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space</title> <meta name="description" content="Search results for: Hilbert space"> <meta name="keywords" content="Hilbert space"> <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="Hilbert space"> <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> 3720</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Hilbert space</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3720</span> Every g-Riesz Basis is a Riesz Basis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehdi%20Rashidi-Kouchi">Mehdi Rashidi-Kouchi</a>, <a href="https://publications.waset.org/abstracts/search?q=Asghar%20Rahimi"> Asghar Rahimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Sun introduced a generalization of frames and showed that this includes more other cases of generalizations of frame concept and proved that many basic properties can be derived within this more general context. Another generalization of frames is frames in Hilbert C*-module. It has been proved that every g-frame in Hilbert space H respect to Hilbert space K is a frame for B(H;K) as Hilbert C*-module. We show that every g-Riesz basis for Hilbert space H respect to K by add a condition is a Riesz basis for Hilbert B(K)-module B(H;K). Also, we investigate similar result for g-orthonormal and orthogonal bases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=frame" title="frame">frame</a>, <a href="https://publications.waset.org/abstracts/search?q=g-frame" title=" g-frame"> g-frame</a>, <a href="https://publications.waset.org/abstracts/search?q=Riesz%20basis" title=" Riesz basis"> Riesz basis</a>, <a href="https://publications.waset.org/abstracts/search?q=g-Riesz%20basis" title=" g-Riesz basis"> g-Riesz basis</a>, <a href="https://publications.waset.org/abstracts/search?q=Hilbert%20C%2A-module" title=" Hilbert C*-module"> Hilbert C*-module</a> </p> <a href="https://publications.waset.org/abstracts/17888/every-g-riesz-basis-is-a-riesz-basis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17888.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">471</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">3719</span> Heinz-Type Inequalities in Hilbert Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jin%20Liang">Jin Liang</a>, <a href="https://publications.waset.org/abstracts/search?q=Guanghua%20Shi"> Guanghua Shi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we are concerned with the further refinements of the Heinz operator inequalities in Hilbert spaces. Our purpose is to derive several new Heinz-type operator inequalities. First, with the help of the Taylor series of some hyperbolic functions, we obtain some refinements of the ordering relations among Heinz means defined by Bhatia with different parameters, which would be more suitable in obtaining the corresponding operator inequalities. Second, we present some generalizations of Heinz operator inequalities. Finally, we give a matrix version of the Heinz inequality for the Hilbert-Schmidt norm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hilbert%20space" title="Hilbert space">Hilbert space</a>, <a href="https://publications.waset.org/abstracts/search?q=means%20inequality" title=" means inequality"> means inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=norm%20inequality" title=" norm inequality"> norm inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20linear%20operator" title=" positive linear operator"> positive linear operator</a> </p> <a href="https://publications.waset.org/abstracts/54127/heinz-type-inequalities-in-hilbert-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54127.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">3718</span> Construction of Finite Woven Frames through Bounded Linear Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Bhandari">A. Bhandari</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Mukherjee"> S. Mukherjee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two frames in a Hilbert space are called woven or weaving if all possible merge combinations between them generate frames of the Hilbert space with uniform frame bounds. Weaving frames are powerful tools in wireless sensor networks which require distributed data processing. Considering the practical applications, this article deals with finite woven frames. We provide methods of constructing finite woven frames, in particular, bounded linear operators are used to construct woven frames from a given frame. Several examples are discussed. We also introduce the notion of woven frame sequences and characterize them through the concepts of gaps and angles between spaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=frames" title="frames">frames</a>, <a href="https://publications.waset.org/abstracts/search?q=woven%20frames" title=" woven frames"> woven frames</a>, <a href="https://publications.waset.org/abstracts/search?q=gap" title=" gap"> gap</a>, <a href="https://publications.waset.org/abstracts/search?q=angle" title=" angle"> angle</a> </p> <a href="https://publications.waset.org/abstracts/100698/construction-of-finite-woven-frames-through-bounded-linear-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100698.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">193</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">3717</span> A General Approach to Define Adjoint of Linear and Non-linear Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehdi%20Jafari%20Matehkolaee">Mehdi Jafari Matehkolaee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adjoint%20operator" title="adjoint operator">adjoint operator</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20operator" title=" non-linear operator"> non-linear operator</a>, <a href="https://publications.waset.org/abstracts/search?q=differentiable%20operator" title=" differentiable operator"> differentiable operator</a>, <a href="https://publications.waset.org/abstracts/search?q=manifold" title=" manifold"> manifold</a> </p> <a href="https://publications.waset.org/abstracts/166456/a-general-approach-to-define-adjoint-of-linear-and-non-linear-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166456.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">119</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">3716</span> A Family of Distributions on Learnable Problems without Uniform Convergence</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=C%C3%A9sar%20Garza">César Garza</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=statistical%20learning%20theory" title="statistical learning theory">statistical learning theory</a>, <a href="https://publications.waset.org/abstracts/search?q=learnability" title=" learnability"> learnability</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20convergence" title=" uniform convergence"> uniform convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=regularized%20loss%20minimization" title=" regularized loss minimization"> regularized loss minimization</a> </p> <a href="https://publications.waset.org/abstracts/151038/a-family-of-distributions-on-learnable-problems-without-uniform-convergence" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151038.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">129</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">3715</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">3714</span> Facial Pose Classification Using Hilbert Space Filling Curve and Multidimensional Scaling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mekam%C4%B1%20Hayet">Mekamı Hayet</a>, <a href="https://publications.waset.org/abstracts/search?q=Bounoua%20Nacer"> Bounoua Nacer</a>, <a href="https://publications.waset.org/abstracts/search?q=Benabderrahmane%20Sidahmed"> Benabderrahmane Sidahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Taleb%20Ahmed"> Taleb Ahmed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Pose estimation is an important task in computer vision. Though the majority of the existing solutions provide good accuracy results, they are often overly complex and computationally expensive. In this perspective, we propose the use of dimensionality reduction techniques to address the problem of facial pose estimation. Firstly, a face image is converted into one-dimensional time series using Hilbert space filling curve, then the approach converts these time series data to a symbolic representation. Furthermore, a distance matrix is calculated between symbolic series of an input learning dataset of images, to generate classifiers of frontal vs. profile face pose. The proposed method is evaluated with three public datasets. Experimental results have shown that our approach is able to achieve a correct classification rate exceeding 97% with K-NN algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=machine%20learning" title="machine learning">machine learning</a>, <a href="https://publications.waset.org/abstracts/search?q=pattern%20recognition" title=" pattern recognition"> pattern recognition</a>, <a href="https://publications.waset.org/abstracts/search?q=facial%20pose%20classification" title=" facial pose classification"> facial pose classification</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20series" title=" time series "> time series </a> </p> <a href="https://publications.waset.org/abstracts/33324/facial-pose-classification-using-hilbert-space-filling-curve-and-multidimensional-scaling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33324.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">350</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">3713</span> Explicit Iterative Scheme for Approximating a Common Solution of Generalized Mixed Equilibrium Problem and Fixed Point Problem for a Nonexpansive Semigroup in Hilbert Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Farid">Mohammad Farid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20mixed%20equilibrium%20problem" title="generalized mixed equilibrium problem">generalized mixed equilibrium problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed-point%20problem" title=" fixed-point problem"> fixed-point problem</a>, <a href="https://publications.waset.org/abstracts/search?q=nonexpansive%20semigroup" title=" nonexpansive semigroup"> nonexpansive semigroup</a>, <a href="https://publications.waset.org/abstracts/search?q=variational%20inequality%20problem" title=" variational inequality problem"> variational inequality problem</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20algorithms" title=" iterative algorithms"> iterative algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20extragradient%20method" title=" hybrid extragradient method"> hybrid extragradient method</a> </p> <a href="https://publications.waset.org/abstracts/14070/explicit-iterative-scheme-for-approximating-a-common-solution-of-generalized-mixed-equilibrium-problem-and-fixed-point-problem-for-a-nonexpansive-semigroup-in-hilbert-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14070.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">475</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">3712</span> Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Apirak%20Sombat">Apirak Sombat</a>, <a href="https://publications.waset.org/abstracts/search?q=Teerapol%20Saleewong"> Teerapol Saleewong</a>, <a href="https://publications.waset.org/abstracts/search?q=Poom%20Kumam"> Poom Kumam</a>, <a href="https://publications.waset.org/abstracts/search?q=Parin%20Chaipunya"> Parin Chaipunya</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiyada%20Kumam"> Wiyada Kumam</a>, <a href="https://publications.waset.org/abstracts/search?q=Anantachai%20Padcharoen"> Anantachai Padcharoen</a>, <a href="https://publications.waset.org/abstracts/search?q=Yeol%20Je%20Cho"> Yeol Je Cho</a>, <a href="https://publications.waset.org/abstracts/search?q=Thana%20Sutthibutpong"> Thana Sutthibutpong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotically%20quasi-nonexpansive%20nonself-mapping" title="asymptotically quasi-nonexpansive nonself-mapping">asymptotically quasi-nonexpansive nonself-mapping</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20convergence" title=" strong convergence"> strong convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convex%20and%20uniformly%20smooth%20Banach%20space" title=" uniformly convex and uniformly smooth Banach space"> uniformly convex and uniformly smooth Banach space</a> </p> <a href="https://publications.waset.org/abstracts/58622/algorithms-for-computing-of-optimization-problems-with-a-common-minimum-norm-fixed-point-with-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58622.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">260</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">3711</span> Online Prediction of Nonlinear Signal Processing Problems Based Kernel Adaptive Filtering</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamza%20Nejib">Hamza Nejib</a>, <a href="https://publications.waset.org/abstracts/search?q=Okba%20Taouali"> Okba Taouali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=online%20prediction" title="online prediction">online prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=KAF" title=" KAF"> KAF</a>, <a href="https://publications.waset.org/abstracts/search?q=signal%20processing" title=" signal processing"> signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=RKHS" title=" RKHS"> RKHS</a>, <a href="https://publications.waset.org/abstracts/search?q=Kernel%20methods" title=" Kernel methods"> Kernel methods</a>, <a href="https://publications.waset.org/abstracts/search?q=KRLS" title=" KRLS"> KRLS</a>, <a href="https://publications.waset.org/abstracts/search?q=KLMS" title=" KLMS"> KLMS</a> </p> <a href="https://publications.waset.org/abstracts/63627/online-prediction-of-nonlinear-signal-processing-problems-based-kernel-adaptive-filtering" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63627.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">399</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">3710</span> Agegraphic Dark Energy with GUP</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20R.%20Fazlollahi">H. R. Fazlollahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dark Energy origin is unknown and so describing this mysterious component in large scale structure needs to manipulate our theories in general relativity. Although in most models, dark energy arises from extra terms through modifying Einstein-Hilbert action, maybe its origin traces back to fundamental aspects of ground energy of space-time given in quantum mechanics. Hence, diluting space-time in general relativity with quantum mechanics properties leads to the Karolyhazy relation corresponding energy density of quantum fluctuations of space-time. Through generalized uncertainty principle and an eye to Karolyhazy approach in this study we extend energy density of quantum fluctuations of space-time. Also, the application of this idea is considered in late time evolution and we have shown how extra term in generalized uncertainty principle plays as a plausible interaction term role in suggested model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20uncertainty%20principle" title="generalized uncertainty principle">generalized uncertainty principle</a>, <a href="https://publications.waset.org/abstracts/search?q=karolyhazy%20approach" title=" karolyhazy approach"> karolyhazy approach</a>, <a href="https://publications.waset.org/abstracts/search?q=agegraphic%20dark%20energy" title=" agegraphic dark energy"> agegraphic dark energy</a>, <a href="https://publications.waset.org/abstracts/search?q=cosmology" title=" cosmology"> cosmology</a> </p> <a href="https://publications.waset.org/abstracts/165000/agegraphic-dark-energy-with-gup" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165000.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">73</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">3709</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">3708</span> Weyl Type Theorem and the Fuglede Property</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20H.%20M.%20Rashid">M. H. M. Rashid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuglede%20Property" title="Fuglede Property">Fuglede Property</a>, <a href="https://publications.waset.org/abstracts/search?q=Weyl%E2%80%99s%20theorem" title=" Weyl’s theorem"> Weyl’s theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20derivation" title=" generalized derivation"> generalized derivation</a>, <a href="https://publications.waset.org/abstracts/search?q=Aluthge%20transform" title=" Aluthge transform"> Aluthge transform</a> </p> <a href="https://publications.waset.org/abstracts/113531/weyl-type-theorem-and-the-fuglede-property" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113531.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">128</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">3707</span> On the System of Split Equilibrium and Fixed Point Problems in Real Hilbert Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francis%20O.%20Nwawuru">Francis O. Nwawuru</a>, <a href="https://publications.waset.org/abstracts/search?q=Jeremiah%20N.%20Ezeora"> Jeremiah N. Ezeora</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a new algorithm for solving the system of split equilibrium and fixed point problems in real Hilbert spaces is considered. The equilibrium bifunction involves a nite family of pseudo-monotone mappings, which is an improvement over monotone operators. More so, it turns out that the solution of the finite family of nonexpansive mappings. The regularized parameters do not depend on Lipschitz constants. Also, the computations of the stepsize, which plays a crucial role in the convergence analysis of the proposed method, do require prior knowledge of the norm of the involved bounded linear map. Furthermore, to speed up the rate of convergence, an inertial term technique is introduced in the proposed method. Under standard assumptions on the operators and the control sequences, using a modified Halpern iteration method, we establish strong convergence, a desired result in applications. Finally, the proposed scheme is applied to solve some optimization problems. The result obtained improves numerous results announced earlier in this direction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=equilibrium" title="equilibrium">equilibrium</a>, <a href="https://publications.waset.org/abstracts/search?q=Hilbert%20spaces" title=" Hilbert spaces"> Hilbert spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=nonexpansive%20mapping" title=" nonexpansive mapping"> nonexpansive mapping</a>, <a href="https://publications.waset.org/abstracts/search?q=extragradient%20method" title=" extragradient method"> extragradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=regularized%20equilibrium" title=" regularized equilibrium"> regularized equilibrium</a> </p> <a href="https://publications.waset.org/abstracts/184412/on-the-system-of-split-equilibrium-and-fixed-point-problems-in-real-hilbert-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184412.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">48</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">3706</span> Split Monotone Inclusion and Fixed Point Problems in Real Hilbert Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francis%20O.%20Nwawuru">Francis O. Nwawuru</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fixedpoint" title="fixedpoint">fixedpoint</a>, <a href="https://publications.waset.org/abstracts/search?q=hilbertspace" title=" hilbertspace"> hilbertspace</a>, <a href="https://publications.waset.org/abstracts/search?q=monotonemapping" title=" monotonemapping"> monotonemapping</a>, <a href="https://publications.waset.org/abstracts/search?q=resolventoperators" title=" resolventoperators"> resolventoperators</a> </p> <a href="https://publications.waset.org/abstracts/183967/split-monotone-inclusion-and-fixed-point-problems-in-real-hilbert-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/183967.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">52</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">3705</span> Powers of Class p-w A (s, t) Operators Associated with Generalized Aluthge Transformations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Husein%20Mohammed%20Rashid">Mohammed Husein Mohammed Rashid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let Τ = U |Τ| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with ker U = ker |T|. T is said to be class p-w A(s,t) if (|T*|ᵗ|T|²ˢ|T*|ᵗ )ᵗᵖ/ˢ⁺ᵗ ≥|T*|²ᵗᵖ and |T|²ˢᵖ ≥ (|T|ˢ|T*|²ᵗ|T|ˢ)ˢᵖ/ˢ⁺ᵗ with 0<p≤1 and 0<s,t,s + t≤1. This is a generalization of p-hyponormal or class A operators. In this paper, we shall show that if T belongs to class p-w A (s, t) operator for 0<s,t≤1 and 0<p≤1, then Tⁿ belongs to class p₁-w A (s/n, t/n) for 0<p₁≤p and for all positive integer n. As an immediate corollary of this result, we shall also show that if T is a p-w-hyponormal operator, then Tⁿ is also p₁-w-hyponormal for 0<p₁≤p and for all positive integer n. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=class%20p-w%20A%20%28s" title="class p-w A (s">class p-w A (s</a>, <a href="https://publications.waset.org/abstracts/search?q=t%29" title=" t)"> t)</a>, <a href="https://publications.waset.org/abstracts/search?q=normaloid" title=" normaloid"> normaloid</a>, <a href="https://publications.waset.org/abstracts/search?q=isoloid" title=" isoloid"> isoloid</a>, <a href="https://publications.waset.org/abstracts/search?q=finite" title=" finite"> finite</a>, <a href="https://publications.waset.org/abstracts/search?q=orthogonality" title=" orthogonality"> orthogonality</a> </p> <a href="https://publications.waset.org/abstracts/158688/powers-of-class-p-w-a-s-t-operators-associated-with-generalized-aluthge-transformations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158688.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">117</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">3704</span> Quantification of Site Nonlinearity Based on HHT Analysis of Seismic Recordings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ruichong%20Zhang">Ruichong Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time-frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=site%20nonlinearity" title="site nonlinearity">site nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=site%20amplification" title=" site amplification"> site amplification</a>, <a href="https://publications.waset.org/abstracts/search?q=site%20damping" title=" site damping"> site damping</a>, <a href="https://publications.waset.org/abstracts/search?q=Hilbert-Huang%20Transform%20%28HHT%29" title=" Hilbert-Huang Transform (HHT)"> Hilbert-Huang Transform (HHT)</a>, <a href="https://publications.waset.org/abstracts/search?q=liquefaction" title=" liquefaction"> liquefaction</a>, <a href="https://publications.waset.org/abstracts/search?q=2001%20Nisqually%20Earthquake" title=" 2001 Nisqually Earthquake"> 2001 Nisqually Earthquake</a> </p> <a href="https://publications.waset.org/abstracts/23109/quantification-of-site-nonlinearity-based-on-hht-analysis-of-seismic-recordings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23109.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">486</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">3703</span> Analysis of Nonlinear and Non-Stationary Signal to Extract the Features Using Hilbert Huang Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Paithane">A. N. Paithane</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20S.%20Bormane"> D. S. Bormane</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20D.%20Shirbahadurkar"> S. D. Shirbahadurkar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has been seen that emotion recognition is an important research topic in the field of Human and computer interface. A novel technique for Feature Extraction (FE) has been presented here, further a new method has been used for human emotion recognition which is based on HHT method. This method is feasible for analyzing the nonlinear and non-stationary signals. Each signal has been decomposed into the IMF using the EMD. These functions are used to extract the features using fission and fusion process. The decomposition technique which we adopt is a new technique for adaptively decomposing signals. In this perspective, we have reported here potential usefulness of EMD based techniques.We evaluated the algorithm on Augsburg University Database; the manually annotated database. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=intrinsic%20mode%20function%20%28IMF%29" title="intrinsic mode function (IMF)">intrinsic mode function (IMF)</a>, <a href="https://publications.waset.org/abstracts/search?q=Hilbert-Huang%20transform%20%28HHT%29" title=" Hilbert-Huang transform (HHT)"> Hilbert-Huang transform (HHT)</a>, <a href="https://publications.waset.org/abstracts/search?q=empirical%20mode%20decomposition%20%28EMD%29" title=" empirical mode decomposition (EMD)"> empirical mode decomposition (EMD)</a>, <a href="https://publications.waset.org/abstracts/search?q=emotion%20detection" title=" emotion detection"> emotion detection</a>, <a href="https://publications.waset.org/abstracts/search?q=electrocardiogram%20%28ECG%29" title=" electrocardiogram (ECG)"> electrocardiogram (ECG)</a> </p> <a href="https://publications.waset.org/abstracts/19551/analysis-of-nonlinear-and-non-stationary-signal-to-extract-the-features-using-hilbert-huang-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19551.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">580</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">3702</span> Fuglede-Putnam Theorem for ∗-Class A Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Husein%20Mohammad%20Rashid">Mohammed Husein Mohammad Rashid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For a bounded linear operator T acting on a complex inﬁnite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuglede-putnam%20theorem" title="fuglede-putnam theorem">fuglede-putnam theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=normal%20operators" title=" normal operators"> normal operators</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%88%97-class%20a%20operators" title=" ∗-class a operators"> ∗-class a operators</a>, <a href="https://publications.waset.org/abstracts/search?q=dominant%20operators" title=" dominant operators"> dominant operators</a> </p> <a href="https://publications.waset.org/abstracts/159132/fuglede-putnam-theorem-for-class-a-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/159132.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">88</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">3701</span> State’s Responsibility of Space Debris</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Athari%20Farhani">Athari Farhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Abstract The existence of space debris is a direct implication of human activities in outer space. The amount of orbital debris resulting from human exploration and use of outer space has been steadily increasing in the history of human exploration and use of outer space, so that space debris in the responsibility of the launching state. Space debris not only hs a direct impact on environmentalpollution but can also harm and endanger the safety of human life. Despite the legal provisions governing the exploration and use of outer space, both international space law and liability convention, however, these legal provisions are only basic prinsiples, so that further thought or effort are needed, such as new international legal instruments to regulate the existence of space debris. The method used in this research is normative juridical with an approach to written legal regulation, especially international agreements related to space law. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=state%E2%80%99s%20responsibility" title="state’s responsibility">state’s responsibility</a>, <a href="https://publications.waset.org/abstracts/search?q=space%20debris" title=" space debris"> space debris</a>, <a href="https://publications.waset.org/abstracts/search?q=outerspace" title=" outerspace"> outerspace</a>, <a href="https://publications.waset.org/abstracts/search?q=international%20law" title=" international law"> international law</a> </p> <a href="https://publications.waset.org/abstracts/167497/states-responsibility-of-space-debris" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167497.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">105</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">3700</span> Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benedict%20Barnes">Benedict Barnes</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Y.%20Aidoo"> Anthony Y. Aidoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=divergence%20regularization%20method" title="divergence regularization method">divergence regularization method</a>, <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title=" Helmholtz equation"> Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20inhomogeneous%20Cauchy%20boundary%20conditions" title=" ill-posed inhomogeneous Cauchy boundary conditions"> ill-posed inhomogeneous Cauchy boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/137727/divergence-regularization-method-for-solving-ill-posed-cauchy-problem-for-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137727.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">189</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">3699</span> Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fethi%20Soltani">Fethi Soltani</a>, <a href="https://publications.waset.org/abstracts/search?q=Adel%20Almarashi"> Adel Almarashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Idir%20Mechai"> Idir Mechai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourier%20multiplier%20operators" title="fourier multiplier operators">fourier multiplier operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Gauss-Kronrod%20method%20of%20integration" title=" Gauss-Kronrod method of integration"> Gauss-Kronrod method of integration</a>, <a href="https://publications.waset.org/abstracts/search?q=Paley-Wiener%20space" title=" Paley-Wiener space"> Paley-Wiener space</a>, <a href="https://publications.waset.org/abstracts/search?q=Tikhonov%20regularization" title=" Tikhonov regularization"> Tikhonov regularization</a> </p> <a href="https://publications.waset.org/abstracts/38538/numerical-applications-of-tikhonov-regularization-for-the-fourier-multiplier-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38538.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">318</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">3698</span> A Sliding Model Control for a Hybrid Hyperbolic Dynamic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xuezhang%20Hou">Xuezhang Hou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hyperbolic%20dynamic%20system" title="hyperbolic dynamic system">hyperbolic dynamic system</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20model%20control" title=" sliding model control"> sliding model control</a>, <a href="https://publications.waset.org/abstracts/search?q=semigroup%20of%20linear%20operators" title=" semigroup of linear operators"> semigroup of linear operators</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a> </p> <a href="https://publications.waset.org/abstracts/148599/a-sliding-model-control-for-a-hybrid-hyperbolic-dynamic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148599.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">136</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">3697</span> A Study of Evolutional Control Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ti-Jun%20Xiao">Ti-Jun Xiao</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhe%20Xu"> Zhe Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=evolutional%20control%20system" title="evolutional control system">evolutional control system</a>, <a href="https://publications.waset.org/abstracts/search?q=controllability" title=" controllability"> controllability</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20control" title=" boundary control"> boundary control</a>, <a href="https://publications.waset.org/abstracts/search?q=existence%20and%20uniqueness" title=" existence and uniqueness"> existence and uniqueness</a> </p> <a href="https://publications.waset.org/abstracts/93935/a-study-of-evolutional-control-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93935.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">222</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">3696</span> Information Society-Education Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Monica%20Lia">Monica Lia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper has set the objective of researching how education is influenced by the information society. The first step was to define more precisely the information space. Second step was to identify how information space intersects the family space and institutional space educational levels represented by pre-school / school and pre-university (kindergarten, at elementary / middle school / high school). Interrelationship between the above-mentioned areas was another objective of the research. All these elements have been investigated through the original intention to identify how the information space can become an educational tool to support for the family space, education and institutional space. In addition, the aim of this research is to offer some solutions in this regard. Often the educational efforts appear to be blocked by the existence of this space. However, this paper demonstrates that Informational space can be an enemy of the educational system or be support systems if we know the internal structure and mechanisms. We can make the Informational Space to work for accomplish the educational objectives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=informational%20space" title="informational space">informational space</a>, <a href="https://publications.waset.org/abstracts/search?q=education" title=" education"> education</a>, <a href="https://publications.waset.org/abstracts/search?q=educational%20tool" title=" educational tool"> educational tool</a>, <a href="https://publications.waset.org/abstracts/search?q=social%20diagram" title=" social diagram"> social diagram</a>, <a href="https://publications.waset.org/abstracts/search?q=information" title=" information"> information</a>, <a href="https://publications.waset.org/abstracts/search?q=information%20structure" title=" information structure"> information structure</a>, <a href="https://publications.waset.org/abstracts/search?q=lessons" title=" lessons "> lessons </a> </p> <a href="https://publications.waset.org/abstracts/39912/information-society-education-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39912.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">334</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">3695</span> Environmental and Space Travel</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alimohammad">Alimohammad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Man's entry into space is one of the most important results of developments and advances made in information technology. But this human step, like many of his other actions, is not free of danger, as space pollution today has become a major problem for the global community. Paying attention to the issue of preserving the space environment is in the interest of all governments and mankind, and ignoring it can increase the possibility of conflict between countries. What many space powers still do not pay attention to is the freedom to explore and exploit space should be limited by banning pollution of the space environment. Therefore, freedom and prohibition are complementary and should not be considered conflicting concepts. The legal system created by the current space treaties for the effective preservation of the space environment has failed. Customary international law also does not have an effective provision and guarantee of sufficient executions in order to prevent damage to the environment. Considering the responsibility of each generation in the healthy transfer of the environment to the next generation and considering the sustainable development concept, the space environment must also be passed on to future generations in a healthy and undamaged manner. As a result, many environmental policies related to Earth should also be applied to the space environment.. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=law" title="law">law</a>, <a href="https://publications.waset.org/abstracts/search?q=space" title=" space"> space</a>, <a href="https://publications.waset.org/abstracts/search?q=environment" title=" environment"> environment</a>, <a href="https://publications.waset.org/abstracts/search?q=responsibility" title=" responsibility"> responsibility</a> </p> <a href="https://publications.waset.org/abstracts/161584/environmental-and-space-travel" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161584.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">84</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">3694</span> Preliminary Results on a Maximum Mean Discrepancy Approach for Seizure Detection</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boumediene%20Hamzi">Boumediene Hamzi</a>, <a href="https://publications.waset.org/abstracts/search?q=Turky%20N.%20AlOtaiby"> Turky N. AlOtaiby</a>, <a href="https://publications.waset.org/abstracts/search?q=Saleh%20AlShebeili"> Saleh AlShebeili</a>, <a href="https://publications.waset.org/abstracts/search?q=Arwa%20AlAnqary"> Arwa AlAnqary</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We introduce a data-driven method for seizure detection drawing on recent progress in Machine Learning. The method is based on embedding probability measures in a high (or infinite) dimensional reproducing kernel Hilbert space (RKHS) where the Maximum Mean Discrepancy (MMD) is computed. The MMD is metric between probability measures that are computed as the difference between the means of probability measures after being embedded in an RKHS. Working in RKHS provides a convenient, general functional-analytical framework for theoretical understanding of data. We apply this approach to the problem of seizure detection. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=kernel%20methods" title="kernel methods">kernel methods</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20mean%20discrepancy" title=" maximum mean discrepancy"> maximum mean discrepancy</a>, <a href="https://publications.waset.org/abstracts/search?q=seizure%20detection" title=" seizure detection"> seizure detection</a>, <a href="https://publications.waset.org/abstracts/search?q=machine%20learning" title=" machine learning"> machine learning</a> </p> <a href="https://publications.waset.org/abstracts/83558/preliminary-results-on-a-maximum-mean-discrepancy-approach-for-seizure-detection" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/83558.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">238</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">3693</span> Computation of ΔV Requirements for Space Debris Removal Using Orbital Transfer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadhvi%20Gupta">Sadhvi Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Charulatha%20S."> Charulatha S.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Since the dawn of the early 1950s humans have launched numerous vehicles in space. Be it from rockets to rovers humans have done tremendous growth in the technology sector. While there is mostly upside for it for humans the only major downside which cannot be ignored now is the amount of junk produced in space due to it i.e. space debris. All this space junk amounts from objects we launch from earth which so remains in orbit until it re-enters the atmosphere. Space debris can be of various sizes mainly the big ones are of the dead satellites floating in space and small ones can consist of various things like paint flecks, screwdrivers, bolts etc. Tracking of small space debris whose size is less than 10 cm is impossible and can have vast implications. As the amount of space debris increases in space the chances of it hitting a functional satellite also increases. And it is extremely costly to repair or recover the satellite once hit by a revolving space debris. So the proposed solution is, Actively removing space debris while keeping space sustainability in mind. For this solution a total of 8 modules will be launched in LEO and in GEO and these models will be placed in their desired orbits through Hohmann transfer and for that calculating ΔV values is crucial. After which the modules will be placed in their designated positions in STK software and thorough analysis is conducted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20debris" title="space debris">space debris</a>, <a href="https://publications.waset.org/abstracts/search?q=Hohmann%20transfer" title=" Hohmann transfer"> Hohmann transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=STK" title=" STK"> STK</a>, <a href="https://publications.waset.org/abstracts/search?q=delta-V" title=" delta-V"> delta-V</a> </p> <a href="https://publications.waset.org/abstracts/166831/computation-of-dv-requirements-for-space-debris-removal-using-orbital-transfer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166831.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">86</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">3692</span> A Variable Structural Control for a Flexible Lamina</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xuezhang%20Hou">Xuezhang Hou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title="partial differential equations">partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=flexible%20lamina" title=" flexible lamina"> flexible lamina</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20structural%20control" title=" variable structural control"> variable structural control</a>, <a href="https://publications.waset.org/abstracts/search?q=semigroup%20of%20linear%20operators" title=" semigroup of linear operators"> semigroup of linear operators</a> </p> <a href="https://publications.waset.org/abstracts/167218/a-variable-structural-control-for-a-flexible-lamina" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167218.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">85</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">3691</span> Need of National Space Legislation for Space Faring Nations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Naveed">Muhammad Naveed</a>, <a href="https://publications.waset.org/abstracts/search?q=Yang%20Caixia"> Yang Caixia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The need for national space legislation is pivotal, particularly in light of the fact that in recent years space activities have grown immensely both in volume and diversity. Countries are progressively developing capabilities in space exploration and scientific discoveries, market their capabilities to manufacture satellites, provide launch services from their facilities and are looking to privatize and commercialize their space resources. Today, nations are also seeking to comprehend the technological and financial potential of the private sector and are considering to share their financial burdens with them and to limit their exposures to risks, but they are lagging behind in legal framework in this regard. In the perspective of these emerging developments, it is therefore, felt that national space legislation should be enacted with the goal of building and implementing a vibrant and transparent legal framework at the national level to hasten investments and to ensure growth in this capital intensive - highly yield strategic sector. This study looks at (I) the international legal framework that governs space activities; (II) motivation behind making national space laws; and (III) the need for national space legislation. The paper concludes with some recommendations with regards to the conceivable future direction for national space legislation, in particular space empowered sub-areas for countries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=international%20conventions" title="international conventions">international conventions</a>, <a href="https://publications.waset.org/abstracts/search?q=national%20legislation" title=" national legislation"> national legislation</a>, <a href="https://publications.waset.org/abstracts/search?q=space%20faring%20nations" title=" space faring nations"> space faring nations</a>, <a href="https://publications.waset.org/abstracts/search?q=space%20law" title=" space law"> space law</a> </p> <a href="https://publications.waset.org/abstracts/73072/need-of-national-space-legislation-for-space-faring-nations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73072.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">277</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hilbert%20space&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hilbert%20space&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hilbert%20space&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hilbert%20space&page=5">5</a></li> <li class="page-item"><a class="page-link" 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