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MATHEMATICS (645 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: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
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: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
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: 5)
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: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
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: 5)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
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: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
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: 4)
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: 8)
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  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
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: 17)
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: 3)
BIBECHANA     Open Access  
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: 7)
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: 17)
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: 1)
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: 12)
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: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
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: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
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)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Axioms
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   ISSN (Online) 2075-1680
   Published by MDPI Homepage  [148 journals]
  • 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.
      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.
      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.
      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.
      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.
      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

    • Authors: Zengqiang Chen, Matthias Dehmer, Frank Emmert-Streib, 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.
      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.
      PubDate: 2017-05-11
      DOI: 10.3390/axioms6020013
      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.
      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
      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.
      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.
      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.
      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 .
      PubDate: 2017-03-04
      DOI: 10.3390/axioms6010006
      Issue No: Vol. 6, No. 1 (2017)
  • Axioms, Vol. 5, Pages 25: Quantum Quasigroups and the Quantum
           Yang–Baxter Equation

    • Authors: Jonathan Smith
      First page: 25
      Abstract: Quantum quasigroups are algebraic structures providing a general self-dual framework for the nonassociative extension of Hopf algebra techniques. They also have one-sided analogues, which are not self-dual. The paper presents a survey of recent work on these structures, showing how they furnish various solutions to the quantum Yang–Baxter equation.
      PubDate: 2016-11-09
      DOI: 10.3390/axioms5040025
      Issue No: Vol. 5, No. 4 (2016)
  • Axioms, Vol. 5, Pages 26: Forman-Ricci Flow for Change Detection in Large
           Dynamic Data Sets

    • Authors: Melanie Weber, Jürgen Jost, Emil Saucan
      First page: 26
      Abstract: We present a viable geometric solution for the detection of dynamic effects in complex networks. Building on Forman’s discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. We study the classical Ricci-flow in a network-theoretic setting and introduce an analytic tool for characterizing dynamic effects. The formalism suggests a computational method for change detection and the identification of fast evolving network regions and yields insights into topological properties and the structure of the underlying data.
      PubDate: 2016-11-10
      DOI: 10.3390/axioms5040026
      Issue No: Vol. 5, No. 4 (2016)
  • Axioms, Vol. 5, Pages 27: Discrete Geometry—From Theory to
           Applications: A Case Study

    • Authors: David Gu, Emil Saucan
      First page: 27
      Abstract: n/a
      PubDate: 2016-12-09
      DOI: 10.3390/axioms5040027
      Issue No: Vol. 5, No. 4 (2016)
  • Axioms, Vol. 5, Pages 28: Operational Approach and Solutions of Hyperbolic
           Heat Conduction Equations

    • Authors: Konstantin Zhukovsky
      First page: 28
      Abstract: We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Inverse differential operators and operational exponent as well as operational definitions and operational rules for generalized orthogonal polynomials were used together with integral transforms and special functions. Examples of an electric charge in a constant electric field passing under a potential barrier and of heat diffusion were compared and explored in two dimensions. Non-Fourier heat propagation models were studied and compared with each other and with Fourier heat transfer. Exact analytical solutions for the hyperbolic heat equation and for its extensions were explored. The exact analytical solution for the Guyer-Krumhansl type heat equation was derived. Using the latter, the heat surge propagation and relaxation was studied for the Guyer-Krumhansl heat transport model, for the Cattaneo and for the Fourier models. The comparison between them was drawn. Space-time propagation of a power–exponential function and of a periodic signal, obeying the Fourier law, the hyperbolic heat equation and its extended Guyer-Krumhansl form were studied by the operational technique. The role of various terms in the equations was explored and their influence on the solutions demonstrated. The accordance of the solutions with maximum principle is discussed. The application of our theoretical study for heat propagation in thin films is considered. The examples of the relaxation of the initial laser flash, the wide heat spot, and the harmonic function are considered and solved analytically.
      PubDate: 2016-12-12
      DOI: 10.3390/axioms5040028
      Issue No: Vol. 5, No. 4 (2016)
  • Axioms, Vol. 5, Pages 29: Operational Solution of Non-Integer Ordinary and
           Evolution-Type Partial Differential Equations

    • Authors: Konstantin Zhukovsky, Hari Srivastava
      First page: 29
      Abstract: A method for the solution of linear differential equations (DE) of non-integer order and of partial differential equations (PDE) by means of inverse differential operators is proposed. The solutions of non-integer order ordinary differential equations are obtained with recourse to the integral transforms and the exponent operators. The generalized forms of Laguerre and Hermite orthogonal polynomials as members of more general Appèl polynomial family are used to find the solutions. Operational definitions of these polynomials are used in the context of the operational approach. Special functions are employed to write solutions of DE in convolution form. Some linear partial differential equations (PDE) are also explored by the operational method. The Schrödinger and the Black–Scholes-like evolution equations and solved with the help of the operational technique. Examples of the solution of DE of non-integer order and of PDE are considered with various initial functions, such as polynomial, exponential, and their combinations.
      PubDate: 2016-12-13
      DOI: 10.3390/axioms5040029
      Issue No: Vol. 5, No. 4 (2016)
  • Axioms, Vol. 5, Pages 19: A Logical Analysis of Existential Dependence and
           Some Other Ontological Concepts—A Comment to Some Ideas of Eugenia

    • Authors: Marek Magdziak
      First page: 19
      Abstract: This paper deals with several problems concerning notion of existential dependence and ontological notions of existence, necessity and fusion. Following some ideas of Eugenia Ginsberg-Blaustein, the notions are treated in reference to objects, in relation to the concepts of state of affairs and subject of state of affairs. It provides an axiomatic characterization of these concepts within the framework of a multi-modal propositional logic and then presents a semantic analysis of these concepts. The semantics are a slight modification to the standard relational semantics for normal modal propositional logic.
      PubDate: 2016-07-15
      DOI: 10.3390/axioms5030019
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 20: Approach of Complexity in Nature: Entropic

    • Authors: Constantino Tsallis
      First page: 20
      Abstract: Boltzmann introduced in the 1870s a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His celebrated entropic functional for classical systems was then extended by Gibbs to the entire phase space of a many-body system and by von Neumann in order to cover quantum systems, as well. Finally, it was used by Shannon within the theory of information. The simplest expression of this functional corresponds to a discrete set of W microscopic possibilities and is given by S B G = − k ∑ i = 1 W p i ln p i (k is a positive universal constant; BG stands for Boltzmann–Gibbs). This relation enables the construction of BGstatistical mechanics, which, together with the Maxwell equations and classical, quantum and relativistic mechanics, constitutes one of the pillars of contemporary physics. The BG theory has provided uncountable important applications in physics, chemistry, computational sciences, economics, biology, networks and others. As argued in the textbooks, its application in physical systems is legitimate whenever the hypothesis of ergodicity is satisfied, i.e., when ensemble and time averages coincide. However, what can we do when ergodicity and similar simple hypotheses are violated, which indeed happens in very many natural, artificial and social complex systems. The possibility of generalizing BG statistical mechanics through a family of non-additive entropies was advanced in 1988, namely S q = k 1 − ∑ i = 1 W p i q q − 1 , which recovers the additive S B G entropy in the q→ 1 limit. The index q is to be determined from mechanical first principles, corresponding to complexity universality classes. Along three decades, this idea intensively evolved world-wide (see the Bibliography in and led to a plethora of predictions, verifications and applications in physical systems and elsewhere. As expected, whenever a paradigm shift is explored, some controversy naturally emerged, as well, in the community. The present status of the general picture is here described, starting from its dynamical and thermodynamical foundations and ending with its most recent physical applications.
      PubDate: 2016-08-12
      DOI: 10.3390/axioms5030020
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 21: Is Kazimierz Ajdukiewicz’s Concept of a Real
           Definition Still Important?

    • Authors: Robert Kublikowski
      First page: 21
      Abstract: The concept of a real definition worked out by Kazimierz Ajdukiewicz is still important in the theory of definition and can be developed by applying Hilary Putnam’s theory of reference of natural kind terms and Karl Popper’s fallibilism. On the one hand, the definiendum of a real definition refers to a natural kind of things and, on the other hand, the definiens of such a definition expresses actual, empirical, fallible knowledge which can be revised and changed.
      PubDate: 2016-08-17
      DOI: 10.3390/axioms5030021
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 22: A Method for Ordering of LR-Type Fuzzy Numbers:
           An Important Decision Criteria

    • Authors: José González Campos, Ronald Manríquez Peñafiel
      First page: 22
      Abstract: Methods for ordering fuzzy numbers play an important role as decision criteria, with applications in areas such as optimization and data mining, among others. Although there are several proposals for ordering methods in the fuzzy literature, many of them are difficult to apply and present some problems with ranking computation. For that reason, this work proposes an ordering method for fuzzy numbers based on a simple application of a polynomial function. We study some properties of our new method, comparing our results with those generated by other methods previously discussed in literature.
      PubDate: 2016-08-31
      DOI: 10.3390/axioms5030022
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 23: The Universe in Leśniewski’s Mereology: Some
           Comments on Sobociński’s Reflections

    • Authors: Marcin Łyczak, Marek Porwolik, Kordula Świętorzecka
      First page: 23
      Abstract: Stanisław Leśniewski’s mereology was originally conceived as a theory of foundations of mathematics and it is also for this reason that it has philosophical connotations. The ‘philosophical significance’ of mereology was upheld by Bolesław Sobociński who expressed the view in his correspondence with J.M. Bocheński. As he wrote to Bocheński in 1948: “[...] it is interesting that, being such a simple deductive theory, mereology may prove a number of very general theses reminiscent of metaphysical ontology”. The theses which Sobociński had in mind were related to the mereological notion of “the Universe”. Sobociński listed them in the letter adding his philosophical commentary but he did not give proofs for them and did not specify precisely the theory lying behind them. This is what we want to supply in the first part of our paper. We indicate some connections between the notion of the universe and other specific mereological notions. Motivated by Sobociński’s informal suggestions showing his preference for mereology over the axiomatic set theory in application to philosophy we propose to consider Sobociński’s formalism in a new frame which is the ZFM theory—an extension of Zermelo-Fraenkel set theory by mereological axioms, developed by A. Pietruszczak. In this systematic part we investigate reasons of ’philosophical hopes’ mentioned by Sobociński, pinned on the mereological concept of “the Universe”.
      PubDate: 2016-09-06
      DOI: 10.3390/axioms5030023
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 24: On the q-Laplace Transform and Related Special

    • Authors: Shanoja Naik, Hans Haubold
      First page: 24
      Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functions, hypergeometric and H-function, by means of the kernel function of the integral. Traditionally, we have been applying the Laplace transform method to solve differential equations and boundary value problems. Here, we propose an alternative, the q-Laplace transform method, to solve differential equations, such as as the fractional space-time diffusion equation, the generalized kinetic equation and the time fractional heat equation.
      PubDate: 2016-09-06
      DOI: 10.3390/axioms5030024
      Issue No: Vol. 5, No. 3 (2016)
  • Axioms, Vol. 5, Pages 9: The Lvov-Warsaw School and Its Future

    • Authors: Angel Garrido, Piedad Yuste
      First page: 9
      Abstract: The Lvov-Warsaw School (L-WS) was the most important movement in the history of Polish philosophy, and certainly prominent in the general history of philosophy, and 20th century logics and mathematics in particular.[...]
      PubDate: 2016-04-11
      DOI: 10.3390/axioms5020009
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 10: Applications of Skew Models Using Generalized
           Logistic Distribution

    • Authors: Pushpa Rathie, Paulo Silva, Gabriela Olinto
      First page: 10
      Abstract: We use the skew distribution generation procedure proposed by Azzalini [Scand. J. Stat., 1985, 12, 171–178] to create three new probability distribution functions. These models make use of normal, student-t and generalized logistic distribution, see Rathie and Swamee [Technical Research Report No. 07/2006. Department of Statistics, University of Brasilia: Brasilia, Brazil, 2006]. Expressions for the moments about origin are derived. Graphical illustrations are also provided. The distributions derived in this paper can be seen as generalizations of the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. Applications with unimodal and bimodal data are given to illustrate the applicability of the results derived in this paper. The applications include the analysis of the following data sets: (a) spending on public education in various countries in 2003; (b) total expenditure on health in 2009 in various countries and (c) waiting time between eruptions of the Old Faithful Geyser in the Yellow Stone National Park, Wyoming, USA. We compare the fit of the distributions introduced in this paper with the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. The results show that our distributions, in general, fit better the data sets. The general R codes for fitting the distributions introduced in this paper are given in Appendix A.
      PubDate: 2016-04-15
      DOI: 10.3390/axioms5020010
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 11: An Overview of Topological Groups: Yesterday,
           Today, Tomorrow

    • Authors: Sidney Morris
      First page: 11
      Abstract: n/a
      PubDate: 2016-05-05
      DOI: 10.3390/axioms5020011
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 12: Infinite-dimensional Lie Algebras,
           Representations, Hermitian Duality and the Operators of Stochastic

    • Authors: Palle Jorgensen, Feng Tian
      First page: 12
      Abstract: We study densely defined unbounded operators acting between different Hilbert spaces. For these, we introduce a notion of symmetric (closable) pairs of operators. The purpose of our paper is to give applications to selected themes at the cross road of operator commutation relations and stochastic calculus. We study a family of representations of the canonical commutation relations (CCR)-algebra (an infinite number of degrees of freedom), which we call admissible. The family of admissible representations includes the Fock-vacuum representation. We show that, to every admissible representation, there is an associated Gaussian stochastic calculus, and we point out that the case of the Fock-vacuum CCR-representation in a natural way yields the operators of Malliavin calculus. We thus get the operators of Malliavin’s calculus of variation from a more algebraic approach than is common. We further obtain explicit and natural formulas, and rules, for the operators of stochastic calculus. Our approach makes use of a notion of symmetric (closable) pairs of operators. The Fock-vacuum representation yields a maximal symmetric pair. This duality viewpoint has the further advantage that issues with unbounded operators and dense domains can be resolved much easier than what is possible with alternative tools. With the use of CCR representation theory, we also obtain, as a byproduct, a number of new results in multi-variable operator theory which we feel are of independent interest.
      PubDate: 2016-05-17
      DOI: 10.3390/axioms5020012
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 13: Fundamental Results for Pseudo-Differential
           Operators of Type 1, 1

    • Authors: Jon Johnsen
      First page: 13
      Abstract: This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type 1 , 1 in Hörmander’s sense. Thus, it contributes to the long-standing problem of creating a systematic theory of such operators. It is shown that type 1 , 1 -operators are defined and continuous on the full space of temperate distributions, if they fulfil Hörmander’s twisted diagonal condition, or more generally if they belong to the self-adjoint subclass; and that they are always defined on the temperate smooth functions. As a main tool the paradifferential decomposition is derived for type 1 , 1 -operators, and to confirm a natural hypothesis the symmetric term is shown to cause the domain restrictions; whereas the other terms are shown to define nice type 1 , 1 -operators fulfilling the twisted diagonal condition. The decomposition is analysed in the type 1 , 1 -context by combining the Spectral Support Rule and the factorisation inequality, which gives pointwise estimates of pseudo-differential operators in terms of maximal functions.
      PubDate: 2016-05-19
      DOI: 10.3390/axioms5020013
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 14: An Axiomatic Account of Question Evocation: The
           Propositional Case

    • Authors: Andrzej Wiśniewski
      First page: 14
      Abstract: An axiomatic system for question evocation in Classical Propositional Logic is proposed. Soundness and completeness of the system are proven.
      PubDate: 2016-05-26
      DOI: 10.3390/axioms5020014
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 15: On the Mutual Definability of the Notions of
           Entailment, Rejection, and Inconsistency

    • Authors: Urszula Wybraniec-Skardowska
      First page: 15
      Abstract: In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved that the theories T+, T−, and T′ are equivalent.
      PubDate: 2016-06-07
      DOI: 10.3390/axioms5020015
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 16: Contribution of Warsaw Logicians to
           Computational Logic

    • Authors: Damian Niwiński
      First page: 16
      Abstract: The newly emerging branch of research of Computer Science received encouragement from the successors of the Warsaw mathematical school: Kuratowski, Mazur, Mostowski, Grzegorczyk, and Rasiowa. Rasiowa realized very early that the spectrum of computer programs should be incorporated into the realm of mathematical logic in order to make a rigorous treatment of program correctness. This gave rise to the concept of algorithmic logic developed since the 1970s by Rasiowa, Salwicki, Mirkowska, and their followers. Together with Pratt’s dynamic logic, algorithmic logic evolved into a mainstream branch of research: logic of programs. In the late 1980s, Warsaw logicians Tiuryn and Urzyczyn categorized various logics of programs, depending on the class of programs involved. Quite unexpectedly, they discovered that some persistent open questions about the expressive power of logics are equivalent to famous open problems in complexity theory. This, along with parallel discoveries by Harel, Immerman and Vardi, contributed to the creation of an important area of theoretical computer science: descriptive complexity. By that time, the modal μ-calculus was recognized as a sort of a universal logic of programs. The mid 1990s saw a landmark result by Walukiewicz, who showed completeness of a natural axiomatization for the μ-calculus proposed by Kozen. The difficult proof of this result, based on automata theory, opened a path to further investigations. Later, Bojanczyk opened a new chapter by introducing an unboundedness quantifier, which allowed for expressing some quantitative properties of programs. Yet another topic, linking the past with the future, is the subject of automata founded in the Fraenkel-Mostowski set theory. The studies on intuitionism found their continuation in the studies of Curry-Howard isomorphism. ukasiewicz’s landmark idea of many-valued logic found its continuation in various approaches to incompleteness and uncertainty.
      PubDate: 2016-06-03
      DOI: 10.3390/axioms5020016
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 17: An Overview of the Fuzzy Axiomatic Systems and
           Characterizations Proposed at Ghent University

    • Authors: Etienne Kerre, Lynn D´eer, Bart Van Gasse
      First page: 17
      Abstract: During the past 40 years of fuzzy research at the Fuzziness and Uncertainty Modeling research unit of Ghent University several axiomatic systems and characterizations have been introduced. In this paper we highlight some of them. The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. Currently, these attempts are spread over many journals; with this paper they are now collected in a neat overview. In the literature, many axiom systems have been introduced, but as far as we know the axiomatic system of Huntington concerning a Boolean algebra has been the only one where the axioms have been proven independent. Another line of further research could be with respect to the simplification of these systems, in discovering redundancies between the axioms.
      PubDate: 2016-06-07
      DOI: 10.3390/axioms5020017
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 18: Potential Infinity, Abstraction Principles and
           Arithmetic (Leśniewski Style)

    • Authors: Rafal Urbaniak
      First page: 18
      Abstract: This paper starts with an explanation of how the logicist research program can be approached within the framework of Leśniewski’s systems. One nice feature of the system is that Hume’s Principle is derivable in it from an explicit definition of natural numbers. I generalize this result to show that all predicative abstraction principles corresponding to second-level relations, which are provably equivalence relations, are provable. However, the system fails, despite being much neater than the construction of Principia Mathematica (PM). One of the key reasons is that, just as in the case of the system of PM, without the assumption that infinitely many objects exist, (renderings of) most of the standard axioms of Peano Arithmetic are not derivable in the system. I prove that introducing modal quantifiers meant to capture the intuitions behind potential infinity results in the (renderings of) axioms of Peano Arithmetic (PA) being valid in all relational models (i.e. Kripke-style models, to be defined later on) of the extended language. The second, historical part of the paper contains a user-friendly description of Leśniewski’s own arithmetic and a brief investigation into its properties.
      PubDate: 2016-06-15
      DOI: 10.3390/axioms5020018
      Issue No: Vol. 5, No. 2 (2016)
  • Axioms, Vol. 5, Pages 2: Non-Abelian Pseudocompact Groups

    • Authors: W. Comfort, Dieter Remus
      First page: 2
      Abstract: Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2 K -many proper dense pseudocompact subgroups. (B) (2003) Every non-metrizable compact abelian group K admits 22 K -many strictly finer pseudocompact topological group refinements. (C) (2007) Every non-metrizable pseudocompact abelian group has a proper dense pseudocompact subgroup and a strictly finer pseudocompact topological group refinement. (Theorems (A), (B) and (C) become false if the non-metrizable hypothesis is omitted.) With a detailed view toward the relevant literature, the present authors ask: What happens to (A), (B), (C) and to similar known facts about pseudocompact abelian groups if the abelian hypothesis is omitted? Are the resulting statements true, false, true under certain natural additional hypotheses, etc.? Several new results responding in part to these questions are given, and several specific additional questions are posed.
      PubDate: 2016-01-12
      DOI: 10.3390/axioms5010002
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 3: Acknowledgement to Reviewers of Axioms in 2015

    • Authors: Axioms Editorial Office
      First page: 3
      Abstract: The editors of Axioms would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]
      PubDate: 2016-01-25
      DOI: 10.3390/axioms5010003
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 4: Data Farming Process and Initial Network Analysis

    • Authors: Gary Horne, Theodore Meyer
      First page: 4
      Abstract: Data Farming, network applications and approaches to integrate network analysis and processes to the data farming paradigm are presented as approaches to address complex system questions. Data Farming is a quantified approach that examines questions in large possibility spaces using modeling and simulation. It evaluates whole landscapes of outcomes to draw insights from outcome distributions and outliers. Social network analysis and graph theory are widely used techniques for the evaluation of social systems. Incorporation of these techniques into the data farming process provides analysts examining complex systems with a powerful new suite of tools for more fully exploring and understanding the effect of interactions in complex systems. The integration of network analysis with data farming techniques provides modelers with the capability to gain insight into the effect of network attributes, whether the network is explicitly defined or emergent, on the breadth of the model outcome space and the effect of model inputs on the resultant network statistics.
      PubDate: 2016-01-27
      DOI: 10.3390/axioms5010004
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 5: Modular Nuclearity: A Generally Covariant

    • Authors: Gandalf Lechner, Ko Sanders
      First page: 5
      Abstract: A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a modular ℓp -condition, which is an extension of a strengthened modular nuclearity condition to generally covariant theories. The modular nuclearity condition was previously introduced in Minkowski space, where it played an important role in constructive two dimensional algebraic QFT’s. We show that our generally covariant extension of this condition makes sense for a vast range of theories, and that it behaves well under causal propagation and taking mixtures. In addition we show that our modular ℓp -condition holds for every quasi-free Hadamard state of a free scalar quantum field (regardless of mass or scalar curvature coupling). However, our condition is not equivalent to the Hadamard condition.
      PubDate: 2016-01-29
      DOI: 10.3390/axioms5010005
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 6: Entropy Production Rate of a One-Dimensional
           Alpha-Fractional Diffusion Process

    • Authors: Yuri Luchko
      First page: 6
      Abstract: In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation.
      PubDate: 2016-02-05
      DOI: 10.3390/axioms5010006
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 7: Tactical Size Unit as Distribution in a Data
           Farming Environment

    • Authors: Esa Lappi, Bernt Åkesson
      First page: 7
      Abstract: In agent based models, the agents are usually platforms (individual soldiers, tanks, helicopters, etc.), not military units. In the Sandis software, the agents can be platoon size units. As there are about 30 soldiers in a platoon, there is a need for strength distribution in simulations. The contribution of this paper is a conceptual model of the platoon level agent, the needed mathematical models and concepts, and references earlier studies of how simulations have been conducted in a data farming environment with platoon/squad size unit agents with strength distribution.
      PubDate: 2016-02-22
      DOI: 10.3390/axioms5010007
      Issue No: Vol. 5, No. 1 (2016)
  • Axioms, Vol. 5, Pages 8: Summary of Data Farming

    • Authors: Gary Horne, Klaus-Peter Schwierz
      First page: 8
      Abstract: Data Farming is a process that has been developed to support decision-makers by answering questions that are not currently addressed. Data farming uses an inter-disciplinary approach that includes modeling and simulation, high performance computing, and statistical analysis to examine questions of interest with a large number of alternatives. Data farming allows for the examination of uncertain events with numerous possible outcomes and provides the capability of executing enough experiments so that both overall and unexpected results may be captured and examined for insights. Harnessing the power of data farming to apply it to our questions is essential to providing support not currently available to decision-makers. This support is critically needed in answering questions inherent in the scenarios we expect to confront in the future as the challenges our forces face become more complex and uncertain. This article was created on the basis of work conducted by Task Group MSG-088 “Data Farming in Support of NATO”, which is being applied in MSG-124 “Developing Actionable Data Farming Decision Support for NATO” of the Science and Technology Organization, North Atlantic Treaty Organization (STO NATO).
      PubDate: 2016-03-01
      DOI: 10.3390/axioms5010008
      Issue No: Vol. 5, No. 1 (2016)
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