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  Subjects -> MATHEMATICS (Total: 886 journals)
    - APPLIED MATHEMATICS (72 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (656 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 22)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 8)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
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  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 1)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
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: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 8)
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: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     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 Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
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: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Axioms
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   ISSN (Online) 2075-1680
   Published by MDPI Homepage  [156 journals]
  • Axioms, Vol. 6, Pages 17: An Independent Set of Axioms of MV-Algebras and
           Solutions of the Set-Theoretical Yang–Baxter Equation

    • Authors: Tahsin Oner, Ibrahim Senturk, Gulsah Oner
      First page: 17
      Abstract: The aim of this paper is to give a new equivalent set of axioms for MV-algebras, and to show that the axioms are independent. In addition to this, we handle Yang–Baxter equation problem. In conclusion, we construct a new set-theoretical solution for the Yang–Baxter equation by using MV-algebras.
      Citation: Axioms
      PubDate: 2017-06-22
      DOI: 10.3390/axioms6030017
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 18: Fractional Integration and Differentiation of
           the Generalized Mathieu Series

    • Authors: Ram Saxena, Rakesh Parmar
      First page: 18
      Abstract: We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series S μ ( r ) , which are expressed in terms of the Hadamard product of the generalized Mathieu series S μ ( r ) and the Fox–Wright function p Ψ q ( z ) . Corresponding assertions for the classical Riemann–Liouville and Erdélyi–Kober fractional integral and differential operators are deduced. Further, it is emphasized that the results presented here, which are for a seemingly complicated series, can reveal their involved properties via the series of the two known functions.
      Citation: Axioms
      PubDate: 2017-06-27
      DOI: 10.3390/axioms6030018
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 19: Assigning Numerical Scores to Linguistic
           Expressions

    • Authors: María Campión, Edurne Falcó, José García-Lapresta, Esteban Induráin
      First page: 19
      Abstract: In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed.
      Citation: Axioms
      PubDate: 2017-07-06
      DOI: 10.3390/axioms6030019
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 20: Quincunx Fundamental Refinable Functions in
           Arbitrary Dimensions

    • Authors: Xiaosheng Zhuang
      First page: 20
      Abstract: In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension d = 2 , we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks.
      Citation: Axioms
      PubDate: 2017-07-06
      DOI: 10.3390/axioms6030020
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 21: The SIC Question: History and State of Play

    • Authors: Christopher Fuchs, Michael Hoang, Blake Stacey
      First page: 21
      Abstract: Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott’s code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.
      Citation: Axioms
      PubDate: 2017-07-18
      DOI: 10.3390/axioms6030021
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 22: New Order on Type 2 Fuzzy Numbers

    • Authors: Pablo Hernández, Susana Cubillo, Carmen Torres-Blanc, José Guerrero
      First page: 22
      Abstract: Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers.
      Citation: Axioms
      PubDate: 2017-07-28
      DOI: 10.3390/axioms6030022
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 23: Categorically Closed Topological Groups

    • Authors: Taras Banakh
      First page: 23
      Abstract: Let C → be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category C → is called C → -closed if for each morphism Φ ⊂ X × Y in the category C → the image Φ ( X ) = { y ∈ Y : ∃ x ∈ X ( x , y ) ∈ Φ } is closed in Y. In the paper we survey existing and new results on topological groups, which are C → -closed for various categories C → of topologized semigroups.
      Citation: Axioms
      PubDate: 2017-07-30
      DOI: 10.3390/axioms6030023
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 24: Topological Signals of Singularities in Ricci
           Flow

    • Authors: Paul Alsing, Howard Blair, Matthew Corne, Gordon Jones, Warner Miller, Konstantin Mischaikow, Vidit Nanda
      First page: 24
      Abstract: We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point) from local singularity formation (neckpinch). Finally, we discuss the interpretation and implication of these results and future applications.
      Citation: Axioms
      PubDate: 2017-08-01
      DOI: 10.3390/axioms6030024
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 25: Orness For Idempotent Aggregation Functions

    • Authors: Leire Legarreta, Inmaculada Lizasoain, Iraide Mardones-Pérez
      First page: 25
      Abstract: Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.
      Citation: Axioms
      PubDate: 2017-09-20
      DOI: 10.3390/axioms6030025
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 26: From Normal Surfaces to Normal Curves to
           Geodesics on Surfaces

    • Authors: Eli Appleboim
      First page: 26
      Abstract: This paper gives a study of a two dimensional version of the theory of normal surfaces; namely, a study o normal curves and their relations with respect to geodesic curves. This study results with a nice discrete approximation of geodesics embedded in a triangulated orientable Riemannian surface. Experimental results of the two dimensional case are given as well.
      Citation: Axioms
      PubDate: 2017-09-20
      DOI: 10.3390/axioms6030026
      Issue No: Vol. 6, No. 3 (2017)
       
  • Axioms, Vol. 6, Pages 7: Fourier Series for Singular Measures

    • Authors: John Herr, Eric Weber
      First page: 7
      Abstract: Using the Kaczmarz algorithm, we prove that for any singular Borel probability measure μ on [ 0 , 1 ) , every f ∈ L 2 ( μ ) possesses a Fourier series of the form f ( x ) = ∑ n = 0 ∞ c n e 2 π i n x . We show that the coefficients c n can be computed in terms of the quantities f ^ ( n ) = ∫ 0 1 f ( x ) e − 2 π i n x d μ ( x ) . We also demonstrate a Shannon-type sampling theorem for functions that are in a sense μ -bandlimited.
      Citation: Axioms
      PubDate: 2017-03-28
      DOI: 10.3390/axioms6020007
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 8: Expansion of the Kullback-Leibler Divergence, and
           a New Class of Information Metrics

    • Authors: David Galas, Gregory Dewey, James Kunert-Graf, Nikita Sakhanenko
      First page: 8
      Abstract: Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this class of problem. This study takes an approach that simplifies many aspects of these problems by presenting a structured, series expansion of the Kullback-Leibler divergence—a function central to information theory—and devise a distance metric based on this divergence. Using the Möbius inversion duality between multivariable entropies and multivariable interaction information, we express the divergence as an additive series in the number of interacting variables, which provides a restricted and simplified set of distributions to use as approximation and with which to model data. Truncations of this series yield approximations based on the number of interacting variables. The first few terms of the expansion-truncation are illustrated and shown to lead naturally to familiar approximations, including the well-known Kirkwood superposition approximation. Truncation can also induce a simple relation between the multi-information and the interaction information. A measure of distance between distributions, based on Kullback-Leibler divergence, is then described and shown to be a true metric if properly restricted. The expansion is shown to generate a hierarchy of metrics and connects this work to information geometry formalisms. An example of the application of these metrics to a graph comparison problem is given that shows that the formalism can be applied to a wide range of network problems and provides a general approach for systematic approximations in numbers of interactions or connections, as well as a related quantitative metric.
      Citation: Axioms
      PubDate: 2017-04-01
      DOI: 10.3390/axioms6020008
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 9: Euclidean Algorithm for Extension of Symmetric
           Laurent Polynomial Matrix and Its Application in Construction of Multiband
           Symmetric Perfect Reconstruction Filter Bank

    • Authors: Jianzhong Wang
      First page: 9
      Abstract: For a given pair of s-dimensional real Laurent polynomials ( a → ( z ) , b → ( z ) ) , which has a certain type of symmetry and satisfies the dual condition b → ( z ) T a → ( z ) = 1 , an s × s Laurent polynomial matrix A ( z ) (together with its inverse A - 1 ( z ) ) is called a symmetric Laurent polynomial matrix extension of the dual pair ( a → ( z ) , b → ( z ) ) if A ( z ) has similar symmetry, the inverse A - 1 ( Z ) also is a Laurent polynomial matrix, the first column of A ( z ) is a → ( z ) and the first row of A - 1 ( z ) is ( b → ( z ) ) T . In this paper, we introduce the Euclidean symmetric division and the symmetric elementary matrices in the Laurent polynomial ring and reveal their relation. Based on the Euclidean symmetric division algorithm in the Laurent polynomial ring, we develop a novel and effective algorithm for symmetric Laurent polynomial matrix extension. We also apply the algorithm in the construction of multi-band symmetric perfect reconstruction filter banks.
      Citation: Axioms
      PubDate: 2017-04-20
      DOI: 10.3390/axioms6020009
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 10: Orientation Asymmetric Surface Model for
           Membranes: Finsler Geometry Modeling

    • Authors: Evgenii Proutorov, Hiroshi Koibuchi
      First page: 10
      Abstract: We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Euclidean metric δ a b , can be extended to a more general non-Euclidean metric on M in the continuous model. The problem we focus on in this paper is whether such an extension is well defined or not in the discrete model. We find that a discrete surface model with a nontrivial metric becomes well defined if it is treated in the context of Finsler geometry (FG) modeling, where triangle edge length in M depends on the direction. It is also shown that the discrete FG model is orientation asymmetric on invertible surfaces in general, and for this reason, the FG model has a potential advantage for describing real physical membranes, which are expected to have some asymmetries for orientation-changing transformations.
      Citation: Axioms
      PubDate: 2017-04-25
      DOI: 10.3390/axioms6020010
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 11: Multivariate Extended Gamma Distribution

    • Authors: Dhannya Joseph
      First page: 11
      Abstract: In this paper, I consider multivariate analogues of the extended gamma density, which will provide multivariate extensions to Tsallis statistics and superstatistics. By making use of the pathway parameter β , multivariate generalized gamma density can be obtained from the model considered here. Some of its special cases and limiting cases are also mentioned. Conditional density, best predictor function, regression theory, etc., connected with this model are also introduced.
      Citation: Axioms
      PubDate: 2017-04-24
      DOI: 10.3390/axioms6020011
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 12: Toward Measuring Network Aesthetics Based on
           Symmetry

    • Authors: Zengqiang Chen, Matthias Dehmer, Frank Emmert-Streib, Abbe Mowshowitz, Yongtang Shi
      First page: 12
      Abstract: In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer’s perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics.
      Citation: Axioms
      PubDate: 2017-05-06
      DOI: 10.3390/axioms6020012
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 13: No Uncountable Polish Group Can be a
           Right-Angled Artin Group

    • Authors: Gianluca Paolini, Saharon Shelah
      First page: 13
      Abstract: We prove that if G is a Polish group and A a group admitting a system of generators whose associated length function satisfies: (i) if 0 < k < ω , then l g ( x ) ≤ l g ( x k ) ; (ii) if l g ( y ) < k < ω and x k = y , then x = e , then there exists a subgroup G * of G of size b (the bounding number) such that G * is not embeddable in A. In particular, we prove that the automorphism group of a countable structure cannot be an uncountable right-angled Artin group. This generalizes analogous results for free and free abelian uncountable groups.
      Citation: Axioms
      PubDate: 2017-05-11
      DOI: 10.3390/axioms6020013
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 14: Tsallis Entropy and Generalized Shannon
           Additivity

    • Authors: Sonja Jäckle, Karsten Keller
      First page: 14
      Abstract: The Tsallis entropy given for a positive parameter α can be considered as a generalization of the classical Shannon entropy. For the latter, corresponding to α = 1 , there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playing a central role. The main aim of this paper is to discuss this axiom in the context of Tsallis entropy. We show that it is sufficient for characterizing Tsallis entropy, with the exceptions of cases α = 1 , 2 discussed separately.
      Citation: Axioms
      PubDate: 2017-06-14
      DOI: 10.3390/axioms6020014
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 15: Scalable and Fully Distributed Localization in
           Large-Scale Sensor Networks

    • Authors: Miao Jin, Su Xia, Hongyi Wu, Xianfeng Gu
      First page: 15
      Abstract: This work proposes a novel connectivity-based localization algorithm, well suitable for large-scale sensor networks with complex shapes and a non-uniform nodal distribution. In contrast to current state-of-the-art connectivity-based localization methods, the proposed algorithm is highly scalable with linear computation and communication costs with respect to the size of the network; and fully distributed where each node only needs the information of its neighbors without cumbersome partitioning and merging process. The algorithm is theoretically guaranteed and numerically stable. Moreover, the algorithm can be readily extended to the localization of networks with a one-hop transmission range distance measurement, and the propagation of the measurement error at one sensor node is limited within a small area of the network around the node. Extensive simulations and comparison with other methods under various representative network settings are carried out, showing the superior performance of the proposed algorithm.
      Citation: Axioms
      PubDate: 2017-06-15
      DOI: 10.3390/axioms6020015
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 16: An Evaluation of ARFIMA (Autoregressive
           Fractional Integral Moving Average) Programs

    • Authors: Kai Liu, YangQuan Chen, Xi Zhang
      First page: 16
      Abstract: Strong coupling between values at different times that exhibit properties of long range dependence, non-stationary, spiky signals cannot be processed by the conventional time series analysis. The autoregressive fractional integral moving average (ARFIMA) model, a fractional order signal processing technique, is the generalization of the conventional integer order models—autoregressive integral moving average (ARIMA) and autoregressive moving average (ARMA) model. Therefore, it has much wider applications since it could capture both short-range dependence and long range dependence. For now, several software programs have been developed to deal with ARFIMA processes. However, it is unfortunate to see that using different numerical tools for time series analysis usually gives quite different and sometimes radically different results. Users are often puzzled about which tool is suitable for a specific application. We performed a comprehensive survey and evaluation of available ARFIMA tools in the literature in the hope of benefiting researchers with different academic backgrounds. In this paper, four aspects of ARFIMA programs concerning simulation, fractional order difference filter, estimation and forecast are compared and evaluated, respectively, in various software platforms. Our informative comments can serve as useful selection guidelines.
      Citation: Axioms
      PubDate: 2017-06-17
      DOI: 10.3390/axioms6020016
      Issue No: Vol. 6, No. 2 (2017)
       
  • Axioms, Vol. 6, Pages 1: Cuntz Semigroups of Compact-Type Hopf C*-Algebras

    • Authors: Dan Kučerovský
      First page: 1
      Abstract: The classical Cuntz semigroup has an important role in the study of C*-algebras, being one of the main invariants used to classify recalcitrant C*-algebras up to isomorphism. We consider C*-algebras that have Hopf algebra structure, and find additional structure in their Cuntz semigroups. We show that in many cases, isomorphisms of Cuntz semigroups that respect this additional structure can be lifted to Hopf algebra (bi)isomorphisms, up to a possible flip of the co-product. This shows that the Cuntz semigroup provides an interesting invariant of C*-algebraic quantum groups.
      Citation: Axioms
      PubDate: 2017-01-04
      DOI: 10.3390/axioms6010001
      Issue No: Vol. 6, No. 1 (2017)
       
  • Axioms, Vol. 6, Pages 2: Acknowledgement to Reviewers of Axioms in 2016

    • Authors: Axioms Editorial Office
      First page: 2
      Abstract: n/a
      Citation: Axioms
      PubDate: 2017-01-11
      DOI: 10.3390/axioms6010002
      Issue No: Vol. 6, No. 1 (2017)
       
  • Axioms, Vol. 6, Pages 3: Discrete Frames on Finite Dimensional Left
           Quaternion Hilbert Spaces

    • Authors: M. Khokulan, K. Thirulogasanthar, S. Srisatkunarajah
      First page: 3
      Abstract: An introductory theory of frames on finite dimensional left quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
      Citation: Axioms
      PubDate: 2017-02-21
      DOI: 10.3390/axioms6010003
      Issue No: Vol. 6, No. 1 (2017)
       
  • Axioms, Vol. 6, Pages 4: Sparse Wavelet Representation of Differential
           Operators with Piecewise Polynomial Coefficients

    • Authors: Dana Černá, Václav Finĕk
      First page: 4
      Abstract: We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coefficients that are piecewise polynomials of degree at most four on uniform grids are sparse. Numerical examples demonstrate the efficiency of an adaptive wavelet method with the constructed wavelet basis for solving the one-dimensional elliptic equation and the two-dimensional Black–Scholes equation with a quadratic volatility.
      Citation: Axioms
      PubDate: 2017-02-22
      DOI: 10.3390/axioms6010004
      Issue No: Vol. 6, No. 1 (2017)
       
  • Axioms, Vol. 6, Pages 5: Kullback-Leibler Divergence and Mutual
           Information of Experiments in the Fuzzy Case

    • Authors: Dagmar Markechová
      First page: 5
      Abstract: The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of fuzzy partitions and for Kullback-Leibler divergence with respect to fuzzy P-measures are established. In addition, a convexity of Kullback-Leibler divergence and mutual information with respect to fuzzy P-measures is studied.
      Citation: Axioms
      PubDate: 2017-03-03
      DOI: 10.3390/axioms6010005
      Issue No: Vol. 6, No. 1 (2017)
       
  • Axioms, Vol. 6, Pages 6: Norm Retrieval and Phase Retrieval by Projections

    • Authors: Peter Casazza, Dorsa Ghoreishi, Shani Jose, Janet Tremain
      First page: 6
      Abstract: We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is divided into two subsets with spans W 1 , W 2 and W 1 ∩ W 2 = { 0 } , then W 1 ⊥ W 2 .
      Citation: Axioms
      PubDate: 2017-03-04
      DOI: 10.3390/axioms6010006
      Issue No: Vol. 6, No. 1 (2017)
       
 
 
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