Gilani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=BCK-algebra" title="BCK-algebra">BCK-algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-BCK%20algebra" title=" pseudo-BCK algebra"> pseudo-BCK algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-ideal" title=" pseudo-ideal"> pseudo-ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=implicative%20pseudo-ideal" title=" implicative pseudo-ideal"> implicative pseudo-ideal</a> </p> <a href="https://publications.waset.org/abstracts/43353/fuzzy-implicative-pseudo-ideals-of-pesudo-bck-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43353.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">400</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">9</span> Module Valuations and Quasi-Valuations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shai%20Sarussi">Shai Sarussi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Suppose F is a field with valuation v and valuation domain Oᵥ, and R is an Oᵥ-algebra. It is known that there exists a filter quasi-valuation on R; the existence of a quasi-valuation yields several important connections between Oᵥ and R, in particular with respect to their prime spectra. In this paper, the notion of a module valuation is introduced. It is shown that any torsion-free module over Oᵥ has an induced module valuation. Moreover, several results connecting the filter quasi-valuation and module valuations are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=valuations" title="valuations">valuations</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-valuations" title=" quasi-valuations"> quasi-valuations</a>, <a href="https://publications.waset.org/abstracts/search?q=prime%20spectrum" title=" prime spectrum"> prime spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=algebras%20over%20valuation%20domains" title=" algebras over valuation domains"> algebras over valuation domains</a> </p> <a href="https://publications.waset.org/abstracts/139887/module-valuations-and-quasi-valuations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/139887.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8</span> Approximation Property Pass to Free Product</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kankeyanathan%20Kannan">Kankeyanathan Kannan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximation%20property" title="approximation property">approximation property</a>, <a href="https://publications.waset.org/abstracts/search?q=weakly%20amenable" title=" weakly amenable"> weakly amenable</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20invariant%20approximation%20property" title=" strong invariant approximation property"> strong invariant approximation property</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20approximation%20property" title=" invariant approximation property"> invariant approximation property</a> </p> <a href="https://publications.waset.org/abstracts/44414/approximation-property-pass-to-free-product" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44414.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">675</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">7</span> Algebras over an Integral Domain and Immediate Neighbors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shai%20Sarussi">Shai Sarussi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20domains" title="integral domains">integral domains</a>, <a href="https://publications.waset.org/abstracts/search?q=Alexandroff%20topology" title=" Alexandroff topology"> Alexandroff topology</a>, <a href="https://publications.waset.org/abstracts/search?q=immediate%20neighbors" title=" immediate neighbors"> immediate neighbors</a>, <a href="https://publications.waset.org/abstracts/search?q=valuation%20domains" title=" valuation domains"> valuation domains</a> </p> <a href="https://publications.waset.org/abstracts/131023/algebras-over-an-integral-domain-and-immediate-neighbors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131023.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">176</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6</span> Dual Duality for Unifying Spacetime and Internal Symmetry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=David%20C.%20Ni">David C. Ni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20relativity" title="general relativity">general relativity</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20mechanics" title=" quantum mechanics"> quantum mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=string%20theory" title=" string theory"> string theory</a>, <a href="https://publications.waset.org/abstracts/search?q=duality" title=" duality"> duality</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetry" title=" symmetry"> symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=correspondence" title=" correspondence"> correspondence</a>, <a href="https://publications.waset.org/abstracts/search?q=algebra" title=" algebra"> algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=momentum-angular-momentum" title=" momentum-angular-momentum"> momentum-angular-momentum</a> </p> <a href="https://publications.waset.org/abstracts/45918/dual-duality-for-unifying-spacetime-and-internal-symmetry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45918.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5</span> Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zuhier%20Altawallbeh">Zuhier Altawallbeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hochschild%20homology" title="hochschild homology">hochschild homology</a>, <a href="https://publications.waset.org/abstracts/search?q=homotopic%20function" title=" homotopic function"> homotopic function</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20and%20projective%20modules" title=" free and projective modules"> free and projective modules</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20resolution" title=" free resolution"> free resolution</a>, <a href="https://publications.waset.org/abstracts/search?q=exterior%20algebra" title=" exterior algebra"> exterior algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20algebra" title=" symmetric algebra"> symmetric algebra</a> </p> <a href="https://publications.waset.org/abstracts/20251/explicit-chain-homotopic-function-to-compute-hochschild-homology-of-the-polynomial-algebra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20251.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4</span> Algebraic Characterization of Sheaves over Boolean Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=U.%20M.%20Swamy">U. M. Swamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A compact Hausdorff and totally disconnected topological space are known as Boolean space in view of the stone duality between Boolean algebras and such topological spaces. A sheaf over X is a triple (S, p, X) where S and X are topological spaces and p is a local homeomorphism of S onto X (that is, for each element s in S, there exist open sets U and G containing s and p(s) in S and X respectively such that the restriction of p to U is a homeomorphism of U onto G). Here we mainly concern on sheaves over Boolean spaces. From a given sheaf over a Boolean space, we obtain an algebraic structure in such a way that there is a one-to-one correspondence between these algebraic structures and sheaves over Boolean spaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boolean%20algebra" title="Boolean algebra">Boolean algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=Boolean%20space" title=" Boolean space"> Boolean space</a>, <a href="https://publications.waset.org/abstracts/search?q=sheaf" title=" sheaf"> sheaf</a>, <a href="https://publications.waset.org/abstracts/search?q=stone%20duality" title=" stone duality"> stone duality</a> </p> <a href="https://publications.waset.org/abstracts/124439/algebraic-characterization-of-sheaves-over-boolean-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124439.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">349</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3</span> Integral Domains and Their Algebras: Topological Aspects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shai%20Sarussi">Shai Sarussi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20domains" title="integral domains">integral domains</a>, <a href="https://publications.waset.org/abstracts/search?q=Alexandroff%20topology" title=" Alexandroff topology"> Alexandroff topology</a>, <a href="https://publications.waset.org/abstracts/search?q=prime%20spectrum%20of%20a%20ring" title=" prime spectrum of a ring"> prime spectrum of a ring</a>, <a href="https://publications.waset.org/abstracts/search?q=valuation%20domains" title=" valuation domains"> valuation domains</a> </p> <a href="https://publications.waset.org/abstracts/130312/integral-domains-and-their-algebras-topological-aspects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130312.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">130</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> Merging and Comparing Ontologies Generically</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiuzhan%20Guo">Xiuzhan Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Arthur%20Berrill"> Arthur Berrill</a>, <a href="https://publications.waset.org/abstracts/search?q=Ajinkya%20Kulkarni"> Ajinkya Kulkarni</a>, <a href="https://publications.waset.org/abstracts/search?q=Kostya%20Belezko"> Kostya Belezko</a>, <a href="https://publications.waset.org/abstracts/search?q=Min%20Luo"> Min Luo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Ontology operations, e.g., aligning and merging, were studied and implemented extensively in different settings, such as categorical operations, relation algebras, and typed graph grammars, with different concerns. However, aligning and merging operations in the settings share some generic properties, e.g., idempotence, commutativity, associativity, and representativity, labeled by (I), (C), (A), and (R), respectively, which are defined on an ontology merging system (D~M), where D is a non-empty set of the ontologies concerned, ~ is a binary relation on D modeling ontology aligning and M is a partial binary operation on D modeling ontology merging. Given an ontology repository, a finite set O ⊆ D, its merging closure Ô is the smallest set of ontologies, which contains the repository and is closed with respect to merging. If (I), (C), (A), and (R) are satisfied, then both D and Ô are partially ordered naturally by merging, Ô is finite and can be computed, compared, and sorted efficiently, including sorting, selecting, and querying some specific elements, e.g., maximal ontologies and minimal ontologies. We also show that the ontology merging system, given by ontology V -alignment pairs and pushouts, satisfies the properties: (I), (C), (A), and (R) so that the merging system is partially ordered and the merging closure of a given repository with respect to pushouts can be computed efficiently. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ontology%20aligning" title="ontology aligning">ontology aligning</a>, <a href="https://publications.waset.org/abstracts/search?q=ontology%20merging" title=" ontology merging"> ontology merging</a>, <a href="https://publications.waset.org/abstracts/search?q=merging%20system" title=" merging system"> merging system</a>, <a href="https://publications.waset.org/abstracts/search?q=poset" title=" poset"> poset</a>, <a href="https://publications.waset.org/abstracts/search?q=merging%20closure" title=" merging closure"> merging closure</a>, <a href="https://publications.waset.org/abstracts/search?q=ontology%20V-alignment%20pair" title=" ontology V-alignment pair"> ontology V-alignment pair</a>, <a href="https://publications.waset.org/abstracts/search?q=ontology%20homomorphism" title=" ontology homomorphism"> ontology homomorphism</a>, <a href="https://publications.waset.org/abstracts/search?q=ontology%20V-alignment%20pair%20homomorphism" title=" ontology V-alignment pair homomorphism"> ontology V-alignment pair homomorphism</a>, <a href="https://publications.waset.org/abstracts/search?q=pushout" title=" pushout"> pushout</a> </p> <a href="https://publications.waset.org/abstracts/155767/merging-and-comparing-ontologies-generically" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/155767.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">893</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> Formal Group Laws and Toposes in Gauge Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Patrascu%20Andrei%20Tudor">Patrascu Andrei Tudor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the main problems in high energy physics is the fact that we do not have a complete understanding of the interaction between local and global effects in gauge theory. This has an increasing impact on our ability to access the non-perturbative regime of most of our theories. Our theories, while being based on gauge groups considered to be simple or semi-simple and connected, are expected to be described by their simple local linear approximation, namely the Lie algebras. However, higher homotopy properties resulting in gauge anomalies appear frequently in theories of physical interest. Our assumption that the groups we deal with are simple and simply connected is probably not suitable, and ways to go beyond such assumptions, particularly in gauge theories, where the Lie algebra linear approximation is prevalent, are not known. We approach this problem from two directions: on one side we are explaining the potential role of formal group laws in describing certain higher homotopical properties and interferences with local or perturbative effects, and on the other side, we employ a categorical approach leading to synthetic theory and a way of looking at gauge theories. The topos approach is based on a geometry where the fundamental logic is intuitionistic logic, and hence the ‘tertium non datur’ principle is abandoned. This has a remarkable impact on understanding conformal symmetry and its anomalies in string theory in various dimensions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gauge%20theory" title="Gauge theory">Gauge theory</a>, <a href="https://publications.waset.org/abstracts/search?q=formal%20group%20laws" title=" formal group laws"> formal group laws</a>, <a href="https://publications.waset.org/abstracts/search?q=Topos%20theory" title=" Topos theory"> Topos theory</a>, <a href="https://publications.waset.org/abstracts/search?q=conformal%20symmetry" title=" conformal symmetry"> conformal symmetry</a> </p> <a href="https://publications.waset.org/abstracts/188259/formal-group-laws-and-toposes-in-gauge-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188259.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">36</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>