Subjects -> MATHEMATICS (Total: 1061 journals)
    - APPLIED MATHEMATICS (86 journals)
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    - MATHEMATICS (783 journals)
    - MATHEMATICS (GENERAL) (43 journals)
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    - PROBABILITIES AND MATH STATISTICS (103 journals)

MATHEMATICS (783 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 11)
Advances in Materials Science     Open Access   (Followers: 18)
Advances in Mathematical Physics     Open Access   (Followers: 8)
Advances in Mathematics     Full-text available via subscription   (Followers: 17)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in Numerical Analysis     Open Access   (Followers: 9)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 10)
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 9)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 6)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 3)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 12)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 5)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 25)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 22)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (Followers: 1)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Analysis and Applications
Journal Prestige (SJR): 1.188
Citation Impact (citeScore): 2
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0219-5305 - ISSN (Online) 1793-6861
Published by World Scientific Homepage  [119 journals]
  • Asymptotics of solutions to a fifth-order modified Korteweg–de Vries
           equation in the quarter plane
    • Authors: Nan Liu, Boling Guo
      Pages: 1 - 46
      Abstract: Analysis and Applications, Ahead of Print.
      The large-time behavior of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane is established. Our approach uses the unified transform method of Fokas and the nonlinear steepest descent method of Deift and Zhou.
      Citation: Analysis and Applications
      PubDate: 2020-01-23T08:00:00Z
      DOI: 10.1142/S0219530519500210
       
  • Large deviation rates for Markov branching processes
    • Authors: Junping Li, Lan Cheng, Anthony G. Pakes, Anyue Chen, Liuyan Li
      Pages: 1 - 22
      Abstract: Analysis and Applications, Ahead of Print.
      Large deviation rates are determined for quantities associated with a Markov branching process [math] having offspring mean [math] and split rate [math]. The principal quantities examined are [math] and [math], where [math] is the almost sure limit of an appropriately normed version of [math]. Modifications and conditional versions are examined. Some of this requires determination of the asymptotic behavior of harmonic moments [math].
      Citation: Analysis and Applications
      PubDate: 2020-01-21T08:00:00Z
      DOI: 10.1142/S0219530519500209
       
  • Performance analysis of the LapRSSLG algorithm in learning theory
    • Authors: Baohuai Sheng, Haizhang Zhang
      Pages: 79 - 108
      Abstract: Analysis and Applications, Volume 18, Issue 01, Page 79-108, January 2020.
      It is known that one aim of semi-supervised learning is to improve the prediction performance using a few labeled data with a large set of unlabeled data. Recently, a Laplacian regularized semi-supervised learning gradient (LapRSSLG) algorithm associated with data adjacency graph edge weights is proposed in the literature. The algorithm receives success in applications, but there is no theory on the performance analysis. In this paper, an explicit learning rate estimate for the algorithm is provided, which shows that the convergence is indeed controlled by the unlabeled data.
      Citation: Analysis and Applications
      PubDate: 2019-12-16T08:00:00Z
      DOI: 10.1142/S0219530519410033
       
  • Convergence analysis of distributed multi-penalty regularized pairwise
           learning
    • Authors: Ting Hu, Jun Fan, Dao-Hong Xiang
      Pages: 109 - 127
      Abstract: Analysis and Applications, Volume 18, Issue 01, Page 109-127, January 2020.
      In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with [math]-error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization.
      Citation: Analysis and Applications
      PubDate: 2019-12-16T08:00:00Z
      DOI: 10.1142/S0219530519410045
       
  • Optimal learning with Gaussians and correntropy loss
    • Authors: Fusheng Lv, Jun Fan
      Pages: 1 - 18
      Abstract: Analysis and Applications, Ahead of Print.
      Correntropy-based learning has achieved great success in practice during the last decades. It is originated from information-theoretic learning and provides an alternative to classical least squares method in the presence of non-Gaussian noise. In this paper, we investigate the theoretical properties of learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and correntropy loss. By choosing an appropriate scale parameter of Gaussian kernel, we show the polynomial decay of approximation error under a Sobolev smoothness condition. In addition, we employ a tight upper bound for the uniform covering number of Gaussian RKHS in order to improve the estimate of sample error. Based on these two results, we show that the proposed algorithm using varying Gaussian kernel achieves the minimax rate of convergence (up to a logarithmic factor) without knowing the smoothness level of the regression function.
      Citation: Analysis and Applications
      PubDate: 2019-11-11T06:55:29Z
      DOI: 10.1142/S0219530519410124
       
  • A randomized incremental primal-dual method for decentralized consensus
           optimization
    • Authors: Chenxi Chen, Yunmei Chen, Xiaojing Ye
      Pages: 1 - 25
      Abstract: Analysis and Applications, Ahead of Print.
      We consider a class of convex decentralized consensus optimization problems over connected multi-agent networks. Each agent in the network holds its local objective function privately, and can only communicate with its directly connected agents during the computation to find the minimizer of the sum of all objective functions. We propose a randomized incremental primal-dual method to solve this problem, where the dual variable over the network in each iteration is only updated at a randomly selected node, whereas the dual variables elsewhere remain the same as in the previous iteration. Thus, the communication only occurs in the neighborhood of the selected node in each iteration and hence can greatly reduce the chance of communication delay and failure in the standard fully synchronized consensus algorithms. We provide comprehensive convergence analysis including convergence rates of the primal residual and consensus error of the proposed algorithm, and conduct numerical experiments to show its performance using both uniform sampling and important sampling as node selection strategy.
      Citation: Analysis and Applications
      PubDate: 2019-11-07T06:08:24Z
      DOI: 10.1142/S0219530519410082
       
  • Adaptive display images
    • Authors: Meipeng Zhi, Yuesheng Xu
      Pages: 1 - 23
      Abstract: Analysis and Applications, Ahead of Print.
      We develop a numerical method for construction of an adaptive display image from a given display image which is an artificial scene displayed in a computer screen. The adaptive display image is encoded on an adaptive pixel mesh obtained by a merging scheme from the original pixel mesh. The cardinality of the adaptive pixel mesh is significantly less than that of the original pixel mesh. The resulting adaptive display image is the best [math] piecewise constant approximation of the original display image. Under the assumption that a natural image, the real scene that we see, belongs to a Besov space, we provide the optimal [math] error estimate between the adaptive display image and its original natural image. Experimental results are presented to demonstrate the visual quality, the approximation accuracy and the computational complexity of the adaptive display image.
      Citation: Analysis and Applications
      PubDate: 2019-11-07T06:08:24Z
      DOI: 10.1142/S0219530519410112
       
  • Jointly low-rank and bisparse recovery: Questions and partial answers
    • Authors: Simon Foucart, Rémi Gribonval, Laurent Jacques, Holger Rauhut
      Pages: 1 - 24
      Abstract: Analysis and Applications, Ahead of Print.
      We investigate the problem of recovering jointly [math]-rank and [math]-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that [math] measurements make the recovery possible in theory, meaning via a nonpractical algorithm. In case of arbitrary measurements, we investigate the possibility of achieving practical recovery via an iterative-hard-thresholding algorithm when [math] for some exponent [math]. We show that this is feasible for [math], and that the proposed analysis cannot cover the case [math]. The precise value of the optimal exponent [math] is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure. Some related questions are partially answered in passing. For rank-one measurements, we suggest on arcane grounds an iterative-hard-thresholding algorithm modified to exploit the nonstandard restricted isometry property obeyed by this type of measurements.
      Citation: Analysis and Applications
      PubDate: 2019-11-07T06:08:23Z
      DOI: 10.1142/S0219530519410094
       
  • Generalized representer theorems in Banach spaces
    • Authors: Liren Huang, Chunguang Liu, Lulin Tan, Qi Ye
      Pages: 1 - 22
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we generalize the representer theorems in Banach spaces by the theory of nonsmooth analysis. The generalized representer theorems assure that the regularized learning models can be constructed by the nonconvex loss functions, the generalized training data, and the general Banach spaces which are nonreflexive, nonstrictly convex, and nonsmooth. Specially, the sparse representations of the regularized learning in 1-norm reproducing kernel Banach spaces are shown by the generalized representer theorems.
      Citation: Analysis and Applications
      PubDate: 2019-11-07T06:08:23Z
      DOI: 10.1142/S0219530519410100
       
  • A self-adaptive regularized alternating least squares method for tensor
           decomposition problems
    • Authors: Xianpeng Mao, Gonglin Yuan, Yuning Yang
      Pages: 1 - 19
      Abstract: Analysis and Applications, Ahead of Print.
      Though the alternating least squares algorithm (ALS), as a classic and easily implemented algorithm, has been widely applied to tensor decomposition and approximation problems, it has some drawbacks: the convergence of ALS is not guaranteed, and the swamp phenomenon appears in some cases, causing the convergence rate to slow down dramatically. To overcome these shortcomings, the regularized-ALS algorithm (RALS) was proposed in the literature. By employing the optimal step-size selection rule, we develop a self-adaptive regularized alternating least squares method (SA-RALS) to accelerate RALS in this paper. Theoretically, we show that the step-size is always larger than unity, and can be larger than [math], which is quite different from several optimization algorithms. Furthermore, under mild assumptions, we prove that the whole sequence generated by SA-RALS converges to a stationary point of the objective function. Numerical results verify that the SA-RALS performs better than RALS in terms of the number of iterations and the CPU time.
      Citation: Analysis and Applications
      PubDate: 2019-10-29T07:36:38Z
      DOI: 10.1142/S0219530519410057
       
  • Generalized support vector regression: Duality and tensor-kernel
           representation
    • Authors: Saverio Salzo, Johan A. K. Suykens
      Pages: 1 - 35
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel–Rockafellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type of kernels describes Banach spaces of analytic functions and includes generalizations of the exponential and polynomial kernels as well as, in the complex case, generalizations of the Szegö and Bergman kernels.
      Citation: Analysis and Applications
      PubDate: 2019-10-29T07:36:36Z
      DOI: 10.1142/S0219530519410069
       
  • Online regularized pairwise learning with least squares loss
    • Authors: Cheng Wang, Ting Hu
      Pages: 1 - 30
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we study online algorithm for pairwise problems generated from the Tikhonov regularization scheme associated with the least squares loss function and a reproducing kernel Hilbert space (RKHS). This work establishes the convergence for the last iterate of the online pairwise algorithm with the polynomially decaying step sizes and varying regularization parameters. We show that the obtained error rate in [math]-norm can be nearly optimal in the minimax sense under some mild conditions. Our analysis is achieved by a sharp estimate for the norms of the learning sequence and the characterization of RKHS using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.
      Citation: Analysis and Applications
      PubDate: 2019-10-29T07:36:35Z
      DOI: 10.1142/S0219530519410070
       
  • Weighted [math]-regular kernels for reproducing kernel Hilbert spaces and
           Mercer Theorem
    • Authors: L. Agud, J. M. Calabuig, E. A. Sánchez Pérez
      Pages: 1 - 25
      Abstract: Analysis and Applications, Ahead of Print.
      Let [math] be a finite measure space and consider a Banach function space [math]. Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Köthe–Bochner (vector-valued) function spaces. We analyze operator-valued kernels [math] that define integration maps [math] between Köthe–Bochner spaces of Hilbert-valued functions [math] We show a reduction procedure which allows to find a factorization of the corresponding kernel operator through weighted Bochner spaces [math] and [math] — where [math] — under the assumption of [math]-concavity of [math] Equivalently, a new kernel obtained by multiplying [math] by scalar functions can be given in such a way that the kernel operator is defined from [math] to [math] in a natural way. As an application, we prove a new version of Mercer Theorem for matrix-valued weighted kernels.
      Citation: Analysis and Applications
      PubDate: 2019-10-01T06:25:18Z
      DOI: 10.1142/S0219530519500179
       
  • The Cauchy problem for a two-dimensional generalized
           Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces
    • Authors: Wei Yan, Yongsheng Li, Jianhua Huang, Jinqiao Duan
      Pages: 1 - 54
      Abstract: Analysis and Applications, Ahead of Print.
      The goal of this paper is three-fold. First, we prove that the Cauchy problem for a generalized KP-I equation ut + Dx α∂ xu + ∂x−1∂ y2u + 1 2∂x(u2) = 0,α ≥ 4 is locally well-posed in the anisotropic Sobolev spaces [math] with [math] and [math]. Second, we prove that the Cauchy problem is globally well-posed in [math] with [math] if [math]. Finally, we show that the Cauchy problem is globally well-posed in [math] with [math] if [math] Our result improves the result of Saut and Tzvetkov [The Cauchy problem for the fifth order KP equations, J. Math. Pures Appl. 79 (2000) 307–338] and Li and Xiao [Well-posedness of the fifth order Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces with nonnegative indices, J. Math. Pures Appl. 90 (2008) 338–352].
      Citation: Analysis and Applications
      PubDate: 2019-10-01T06:25:18Z
      DOI: 10.1142/S0219530519500180
       
  • On the [math]-functional in learning theory
    • Authors: Bao-Huai Sheng, Jian-Li Wang
      Pages: 1 - 24
      Abstract: Analysis and Applications, Ahead of Print.
      [math]-functionals are used in learning theory literature to study approximation errors in kernel-based regularization schemes. In this paper, we study the approximation error and [math]-functionals in [math] spaces with [math]. To this end, we give a new viewpoint for a reproducing kernel Hilbert space (RKHS) from a fractional derivative and treat powers of the induced integral operator as fractional derivatives of various orders. Then a generalized translation operator is defined by Fourier multipliers, with which a generalized modulus of smoothness is defined. Some general strong equivalent relations between the moduli of smoothness and the [math]-functionals are established. As applications, some strong equivalent relations between these two families of quantities on the unit sphere and the unit ball are provided explicitly.
      Citation: Analysis and Applications
      PubDate: 2019-10-01T06:25:17Z
      DOI: 10.1142/S0219530519500192
       
  • Local strong solutions to the Cauchy problem of two-dimensional
           nonhomogeneous magneto-micropolar fluid equations with nonnegative density
           
    • Authors: Xin Zhong
      Pages: 1 - 29
      Abstract: Analysis and Applications, Ahead of Print.
      We study the Cauchy problem of nonhomogeneous magneto-micropolar fluid system with zero density at infinity in the entire space [math]. We prove that the system admits a unique local strong solution provided the initial density and the initial magnetic field decay not too slowly at infinity. In particular, there is no need to require any Choe–Kim type compatibility condition for the initial data.
      Citation: Analysis and Applications
      PubDate: 2019-09-09T08:02:45Z
      DOI: 10.1142/S0219530519500167
       
  • Approximation by max-product sampling Kantorovich operators with
           generalized kernels
    • Authors: Lucian Coroianu, Danilo Costarelli, Sorin G. Gal, Gianluca Vinti
      Pages: 1 - 26
      Abstract: Analysis and Applications, Ahead of Print.
      In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [math] convergence, and quantitative estimates with respect to the [math] norm, [math]-functionals and [math]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.
      Citation: Analysis and Applications
      PubDate: 2019-08-19T06:31:09Z
      DOI: 10.1142/S0219530519500155
       
  • Error bounds for approximations with deep ReLU neural networks in [math]
           norms
    • Authors: Ingo Gühring, Gitta Kutyniok, Philipp Petersen
      Pages: 1 - 57
      Abstract: Analysis and Applications, Ahead of Print.
      We analyze to what extent deep Rectified Linear Unit (ReLU) neural networks can efficiently approximate Sobolev regular functions if the approximation error is measured with respect to weaker Sobolev norms. In this context, we first establish upper approximation bounds by ReLU neural networks for Sobolev regular functions by explicitly constructing the approximate ReLU neural networks. Then, we establish lower approximation bounds for the same type of function classes. A trade-off between the regularity used in the approximation norm and the complexity of the neural network can be observed in upper and lower bounds. Our results extend recent advances in the approximation theory of ReLU networks to the regime that is most relevant for applications in the numerical analysis of partial differential equations.
      Citation: Analysis and Applications
      PubDate: 2019-08-19T06:31:08Z
      DOI: 10.1142/S0219530519410021
       
  • Superposition, reduction of multivariable problems, and approximation
    • Authors: Palle E. T. Jorgensen, James F. Tian
      Pages: 1 - 31
      Abstract: Analysis and Applications, Ahead of Print.
      We study reduction schemes for functions of “many” variables into system of functions in one variable. Our setting includes infinite dimensions. Following Cybenko–Kolmogorov, the outline for our results is as follows: We present explicit reduction schemes for multivariable problems, covering both a finite, and an infinite, number of variables. Starting with functions in “many” variables, we offer constructive reductions into superposition, with component terms, that make use of only functions in one variable, and specified choices of coordinate directions. Our proofs are transform based, using explicit transforms, Fourier and Radon; as well as multivariable Shannon interpolation.
      Citation: Analysis and Applications
      PubDate: 2019-08-05T06:44:19Z
      DOI: 10.1142/S021953051941001X
       
  • Liftings for ultra-modulation spaces, and one-parameter groups of
           Gevrey-type pseudo-differential operators
    • Authors: Ahmed Abdeljawad, Sandro Coriasco, Joachim Toft
      Pages: 1 - 61
      Abstract: Analysis and Applications, Ahead of Print.
      We deduce one-parameter group properties for pseudo-differential operators [math], where [math] belongs to the class [math] of certain Gevrey symbols. We use this to show that there are pseudo-differential operators [math] and [math] which are inverses to each other, where [math] and [math]. We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions [math] moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) [math] is an isomorphism from [math] to [math] for every [math].
      Citation: Analysis and Applications
      PubDate: 2019-07-30T02:40:53Z
      DOI: 10.1142/S0219530519500143
       
  • Stability and optimization error of stochastic gradient descent for
           pairwise learning
    • Authors: Wei Shen, Zhenhuan Yang, Yiming Ying, Xiaoming Yuan
      Pages: 1 - 41
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking, metric learning, area under ROC curve (AUC) maximization and minimum error entropy (MEE) principle. Our contribution is twofolded. Firstly, we establish the stability results for SGD for pairwise learning in the convex, strongly convex and non-convex settings, from which generalization errors can be naturally derived. Secondly, we establish the trade-off between stability and optimization error of SGD algorithms for pairwise learning. This is achieved by lower-bounding the sum of stability and optimization error by the minimax statistical error over a prescribed class of pairwise loss functions. From this fundamental trade-off, we obtain lower bounds for the optimization error of SGD algorithms and the excess expected risk over a class of pairwise losses. In addition, we illustrate our stability results by giving some specific examples of AUC maximization, metric learning and MEE.
      Citation: Analysis and Applications
      PubDate: 2019-07-24T03:00:36Z
      DOI: 10.1142/S0219530519400062
       
  • PhaseMax: Stable guarantees from noisy sub-Gaussian measurements
    • Authors: Huiping Li, Song Li, Yu Xia
      Pages: 1 - 26
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we consider the noisy phase retrieval problem which occurs in many different areas of science and physics. The PhaseMax algorithm is an efficient convex method to tackle with phase retrieval problem. On the basis of this algorithm, we propose two kinds of extended formulations of the PhaseMax algorithm, namely, PhaseMax with bounded and non-negative noise and PhaseMax with outliers to deal with the phase retrieval problem under different noise corruptions. Then we prove that these extended algorithms can stably recover real signals from independent sub-Gaussian measurements under optimal sample complexity. Specially, such results remain valid in noiseless case. As we can see, these results guarantee that a broad range of random measurements such as Bernoulli measurements with erasures can be applied to reconstruct the original signals by these extended PhaseMax algorithms. Finally, we demonstrate the effectiveness of our extended PhaseMax algorithm through numerical simulations. We find that with the same initialization, extended PhaseMax algorithm outperforms Truncated Wirtinger Flow method, and recovers the signal with corrupted measurements robustly.
      Citation: Analysis and Applications
      PubDate: 2019-07-24T03:00:33Z
      DOI: 10.1142/S0219530519400049
       
  • Limits of the Stokes and Navier–Stokes equations in a punctured
           periodic domain
    • Authors: Michel Chipot, Jérôme Droniou, Gabriela Planas, James C. Robinson, Wei Xue
      Pages: 1 - 25
      Abstract: Analysis and Applications, Ahead of Print.
      We treat three problems on a two-dimensional “punctured periodic domain”: we take [math], where [math] and [math] is the closure of an open connected set that is star-shaped with respect to [math] and has a [math] boundary. We impose periodic boundary conditions on the boundary of [math], and Dirichlet boundary conditions on [math]. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier–Stokes equations, all with a fixed forcing function [math], and examine the behavior of solutions as [math]. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of [math] with periodic boundary conditions.
      Citation: Analysis and Applications
      PubDate: 2019-07-05T08:54:22Z
      DOI: 10.1142/S0219530519500118
       
  • Existence of strong solutions to the rotating shallow water equations with
           degenerate viscosities
    • Authors: Ben Duan, Zhen Luo, Yan Zhou
      Pages: 1 - 26
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we consider the Cauchy problem of a viscous compressible shallow water equations with the Coriolis force term and non-constant viscosities. More precisely, the viscous coefficients are constants multiple of height, the equations are degenerate when vacuum appears. For initial data allowing vacuum, the local existence of strong solution is obtained and a blow-up criterion is established.
      Citation: Analysis and Applications
      PubDate: 2019-07-05T08:54:22Z
      DOI: 10.1142/S021953051950012X
       
  • Solutions of the Al-Salam–Chihara and allied moment problems
    • Authors: Mourad E. H. Ismail
      Pages: 1 - 26
      Abstract: Analysis and Applications, Ahead of Print.
      We study the moment problem associated with the Al-Salam–Chihara polynomials in some detail providing raising (creation) and lowering (annihilation) operators, Rodrigues formula, and a second-order operator equation involving the Askey–Wilson operator. A new infinite family of weight functions is also given. Sufficient conditions for functions to be weight functions for the [math]-Hermite, [math]-Laguerre and Stieltjes–Wigert polynomials are established and used to give new infinite families of absolutely continuous orthogonality measures for each of these polynomials.
      Citation: Analysis and Applications
      PubDate: 2019-06-14T06:00:54Z
      DOI: 10.1142/S0219530519500088
       
  • Three-fold symmetric Hahn-classical multiple orthogonal polynomials
    • Authors: Ana F. Loureiro, Walter Van Assche
      Pages: 1 - 62
      Abstract: Analysis and Applications, Ahead of Print.
      We characterize all the multiple orthogonal three-fold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called the Hahn property and it is an extension of the concept of classical polynomials to the context of multiple orthogonality. The emphasis is on the polynomials whose indices lie on the step line, also known as [math]-orthogonal polynomials. We explain the relation of the asymptotic behavior of the recurrence coefficients to that of the largest zero (in absolute value) of the polynomial set. We provide a full characterization of the Hahn-classical orthogonality measures supported on a [math]-star in the complex plane containing all the zeros of the polynomials. There are essentially three distinct families, one of them [math]-orthogonal with respect to two confluent functions of the second kind. This paper complements earlier research of Douak and Maroni.
      Citation: Analysis and Applications
      PubDate: 2019-06-14T06:00:53Z
      DOI: 10.1142/S0219530519500106
       
  • Asymptotics of the Wilson polynomials
    • Authors: Yu-Tian Li, Xiang-Sheng Wang, Roderick Wong
      Pages: 1 - 34
      Abstract: Analysis and Applications, Ahead of Print.
      In this paper, we study the asymptotic behavior of the Wilson polynomials [math] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable [math] is fixed and (ii) when the variable is rescaled as [math] with [math]. Case (ii) has two subcases, namely, (a) zero-free zone ([math]) and (b) oscillatory region [math]. Corresponding results are also obtained in these cases (iii) when [math] lies in a neighborhood of the transition point [math], and (iv) when [math] is in the neighborhood of the transition point [math]. The expansions in the last two cases hold uniformly in [math]. Case (iv) is also the only unsettled case in a sequence of works on the asymptotic analysis of linear difference equations.
      Citation: Analysis and Applications
      PubDate: 2019-05-16T02:23:12Z
      DOI: 10.1142/S0219530519500076
       
  • Linear perturbations of the Wigner distribution and the Cohen class
    • Authors: Elena Cordero, S. Ivan Trapasso
      Pages: 1 - 38
      Abstract: Analysis and Applications, Ahead of Print.
      The Wigner distribution is a milestone of Time–frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kinds of modifications have been proposed. This contribution fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As a main result, we provide a characterization for the Cohen’s class [L. Cohen, Generalized phase-space distribution functions, J. Math. Phys. 7 (1996) 781–786; Time–frequency Analysis (Prentice Hall, New Jersey, 1995)]. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.
      Citation: Analysis and Applications
      PubDate: 2019-03-25T02:23:53Z
      DOI: 10.1142/S0219530519500052
       
 
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