| 1. |
- Ayman Mursaleen, Mohammad, et al.
(author)
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Statistical Convergence via q-Calculus and a Korovkin's Type Approximation Theorem
- 2022
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In: Axioms. - : MDPI AG. - 2075-1680. ; 11:2
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Journal article (peer-reviewed)abstract
- In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesà ro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesà ro and statistically C1q-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem.
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| 2. |
- Kitouni, Abdennour, 1989-, et al.
(author)
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On Properties and Classification of a Class of 4-Dimensional 3-Hom-Lie Algebras with a Nilpotent Twisting Map
- 2024
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In: AXIOMS. - : MDPI. - 2075-1680. ; 13:6
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Journal article (peer-reviewed)abstract
- The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map alpha and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-isomorphic subclasses. The levels of solvability and nilpotency of the 3-Hom-Lie algebras in these five classes are obtained. Building upon that, all algebras of this class are classified up to Hom-algebra isomorphism. Necessary and sufficient conditions for multiplicativity of general (n+1)-dimensional n-Hom-Lie algebras, as well as for algebras in the considered class, are obtained in terms of the structure constants and the twisting map. Furthermore, for some algebras in this class, it is determined whether the terms of the derived and central descending series are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals.
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| 3. |
- Ekenberg, Love, et al.
(author)
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Second-Order Risk Constraints in Decision Analysis
- 2014
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In: Axioms. - Basel : MDPI AG. - 2075-1680. ; 3:1, s. 31-45
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Journal article (peer-reviewed)abstract
- Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.
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| 4. |
- Ernst, Thomas
(author)
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A New q-Hypergeometric Symbolic Calculus in the Spirit of Horn, Borngässer, Debiard and Gaveau
- 2022
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In: AXIOMS. - : MDPI AG. - 2075-1680. ; 11:2
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Journal article (peer-reviewed)abstract
- The purpose of this article is to introduce a new complete multiple q-hypergeometric symbolic calculus, which leads to q-Euler integrals and a very similar canonical system of q-difference equations for multiple q-hypergeometric functions. q-analogues of recurrence formulas in Horns paper and Borngassers thesis lead to a more exact way to find these Frobenius solutions. To find the right formulas, the parameters in q-shifted factorials can be changed to negative integers, which give no extra q-factors. In proving these q-formulas, in the limit q & RARR;1 we obtain versions of the paper by Debiard and Gaveau for the solution of differential or q-difference equations. The paper is also a correction of some of the statements in the paper by Debiard and Gaveau, e.g., the Euler integrals and other solutions to differential equations for Appell functions, also without references to page numbers in the standard work of Appell and Kampe de Feriet. Sometimes the q-binomial theorem is used to simplify q-integral formulas. By the Horn method, we find another solution to the Appell phi(1) function partial differential equation, which was not mentioned in the thesis by Le Vavasseur 1893.
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| 5. |
- Ernst, Thomas
(author)
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Convergence Aspects for Generalizations of q-Hypergeometric Functions
- 2015
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In: AXIOMS. - : MDPI AG. - 2075-1680. ; 4:2
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Journal article (peer-reviewed)abstract
- In an earlier paper, we found transformation and summation formulas for 43 q-hypergeometric functions of 2 n variables. The aim of the present article is to find convergence regions and a few conjectures of convergence regions for these functions based on a vector version of the Nova q-addition. These convergence regions are given in a purely formal way, extending the results of Karlsson (1976). The q-function and the q-binomial coefficients, which are used in the proofs, are adjusted accordingly. Furthermore, limits and special cases for the new functions, e.g., q-Lauricella functions and q-Horn functions, are pointed out.
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| 6. |
- Ernst, Thomas
(author)
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On Elliptic and Hyperbolic Modular Functions and the Corresponding Gudermann Peeta Functions
- 2015
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In: AXIOMS. - : MDPI AG. - 2075-1680. ; 4:3, s. 235-253
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Journal article (peer-reviewed)abstract
- In this article, we move back almost 200 years to Christoph Gudermann, the great expert on elliptic functions, who successfully put the twelve Jacobi functions in a didactic setting. We prove the second hyperbolic series expansions for elliptic functions again, and express generalizations of many of Gudermann's formulas in Carlson's modern notation. The transformations between squares of elliptic functions can be expressed as general Mobius transformations, and a conjecture of twelve formulas, extending a Gudermannian formula, is presented. In the second part of the paper, we consider the corresponding formulas for hyperbolic modular functions, and show that these Mbius transformations can be used to prove integral formulas for the inverses of hyperbolic modular functions, which are in fact Schwarz-Christoffel transformations. Finally, we present the simplest formulas for the Gudermann Peeta functions, variations of the Jacobi theta functions. 2010 Mathematics Subject Classification: Primary 33E05; Secondary 33D15.
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| 7. |
- Ernst, Thomas
(author)
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On the Triple Lauricella-Horn-Karlsson q-Hypergeometric Functions
- 2020
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In: AXIOMS. - : MDPI. - 2075-1680. ; 9:3
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Journal article (peer-reviewed)abstract
- The Horn-Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are replaced by Ward q-additions. Mostly referring to Krishna Srivastava 1956, we give q-integral representations for these functions.
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| 8. |
- Garoni, Carlo, et al.
(author)
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Block generalized locally Toeplitz sequences : From the theory to the applications
- 2018
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In: Axioms. - : MDPI AG. - 2075-1680. ; 7, s. 49:1-29
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Journal article (peer-reviewed)abstract
- The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices An arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices An give rise to a sequence {An}n, which often turns out to be a GLT sequence or one of its “relatives”, i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.
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| 9. |
- Goranko, Valentin, 1959-
(author)
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Hybrid Deduction–Refutation Systems
- 2019
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In: Axioms. - : MDPI AG. - 2075-1680. ; 8:4
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Journal article (peer-reviewed)abstract
- Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.
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| 10. |
- Goranko, Valentin, 1959-
(author)
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Transformations of Multi-Player Normal form Games by Preplay Offers between Players
- 2022
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In: Axioms. - : MDPI AG. - 2075-1680. ; 11:2
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Journal article (peer-reviewed)abstract
- The paper deals with multiplayer normal form games which are preceded by a ‘preplay negotiation phase’ consisting of exchange of preplay offers by players for payments of utility to other players conditional on them playing designated in the offers strategies. The game-theoretic effect of such preplay offers is a transformation of the payoff matrix of the game, obtained by transferring the offered payments between the payoffs of the respective players; thus, certain groups of game matrix transformations naturally emerge. The main result is an explicit and rather transparent algebraic characterization of the possible transformations of the payoff matrix of any given N-person normal form game induced by preplay offers for transfer of payments. That result can be used to describe the ‘bargaining space’ of the game and to determine the mutually optimal game transformations that rational players can achieve by exchange of preplay offers.
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