Axioms

11 pages, 302 KiB

Open AccessArticle

The Stereographic Projection in Topological Modules

by Francisco Javier García-Pacheco

Axioms 2023, 12(2), 225; https://doi.org/10.3390/axioms12020225 - 20 Feb 2023

Cited by 2 | Viewed by 1361

The stereographic projection is constructed in topological modules. Let A be an additively symmetric closed subset of a topological R-module M such that

0 \in int (A)

. If there exists a continuous functional

m^{*} : M \to R

[...] Read more.

The stereographic projection is constructed in topological modules. Let A be an additively symmetric closed subset of a topological R-module M such that

0 \in int (A)

. If there exists a continuous functional

m^{*} : M \to R

in the dual module

M^{*}

, an invertible

s \in U (R)

and an element a in the topological boundary

bd (A)

of A in such a way that

{(m^{*})}^{- 1} ({s}) \cap int (A) = ⌀

,

a \in {(m^{*})}^{- 1} ({s}) \cap bd (A)

, and

s + m^{*} (bd (A) \ {- a}) \subseteq U (R)

, then the following function

b \mapsto - a + 2 s {(m^{*} (b) + s)}^{- 1} (b + a)

, from

bd (A) \ {- a}

to

{(m^{*})}^{- 1} ({s})

, is a well-defined stereographic projection (also continuous if multiplicative inversion is continuous on R). Finally, we provide sufficient conditions for the previous stereographic projection to become a homeomorphism. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Geometry and Topology)

23 pages, 1277 KiB

Open AccessArticle

Aczel–Alsina Hamy Mean Aggregation Operators in T-Spherical Fuzzy Multi-Criteria Decision-Making

by Haolun Wang, Tingjun Xu, Liangqing Feng, Tahir Mahmood and Kifayat Ullah

Axioms 2023, 12(2), 224; https://doi.org/10.3390/axioms12020224 - 20 Feb 2023

Cited by 8 | Viewed by 2195

Abstract

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and [...] Read more.

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)

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14 pages, 2367 KiB

Open AccessArticle

Impact of Goodwill on Consumer Buying through Advertising in a Segmented Market: An Optimal Control Theoretic Approach

by Pradeep Kumar, Kuldeep Chaudhary, Vijay Kumar and Sudipa Chauhan

Axioms 2023, 12(2), 223; https://doi.org/10.3390/axioms12020223 - 20 Feb 2023

Cited by 2 | Viewed by 1958

Abstract

Market segmentation is one of the key marketing activities to target the potential market for a product, which allows the firm to have a better understanding of their customers. This paper considers an optimal control problem to determine the dynamic price and advertising [...] Read more.

Market segmentation is one of the key marketing activities to target the potential market for a product, which allows the firm to have a better understanding of their customers. This paper considers an optimal control problem to determine the dynamic price and advertising policies of a new product introduction in a segment-specific market incorporating advertising-based goodwill. Under differentiated advertising and single-channel advertising, advertising efforts increase the stock of goodwill in each segment. Single-channel advertising starts in all segments with a fixed segment spectrum, while the differentiated advertising process deals with each segment independently. The explicit optimal dynamic advertising effort and price strategies are obtained by applying Pontryagin’s maximum principle, and local stability of equilibria have also been examined. The effectiveness of the proposed method is validated through numerical examples, and a local sensitivity analysis is performed to find the sensitive parameters that can affect the optimal values of price and advertising effort rates. Full article

(This article belongs to the Special Issue Applied Optimization for Solving Real-World Problems)

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17 pages, 557 KiB

Open AccessArticle

A New Framework for Numerical Techniques for Fuzzy Nonlinear Equations

by Fazlollah Abbasi, Tofigh Allahviranloo and Muhammad Akram

Axioms 2023, 12(2), 222; https://doi.org/10.3390/axioms12020222 - 20 Feb 2023

Viewed by 1820

Abstract

This paper describes a computational method for solving the nonlinear equations with fuzzy input parameters that we encounter in engineering system analysis. In addition to discussing the existence of solutions, the definition and formalization of numerical solutions is based on a new fuzzy [...] Read more.

This paper describes a computational method for solving the nonlinear equations with fuzzy input parameters that we encounter in engineering system analysis. In addition to discussing the existence of solutions, the definition and formalization of numerical solutions is based on a new fuzzy computation operation as a transmission average. Error analysis in numerical solutions is described. Finally, some examples are presented to implement the proposed method and its effectiveness compared to other previous methods. Full article

(This article belongs to the Special Issue Differential Equations and Related Topics)

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14 pages, 316 KiB

Open AccessArticle

On a Resolution of Another Isolated Case of a Kummer’s Quadratic Transformation for ₂F₁

by Mohamed Jalel Atia and Ahmed Saleh Al-Mohaimeed

Axioms 2023, 12(2), 221; https://doi.org/10.3390/axioms12020221 - 20 Feb 2023

Cited by 1 | Viewed by 1363

Abstract

It is well-known that the Kummer quadratic transformation formula is valid provided that its parameters fulfill some specific conditions (see Gradshteyn, Ryzhik, Tables of Integrals, Series and Products, 9.130, 9.134.1). Very recently, one of us established a new identity when one of these [...] Read more.

It is well-known that the Kummer quadratic transformation formula is valid provided that its parameters fulfill some specific conditions (see Gradshteyn, Ryzhik, Tables of Integrals, Series and Products, 9.130, 9.134.1). Very recently, one of us established a new identity when one of these conditions is not fulfilled. In this paper, we aim to discuss another isolated case which completely different from the first. Moreover, in the end, we mention two interesting consequences of these two new results. Full article

(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications: 2nd Edition)

24 pages, 1332 KiB

Open AccessArticle

Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data

by Eid A. A. Hassan, Mohammed Elgarhy, Eman A. Eldessouky, Osama H. Mahmoud Hassan, Essam A. Amin and Ehab M. Almetwally

Axioms 2023, 12(2), 220; https://doi.org/10.3390/axioms12020220 - 20 Feb 2023

Cited by 7 | Viewed by 2435

Abstract

In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the [...] Read more.

In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models. Full article

(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics II)

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16 pages, 311 KiB

Open AccessArticle

New Conditions for Testing the Asymptotic and Oscillatory Behavior of Solutions of Neutral Differential Equations of the Fourth Order

by Amany Nabih, Osama Moaaz, Ghada AlNemer and Elmetwally M. Elabbasy

Axioms 2023, 12(2), 219; https://doi.org/10.3390/axioms12020219 - 20 Feb 2023

Cited by 1 | Viewed by 1073

Abstract

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that [...] Read more.

In this work, in the noncanonical case, we find new properties for a class of positive solutions of fourth-order differential equations. These properties allow us to obtain iterative criteria that exclude positive decreasing solutions, and we then establish sufficient conditions to guarantee that all solutions to the examined equation oscillate. The importance of applying the results to a special case of the investigated equation is demonstrated. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

15 pages, 342 KiB

Open AccessArticle

Quadratic-Phase Hilbert Transform and the Associated Bedrosian Theorem

by Hari M. Srivastava, Firdous A. Shah, Huzaifa L. Qadri, Waseem Z. Lone and Musadiq S. Gojree

Axioms 2023, 12(2), 218; https://doi.org/10.3390/axioms12020218 - 19 Feb 2023

Cited by 1 | Viewed by 1814

Abstract

The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in [...] Read more.

The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in generalized domains. To address this limitation, we propose a novel integral transform, coined the quadratic-phase Hilbert transform. The preliminary study encompasses the formulation of all the fundamental properties of the generalized Hilbert transform. Additionally, we examine the relationship between the quadratic-phase Fourier transform and the proposed transform, and delve into the convolution theorem for the quadratic-phase Hilbert transform. The Bedrosian theorem associated with the quadratic-phase Hilbert transform is explored in detail. The validity and accuracy of the obtained results were verified through simulations. Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications IV)

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27 pages, 2779 KiB

Open AccessArticle

Pseudo-Quasi Overlap Functions and Related Fuzzy Inference Methods

by Mei Jing and Xiaohong Zhang

Axioms 2023, 12(2), 217; https://doi.org/10.3390/axioms12020217 - 19 Feb 2023

Cited by 6 | Viewed by 1393

Abstract

The overlap function, a particular kind of binary aggregate function, has been extensively utilized in decision-making, image manipulation, classification, and other fields. With regard to overlap function theory, many scholars have also obtained many achievements, such as pseudo-overlap function, quasi-overlap function, semi-overlap function, [...] Read more.

The overlap function, a particular kind of binary aggregate function, has been extensively utilized in decision-making, image manipulation, classification, and other fields. With regard to overlap function theory, many scholars have also obtained many achievements, such as pseudo-overlap function, quasi-overlap function, semi-overlap function, etc. The above generalized overlap functions contain commutativity and continuity, which makes them have some limitations in practical applications. In this essay, we give the definition of pseudo-quasi overlap functions by removing the commutativity and continuity of overlap functions, and analyze the relationship of pseudo-t-norms and pseudo-quasi overlap functions. Moreover, we present a structure method for pseudo-quasi overlap functions. Then, we extend additive generators to pseudo-quasi overlap functions, and we discuss additive generators of pseudo-quasi overlap functions. The results show that, compared with the additive generators generated by overlap functions, the additive generators generated by pseudo-quasi overlap functions have fewer restraint conditions. In addition, we also provide a method for creating quasi-overlap functions by utilizing pseudo-t-norms and pseudo automorphisms. Finally, we introduce the idea of left-continuous pseudo-quasi overlap functions, and we study fuzzy inference triple I methods of residual implication operators induced by left-continuous pseudo-quasi overlap functions. On the basis of the above, we give solutions of pseudo-quasi overlap function fuzzy inference triple I methods based on FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems. Full article

(This article belongs to the Special Issue Swarm Intelligence with Mathematical Fuzzy Logic for Computer Science in Real-World Applications)

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11 pages, 581 KiB

Open AccessArticle

Electrothermal Monte Carlo Simulation of a GaAs Resonant Tunneling Diode

by Orazio Muscato

Axioms 2023, 12(2), 216; https://doi.org/10.3390/axioms12020216 - 19 Feb 2023

Viewed by 1384

Abstract

This paper deals with the electron transport and heat generation in a Resonant Tunneling Diode semiconductor device. A new electrothermal Monte Carlo method is introduced. The method couples a Monte Carlo solver of the Boltzmann–Wigner transport equation with a steady-state solution of the [...] Read more.

This paper deals with the electron transport and heat generation in a Resonant Tunneling Diode semiconductor device. A new electrothermal Monte Carlo method is introduced. The method couples a Monte Carlo solver of the Boltzmann–Wigner transport equation with a steady-state solution of the heat diffusion equation. This methodology provides an accurate microscopic description of the spatial distribution of self-heating and its effect on the detailed nonequilibrium carrier dynamics. Full article

(This article belongs to the Special Issue Mathematical Models and Simulations)

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17 pages, 2768 KiB

Open AccessArticle

Stability Analysis of Simple Root Seeker for Nonlinear Equation

by Xiaofeng Wang and Wenshuo Li

Axioms 2023, 12(2), 215; https://doi.org/10.3390/axioms12020215 - 18 Feb 2023

Cited by 6 | Viewed by 1413

Abstract

In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of [...] Read more.

In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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12 pages, 1374 KiB

Open AccessArticle

Parameter Estimation Analysis in a Model of Honey Production

by Atanas Z. Atanasov, Slavi G. Georgiev and Lubin G. Vulkov

Axioms 2023, 12(2), 214; https://doi.org/10.3390/axioms12020214 - 17 Feb 2023

Cited by 4 | Viewed by 2013

Abstract

Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. [...] Read more.

Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. In the present paper, the issue of an adequate model recovery is addressed and the parameter identification inverse problem is solved. An adjoint equation procedure to obtain the unknown parameter values by minimizing the functional error during a period of time is proposed. Numerical simulations with realistic data are discussed. Full article

(This article belongs to the Special Issue Differential Equations and Asymptotic Analysis: Recent Advances and Applications)

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14 pages, 7518 KiB

Open AccessArticle

Turbulent Free Convection and Thermal Radiation in an Air-Filled Cabinet with Partition on the Bottom Wall

by Igor V. Miroshnichenko and Mikhail A. Sheremet

Axioms 2023, 12(2), 213; https://doi.org/10.3390/axioms12020213 - 17 Feb 2023

Cited by 1 | Viewed by 1499

Abstract

Computational analysis is performed for turbulent free convection and surface thermal radiation in an air-filled cavity with solid obstacle on the bottom wall. A partition of finite thickness is considered, the position, length, and heat conductivity of which vary for certain values of [...] Read more.

Computational analysis is performed for turbulent free convection and surface thermal radiation in an air-filled cavity with solid obstacle on the bottom wall. A partition of finite thickness is considered, the position, length, and heat conductivity of which vary for certain values of the Rayleigh number. The coupled heat transmission by thermal radiation, free convection and heat conduction through the solid obstacle and walls is studied. The governing equations are solved by the finite difference method. This work also contains a detailed description of the computational grid thickening procedure. Temperature patterns and airflow field are scrutinized for some specific conditions using streamlines and isotherms. The overall heat transfer within the cavity is analyzed in terms of the mean convective and radiative Nusselt numbers, and many of the data are presented in detail for various partition positions, heat conductivities of the partition and walls of the cavity, and Rayleigh numbers. The results report that the participation of partitions within the cavities in the heat exchange processes decreases the overall heat transfer rate compared to the simpler case of cavities without partitions. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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27 pages, 5972 KiB

Open AccessArticle

Flow Modeling over Airfoils and Vertical Axis Wind Turbines Using Fourier Pseudo-Spectral Method and Coupled Immersed Boundary Method

by Lucas Marques Monteiro and Felipe Pamplona Mariano

Axioms 2023, 12(2), 212; https://doi.org/10.3390/axioms12020212 - 17 Feb 2023

Cited by 2 | Viewed by 1820

Abstract

In the present work, verifying the applicability and potentiality of the IMERSPEC methodology for numerical and computational modeling of two-dimensional flows over airfoils and vertical axis wind turbines is proposed. It is a high-order convergence methodology with low computational cost when compared to [...] Read more.

In the present work, verifying the applicability and potentiality of the IMERSPEC methodology for numerical and computational modeling of two-dimensional flows over airfoils and vertical axis wind turbines is proposed. It is a high-order convergence methodology with low computational cost when compared to other high-order methods, resulting from the coupling of the Fourier pseudo-spectral method and the immersed boundary method. To validate the proposed methodology, flow simulations are carried out over an airfoil NACA 0012 for a Reynolds number equal to 1000. From the spatial discretization procedure, there is convergence and good agreement of the lift and drag coefficients and the Strouhal number in relation to reference works. The behavior of the flows over the airfoil, as a function of the angle of attack, is evaluated by pressure and vorticity fields. From the analyzed flows, it is observed that the formation of different wake modes, constituted by swirling structures that vary their characteristic sizes, is influenced by the angle of attack. A case study is proposed based on the analysis of the main fluid dynamic aspects of flows over wind turbines with a vertical axis of three blades for a Reynolds number equal to 100. For this, a mathematical model responsible for the imposition of the rotational movement on the blades is presented in the turbine. Performance parameters, such as the coefficient of tangential force and normal force, and the analysis of velocity fields on the simulated turbine were presented and compared with other numerical methods. The good level of convergence and the accuracy of the obtained results show the promising capacity of the IMERSPEC methodology in solving problems of this nature. Full article

(This article belongs to the Special Issue Computational and Experimental Fluid Dynamics)

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13 pages, 290 KiB

Open AccessArticle

A More Accurate Half-Discrete Multidimensional Hilbert-Type Inequality Involving One Multiple Upper Limit Function

by Yong Hong, Yanru Zhong and Bicheng Yang

Axioms 2023, 12(2), 211; https://doi.org/10.3390/axioms12020211 - 16 Feb 2023

Cited by 3 | Viewed by 1302

Abstract

By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as [...] Read more.

By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as

{\frac{1}{{(x + | | k - ξ | |_{α})}^{λ}}}^{} (x, λ > 0)

involving one multiple upper limit function is given, which is a new application of Hilbert-type inequalities. The equivalent conditions of the best possible constant factor related to several parameters are considered. The equivalent forms the operator expressions and some particular inequalities are obtained. Full article

13 pages, 282 KiB

Open AccessArticle

On r-Compactness in Topological and Bitopological Spaces

by Jamal Oudetallah, Rehab Alharbi and Iqbal M. Batiha

Axioms 2023, 12(2), 210; https://doi.org/10.3390/axioms12020210 - 16 Feb 2023

Cited by 9 | Viewed by 1488

Abstract

This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the [...] Read more.

This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the r-compact space are generalized on the pairwise r-compact space. The results established in this research paper are new in the field of topology. Full article

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

22 pages, 1094 KiB

Open AccessArticle

Applying the Fuzzy BWM to Determine the Cryptocurrency Trading System under Uncertain Decision Process

by Yeh-Cheng Yang, Wen-Sheng Shieh and Chun-Yueh Lin

Axioms 2023, 12(2), 209; https://doi.org/10.3390/axioms12020209 - 16 Feb 2023

Cited by 3 | Viewed by 1972

Abstract

The crypto and digital assets ecosystems have attracted investment, regulators, and speculators to their environment. As the blockchain-based framework can reduce transaction costs, generate distributed trust, and enable decentralized platforms, it has become a potential new base for decentralized business models. Previous studies [...] Read more.

The crypto and digital assets ecosystems have attracted investment, regulators, and speculators to their environment. As the blockchain-based framework can reduce transaction costs, generate distributed trust, and enable decentralized platforms, it has become a potential new base for decentralized business models. Previous studies have highlighted the advantages and drawbacks of each platform, such as interest rates, cost concerns, transparency issues, hacking issues, and hazards. Consequently, it is challenging for investors to evaluate the cryptocurrency trading system which determines the optimum exchanges and crucial aspects. Therefore, in order to rank the optimal digital token trading system, this paper develops an evaluation architecture to determine the various token trading systems. The developed architecture integrates fuzzy theory and the best-worst method (BWM) into the decision-making process to assess decision behaviors regarding preference for digital token trading systems in investors in Taiwan. First, this work establishes the views and parameters by modifying the Delphi method based on a literature review and survey. Second, the fuzzy-BWM is applied to obtain the fuzzy weights of the views and parameters. Then, defuzzification and BWM are used to rank the optimal alternatives of the digital token trading systems for investors. The results indicate that the optimal digital token trading system is the decentralized platform, and the critical parameters are gas fees, interest rates, and the mechanism of savings under fuzzy uncertain scenarios. This means that when considering the uncertain and ambiguous characteristics of the expert decision process in digital token trading systems, the evaluation is decentralized and the gas fees are the most important parameter in the digital token investment platform. Academically, the fuzzy BWM-based decision-making architecture can provide corporations and investors with valuable guidance to rank the optimal digital token trading systems based on fuzzy uncertain scenarios. Commercially, the proposed architecture could provide corporations and investors with a useful model to measure the optimal digital token trading system. Full article

(This article belongs to the Special Issue Applied Mathematics and Information Sciences)

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11 pages, 279 KiB

Open AccessArticle

Periodic Solutions of Quasi-Monotone Semilinear Multidimensional Hyperbolic Systems

by Corrado Mascia

Axioms 2023, 12(2), 208; https://doi.org/10.3390/axioms12020208 - 16 Feb 2023

Viewed by 1284

Abstract

This paper deals with the Cauchy problem for a class of first-order semilinear hyperbolic equations of the form

\partial_{t} f_{i} + \sum_{j = 1}^{d} λ_{i j} \partial_{x_{j}} f_{i} = Q_{i} (f) .

[...] Read more.

This paper deals with the Cauchy problem for a class of first-order semilinear hyperbolic equations of the form

\partial_{t} f_{i} + \sum_{j = 1}^{d} λ_{i j} \partial_{x_{j}} f_{i} = Q_{i} (f) .

where

f_{i} = f_{i} (x, t)

(

i = 1, \dots, n

) and

x = (x_{1}, \dots, x_{d}) \in {I R}^{d}

(

n \geq 2, d \geq 1

). Under assumption of the existence of a conserved quantity

\sum_{i} α_{i} f_{i}

for some

α_{1}, \dots, α_{n} > 0

, of (strong) quasimonotonicity and an additional assumption on the speed vectors

Λ_{i} = (λ_{i 1}, \dots, λ_{i d}) \in {I R}^{d}

—namely,

span {Λ_{j} - Λ_{k} : j = 1, \dots, n} = {I R}^{d}

for any k—it is proved that the set of constant steady state

{\bar{f} \in {I R}^{n} : Q (\bar{f}) = 0}

is asymptotically stable with respect to periodic perturbations, i.e., any initial data given by an periodic

L^{1}

–perturbations of a constant steady state

\bar{f}

leads to a solution converging to another constant steady state

\bar{g}

(uniquely determined by the initial condition) as

t \to + \infty

. Full article

(This article belongs to the Special Issue Special Topics in Differential Equations with Applications)

12 pages, 323 KiB

Open AccessArticle

Basic Properties for Certain Subclasses of Meromorphic p-Valent Functions with Connected q-Analogue of Linear Differential Operator

by Sheza M. El-Deeb and Luminiţa-Ioana Cotîrlă

Axioms 2023, 12(2), 207; https://doi.org/10.3390/axioms12020207 - 15 Feb 2023

Cited by 2 | Viewed by 1281

Abstract

In this paper, we define three subclasses

M_{p, α}^{n, q} (η, A, B), I_{p, α}^{n} (λ, μ, γ),

, R [...] Read more.

In this paper, we define three subclasses

M_{p, α}^{n, q} (η, A, B), I_{p, α}^{n} (λ, μ, γ),

, R

_{p}^{n, q} (λ, μ, γ)

connected with a q-analogue of linear differential operator

D_{α, p, G}^{n, q}

which consist of functions

F

of the form

F (ζ) = ζ^{- p} + \sum_{j = 1 - p}^{\infty} a_{j} ζ^{j}

(p \in N)

satisfying the subordination condition

p - \frac{1}{η} \{\frac{ζ {(D_{α, p, G}^{n, q} F (ζ))}^{^{'}}}{D_{α, p, G}^{n, q} F (ζ)} + p\} ≺ p \frac{1 + A ζ}{1 + B ζ} .

Also, we study the various properties and characteristics of this subclass

M_{p, α}^{n, q, *} (η, A, B)

such as coefficients estimate, distortion bounds and convex family. Also the concept of

δ

neighborhoods and partial sums of analytic functions to the class

M_{p, α}^{n, q} (η, A, B)

. Full article

(This article belongs to the Special Issue Recent Advances in Fractional Calculus)

13 pages, 7640 KiB

Open AccessArticle

Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials

by Diego Caratelli, Ruben Sabbadini and Paolo Emilio Ricci

Axioms 2023, 12(2), 206; https://doi.org/10.3390/axioms12020206 - 15 Feb 2023

Viewed by 1575

Abstract

Bell’s polynomials are used in many different fields of mathematics, ranging from number theory to operator theory. This paper shows a relevant application in probability theory aimed at computing the moments of generalized Gaussian distributions. To this end, a table containing the first [...] Read more.

Bell’s polynomials are used in many different fields of mathematics, ranging from number theory to operator theory. This paper shows a relevant application in probability theory aimed at computing the moments of generalized Gaussian distributions. To this end, a table containing the first values of the complete Bell’s polynomials is provided. Furthermore, a dedicated code for approximating the moments of the general distributions in terms of complete Bell’s polynomials is detailed. Several test cases concerning different nested functions are discussed. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

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16 pages, 532 KiB

Open AccessArticle

Axiomatics of the Observer Manifold and Relativity

by Satyanad Kichenassamy

Axioms 2023, 12(2), 205; https://doi.org/10.3390/axioms12020205 - 15 Feb 2023

Cited by 1 | Viewed by 1601

Abstract

We show that Special and General Relativity lead to the introduction of an observer manifold, in addition to the usual event manifold. Axiomatics that require that manifolds be Hausdorff are not appropriate for the observer manifold. We propose an alternative axiomatics and show [...] Read more.

We show that Special and General Relativity lead to the introduction of an observer manifold, in addition to the usual event manifold. Axiomatics that require that manifolds be Hausdorff are not appropriate for the observer manifold. We propose an alternative axiomatics and show how most of the usual local computations extend to this framework without difficulty. The derivation of the Lorentz transformation takes a new meaning in this context, enabling the identification of the representations of several observers and hence reducing the observer manifold to the event manifold. However, we show in an example relevant to the radiation of accelerated electrons that this identification is not always correct. This appears to be relevant in any situation where gravitational fields in remote locations have to be measured on Earth, such as the detection of gravitational waves, or when high accelerations are involved, such as in electron radiation or laser cooling. Full article

(This article belongs to the Section Hilbert’s Sixth Problem)

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22 pages, 7280 KiB

Open AccessArticle

L₁-Norm Robust Regularized Extreme Learning Machine with Asymmetric C-Loss for Regression

by Qing Wu, Fan Wang, Yu An and Ke Li

Axioms 2023, 12(2), 204; https://doi.org/10.3390/axioms12020204 - 15 Feb 2023

Cited by 1 | Viewed by 1769

Abstract

Extreme learning machines (ELMs) have recently attracted significant attention due to their fast training speeds and good prediction effect. However, ELMs ignore the inherent distribution of the original samples, and they are prone to overfitting, which fails at achieving good generalization performance. In [...] Read more.

Extreme learning machines (ELMs) have recently attracted significant attention due to their fast training speeds and good prediction effect. However, ELMs ignore the inherent distribution of the original samples, and they are prone to overfitting, which fails at achieving good generalization performance. In this paper, based on expectile penalty and correntropy, an asymmetric C-loss function (called AC-loss) is proposed, which is non-convex, bounded, and relatively insensitive to noise. Further, a novel extreme learning machine called L₁ norm robust regularized extreme learning machine with asymmetric C-loss (L₁-ACELM) is presented to handle the overfitting problem. The proposed algorithm benefits from L₁ norm and replaces the square loss function with the AC-loss function. The L₁-ACELM can generate a more compact network with fewer hidden nodes and reduce the impact of noise. To evaluate the effectiveness of the proposed algorithm on noisy datasets, different levels of noise are added in numerical experiments. The results for different types of artificial and benchmark datasets demonstrate that L₁-ACELM achieves better generalization performance compared to other state-of-the-art algorithms, especially when noise exists in the datasets. Full article

(This article belongs to the Special Issue Fractional-Order Equations and Optimization Models in Engineering)

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13 pages, 384 KiB

Open AccessArticle

Extremal Graphs for Sombor Index with Given Parameters

by Wanping Zhang, Jixiang Meng and Na Wang

Axioms 2023, 12(2), 203; https://doi.org/10.3390/axioms12020203 - 15 Feb 2023

Cited by 2 | Viewed by 1673

Abstract

In this paper, we present the upper and lower bounds on Sombor index

S O (G)

among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on

S O (G)

among connected graphs [...] Read more.

In this paper, we present the upper and lower bounds on Sombor index

S O (G)

among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on

S O (G)

among connected graphs in terms of some parameters, including chromatic, girth and matching number. Meanwhile, we characterize the extremal graphs attaining those bounds. In addition, we give upper bounds on

S O (G)

among connected bipartite graphs with given matching number and/or connectivity and determine the corresponding extremal connected bipartite graphs. Full article

(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)

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22 pages, 362 KiB

Open AccessArticle

On the Structure of Coisometric Extensions

by Dan Popovici

Axioms 2023, 12(2), 202; https://doi.org/10.3390/axioms12020202 - 14 Feb 2023

Viewed by 1410

Abstract

If T is a bounded linear operator on a Hilbert space

H

and V is a given linear isometry on a Hilbert space

K

, we present necessary and sufficient conditions on T in order to ensure the existence of a linear isometry [...] Read more.

If T is a bounded linear operator on a Hilbert space

H

and V is a given linear isometry on a Hilbert space

K

, we present necessary and sufficient conditions on T in order to ensure the existence of a linear isometry

π : H \to K

such that

π T = V^{*} π

(i.e.,

(π, V^{*})

extends T). We parametrize the set of all solutions

π

of this equation. We show, for example, that for a given unitary operator U on a Hilbert space

E

and for the multiplication operator by the independent variable

M_{z}

on the Hardy space

H_{D}^{2} (D)

, there exists an isometric operator

π : H \to E \oplus H_{D}^{2} (D)

such that

(π, {(U \oplus M_{z})}^{*})

extends T if and only if T is a contraction, the defect index

δ_{T} \leq dim D

and, for some

Y : A_{T} \to E

,

(Y, U^{*})

extends the isometric operator

A_{T}^{1 / 2} h \mapsto A_{T}^{1 / 2} T h

on the space

A_{T} = \bar{A_{T} H}

, where

A_{T}

is the asymptotic limit associated with T. We also prove that if T is isometric and V is unitary, there exists an isometric operator

π : H \to K

such that

(π, V)

extends T if and only if (a) the spectral measures of the unitary part of T (in its Wold decomposition) and the restriction of V to one of its reducing subspaces

K_{0}

possess identical multiplicity functions and (b)

dim (ker T^{*}) = dim (K_{1} ⊖ V K_{1})

for a certain subspace

K_{1}

of

K

that contains

K_{0}

and is invariant under V. The precise form of

π

, in each situation, and characterizations of the minimality conditions are also included. Several examples are given for illustrative purposes. Full article

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

26 pages, 2331 KiB

Open AccessArticle

Dynamical Properties of Discrete-Time HTLV-I and HIV-1 within-Host Coinfection Model

by Ahmed M. Elaiw, Abdulaziz K. Aljahdali and Aatef D. Hobiny

Axioms 2023, 12(2), 201; https://doi.org/10.3390/axioms12020201 - 14 Feb 2023

Cited by 5 | Viewed by 3991

Abstract

Infection with human immunodeficiency virus type 1 (HIV-1) or human T-lymphotropic virus type I (HTLV-I) or both can lead to mortality. CD4⁺T cells are the target for both HTLV-I and HIV-1. In addition, HIV-1 can infect macrophages. CD4⁺T cells [...] Read more.

Infection with human immunodeficiency virus type 1 (HIV-1) or human T-lymphotropic virus type I (HTLV-I) or both can lead to mortality. CD4⁺T cells are the target for both HTLV-I and HIV-1. In addition, HIV-1 can infect macrophages. CD4⁺T cells and macrophages play important roles in the immune system response. This article develops and analyzes a discrete-time HTLV-I and HIV-1 co-infection model. The model depicts the within-host interaction of six compartments: uninfected CD4⁺T cells, HIV-1-infected CD4⁺T cells, uninfected macrophages, HIV-1-infected macrophages, free HIV-1 particles and HTLV-I-infected CD4⁺T cells. The discrete-time model is obtained by discretizing the continuous-time model via the nonstandard finite difference (NSFD) approach. We show that NSFD preserves the positivity and boundedness of the model’s solutions. We deduce four threshold parameters that control the existence and stability of the four equilibria of the model. The Lyapunov method is used to examine the global stability of all equilibria. The analytical findings are supported via numerical simulation. The model can be useful when one seeks to design optimal treatment schedules using optimal control theory. Full article

(This article belongs to the Special Issue Control Theory and Its Application in Mathematical Biology)

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13 pages, 2531 KiB

Open AccessArticle

Identification of Chaotic Dynamics in Jerky-Based Systems by Recurrent Wavelet First-Order Neural Networks with a Morlet Wavelet Activation Function

by Daniel Alejandro Magallón-García, Luis Javier Ontanon-Garcia, Juan Hugo García-López, Guillermo Huerta-Cuéllar and Carlos Soubervielle-Montalvo

Axioms 2023, 12(2), 200; https://doi.org/10.3390/axioms12020200 - 14 Feb 2023

Cited by 7 | Viewed by 1740

Abstract

Considering that chaotic systems are immersed in multiple areas of science and nature and that their dynamics are governed by a great sensitivity to the initial conditions and variations in their parameters, it is of great interest for the scientific community to have [...] Read more.

Considering that chaotic systems are immersed in multiple areas of science and nature and that their dynamics are governed by a great sensitivity to the initial conditions and variations in their parameters, it is of great interest for the scientific community to have tools to characterize and reproduce these trajectories. Two dynamic chaotic systems whose equations are based on the jerky system are used as benchmarks, i.e., the Memristive Shaking Chaotic System (MSCS) and the Unstable Dissipative System of type I (UDSI). One characteristic common to them is their simple mathematical structure and the complexity of their solutions. Therefore, this paper presents a strategy for identifying chaotic trajectories using a recurrent wavelet first-order neural network (RWFONN) that is trained online with an error filtering algorithm and considering the Morlet-wavelet as an activation function. The parameters of the network are adjusted considering the Euclidean distance between the solutions. Finally, the results depict proper identification of the chaotic systems studied through analysis and numerical simulation to validate the behavior and functionality of the proposed network. Full article

(This article belongs to the Section Mathematical Physics)

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29 pages, 17111 KiB

Open AccessArticle

LBM-MHD Data-Driven Approach to Predict Rayleigh–Bénard Convective Heat Transfer by Levenberg–Marquardt Algorithm

by Taasnim Ahmed Himika, Md Farhad Hasan, Md. Mamun Molla and Md Amirul Islam Khan

Axioms 2023, 12(2), 199; https://doi.org/10.3390/axioms12020199 - 13 Feb 2023

Cited by 7 | Viewed by 1935

Abstract

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the [...] Read more.

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top wall is kept cold. Rayleigh–Bénard (RB) convection was considered a heat-transfer phenomenon within the cavity. The Hartmann (

H a

) number, by varying the inclination angle (

θ

), was considered in developing the equations by considering the input parameters, namely, the Rayleigh (

R a

) numbers, Darcy (

D a

) numbers, and porosity (

ϵ

) of the cavity in different segments. Each segment considers a data-driven approach to calibrate the Levenberg–Marquardt (LM) algorithm, which is highly linked with the artificial neural network (ANN) machine learning method. Separate validations have been conducted in corresponding sections to showcase the accuracy of the equations. Overall, coefficients of determination (

R^{2}

) were found to be within 0.85 to 0.99. The significant findings of this study present mathematical equations to predict the average Nusselt number (

\bar{N u}

). The equations can be used to quantitatively predict the heat transfer without directly simulating LBM. In other words, the equations can be considered validations methods for any LBM-MHD model, which considers RB convection within the range of the parameters in each equation. Full article

(This article belongs to the Special Issue Applied Mathematics in Energy and Mechanical Engineering)

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19 pages, 424 KiB

Open AccessArticle

Partially Linear Additive Hazards Regression for Bivariate Interval-Censored Data

by Ximeng Zhang, Shishun Zhao, Tao Hu and Jianguo Sun

Axioms 2023, 12(2), 198; https://doi.org/10.3390/axioms12020198 - 13 Feb 2023

Viewed by 1541

Abstract

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow [...] Read more.

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow for both time-dependent covariates and possible nonlinear effects. For inference, a sieve maximum likelihood estimation approach based on Bernstein polynomials is proposed to estimate the baseline hazard functions and nonlinear covariate effects. The resulting estimators of regression parameters are shown to be consistent, asymptotically efficient and normal. A simulation study is conducted to assess the finite-sample performance of this method and the results show that it is effective in practice. Moreover, an illustration is provided. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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22 pages, 7729 KiB

Open AccessArticle

PSEV-BF Methodology for Object Recognition of Birds in Uncontrolled Environments

by Lucía J. Hernández-González, Juan Frausto-Solís, Juan J. González-Barbosa, Juan Paulo Sánchez-Hernández, Deny Lizbeth Hernández-Rabadán and Edgar Román-Rangel

Axioms 2023, 12(2), 197; https://doi.org/10.3390/axioms12020197 - 13 Feb 2023

Cited by 1 | Viewed by 1939

Abstract

Computer vision methodologies using machine learning techniques usually consist of the following phases: pre-processing, segmentation, feature extraction, selection of relevant variables, classification, and evaluation. In this work, a methodology for object recognition is proposed. The methodology is called PSEV-BF (pre-segmentation and enhanced variables [...] Read more.

Computer vision methodologies using machine learning techniques usually consist of the following phases: pre-processing, segmentation, feature extraction, selection of relevant variables, classification, and evaluation. In this work, a methodology for object recognition is proposed. The methodology is called PSEV-BF (pre-segmentation and enhanced variables for bird features). PSEV-BF includes two new phases compared to the traditional computer vision methodologies, namely: pre-segmentation and enhancement of variables. Pre-segmentation is performed using the third version of YOLO (you only look once), a convolutional neural network (CNN) architecture designed for object detection. Additionally, a simulated annealing (SA) algorithm is proposed for the selection and enhancement of relevant variables. To test PSEV-BF, the repository commons object in Context (COCO) was used with images exhibiting uncontrolled environments. Finally, the APIoU metric (average precision intersection over union) is used as an evaluation benchmark to compare our methodology with standard configurations. The results show that PSEV-BF has the highest performance in all tests. Full article

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10 pages, 317 KiB

Open AccessArticle

A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

by Yunlu Jiang and Zehong Zhuang

Axioms 2023, 12(2), 196; https://doi.org/10.3390/axioms12020196 - 13 Feb 2023

Viewed by 1619

Abstract

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. [...] Read more.

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods. Full article

(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis)

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