Axioms

10 pages, 284 KiB

Open AccessArticle

Generalized k-Fractional Chebyshev-Type Inequalities via Mittag-Leffler Functions

by Zhiqiang Zhang, Ghulam Farid, Sajid Mehmood, Chahn-Yong Jung and Tao Yan

Axioms 2022, 11(2), 82; https://doi.org/10.3390/axioms11020082 - 21 Feb 2022

Cited by 4 | Viewed by 1824

Mathematical inequalities have gained importance and popularity due to the application of integral operators of different types. The present paper aims to give Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels. Several new results can be deduced for [...] Read more.

Mathematical inequalities have gained importance and popularity due to the application of integral operators of different types. The present paper aims to give Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels. Several new results can be deduced for different integral operators, along with Riemann–Liouville fractional integrals by substituting convenient parameters. Moreover, the presented results generalize several already published inequalities. Full article

(This article belongs to the Special Issue Special Functions and Polynomials: Theory, Practice, Applications, and Modeling)

21 pages, 5043 KiB

Open AccessArticle

Reliability-Based Design Optimization of Structures Considering Uncertainties of Earthquakes Based on Efficient Gaussian Process Regression Metamodeling

by Yanjie Xiao, Feng Yue, Xinwei Wang and Xun’an Zhang

Axioms 2022, 11(2), 81; https://doi.org/10.3390/axioms11020081 - 20 Feb 2022

Cited by 6 | Viewed by 2569

Abstract

The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under [...] Read more.

The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under stochastic earthquakes based on adaptive Gaussian process regression (GPR) metamodeling is proposed in this study. In this method, the uncertainties of ground motions are described by the record-to-record variation and the randomness of intensity measure (IM). A GPR model is constructed to obtain the approximations of the engineering demand parameter (EDP), and an active learning (AL) strategy is presented to adaptively update the design of experiments (DoE) of this metamodel. Based on the reliability of design variables calculated by Monte Carlo simulation (MCS), an optimal solution can be obtained by an efficient global optimization (EGO) algorithm. To validate the effectiveness and efficiency of the developed method, it is applied to the optimization problems of a steel frame and a reinforced concrete frame and compared with the existing methods. The results show that this method can provide accurate reliability information for seismic design and can deal with the problems of minimizing costs under the probabilistic constraint and problems of improving the seismic reliability under limited costs. Full article

(This article belongs to the Special Issue Computing Methods in Mathematics and Engineering)

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18 pages, 306 KiB

Open AccessEditor’s ChoiceArticle

Mathematical Neural Networks

by Julia García Cabello

Axioms 2022, 11(2), 80; https://doi.org/10.3390/axioms11020080 - 17 Feb 2022

Cited by 4 | Viewed by 5492

Abstract

ANNs succeed in several tasks for real scenarios due to their high learning abilities. This paper focuses on theoretical aspects of ANNs to enhance the capacity of implementing those modifications that make ANNs absorb the defining features of each scenario. This work may [...] Read more.

ANNs succeed in several tasks for real scenarios due to their high learning abilities. This paper focuses on theoretical aspects of ANNs to enhance the capacity of implementing those modifications that make ANNs absorb the defining features of each scenario. This work may be also encompassed within the trend devoted to providing mathematical explanations of ANN performance, with special attention to activation functions. The base algorithm has been mathematically decoded to analyse the required features of activation functions regarding their impact on the training process and on the applicability of the Universal Approximation Theorem. Particularly, significant new results to identify those activation functions which undergo some usual failings (gradient preserving) are presented here. This is the first paper—to the best of the author’s knowledge—that stresses the role of injectivity for activation functions, which has received scant attention in literature but has great incidence on the ANN performance. In this line, a characterization of injective activation functions has been provided related to monotonic functions which satisfy the classical contractive condition as a particular case of Lipschitz functions. A summary table on these is also provided, targeted at documenting how to select the best activation function for each situation. Full article

(This article belongs to the Special Issue Mathematics Behind Machine Learning)

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8 pages, 255 KiB

Open AccessArticle

Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach

by Asha B. Nale, Vaijanath L. Chinchane, Satish K. Panchal and Christophe Chesneau

Axioms 2022, 11(2), 79; https://doi.org/10.3390/axioms11020079 - 17 Feb 2022

Cited by 2 | Viewed by 1728

Abstract

In this article, we establish some of the Pólya–Szegö and Minkowsky-type fractional integral inequalities by considering the Caputo–Fabrizio fractional integral. Moreover, we give some special cases of Pólya–Szegö inequalities. Full article

(This article belongs to the Special Issue Current Research on Mathematical Inequalities)

18 pages, 365 KiB

Open AccessArticle

On Cohomology of Simple Modules for Modular Classical Lie Algebras

by Sherali S. Ibraev, Larissa S. Kainbaeva and Saulesh K. Menlikozhaeva

Axioms 2022, 11(2), 78; https://doi.org/10.3390/axioms11020078 - 16 Feb 2022

Cited by 1 | Viewed by 2443

Abstract

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic

p > h,

where

h

is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras [...] Read more.

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic

p > h,

where

h

is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras. Full article

(This article belongs to the Special Issue Algebra, Logic and Applications)

10 pages, 416 KiB

Open AccessArticle

The Relationships among Three Kinds of Divisions of Type-1 Fuzzy Numbers

by Yadan Jiang and Dong Qiu

Axioms 2022, 11(2), 77; https://doi.org/10.3390/axioms11020077 - 15 Feb 2022

Cited by 3 | Viewed by 2378

Abstract

The division operation for type-1 fuzzy numbers in its original form is not invertible for the multiplication operation. This is an essential drawback in some applications. To eliminate this drawback several approaches are proposed: the generalized Hukuhara division, generalized division and granular division. [...] Read more.

The division operation for type-1 fuzzy numbers in its original form is not invertible for the multiplication operation. This is an essential drawback in some applications. To eliminate this drawback several approaches are proposed: the generalized Hukuhara division, generalized division and granular division. In this paper, the expression of granular division is introduced, and the relationships among generalized Hukuhara division, generalized division and granular division are clarified. Full article

(This article belongs to the Special Issue Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences)

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9 pages, 920 KiB

Open AccessArticle

Some New Results for a Class of Multivalued Interpolative Kannan-Type Contractions

by Nabanita Konwar, Rekha Srivastava, Pradip Debnath and Hari Mohan Srivastava

Axioms 2022, 11(2), 76; https://doi.org/10.3390/axioms11020076 - 15 Feb 2022

Cited by 2 | Viewed by 2573

Abstract

In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions. We also introduce a more general version of this notion by relaxing the degrees of freedom of the powers arising in the contractive condition. Gaba et al. (2021) recently pointed out [...] Read more.

In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions. We also introduce a more general version of this notion by relaxing the degrees of freedom of the powers arising in the contractive condition. Gaba et al. (2021) recently pointed out a significant error in the paper of Gaba and Karapinar (2019), showing that a particular type of generalized interpolative Kannan-type contraction does not posses a fixed point in general in a complete metric space. Thus, the study of generalized Kannan-type mappings remains an interesting and mathematically challenging area of research. The main aim of this article is to address such existing results for multivalued mappings. We also investigate common fixed points for this type of contractions. Our results extend and unify some existing results in the literature. Full article

(This article belongs to the Collection Mathematical Analysis and Applications)

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15 pages, 307 KiB

Open AccessArticle

g-Expectation for Conformable Backward Stochastic Differential Equations

by Mei Luo, Michal Fečkan, Jin-Rong Wang and Donal O’Regan

Axioms 2022, 11(2), 75; https://doi.org/10.3390/axioms11020075 - 14 Feb 2022

Cited by 2 | Viewed by 2397

Abstract

In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In [...] Read more.

In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases. Full article

(This article belongs to the Special Issue Mathematical Analysis Is the Theoretical Basis of a Number of Mathematical Disciplines)

21 pages, 518 KiB

Open AccessArticle

Analyzing the Main Determinants for Being an Immigrant in Cuenca (Ecuador) Based on a Fuzzy Clustering Approach

by Juan Carlos Martin, Natalia Soledad Bustamante-Sánchez and Alessandro Indelicato

Axioms 2022, 11(2), 74; https://doi.org/10.3390/axioms11020074 - 14 Feb 2022

Cited by 5 | Viewed by 3072

Abstract

The study aims to analyze the determinants for being an immigrant in Cuenca (Ecuador). Our analysis is based on the answers given to a scale formed by 30 items included in a questionnaire administered to a representative sample of 369 immigrants. A fuzzy [...] Read more.

The study aims to analyze the determinants for being an immigrant in Cuenca (Ecuador). Our analysis is based on the answers given to a scale formed by 30 items included in a questionnaire administered to a representative sample of 369 immigrants. A fuzzy hybrid multi-criteria decision-making method, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), is used to analyze whether immigrants are more or less exigent regarding the items included in the scale to reside in Cuenca. Then, a fuzzy clustering method is applied to analyze the differences observed in the main determinants observed over a number of traits according to their similarities to three obtained profiles: (1) extreme exigent immigrants; (2) extreme unneedful immigrants; and (3) intermediate exigent immigrants. Results show that items such as access to internet and benefits for retirees were highly valued by some immigrants. In addition, the authors found that information channels, reasons for immigrating, house location, main transport mode, income and main income source are the main determinants that differentiate whether the immigrants in Cuenca (Ecuador) are more or less demanding with respect to the exigency scale developed in the study. The main contributions to the body of knowledge, the policy implications and lines for future research are finally discussed. Full article

(This article belongs to the Special Issue Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences)

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15 pages, 284 KiB

Open AccessFeature PaperArticle

Transformations of Multi-Player Normal form Games by Preplay Offers between Players

by Valentin Goranko

Axioms 2022, 11(2), 73; https://doi.org/10.3390/axioms11020073 - 12 Feb 2022

Cited by 2 | Viewed by 2041

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 [...] Read more.

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. Full article

20 pages, 326 KiB

Open AccessArticle

A Class of BCI-Algebra and Quasi-Hyper BCI-Algebra

by Xiaohong Zhang and Yudan Du

Axioms 2022, 11(2), 72; https://doi.org/10.3390/axioms11020072 - 10 Feb 2022

Cited by 9 | Viewed by 2697

Abstract

In this paper, we study the connection between generalized quasi-left alter

B C I

-algebra and commutative Clifford semigroup by introducing the concept of an adjoint semigroup. We introduce QM-

B C I

algebra, in which every element is a quasi-minimal element, and [...] Read more.

In this paper, we study the connection between generalized quasi-left alter

B C I

-algebra and commutative Clifford semigroup by introducing the concept of an adjoint semigroup. We introduce QM-

B C I

algebra, in which every element is a quasi-minimal element, and prove that each QM-

B C I

algebra is equivalent to generalized quasi-left alter

B C I

-algebra. Then, we introduce the notion of generalized quasi-left alter-hyper

B C I

-algebra and prove that every generalized quasi-left alter-hyper

B C I

-algebra is a generalized quasi-left alter

B C I

-algebra. Next, we propose a new notion of quasi-hyper

B C I

algebra and discuss the relationship among them. Moreover, we study the subalgebras of quasi-hyper

B C I

algebra and the relationships between

H_{v}

-group and quasi-hyper

B C I

-algebra, hypergroup and quasi-hyper

B C I

-algebra. Finally, we propose the concept of a generalized quasi-left alter quasi-hyper

B C I

algebra and QM-quasi hyper

B C I

-algebra and discuss the relationships between them and related

B C I

-algebra. Full article

(This article belongs to the Special Issue Algebra, Logic and Applications)

8 pages, 261 KiB

Open AccessFeature PaperArticle

Bounded Sets in Topological Spaces

by Cristina Bors, María V. Ferrer and Salvador Hernández

Axioms 2022, 11(2), 71; https://doi.org/10.3390/axioms11020071 - 10 Feb 2022

Viewed by 2320

Abstract

Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point

x_{0} \in X

with

G U = X

for each neighbourhood U of

x_{0}

. A subset A of X is [...] Read more.

Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point

x_{0} \in X

with

G U = X

for each neighbourhood U of

x_{0}

. A subset A of X is said to be G-bounded if for each neighbourhood U of

x_{0}

there is a finite subset F of G with

A \subseteq F U

. We prove that for a metrizable and separable G-space X, the bounded subsets of X are completely determined by the bounded subsets of any dense subspace. We also obtain sufficient conditions for a G-space X to be locally G-bounded, which apply to topological groups. Thereby, we extend some previous results accomplished for locally convex spaces and topological groups. Full article

(This article belongs to the Special Issue Advance in Topology and Functional Analysis——In Honour of María Jesús Chasco's 65th Birthday)

10 pages, 778 KiB

Open AccessEditor’s ChoiceArticle

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

by Mohammad Ayman Mursaleen and Stefano Serra-Capizzano

Axioms 2022, 11(2), 70; https://doi.org/10.3390/axioms11020070 - 9 Feb 2022

Cited by 34 | Viewed by 3253

Abstract

In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically

C_{1}^{q}

-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesàro and [...] Read more.

In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically

C_{1}^{q}

-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesàro and statistically

C_{1}^{q}

-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem. Full article

(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications)

12 pages, 406 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Positive Numerical Approximation of Integro-Differential Epidemic Model

by Eleonora Messina, Mario Pezzella and Antonia Vecchio

Axioms 2022, 11(2), 69; https://doi.org/10.3390/axioms11020069 - 9 Feb 2022

Cited by 7 | Viewed by 2815

Abstract

In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive [...] Read more.

In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive conditions on the step-length of integration h, some of the essential properties of the continuous system. In particular, the numerical solution is positive and bounded and, in cases of interest in applications, it is monotone. We prove an order of convergence theorem and show by numerical experiments that the discrete final size tends to its continuous equivalent as h tends to zero. Full article

(This article belongs to the Special Issue Differential Equations: Theories, Methods and Modern Applications)

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8 pages, 235 KiB

Open AccessArticle

A New Equilibrium Version of Ekeland’s Variational Principle and Its Applications

by Yuqiang Feng, Juntao Xie and Bo Wu

Axioms 2022, 11(2), 68; https://doi.org/10.3390/axioms11020068 - 9 Feb 2022

Viewed by 2002

Abstract

In this note, a new equilibrium version of Ekeland’s variational principle is presented. It is a modification and promotion of previous results. Subsequently, the principle is applied to discuss the equilibrium points for binary functions and the fixed points for nonlinear mappings. Full article

(This article belongs to the Special Issue Calculus of Variations and Nonlinear Partial Differential Equations)

17 pages, 774 KiB

Open AccessArticle

Research on the n-Stage Delay Distribution Method Based on a Compensation Mechanism in a Random Environment

by Lei Zhou, Yue Qi and Fachao Li

Axioms 2022, 11(2), 67; https://doi.org/10.3390/axioms11020067 - 8 Feb 2022

Viewed by 2167

Abstract

With the development of logistics, the delayed distribution problem based on a compensation mechanism has appeared. The core of this problem is to decide whether to delay the distribution at the beginning of each stage and how to compensate the customers if delay [...] Read more.

With the development of logistics, the delayed distribution problem based on a compensation mechanism has appeared. The core of this problem is to decide whether to delay the distribution at the beginning of each stage and how to compensate the customers if delay occurs. In this paper, beginning with the 2 and 3-stage delay distribution problem, the characteristics and computational complexity of the model are analyzed, and a formal model description of the n-stage problem is given. The expected value and variance are used as the centralized quantization description strategy for random variables, and the expected value model and the generalized expectation value model for solving the delay distribution problem are given. The solution algorithm is given, and the dependence of the single transport cost of each transport vehicle and the penalty for each car delay in a period-of-time distribution are analyzed. Combined with specific examples, theoretical analysis and example calculations show that the formal description model is a good platform for further combinations of solution methods. This method extends the general delayed distribution problem to multi-stage delayed distribution, which has guiding significance for decision-makers. The proposed model has solid system structure features and interpretability, and could be used in a wide variety of applications. Full article

(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)

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19 pages, 387 KiB

Open AccessFeature PaperArticle

Logarithmic SAT Solution with Membrane Computing

by Radu Nicolescu, Michael J. Dinneen, James Cooper, Alec Henderson and Yezhou Liu

Axioms 2022, 11(2), 66; https://doi.org/10.3390/axioms11020066 - 8 Feb 2022

Cited by 1 | Viewed by 2543

Abstract

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a [...] Read more.

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., which solves SAT in square-root-sublinear time, this paper proposes an orders-of-magnitude-faster solution, running in logarithmic time, and using a small fixed-sized alphabet and ruleset (25 rules). To the best of our knowledge, this is the fastest deterministic solution across all extant P system variants. Like all other cP solutions, it is a complete solution that is not a member of a uniform family (and thus does not require any preprocessing). Consequently, according to another reduction result by Henderson et al., cP systems can also solve k-colouring and several other NP-complete problems in logarithmic time. Full article

(This article belongs to the Special Issue In Memoriam, Solomon Marcus)

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6 pages, 268 KiB

Open AccessArticle

Products of K-Analytic Sets in Locally Compact Groups and Kuczma–Ger Classes

by Taras Banakh, Iryna Banakh and Eliza Jabłońska

Axioms 2022, 11(2), 65; https://doi.org/10.3390/axioms11020065 - 7 Feb 2022

Cited by 1 | Viewed by 1895

Abstract

We prove that for any K-analytic subsets

A, B

of a locally compact group X if the product

A B

has empty interior (and is meager) in X, then one of the sets A or B can be covered by [...] Read more.

We prove that for any K-analytic subsets

A, B

of a locally compact group X if the product

A B

has empty interior (and is meager) in X, then one of the sets A or B can be covered by countably many closed nowhere dense subsets (of Haar measure zero) in X. This implies that a K-analytic subset A of X can be covered by countably many closed Haar-null sets if the set

A A A A

has an empty interior in X. It also implies that every non-open K-analytic subgroup of a locally compact group X can be covered by countably many closed Haar-null sets in X (for analytic subgroups of the real line this fact was proved by Laczkovich in 1998). Applying this result to the Kuczma–Ger classes, we prove that an additive function

f : X \to R

on a locally compact topological group X is continuous if and only if f is upper bounded on some K-analytic subset

A \subseteq X

that cannot be covered by countably many closed Haar-null sets. Full article

(This article belongs to the Special Issue Topological Groups and Dynamics)

19 pages, 304 KiB

Open AccessArticle

A New q-Hypergeometric Symbolic Calculus in the Spirit of Horn, Borngässer, Debiard and Gaveau

by Thomas Ernst

Axioms 2022, 11(2), 64; https://doi.org/10.3390/axioms11020064 - 4 Feb 2022

Cited by 2 | Viewed by 2216

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 [...] Read more.

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 Borngässers 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 \to 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 Kampé de Fériet. Sometimes the q-binomial theorem is used to simplify q-integral formulas. By the Horn method, we find another solution to the Appell

Φ_{1}

function partial differential equation, which was not mentioned in the thesis by Le Vavasseur 1893. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Physics)

9 pages, 378 KiB

Open AccessArticle

Perturbation of One-Dimensional Time-Independent Schrödinger Equation with a Near-Hyperbolic Potential

by Byungbae Kim and Soon-Mo Jung

Axioms 2022, 11(2), 63; https://doi.org/10.3390/axioms11020063 - 2 Feb 2022

Cited by 2 | Viewed by 2083

Abstract

The authors have recently investigated a type of Hyers–Ulam stability of one-dimensional time-independent Schrödinger equation with a symmetric parabolic potential wall. In this paper, we investigate a type of Hyers–Ulam stability of the Schrödinger equation with a near-hyperbolic potential. Full article

(This article belongs to the Special Issue Current Research on Mathematical Inequalities)

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18 pages, 307 KiB

Open AccessArticle

Fixed Point Results on Partial Modular Metric Space

by Dipankar Das, Santanu Narzary, Yumnam Mahendra Singh, Mohammad Saeed Khan and Salvatore Sessa

Axioms 2022, 11(2), 62; https://doi.org/10.3390/axioms11020062 - 1 Feb 2022

Cited by 3 | Viewed by 2620

Abstract

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a [...] Read more.

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed. Full article

(This article belongs to the Special Issue Approximation Theory and Related Applications)

27 pages, 682 KiB

Open AccessArticle

Three Hybrid Scatter Search Algorithms for Multi-Objective Job Shop Scheduling Problem

by Leo Hernández-Ramírez, Juan Frausto-Solís, Guadalupe Castilla-Valdez, Javier González-Barbosa and Juan-Paulo Sánchez Hernández

Axioms 2022, 11(2), 61; https://doi.org/10.3390/axioms11020061 - 31 Jan 2022

Cited by 6 | Viewed by 2826

Abstract

The Job Shop Scheduling Problem (JSSP) consists of finding the best scheduling for a set of jobs that should be processed in a specific order using a set of machines. This problem belongs to the NP-hard class problems and has enormous industrial applicability. [...] Read more.

The Job Shop Scheduling Problem (JSSP) consists of finding the best scheduling for a set of jobs that should be processed in a specific order using a set of machines. This problem belongs to the NP-hard class problems and has enormous industrial applicability. In the manufacturing area, decision-makers consider several criteria to elaborate their production schedules. These cases are studied in multi-objective optimization. However, few works are addressed from this multi-objective perspective. The literature shows that multi-objective evolutionary algorithms can solve these problems efficiently; nevertheless, multi-objective algorithms have slow convergence to the Pareto optimal front. This paper proposes three multi-objective Scatter Search hybrid algorithms that improve the convergence speed evolving on a reduced set of solutions. These algorithms are: Scatter Search/Local Search (SS/LS), Scatter Search/Chaotic Multi-Objective Threshold Accepting (SS/CMOTA), and Scatter Search/Chaotic Multi-Objective Simulated Annealing (SS/CMOSA). The proposed algorithms are compared with the state-of-the-art algorithms IMOEA/D, CMOSA, and CMOTA, using the MID, Spacing, HV, Spread, and IGD metrics; according to the experimental results, the proposed algorithms achieved the best performance. Notably, they obtained a 47% reduction in the convergence time to reach the optimal Pareto front. Full article

(This article belongs to the Special Issue Softcomputing: Theories and Applications II)

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25 pages, 3190 KiB

Open AccessArticle

Sustainable Integrated Fuzzy Optimization for Multimodal Petroleum Supply Chain Design with Pipeline System: The Case Study of Vietnam

by Chia-Nan Wang, Nhat-Luong Nhieu, Kim-Phong Tran and Yen-Hui Wang

Axioms 2022, 11(2), 60; https://doi.org/10.3390/axioms11020060 - 31 Jan 2022

Cited by 12 | Viewed by 4886

Abstract

Over the years, oil-related energy sources have played an irreplaceable role in both developed and developing countries. Therefore, the efficiency of petroleum supply chains is a key factor that significantly affects the economy. This research aimed to optimize the configuration of the uncertainty [...] Read more.

Over the years, oil-related energy sources have played an irreplaceable role in both developed and developing countries. Therefore, the efficiency of petroleum supply chains is a key factor that significantly affects the economy. This research aimed to optimize the configuration of the uncertainty multimodal petroleum supply chain in terms of economy, energy and environment (3E assessment). This study proposes a novel integration methodology between a heuristic algorithm and exact solution optimization. In the first stage, this study determines the facilities’ potential geographical coordinates using heuristic algorithm. Then, the fuzzy min-max goal programming model (FMMGPM) was developed to find the multi-objective solutions. In particular, this model allows analysis of supply chain uncertainty through simultaneous factors such as demand, resource, cost and price. These uncertainty factors are expressed as triangular fuzzy parameters that can be analyzed in terms of both probability and magnitude. Moreover, the model is applied to the entire petroleum supply chain in Vietnam, including downstream and upstream activities. In addition, another novelty is that for the first time, pipeline systems in logistics activities are considered in Vietnam’s petroleum supply chain optimization study. The results also show the short-term and long-term benefits of developing a pipeline system for oil transportation in Vietnam’s petroleum supply chain. To evaluate the effects of uncertainty on design decisions, this study also performed a sensitivity analysis with scenarios constructed based on different magnitudes and probabilities of uncertainty. Full article

(This article belongs to the Special Issue Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences)

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12 pages, 297 KiB

Open AccessArticle

Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms

by Muhittin Evren Aydın, Adela Mihai and Cihan Özgür

Axioms 2022, 11(2), 59; https://doi.org/10.3390/axioms11020059 - 30 Jan 2022

Cited by 2 | Viewed by 2453

Abstract

We introduce the notion of a Pythagorean hypersurface immersed into an

(n + 1)

-dimensional pseudo-Riemannian space form of constant sectional curvature

c \in \{- 1, 0, 1\}

. By using this definition, we prove in Riemannian setting that if an [...] Read more.

We introduce the notion of a Pythagorean hypersurface immersed into an

(n + 1)

-dimensional pseudo-Riemannian space form of constant sectional curvature

c \in \{- 1, 0, 1\}

. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature

φ + c,

where

φ

is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application)

13 pages, 301 KiB

Open AccessArticle

Nonlinear Eigenvalue Problems for the Dirichlet (p,2)-Laplacian

by Yunru Bai, Leszek Gasiński and Nikolaos S. Papageorgiou

Axioms 2022, 11(2), 58; https://doi.org/10.3390/axioms11020058 - 30 Jan 2022

Cited by 2 | Viewed by 1953

Abstract

We consider a nonlinear eigenvalue problem driven by the Dirichlet

(p, 2)

-Laplacian. The parametric reaction is a Carathéodory function which exhibits

(p - 1)

-sublinear growth as

x \to + \infty

and as

x \to 0^{+}

[...] Read more.

We consider a nonlinear eigenvalue problem driven by the Dirichlet

(p, 2)

-Laplacian. The parametric reaction is a Carathéodory function which exhibits

(p - 1)

-sublinear growth as

x \to + \infty

and as

x \to 0^{+}

. Using variational tools and truncation and comparison techniques, we prove a bifurcation-type theorem describing the “spectrum” as

λ > 0

varies. We also prove the existence of a smallest positive eigenfunction for every eigenvalue. Finally, we indicate how the result can be extended to

(p, q)

-equations (

q \neq 2

). Full article

(This article belongs to the Special Issue Nonlinear Dynamical Systems with Applications)

13 pages, 1980 KiB

Open AccessArticle

A New Hybrid Triple Bottom Line Metrics and Fuzzy MCDM Model: Sustainable Supplier Selection in the Food-Processing Industry

by Nguyen Van Thanh and Nguyen Thi Kim Lan

Axioms 2022, 11(2), 57; https://doi.org/10.3390/axioms11020057 - 29 Jan 2022

Cited by 24 | Viewed by 4674

Abstract

Vietnam’s food processing and production industries in the past have managed to receive many achievements, contributing heavily to the growth of the country’s economic growth, especially the production index. Even with an increase of 7% per year over the past five years, the [...] Read more.

Vietnam’s food processing and production industries in the past have managed to receive many achievements, contributing heavily to the growth of the country’s economic growth, especially the production index. Even with an increase of 7% per year over the past five years, the industry currently also faces problems and struggles that require business managers to rewrite legal documents and redevelop the business environment as well as the production conditions in order to compete better and use the available resources. Xanthan gum (a food additive and a thickener) is one of the most used ingredients in the food-processing industry. Xanthan gum is utilized in a number of variety of products such as canned products, ice cream, meats, breads, candies, drinks, milk products, and many others. Therefore, in order to improve competitiveness, the stage of selecting raw-material suppliers is a complicated task. The purpose of this study was to develop a new composite model using Triple Bottom Line Metrics, the Fuzzy Analytical Hierarchy Process (FAHP) method, and the Combined Compromise Solution (CoCoSo) algorithm for the selection of suppliers. The application process was accomplished for the Xanthan-gum (β-glucopyranose (C₃₅H₄₉O₂₉)n) supplier selection in a food processing industry. In this study, the model building, solution, and application processes of the proposed integrated model for the supplier selection in the food-processing industry are presented. Full article

(This article belongs to the Special Issue Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences)

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15 pages, 1356 KiB

Open AccessArticle

Hopf Bifurcation Analysis of a Diffusive Nutrient–Phytoplankton Model with Time Delay

by Ruizhi Yang, Liye Wang and Dan Jin

Axioms 2022, 11(2), 56; https://doi.org/10.3390/axioms11020056 - 29 Jan 2022

Cited by 4 | Viewed by 2439

Abstract

In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation. Some formulas are obtained to determine the direction of the bifurcation and the stability of periodic [...] Read more.

In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation. Some formulas are obtained to determine the direction of the bifurcation and the stability of periodic solutions by the central manifold theory and normal form method. Finally, we verify the above conclusion through numerical simulation. Full article

(This article belongs to the Special Issue Nonlinear Dynamical Systems with Applications)

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16 pages, 277 KiB

Open AccessArticle

A Straightforward Sufficiency Proof for a Nonparametric Problem of Bolza in the Calculus of Variations

by Gerardo Sánchez Licea

Axioms 2022, 11(2), 55; https://doi.org/10.3390/axioms11020055 - 29 Jan 2022

Cited by 1 | Viewed by 2004

Abstract

We study a variable end-points calculus of variations problem of Bolza containing inequality and equality constraints. The proof of the principal theorem of the paper has a direct nature since it is independent of some classical sufficiency approaches invoking the Hamiltonian-Jacobi theory, Riccati [...] Read more.

We study a variable end-points calculus of variations problem of Bolza containing inequality and equality constraints. The proof of the principal theorem of the paper has a direct nature since it is independent of some classical sufficiency approaches invoking the Hamiltonian-Jacobi theory, Riccati equations, fields of extremals or the theory of conjugate points. In contrast, the algorithm employed to prove the principal theorem of the article is based on elementary tools of the real analysis. Full article

(This article belongs to the Special Issue Calculus of Variations and Nonlinear Partial Differential Equations)

5 pages, 187 KiB

Open AccessEditorial

Acknowledgment to Reviewers of Axioms in 2021

by Axioms Editorial Office

Axioms 2022, 11(2), 54; https://doi.org/10.3390/axioms11020054 - 28 Jan 2022

Viewed by 1743

Abstract

Rigorous peer-reviews are the basis of high-quality academic publishing [...] Full article

13 pages, 656 KiB

Open AccessArticle

Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems

by Stephan Daniel Schwoebel, Markus Mueller, Thomas Mehner and Thomas Lampke

Axioms 2022, 11(2), 53; https://doi.org/10.3390/axioms11020053 - 28 Jan 2022

Cited by 4 | Viewed by 3454

Abstract

The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity [...] Read more.

The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity of the thickness of the deposited metal layer. For these reasons, a major interest in the limiting current density is given in practical applications. Usually, the limiting current density is determined via measurements. In this article, a simple model to compute the limiting current density is presented, basing on a system of diffusion–reaction equations in one spatial dimension. Although the model formulations need many assumptions, it is of special interest for screenings, as well as for comparative work, and could easily be adjusted to measurements. Full article

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Axioms, Volume 11, Issue 2 (February 2022) – 48 articles

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