Axioms

20 pages, 333 KiB

Open AccessArticle

Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators

by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki

Axioms 2023, 12(3), 316; https://doi.org/10.3390/axioms12030316 - 22 Mar 2023

Viewed by 1084

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space

H

, which leads to the special case of the well-known A-numerical radius [...] Read more.

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space

H

, which leads to the special case of the well-known A-numerical radius for

d = 1

. Here, A is a positive operator on

H

. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated. Full article

(This article belongs to the Special Issue A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi)

14 pages, 355 KiB

Open AccessArticle

Existence and Stability of a Nonlinear Distributed Delayed Periodic AG-Ecosystem with Competition on Time Scales

by Kaihong Zhao

Axioms 2023, 12(3), 315; https://doi.org/10.3390/axioms12030315 - 22 Mar 2023

Cited by 15 | Viewed by 970

Abstract

The Ayala-Gilpin (AG) kinetics system is one of the famous mathematical models of ecosystem. This model has been widely concerned and studied since it was proposed. This paper stresses on a nonlinear distributed delayed periodic AG-ecosystem with competition on time scales. In the [...] Read more.

The Ayala-Gilpin (AG) kinetics system is one of the famous mathematical models of ecosystem. This model has been widely concerned and studied since it was proposed. This paper stresses on a nonlinear distributed delayed periodic AG-ecosystem with competition on time scales. In the sense of time scale, our model unifies and generalizes the discrete and continuous cases. Firstly, with the aid of the auxiliary function having only two zeros in the real number field, we apply inequality technique and coincidence degree theory to obtain some sufficient criteria which ensure that this model has periodic solutions on time scales. Meanwhile, the global asymptotic stability of the periodic solution is founded by employing stability theory in the sense of Lyapunov. Eventually, we provide an illustrative example and conduct numerical simulation by means of MATLAB tools. Full article

(This article belongs to the Special Issue Differential Equations in Applied Mathematics)

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11 pages, 356 KiB

Open AccessArticle

Interpreting Infinite Numbers

by Carles M. Cuadras

Axioms 2023, 12(3), 314; https://doi.org/10.3390/axioms12030314 - 22 Mar 2023

Viewed by 1128

Abstract

The mathematical concept of infinity, in the sense of Cantor, is rather far from applied mathematics and statistics. These fields can be linked. We comment on the properties of infinite numbers and relate them to some operations with random variables. The existence of [...] Read more.

The mathematical concept of infinity, in the sense of Cantor, is rather far from applied mathematics and statistics. These fields can be linked. We comment on the properties of infinite numbers and relate them to some operations with random variables. The existence of statistical parametric models can be studied in terms of cardinal numbers. Some probabilistic interpretations of Gödel’s theorem, Turing’s halting problem, and the Banach-Tarski paradox are commented upon, as well as the axiom of choice and the continuum hypothesis. We use a basic but sufficient mathematical level. Full article

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11 pages, 282 KiB

Open AccessArticle

Some Subordination Results Defined by Using the Symmetric q-Differential Operator for Multivalent Functions

by Saima Noor, Sa’ud Al-Sa’di and Saqib Hussain

Axioms 2023, 12(3), 313; https://doi.org/10.3390/axioms12030313 - 22 Mar 2023

Cited by 1 | Viewed by 837

Abstract

In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, [...] Read more.

In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, we derive several interesting applications of the newly defined operator for multivalent functions. Full article

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

11 pages, 284 KiB

Open AccessArticle

One-Stage Multiple Comparisons of the Mean Lifetimes of k Treatments with the Average for Exponential Distributions under Heteroscedasticity

by Shu-Fei Wu

Axioms 2023, 12(3), 312; https://doi.org/10.3390/axioms12030312 - 21 Mar 2023

Viewed by 823

Abstract

Making use of uniformly minimum-variance unbiased estimators for the parameters of two-parameter exponential distributions and the distribution of pivotal quantities, we propose one-stage multiple comparison procedures for k mean lifetimes with the average under heteroscedasticity. The multiple comparison procedures include one-sided and two-sided [...] Read more.

Making use of uniformly minimum-variance unbiased estimators for the parameters of two-parameter exponential distributions and the distribution of pivotal quantities, we propose one-stage multiple comparison procedures for k mean lifetimes with the average under heteroscedasticity. The multiple comparison procedures include one-sided and two-sided confidence intervals. These intervals can be applied to identify which treatment’s mean lifetime is better than the average or worse than the average in terms of the mean lifetimes of all treatments. Critical values are obtained in order to assure users that the given confidence coefficient has been reached; they are organized in table format for practical and convenient use. An example is provided to demonstrate the proposed techniques, wherein the mean survival times of four different lung cancer categories are compared with the average. Full article

(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)

13 pages, 291 KiB

Open AccessArticle

Between Soft θ-Openness and Soft ω⁰-Openness

by Samer Al Ghour

Axioms 2023, 12(3), 311; https://doi.org/10.3390/axioms12030311 - 20 Mar 2023

Cited by 3 | Viewed by 935

Abstract

In this paper, we define and investigate soft

ω_{θ}

-open sets as a novel type of soft set. We characterize them and demonstrate that they form a soft topology that lies strictly between the soft topologies of soft

θ

-open sets and [...] Read more.

In this paper, we define and investigate soft

ω_{θ}

-open sets as a novel type of soft set. We characterize them and demonstrate that they form a soft topology that lies strictly between the soft topologies of soft

θ

-open sets and soft

ω^{0}

-open sets. Moreover, we show that soft

ω_{θ}

-open sets and soft

ω^{0}

-open sets are equivalent for soft regular spaces. Furthermore, we investigate the connections between particular types of soft sets in a given soft anti-locally countable space and the soft topological space of soft

ω_{θ}

-open sets generated by it. In addition to these, we define soft

(ω_{θ}, ω)

-sets and soft

(ω_{θ}, θ)

-sets as two classes of sets, and via these sets, we introduce two decompositions of soft

θ

-open sets and soft

ω_{θ}

-open sets, respectively. Finally, the relationships between these three new classes of soft sets and their analogs in general topology are examined. Full article

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

11 pages, 257 KiB

Open AccessArticle

New Iterative Scheme Involving Self-Adaptive Method for Solving Mixed Variational Inequalities

by Aiman Mukheimer, Saleem Ullah, Muhammad Bux, Muhammad Shoaib Arif and Kamaleldin Abodayeh

Axioms 2023, 12(3), 310; https://doi.org/10.3390/axioms12030310 - 20 Mar 2023

Cited by 1 | Viewed by 897

Abstract

Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point [...] Read more.

Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point theory. The concept of fixed-point theory can be considered an inherent component of the VI. We consider a mixed variational inequality (MVI) a useful generalization of a classical variational inequality. The projection method is not applicable to solve MVI due to the involvement of the nonlinear term

ϕ

. MVI is equivalent to fixed-point problems and the resolvent equation techniques. This technique is commonly used in the research on the existence of a solution to the MVI. This paper uses a new self-adaptive method using step size to modify the fixed-point formulation for solving the MVI. We will also provide the convergence of the proposed scheme. Our output could be seen as a significant refinement of the previously known results for MVI. A numerical example is also provided for the implementation of the generated algorithm. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics IV)

16 pages, 10110 KiB

Open AccessArticle

On Construction and Estimation of Mixture of Log-Bilal Distributions

by Showkat Ahmad Lone, Tabassum Naz Sindhu, Sadia Anwar, Marwa K. H. Hassan, Sarah A. Alsahli and Tahani A. Abushal

Axioms 2023, 12(3), 309; https://doi.org/10.3390/axioms12030309 - 19 Mar 2023

Cited by 2 | Viewed by 1174

Abstract

Recently, the use of mixed models for analyzing real data sets with infinite domains has gained favor. However, only a specific type of mixture model using mostly maximum likelihood estimation technique has been exercised in the literature, and fitting the mixture models for [...] Read more.

Recently, the use of mixed models for analyzing real data sets with infinite domains has gained favor. However, only a specific type of mixture model using mostly maximum likelihood estimation technique has been exercised in the literature, and fitting the mixture models for bounded data (between zero and one) has been neglected. In statistical mechanics, unit distributions are widely utilized to explain practical numeric values ranging between zero and one. We presented a classical examination for the trade share data set using a mixture of two log-Bilal distributions (MLBDs). We examine the features and statistical estimation of the MLBD in connection with three techniques. The sensitivity of the presented estimators with respect to model parameters, weighting proportions, sample size, and different evaluation methodologies has also been discussed. A simulation investigation is also used to endorse the estimation results. The findings on maximum likelihood estimation were more persuasive than those of existing mixture models. The flexibility and importance of the proposed distribution are illustrated by means of real datasets. Full article

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

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21 pages, 1274 KiB

Open AccessArticle

Quantum-Inspired Fully Complex-Valued Neutral Network for Sentiment Analysis

by Wei Lai, Jinjing Shi and Yan Chang

Axioms 2023, 12(3), 308; https://doi.org/10.3390/axioms12030308 - 19 Mar 2023

Cited by 3 | Viewed by 2145

Abstract

Most of the existing quantum-inspired models are based on amplitude-phase embedding to model natural language, which maps words into Hilbert space. In quantum-computing theory, the vectors corresponding to quantum states are all complex values, so there is a gap between these two areas. [...] Read more.

Most of the existing quantum-inspired models are based on amplitude-phase embedding to model natural language, which maps words into Hilbert space. In quantum-computing theory, the vectors corresponding to quantum states are all complex values, so there is a gap between these two areas. Presently, complex-valued neural networks have been studied, but their practical applications are few, let alone in the downstream tasks of natural language processing such as sentiment analysis and language modeling. In fact, the complex-valued neural network can use the imaginary part information to embed hidden information and can express more complex information, which is suitable for modeling complex natural language. Meanwhile, quantum-inspired models are defined in Hilbert space, which is also a complex space. So it is natural to construct quantum-inspired models based on complex-valued neural networks. Therefore, we propose a new quantum-inspired model for NLP, ComplexQNN, which contains a complex-valued embedding layer, a quantum encoding layer, and a measurement layer. The modules of ComplexQNN are fully based on complex-valued neural networks. It is more in line with quantum-computing theory and easier to transfer to quantum computers in the future to achieve exponential acceleration. We conducted experiments on six sentiment-classification datasets comparing with five classical models (TextCNN, GRU, ELMo, BERT, and RoBERTa). The results show that our model has improved by 10% in accuracy metric compared with TextCNN and GRU, and has competitive experimental results with ELMo, BERT, and RoBERTa. Full article

(This article belongs to the Topic Multimodal Sentiment Analysis Based on Deep Learning Methods Such as Convolutional Neural Networks)

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19 pages, 342 KiB

Open AccessArticle

Decision Making of Agile Patterns in Offshore Software Development Outsourcing: A Fuzzy Logic-Based Analysis

by Maryam Kausar, Noushin Mazhar, Muhammad Ishtiaq and Amerah Alabrah

Axioms 2023, 12(3), 307; https://doi.org/10.3390/axioms12030307 - 18 Mar 2023

Cited by 2 | Viewed by 1521

Abstract

Computation intelligence techniques are important for making decisions in an agile-based offshore software development paradigm. Offshore development faces additional challenges, such as trust, communication and coordination, and socio-cultural and knowledge transfer. There is a need to determine the rankings of challenges considering their [...] Read more.

Computation intelligence techniques are important for making decisions in an agile-based offshore software development paradigm. Offshore development faces additional challenges, such as trust, communication and coordination, and socio-cultural and knowledge transfer. There is a need to determine the rankings of challenges considering their criticality concerning practitioners working in agile-based offshore software development. This paper aims to identify and rank agile challenges in offshore software development by applying computational intelligence techniques. From the systematic literature review, we identified 30 communication and coordination challenges. The distributed agile pattern catalog consists of 15 patterns, from which eight were used to solve communication and collaboration challenges. Many researchers have used fuzzy logic to quantify their results. We further applied the fuzzy analytical technique to determine the priority order concerning the criticality of the identified agile pattern catalog. The results showed that Central Code Repository Pattern ranked the most significant for solving communication and coordination challenges. Global Scrum Board Pattern and Synchronous Communication Pattern ranked second. Full article

(This article belongs to the Special Issue Computational Intelligence and Software Engineering)

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12 pages, 349 KiB

Open AccessArticle

A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles

by Iqbal M. Batiha, Osama Y. Ababneh, Abeer A. Al-Nana, Waseem G. Alshanti, Shameseddin Alshorm and Shaher Momani

Axioms 2023, 12(3), 306; https://doi.org/10.3390/axioms12030306 - 17 Mar 2023

Cited by 6 | Viewed by 1500

Abstract

In the context of reaching the best way to control the movement of autonomous cars linearly and angularly, making them more stable and balanced on different roads and ensuring that they avoid road obstacles, this manuscript chiefly aims to reach the optimal approach [...] Read more.

In the context of reaching the best way to control the movement of autonomous cars linearly and angularly, making them more stable and balanced on different roads and ensuring that they avoid road obstacles, this manuscript chiefly aims to reach the optimal approach for a fractional-order PID controller (or

P I^{γ} D^{ρ}

-controller) instead of the already classical one used to provide smooth automatic parking for electrical autonomous cars. The fractional-order

P I^{γ} D^{ρ}

-controller is based on the particle swarm optimization (PSO) algorithm for its design, with two different approximations: Oustaloup’s approximation and the continued fractional expansion (CFE) approximation. Our approaches to the fractional-order PID using the results of the PSO algorithm are compared with the classical PID that was designed using the results of the Cohen–Coon, Ziegler–Nichols and bacteria foraging algorithms. The scheme represented by the proposed

P I^{γ} D^{ρ}

-controller can provide the system of the autonomous vehicle with more stable results than that of the PID controller. Full article

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

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20 pages, 353 KiB

Open AccessArticle

A Bi-Level Vaccination Points Location Problem That Aims at Social Distancing and Equity for the Inhabitants

by Edith Salinas, José-Fernando Camacho-Vallejo and Samuel Nucamendi-Guillén

Axioms 2023, 12(3), 305; https://doi.org/10.3390/axioms12030305 - 17 Mar 2023

Cited by 1 | Viewed by 1300

Abstract

Designing efficient vaccination programs that consider the needs of the population is very relevant to prevent reoccurrence of the COVID-19 pandemic. The government needs to provide vaccination points to give out vaccine doses to the population. In this paper, the authors analyze the [...] Read more.

Designing efficient vaccination programs that consider the needs of the population is very relevant to prevent reoccurrence of the COVID-19 pandemic. The government needs to provide vaccination points to give out vaccine doses to the population. In this paper, the authors analyze the location of vaccination points whilst addressing the inhabitants’ preferences. Two objectives that prevent crowding of inhabitants are considered. The government aims for the minimum distance between located vaccination points is maximized, and for the number of inhabitants that attend the different vaccination points to be equitable. One of the key aspects of this problem is the assumption that inhabitants freely choose the located vaccination point to go. That decision affects the objectives of the government, since crowding at vaccination points may appear due to the inhabitants’ decisions. This problem is modeled as a bi-objective, bi-level program, in which the upper level is associated to the government and the lower level to the inhabitants. To approximate the Pareto front of this problem, a cross-entropy metaheuristic is proposed. The algorithm incorporates criteria to handle two objective functions in a simultaneous manner, and optimally solve the lower-level problem for each government decision. The proposed algorithm is tested over an adapted set of benchmark instances and pertinent analysis of the results is included. An important managerial insight is that locating far vaccination points does not lead us to a more equitable allocation of inhabitants. Full article

(This article belongs to the Special Issue Post-pandemic Operational Research Applications: Models and Algorithms)

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15 pages, 810 KiB

Open AccessArticle

An IND-CPA Analysis of a Cryptosystem Based on Bivariate Polynomial Reconstruction Problem

by Siti Nabilah Yusof, Muhammad Rezal Kamel Ariffin, Terry Shue Chien Lau, Nur Raidah Salim, Sook-Chin Yip and Timothy Tzen Vun Yap

Axioms 2023, 12(3), 304; https://doi.org/10.3390/axioms12030304 - 17 Mar 2023

Cited by 2 | Viewed by 994

Abstract

The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in [...] Read more.

The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in 2004. In 2013, a bivariate PRP was proposed. The design is a modified version of Augot and Finiasz’s design. Our strategic method, comprising the modified Berlekamp–Welch algorithm and Coron strategies, allowed us to obtain certain secret parameters of the bivariate PRP. This finding resulted in us concluding that the bivariate PRP is not secure against Indistinguishable Chosen-Plaintext Attack (IND-CPA). Full article

(This article belongs to the Special Issue Computation Methods on Quantum Systems)

16 pages, 441 KiB

Open AccessArticle

Research on PDF Shape Control for Nonlinear Stochastic System Using an Approximate Solution of FPK Equation

by Lingzhi Wang, Kun Zhang, Fucai Qian and Xiaoli Zhang

Axioms 2023, 12(3), 303; https://doi.org/10.3390/axioms12030303 - 17 Mar 2023

Viewed by 1068

Abstract

In this paper, we developed a probability density function (PDF) shape control method for non-linear stochastic systems using a hybrid logistic function (HLF) as an approximate PDF of the state variable. First, the functional relationship between the hybrid logistic probability density function and [...] Read more.

In this paper, we developed a probability density function (PDF) shape control method for non-linear stochastic systems using a hybrid logistic function (HLF) as an approximate PDF of the state variable. First, the functional relationship between the hybrid logistic probability density function and the controller was established based on the Fokker–Planck–Kolmogorov (FPK) equation. Then, the optimal PDF shape controller derivation was completed using the optimization method and the inner product definition of Hilbert space. This approach is suitable for any non-linear stochastic system. To evaluate the effectiveness and performance of the proposed method, we conducted a comparison experiment with the multi-Gaussian closure (MGC) method and the exponential polynomial (EP) method. The experimental results show that, for different types of targeted PDFs (symmetric unimodal, asymmetric unimodal, bimodal, and trimodal shapes), the PDF shape controller obtained using the HLF approach can make the PDF shape of the state variable track the targeted PDF effectively. In particular, when the targeted PDF has an asymmetric or complex trimodal shape, the proposed technique has comparatively better control effects. Compared with the EP method, our method requires a much smaller number of parameters, greatly reducing the computational complexity while achieving the same control effects. This study provides another approach for controlling the PDF shape of state variables in non-linear stochastic systems, which has important research significance. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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20 pages, 4619 KiB

Open AccessArticle

Analysis of

ℝ = P [Y < X < Z]

Using Ranked Set Sampling for a Generalized Inverse Exponential Model

by Amal S. Hassan, Najwan Alsadat, Mohammed Elgarhy, Christophe Chesneau and Heba F. Nagy

Axioms 2023, 12(3), 302; https://doi.org/10.3390/axioms12030302 - 15 Mar 2023

Cited by 5 | Viewed by 1271

Abstract

In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component [...] Read more.

In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component with a strength (

X

) that is independent of the opposing lower bound stress (

Y

) and upper bound stress (

Z

). We assumed that the strength and stress random variables followed a generalized inverse exponential distribution with different shape parameters. Under ranked set sampling (RSS) and simple random sampling (SRS) designs, we obtained four reliability estimators using the maximum likelihood method. The first and second reliability estimators were deduced when the sample data of the strength and stress distributions used the sample design (RSS/SRS). The third reliability estimator was determined when the sample data for

Y

and

Z

were received from the RSS and the sample data for

X

were taken from the SRS. The fourth reliability estimator was derived when the sample data of

Y

and

Z

were selected from the SRS, while the sample data of

X

were taken from the RSS. The accuracy of the suggested estimators was compared using a comprehensive computer simulation. Lastly, three real data sets were used to determine the reliability. Full article

(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)

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9 pages, 280 KiB

Open AccessArticle

Lyapunov Inequalities for Two Dimensional Fractional Boundary-Value Problems with Mixed Fractional Derivatives

by Tatiana Odzijewicz

Axioms 2023, 12(3), 301; https://doi.org/10.3390/axioms12030301 - 15 Mar 2023

Viewed by 977

Abstract

We consider two types of partial fractional differential equations in two dimensions with mixed fractional derivatives. Appropriate Lyapunov-type inequalities are proved, and applications to the certain eigenvalue problems are presented. Moreover, some connections with the fractional variational problems are highlighted. Full article

(This article belongs to the Topic Fractional Calculus: Theory and Applications)

24 pages, 3696 KiB

Open AccessArticle

Mathematical Models of the Processes of Operation, Renewal and Degradation of a Fleet of Complex Technical Systems with Metrological Support

by Rustam Khayrullin, Denis Ershov, Alexander Malahov and Tatyana Levina

Axioms 2023, 12(3), 300; https://doi.org/10.3390/axioms12030300 - 15 Mar 2023

Cited by 1 | Viewed by 1069

Abstract

(1) Background: The aim of the study is to develop a set of models for managing a fleet of complex technical systems with metrological support, allowing the simulation and management at all the stages of the life cycle of the complex technical systems, [...] Read more.

(1) Background: The aim of the study is to develop a set of models for managing a fleet of complex technical systems with metrological support, allowing the simulation and management at all the stages of the life cycle of the complex technical systems, as well as to simulate the functioning of large fleets of complex technical systems, including up to several hundred thousand samples; (2) Methods: The authors use methods of mathematical modeling, methods of the theory of Markov and semi-Markov processes, methods of optimization, methods of reliability theory, and methods of probability theory and mathematical statistics; (3) Results: an interconnected set of mathematical models for managing a fleet of complex technical systems with metrological support was developed and the applied software was developed; (4) Conclusions: The set of models presented in the article allows for the adequate simulation of all the stages of the life cycle of large complex technical systems fleets, including up to several hundreds of thousands of samples, to optimize the functioning processes of a fleet of complex technical systems, to form strategies for fleet development, and to assess the risks associated with false and undetected failures, as well as the risks associated with the degradation of complex technical systems. Full article

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

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15 pages, 2559 KiB

Open AccessArticle

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H₄(a,b;c,d;z₁,z₂) Ratios

by Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv and Serhii Sharyn

Axioms 2023, 12(3), 299; https://doi.org/10.3390/axioms12030299 - 15 Mar 2023

Cited by 6 | Viewed by 999

Abstract

The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function

H_{4}

ratios are constructed. The method employed is a two-dimensional generalization of the classical [...] Read more.

The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function

H_{4}

ratios are constructed. The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian continued fraction. It is proven that the branched continued fraction, which is an expansion of one of the ratios, uniformly converges to a holomorphic function of two variables on every compact subset of some domain

H,

H \subset C^{2},

and that this function is an analytic continuation of this ratio in the domain

H .

The application to the approximation of functions of two variables associated with Horn’s double hypergeometric series

H_{4}

is considered, and the expression of solutions of some systems of partial differential equations is indicated. Full article

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

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21 pages, 9738 KiB

Open AccessArticle

A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force

by Bowen Liu and Weiping Shi

Axioms 2023, 12(3), 298; https://doi.org/10.3390/axioms12030298 - 14 Mar 2023

Cited by 1 | Viewed by 1504

Abstract

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and [...] Read more.

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies. Full article

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26 pages, 5485 KiB

Open AccessArticle

Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution

by Aisha Fayomi, Amal S. Hassan, Hanan Baaqeel and Ehab M. Almetwally

Axioms 2023, 12(3), 297; https://doi.org/10.3390/axioms12030297 - 14 Mar 2023

Cited by 12 | Viewed by 1093

Abstract

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. [...] Read more.

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. Full article

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

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15 pages, 322 KiB

Open AccessArticle

Cooperative Games Based on Coalition Functions in Biform Games

by Chenwei Liu, Shuwen Xiang, Yanlong Yang and Enquan Luo

Axioms 2023, 12(3), 296; https://doi.org/10.3390/axioms12030296 - 13 Mar 2023

Cited by 1 | Viewed by 1117

Abstract

In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the [...] Read more.

In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the coalition function and giving the core and Shapley value as cooperative solutions. The relations between the coalition function and the characteristic function are investigated in terms of additivity and convexity, and the properties associated with the characteristic function, such as individual rationalities and cores, are compared with the corresponding results. The relations among the solutions of the normal-form game, biform game, and cooperative game are discussed with several examples. Full article

(This article belongs to the Special Issue Advances in Logic and Game Theory)

9 pages, 276 KiB

Open AccessArticle

Some New Sufficient Conditions on p-Valency for Certain Analytic Functions

by Lei Shi, Muhammad Arif, Syed Zakar Hussain Bukhari and Malik Ali Raza

Axioms 2023, 12(3), 295; https://doi.org/10.3390/axioms12030295 - 13 Mar 2023

Cited by 1 | Viewed by 968

Abstract

In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be p-valent functions. This work also extends the findings of Nunokawa and others. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications)

20 pages, 1047 KiB

Open AccessArticle

Learning the Parameters of ELECTRE-Based Primal-Dual Sorting Methods that Use Either Characteristic or Limiting Profiles

by Jorge Navarro, Eduardo Fernández, Efrain Solares, Abril Flores and Raymundo Díaz

Axioms 2023, 12(3), 294; https://doi.org/10.3390/axioms12030294 - 11 Mar 2023

Viewed by 894

Abstract

Two multicriteria-sorting methods that generalize the relational paradigm have been recently presented in the literature. One uses objects representative of classes, the other uses objects in the limiting boundaries of classes; both can use either a reflexive or an asymmetric preference relation. However, [...] Read more.

Two multicriteria-sorting methods that generalize the relational paradigm have been recently presented in the literature. One uses objects representative of classes, the other uses objects in the limiting boundaries of classes; both can use either a reflexive or an asymmetric preference relation. However, defining the parameters of relation-based methods is not straightforward. The present work operationalizes those methods with a methodology that takes examples provided by the decision-maker and, using an accuracy measure that specifically fits the characteristics of the methods, exploits an evolutionary algorithm to determine the parameters that best reproduce such examples. The assessment of the proposal showed that (i) it can achieve considerably high levels of out-of-sample effectiveness with only a few decision examples; (ii) the inference process is more effective learning the parameters of the method based on representative objects; (iii) it tends to be more effective with a reflexive relation; (iv) the effectiveness decreases while increasing the number of classes, which is not always the case when increasing the number of criteria. Theoretical properties of the proposed methodology will be investigated in future works. Full article

(This article belongs to the Special Issue Combinatorial Optimization & Applications)

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8 pages, 726 KiB

Open AccessArticle

Nonparametric Directional Dependence Estimation and Its Application to Cryptocurrency

by Hohsuk Noh, Hyuna Jang, Kun Ho Kim and Jong-Min Kim

Axioms 2023, 12(3), 293; https://doi.org/10.3390/axioms12030293 - 11 Mar 2023

Viewed by 1013

Abstract

This paper proposes a nonparametric directional dependence by using the local polynomial regression technique. With data generated from a bivariate copula having a nonmonotone regression structure, we show that our nonparametric directional dependence is superior to the copula directional dependence method in terms [...] Read more.

This paper proposes a nonparametric directional dependence by using the local polynomial regression technique. With data generated from a bivariate copula having a nonmonotone regression structure, we show that our nonparametric directional dependence is superior to the copula directional dependence method in terms of the root-mean-square error. To validate the directional dependence with real data, we use the log returns of daily prices of Bitcoin, Ethereum, Ripple, and Stellar. We conclude that our nonparametric directional dependence, by using the local polynomial regression technique with asymmetric-threshold GARCH models for marginal distributions, detects the directional dependence better than the copula directional dependence method by an asymmetric GARCH model. Full article

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

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17 pages, 941 KiB

Open AccessArticle

On Using Piecewise Fractional Differential Operator to Study a Dynamical System

by Shahid Khan, Zareen A. Khan, Hussam Alrabaiah and Salman Zeb

Axioms 2023, 12(3), 292; https://doi.org/10.3390/axioms12030292 - 10 Mar 2023

Cited by 2 | Viewed by 1280

Abstract

This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that [...] Read more.

This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that for such disruption, piecewise operators of fractional derivatives have been found useful in many cases. Therefore, we study a compartmental model of susceptible and infected individuals under the concept of piecewise derivative. We establish the existence theory of the considered model by using some Banach and Schauder fixed-point theorems. Keeping the importance of stability, a pertinent result related to the said area is also developed. The said concept of stability is based on the concept given by Ulam and Hyers. Further, to derive the numerical results, we use the Euler method to develop a numerical scheme for the considered model. Using real available data, we have presented various graphical presentations of two compartments against different fractional orders and various values of isolation parameters. The crossover behaviors in the dynamics can be clearly observed, which is explained by the piecewise operators, not the usual fractional-order derivative. Full article

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

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15 pages, 308 KiB

Open AccessArticle

Further Closed Formulae of Exotic ₃F₂-Series

by Wenchang Chu

Axioms 2023, 12(3), 291; https://doi.org/10.3390/axioms12030291 - 10 Mar 2023

Viewed by 790

Abstract

By making use of the linearization method, we examine a class of nonterminating

_{3} F_{2}

-series with five free integer parameters that yields twenty summation formulae. Under the Kummer and Thomae transformations, six classes of exotic

_{3} F_{2}

-series are consequently [...] Read more.

By making use of the linearization method, we examine a class of nonterminating

_{3} F_{2}

-series with five free integer parameters that yields twenty summation formulae. Under the Kummer and Thomae transformations, six classes of exotic

_{3} F_{2}

-series are consequently evaluated in closed forms. There are overall 100 identities recorded in the present paper Full article

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

16 pages, 3443 KiB

Open AccessArticle

The Qualitative Analysis of Host–Parasitoid Model with Inclusion of Spatial Refuge Effect

by Muhammad Sajjad Shabbir, Qamar Din, Wafa F. Alfwzan and Manuel De la Sen

Axioms 2023, 12(3), 290; https://doi.org/10.3390/axioms12030290 - 10 Mar 2023

Cited by 2 | Viewed by 917

Abstract

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an [...] Read more.

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting the existence of the equilibrium points and uniqueness of equilibrium points. A local stability analysis of host–parasitoid models was also carried out. Bifurcation theory was used to observe that the host–parasitoid models undergo Neimark–Sacker bifurcation. The effect of the existence of constant refuge effect on the local stability and bifurcation of models was also explored. Hybrid chaos control methodology was used to control the chaotic behavior of model. In addition, numerical simulations, bifurcation diagrams, and phase portraits of the models are also presented. Full article

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

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16 pages, 1444 KiB

Open AccessArticle

An Improved Algorithm for Identification of Dominating Vertex Set in Intuitionistic Fuzzy Graphs

by Nazia Nazir, Tanzeela Shaheen, LeSheng Jin and Tapan Senapati

Axioms 2023, 12(3), 289; https://doi.org/10.3390/axioms12030289 - 09 Mar 2023

Cited by 2 | Viewed by 1058

Abstract

In graph theory, a “dominating vertex set” is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in [...] Read more.

In graph theory, a “dominating vertex set” is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in the dominating set “dominate” the remaining vertices in the graph. Dominating vertex sets are important in graph theory because they can help us understand and analyze the behavior of a graph. For example, in network analysis, a set of dominant vertices may represent key nodes in a network that can influence the behavior of other nodes. Identifying dominant sets in a graph can also help in optimization problems, as it can help us find the minimum set of vertices that can control the entire graph. Now that there are theories about vagueness, it is important to define parallel ideas in vague structures, such as intuitionistic fuzzy graphs. This paper describes a better way to find dominating vertex sets (DVSs) in intuitive fuzzy graphs (IFGs). Even though there is already an algorithm for finding DVSs in IFGs, it has some problems. For example, it does not take into account the vertex volume, which has a direct effect on how DVSs are calculated. To address these limitations, we propose a new algorithm that can handle large-scale IFGs more efficiently. We show how effective and scalable the method is by comparing it to other methods and applying it to water flow. This work’s contributions can be used in many areas, such as social network analysis, transportation planning, and telecommunications. Full article

(This article belongs to the Special Issue Fuzzy Systems and Decision Making Theory)

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29 pages, 3304 KiB

Open AccessArticle

Tax Fraud Reduction Using Analytics in an East European Country

by Tomas Ruzgas, Laura Kižauskienė, Mantas Lukauskas, Egidijus Sinkevičius, Melita Frolovaitė and Jurgita Arnastauskaitė

Axioms 2023, 12(3), 288; https://doi.org/10.3390/axioms12030288 - 09 Mar 2023

Cited by 2 | Viewed by 2929

Abstract

Tax authorities face the challenge of effectively identifying companies that avoid paying taxes, which is not unique to European Union countries. Limited resources often constrain tax administrators, who traditionally rely on time-consuming and labour-intensive tax audit tools. As a result of this established [...] Read more.

Tax authorities face the challenge of effectively identifying companies that avoid paying taxes, which is not unique to European Union countries. Limited resources often constrain tax administrators, who traditionally rely on time-consuming and labour-intensive tax audit tools. As a result of this established practice, governments are losing a lot of tax revenue. The main objective of this study is to increase the efficiency of the detection of tax evasion by applying data mining methods in the East European country Lithuania, which has a rapidly developing economy, by applying data mining methods concerning affluence-related impacts. The study develops various models for segmentation, risk assessment, behavioral templates, and tax crime detection. Results show that the data mining technique can effectively detect tax evasion and extract hidden knowledge that can be used to reduce revenue losses resulting from tax evasion. This study’s methods, software, and findings can assist decision-makers, experts, and scientists in developing countries in predicting tax fraud detection. Full article

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

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18 pages, 1651 KiB

Open AccessArticle

An Accelerated Double-Integral ZNN with Resisting Linear Noise for Dynamic Sylvester Equation Solving and Its Application to the Control of the SFM Chaotic System

by Luyang Han, Yongjun He, Bolin Liao and Cheng Hua

Axioms 2023, 12(3), 287; https://doi.org/10.3390/axioms12030287 - 09 Mar 2023

Cited by 3 | Viewed by 1169

Abstract

The dynamic Sylvester equation (DSE) is frequently encountered in engineering and mathematics fields. The original zeroing neural network (OZNN) can work well to handle DSE under a noise-free environment, but may not work in noise. Though an integral-enhanced zeroing neural network (IEZNN) can [...] Read more.

The dynamic Sylvester equation (DSE) is frequently encountered in engineering and mathematics fields. The original zeroing neural network (OZNN) can work well to handle DSE under a noise-free environment, but may not work in noise. Though an integral-enhanced zeroing neural network (IEZNN) can be employed to solve the DSE under multiple-noise, it may fall flat under linear noise, and its convergence speed is unsatisfactory. Therefore, an accelerated double-integral zeroing neural network (ADIZNN) is proposed based on an innovative design formula to resist linear noise and accelerate convergence. Besides, theoretical proofs verify the convergence and robustness of the ADIZNN model. Moreover, simulation experiments indicate that the convergence rate and anti-noise ability of the ADIZNN are far superior to the OZNN and IEZNN under linear noise. Finally, chaos control of the sine function memristor (SFM) chaotic system is provided to suggest that the controller based on the ADIZNN has a smaller amount of error and higher accuracy than other ZNNs. Full article

(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences)

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