Axioms

66 pages, 702 KiB

Open AccessArticle

A New Survey of Measures of Noncompactness and Their Applications

by Moosa Gabeleh, Eberhard Malkowsky, Mohammad Mursaleen and Vladimir Rakočević

Axioms 2022, 11(6), 299; https://doi.org/10.3390/axioms11060299 - 20 Jun 2022

Cited by 12 | Viewed by 2787

We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite [...] Read more.

We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also present some recent results related to the existence of best proximity points (pairs) for some classes of cyclic and noncyclic condensing operators in Banach spaces equipped with a suitable measure of noncompactness. Finally, we discuss the existence of an optimal solution for systems of integro–differentials. Full article

(This article belongs to the Special Issue Operator Theory and Its Applications)

14 pages, 386 KiB

Open AccessArticle

Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley–Martin Functional Responses

by Lili Xu, Yalong Xue, Xiangdong Xie and Qifa Lin

Axioms 2022, 11(6), 298; https://doi.org/10.3390/axioms11060298 - 20 Jun 2022

Cited by 10 | Viewed by 1826

Abstract

A two species obligate commensal symbiosis model with Crowley–Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium [...] Read more.

A two species obligate commensal symbiosis model with Crowley–Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium is coincidentla to the conditions of global stability of a positive equilibrium. For nonautonomous cases, persistent and extinction properties of the system are investigated. Full article

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

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10 pages, 260 KiB

Open AccessArticle

Context-Free Grammars for Several Triangular Arrays

by Roberta Rui Zhou, Jean Yeh and Fuquan Ren

Axioms 2022, 11(6), 297; https://doi.org/10.3390/axioms11060297 - 20 Jun 2022

Viewed by 1809

Abstract

In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros [...] Read more.

In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros of row-generating polynomials is also presented. 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)

19 pages, 2409 KiB

Open AccessArticle

Public Opinion Spread and Guidance Strategy under COVID-19: A SIS Model Analysis

by Ge You, Shangqian Gan, Hao Guo and Abd Alwahed Dagestani

Axioms 2022, 11(6), 296; https://doi.org/10.3390/axioms11060296 - 17 Jun 2022

Cited by 29 | Viewed by 3936

Abstract

Both the suddenness and seriousness of COVID-19 have caused a variety of public opinions on social media, which becomes the focus of social attention. This paper aims to analyze the strategies regarding the prevention and guidance of public opinion spread under COVID-19 in [...] Read more.

Both the suddenness and seriousness of COVID-19 have caused a variety of public opinions on social media, which becomes the focus of social attention. This paper aims to analyze the strategies regarding the prevention and guidance of public opinion spread under COVID-19 in social networks from the perspective of the emotional characteristics of user texts. Firstly, a model is established to mine text-based emotional tendency based on the Susceptible-Infectious-Susceptible (SIS) model. In addition, a mathematical and simulation analysis of the model is presented. Finally, an empirical study based on the data of microblog contents regarding COVID-19 public opinion in the Sina Weibo platform from January to March 2020 is conducted to analyze the factors that boost and hinder COVID-19 public opinion. The results show that when positive emotion is higher than 0.8, the spread of negative public opinion can be blocked. When the negative emotion and neutral emotion are both below 0.2, the spread of COVID-19 public opinion would be weakened. To accurately guide public opinion on COVID-19, the government authorities should establish a public opinion risk evaluation and an early warning mechanism. Platforms should strengthen public opinion supervision and users should improve their media literacy. The media organizations should insist on positive reporting, improve social cohesion, and guide the trend of public opinion. Full article

(This article belongs to the Special Issue Soft Computing with Applications to Decision Making and Data Mining)

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12 pages, 283 KiB

Open AccessArticle

Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

by Djalal Boucenna, Amar Chidouh and Delfim F. M. Torres

Axioms 2022, 11(6), 295; https://doi.org/10.3390/axioms11060295 - 16 Jun 2022

Viewed by 1703

Abstract

We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel’skii fixed-point theorem we prove, via the Kolmogorov–Riesz criteria, the existence of solutions. The existence results are established in [...] Read more.

We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel’skii fixed-point theorem we prove, via the Kolmogorov–Riesz criteria, the existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples. Full article

(This article belongs to the Special Issue Calculus of Variations, Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday)

21 pages, 402 KiB

Open AccessArticle

RbfDeSolver: A Software Tool to Approximate Differential Equations Using Radial Basis Functions

by Ioannis G. Tsoulos, Alexandros Tzallas and Evangelos Karvounis

Axioms 2022, 11(6), 294; https://doi.org/10.3390/axioms11060294 - 16 Jun 2022

Viewed by 2055

Abstract

A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with [...] Read more.

A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with a hybrid genetic algorithm. In addition, this text presents in detail the software developed for the above method in ANSI C++. The user can code the underlying differential equation either in C++ or in Fortran format. The method was applied to a wide range of test functions of different types and the results are presented and analyzed in detail. Full article

(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)

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9 pages, 991 KiB

Open AccessArticle

Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling

by Hossein Jabbari Khamnei, Ieva Meidute-Kavaliauskiene, Masood Fathi, Asta Valackienė and Shahryar Ghorbani

Axioms 2022, 11(6), 293; https://doi.org/10.3390/axioms11060293 - 15 Jun 2022

Cited by 3 | Viewed by 3009

Abstract

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no [...] Read more.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision-Making and Computational Intelligence: Recent Applications)

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22 pages, 6653 KiB

Open AccessArticle

Multitask Learning Based on Least Squares Support Vector Regression for Stock Forecast

by Heng-Chang Zhang, Qing Wu, Fei-Yan Li and Hong Li

Axioms 2022, 11(6), 292; https://doi.org/10.3390/axioms11060292 - 15 Jun 2022

Cited by 6 | Viewed by 2072

Abstract

Various factors make stock market forecasting difficult and arduous. Single-task learning models fail to achieve good results because they ignore the correlation between multiple related tasks. Multitask learning methods can capture the cross-correlation among subtasks and achieve a satisfactory learning effect by training [...] Read more.

Various factors make stock market forecasting difficult and arduous. Single-task learning models fail to achieve good results because they ignore the correlation between multiple related tasks. Multitask learning methods can capture the cross-correlation among subtasks and achieve a satisfactory learning effect by training all tasks simultaneously. With this motivation, we assume that the related tasks are close enough to share a common model whereas having their own independent models. Based on this hypothesis, we propose a multitask learning least squares support vector regression (MTL-LS-SVR) algorithm, and an extension, EMTL-LS-SVR. Theoretical analysis shows that these models can be converted to linear systems. A Krylov-Cholesky algorithm is introduced to determine the optimal solutions of the models. We tested the proposed models by applying them to forecasts of the Chinese stock market index trend and the stock prices of five stated-owned banks. The experimental results demonstrate their validity. Full article

(This article belongs to the Special Issue Soft Computing with Applications to Decision Making and Data Mining)

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15 pages, 283 KiB

Open AccessArticle

Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products

by Yongge Tian

Axioms 2022, 11(6), 291; https://doi.org/10.3390/axioms11060291 - 14 Jun 2022

Cited by 2 | Viewed by 2024

Abstract

This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses. We select a group of known and new reverse-order laws for generalized inverses of several matrix products and derive various necessary [...] Read more.

This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses. We select a group of known and new reverse-order laws for generalized inverses of several matrix products and derive various necessary and sufficient conditions for them to hold using the matrix rank method and the block matrix method. Full article

9 pages, 291 KiB

Open AccessEditor’s ChoiceArticle

Some Cardinal and Geometric Properties of the Space of Permutation Degree

by Ljubiša D. R. Kočinac, Farkhod G. Mukhamadiev and Anvar K. Sadullaev

Axioms 2022, 11(6), 290; https://doi.org/10.3390/axioms11060290 - 14 Jun 2022

Cited by 12 | Viewed by 2033

Abstract

This paper is devoted to the investigation of cardinal invariants such as the hereditary density, hereditary weak density, and hereditary Lindelöf number. The relation between the spread and the extent of the space

{SP}^{2} (R, τ (A))

[...] Read more.

This paper is devoted to the investigation of cardinal invariants such as the hereditary density, hereditary weak density, and hereditary Lindelöf number. The relation between the spread and the extent of the space

{SP}^{2} (R, τ (A))

of permutation degree of the Hattori space is discussed. In particular, it is shown that the space

{SP}^{2} (R, τ_{S})

contains a closed discrete subset of cardinality

c

. Moreover, it is shown that the functor

{SP}_{G}^{n}

preserves the homotopy and the retraction of topological spaces. In addition, we prove that if the spaces X and Y are homotopically equivalent, then the spaces

{SP}_{G}^{n} X

and

{SP}_{G}^{n} Y

are also homotopically equivalent. As a result, it has been proved that the functor

{SP}_{G}^{n}

is a covariant homotopy functor. Full article

(This article belongs to the Special Issue Advances in General Topology and Its Application)

14 pages, 8145 KiB

Open AccessArticle

Pipeline Corrosion Prediction Using the Grey Model and Artificial Bee Colony Algorithm

by Shiguo Li, Hualong Du, Qiuyu Cui, Pengfei Liu, Xin Ma and He Wang

Axioms 2022, 11(6), 289; https://doi.org/10.3390/axioms11060289 - 14 Jun 2022

Cited by 3 | Viewed by 1775

Abstract

Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named [...] Read more.

Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named ETGM(1,1)-RABC. The proposed method consists of two parts. First, the exponentially transformed grey model (ETGM(1,1)) is an improvement of the GM(1,1), in which exponential transformation (ET) is used to preprocess the raw data. Next, dynamic coefficients, instead of background fixed coefficients, are optimized by the reformative artificial bee colony (RABC) algorithm, which is a variation of the artificial bee colony (ABC) algorithm. Experiments are performed on actual pipe corrosion data, and four different methods are included in the comparative study, including GM(1,1), ETGM(1,1), and three ETGM(1,1)-ABC variants. The results show that the proposed method proves to be superior for the PCP in terms of Taylor diagram and absolute error. Full article

(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)

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7 pages, 248 KiB

Open AccessArticle

On Unique Factorization Modules: A Submodule Approach

by Sri Wahyuni, Hidetoshi Marubayashi, Iwan Ernanto and I Putu Yudi Prabhadika

Axioms 2022, 11(6), 288; https://doi.org/10.3390/axioms11060288 - 14 Jun 2022

Cited by 2 | Viewed by 1926

Abstract

Let M be a torsion-free module over an integral domain D. We define a concept of a unique factorization module in terms of v-submodules of M. If M is a unique factorization module (UFM), then D is a unique factorization [...] Read more.

Let M be a torsion-free module over an integral domain D. We define a concept of a unique factorization module in terms of v-submodules of M. If M is a unique factorization module (UFM), then D is a unique factorization domain. However, the converse situation is not necessarily to be held, and we give four different characterizations of unique factorization modules. Further, it is shown that the concept of the UFM is equivalent to Nicolas’s UFM, which is defined in terms of irreducible elements of D and M. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Algebra and Number Theory)

14 pages, 588 KiB

Open AccessArticle

A Story of Computational Science: Colonel Titus’ Problem from the 17th Century

by Trond Steihaug

Axioms 2022, 11(6), 287; https://doi.org/10.3390/axioms11060287 - 14 Jun 2022

Viewed by 2094

Abstract

Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow a single test example over more than 250 years. In 1685, John Wallis published A treatise of algebra, both historical and practical, containing a solution [...] Read more.

Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow a single test example over more than 250 years. In 1685, John Wallis published A treatise of algebra, both historical and practical, containing a solution of Colonel Titus’ problem that was proposed to him around 1650. The Colonel Titus problem consists of three algebraic quadratic equations in three unknowns, which Wallis transformed into the problem of finding the roots of a fourth-order (quartic) polynomial. When Joseph Raphson published his method in 1690, he demonstrated the method on 32 algebraic equations and one of the examples was this quartic equation. Edmund Halley later used the same polynomial as an example for his new methods in 1694. Although Wallis used the method of Vietè, which is a digit–by–digit method, the more efficient methods of Halley and Raphson are clearly demonstrated in the works by Raphson and Halley. For more than 250 years the quartic equation has been used as an example in a wide range of solution methods for nonlinear equations. This paper provides an overview of the Colonel Titus problem and the equation first derived by Wallis. The quartic equation has four positive roots and the equation has been found to be very useful for analyzing the number of roots and finding intervals for the individual roots, in the Cardan–Ferrari direct approach for solving quartic equations, and in Sturm’s method of determining the number of real roots of an algebraic equation. The quartic equation, together with two other algebraic equations, have likely been the first set of test examples used to compare different iteration methods of solving algebraic equations. Full article

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

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13 pages, 388 KiB

Open AccessArticle

A Selection Principle and Products in Topological Groups

by Marion Scheepers

Axioms 2022, 11(6), 286; https://doi.org/10.3390/axioms11060286 - 13 Jun 2022

Cited by 1 | Viewed by 1894

Abstract

We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of

T_{0}

topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded [...] Read more.

We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of

T_{0}

topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of

ℵ_{1}

Hechler reals the product of any o-bounded group with a ground model

ℵ_{0}

bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model

ℵ_{0}

bounded group is an o-bounded group—Theorem 12. Full article

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

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16 pages, 293 KiB

Open AccessArticle

Some Generalized Euclidean Operator Radius Inequalities

by Mohammad W. Alomari, Khalid Shebrawi and Christophe Chesneau

Axioms 2022, 11(6), 285; https://doi.org/10.3390/axioms11060285 - 13 Jun 2022

Cited by 9 | Viewed by 1870

Abstract

In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator are proven. Full article

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

14 pages, 611 KiB

Open AccessArticle

Evaluating the Digital Transformation Performance of Retail by the DEA Approach

by Ling-Jing Kao, Chih-Chou Chiu, Hung-Tse Lin, Yun-Wei Hung and Cheng-Chin Lu

Axioms 2022, 11(6), 284; https://doi.org/10.3390/axioms11060284 - 13 Jun 2022

Cited by 3 | Viewed by 3278

Abstract

In recent years, under the impact of digitization, all industries around the world have undergone unprecedented changes. Such changes have not only altered people’s consumption behavior but have also forced enterprises to accelerate the pace of digitization and actively start digital transformation. In [...] Read more.

In recent years, under the impact of digitization, all industries around the world have undergone unprecedented changes. Such changes have not only altered people’s consumption behavior but have also forced enterprises to accelerate the pace of digitization and actively start digital transformation. In this study, a literature review and focus group interview (FGI) were used to develop the dimensions and criteria to assess enterprise digital transformation status. To illustrate the digital transformation criteria proposed in this research, the retail industry was used as an example to measure the overall digital transformation performance by data envelopment analysis (DEA). The results show that the poor technical efficiency demonstrated by a vendor was not only due to the gradually decreasing returns to scale of the market; a decline in pure technical efficiency was also a contributor. In addition to adjusting their production on the basis of market conditions, vendors should properly manage their internal operations and pay attention to their resource and scale allocations to prevent reductions in their pure technical efficiency. Full article

(This article belongs to the Special Issue A Hybrid Analysis of Information Technology and Decision Making)

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19 pages, 309 KiB

Open AccessArticle

Controllability of a Class of Impulsive ψ-Caputo Fractional Evolution Equations of Sobolev Type

by Qing Yang, Chuanzhi Bai and Dandan Yang

Axioms 2022, 11(6), 283; https://doi.org/10.3390/axioms11060283 - 10 Jun 2022

Cited by 2 | Viewed by 1582

Abstract

In this paper, we investigate the controllability of a class of impulsive

ψ

-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calculus, and Schauder fixed point theorem. Our works are [...] Read more.

In this paper, we investigate the controllability of a class of impulsive

ψ

-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calculus, and Schauder fixed point theorem. Our works are generalizations and continuations of the recent results about controllability of a class of impulsive

ψ

-Caputo fractional evolution equations. Finally, an example is given to illustrate the effectiveness of the main results. Full article

(This article belongs to the Special Issue Impulsive, Delay and Fractional Order Systems)

16 pages, 296 KiB

Open AccessArticle

The Existence of Radial Solutions to the Schrödinger System Containing a Nonlinear Operator

by Guotao Wang, Zhuobin Zhang and Zedong Yang

Axioms 2022, 11(6), 282; https://doi.org/10.3390/axioms11060282 - 10 Jun 2022

Cited by 1 | Viewed by 1563

Abstract

In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components

μ

[...] Read more.

In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components

μ

and

ν

are bounded,

μ

and

ν

are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results. Full article

(This article belongs to the Special Issue Fractional Calculus and Differential Equations)

11 pages, 284 KiB

Open AccessArticle

Nonoscillation and Oscillation Criteria for a Class of Second-Order Nonlinear Neutral Delay Differential Equations with Positive and Negative Coefficients

by Rongrong Guo, Qingdao Huang and Haifeng Tian

Axioms 2022, 11(6), 281; https://doi.org/10.3390/axioms11060281 - 10 Jun 2022

Cited by 1 | Viewed by 1635

Abstract

In this paper, we investigate some nonoscillatory and oscillatory solutions for a class of second-order nonlinear neutral delay differential equations with positive and negative coefficients. By means of the method of contraction mapping principle and some integral inequality techniques, we extend the recent [...] Read more.

In this paper, we investigate some nonoscillatory and oscillatory solutions for a class of second-order nonlinear neutral delay differential equations with positive and negative coefficients. By means of the method of contraction mapping principle and some integral inequality techniques, we extend the recent results provided in the literature. Full article

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

18 pages, 371 KiB

Open AccessArticle

Application of Deep Learning and Neural Network to Speeding Ticket and Insurance Claim Count Data

by Jong-Min Kim, Jihun Kim and Il Do Ha

Axioms 2022, 11(6), 280; https://doi.org/10.3390/axioms11060280 - 10 Jun 2022

Cited by 1 | Viewed by 3049

Abstract

With the popularity of big data analysis with insurance claim count data, diverse regression models for count response variable have been developed. However, there is a multicollinearlity issue with multivariate input variables to the count response regression models. Recently, deep learning and neural [...] Read more.

With the popularity of big data analysis with insurance claim count data, diverse regression models for count response variable have been developed. However, there is a multicollinearlity issue with multivariate input variables to the count response regression models. Recently, deep learning and neural network models for count response have been proposed, and a Keras and Tensorflow-based deep learning model has been also proposed. To apply the deep learning and neural network models to non-normal insurance claim count data, we perform the root mean square error accuracy comparison of gradient boosting machines (a popular machine learning regression tree algorithm), principal component analysis (PCA)-based Poisson regression, PCA-based negative binomial regression, and PCA-based zero inflated poisson regression to avoid the multicollinearity of multivariate input variables with the simulated normal distribution data and the non-normal simulated data combined with normally distributed data, binary data, copula-based asymmetrical data, and two real data sets, which consist of speeding ticket and Singapore insurance claim count data. Full article

(This article belongs to the Special Issue Machine Learning: Theory, Algorithms and Applications)

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8 pages, 245 KiB

Open AccessArticle

New Inequalities and Generalizations for Symmetric Means Induced by Majorization Theory

by Huan-Nan Shi and Wei-Shih Du

Axioms 2022, 11(6), 279; https://doi.org/10.3390/axioms11060279 - 9 Jun 2022

Viewed by 1981

Abstract

In this paper, the authors study new inequalities and generalizations for symmetric means and give new proofs for some known results by applying majorization theory. 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)

18 pages, 339 KiB

Open AccessArticle

On the Laplacian, the Kirchhoff Index, and the Number of Spanning Trees of the Linear Pentagonal Derivation Chain

by Yue Tu, Xiaoling Ma, Yuqing Zhang and Junyu Ren

Axioms 2022, 11(6), 278; https://doi.org/10.3390/axioms11060278 - 9 Jun 2022

Cited by 2 | Viewed by 2092

Abstract

Let

P_{n}

be a pentagonal chain with

2 n

pentagons in which two pentagons with two edges in common can be regarded as adding one vertex and two edges to a hexagon. Thus, the linear pentagonal derivation chains

Q P_{n}

represent [...] Read more.

Let

P_{n}

be a pentagonal chain with

2 n

pentagons in which two pentagons with two edges in common can be regarded as adding one vertex and two edges to a hexagon. Thus, the linear pentagonal derivation chains

Q P_{n}

represent the graph obtained by attaching four-membered rings to every two pentagons of

P_{n}

. In this article, the Laplacian spectrum of

Q P_{n}

consisting of the eigenvalues of two symmetric matrices is determined. Next, the formulas for two graph invariants that can be represented by the Laplacian spectrum, namely, the Kirchhoff index and the number of spanning trees, are studied. Surprisingly, the Kirchhoff index is almost one half of the Wiener index of a linear pentagonal derivation chain

Q P_{n}

. Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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7 pages, 440 KiB

Open AccessArticle

Super Connected Direct Product of Graphs and Cycles

by Jiaqiong Yin and Yingzhi Tian

Axioms 2022, 11(6), 277; https://doi.org/10.3390/axioms11060277 - 9 Jun 2022

Viewed by 1885

Abstract

The topology of an interconnection network can be modeled by a graph

G = (V (G), E (G))

. The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. [...] Read more.

The topology of an interconnection network can be modeled by a graph

G = (V (G), E (G))

. The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. The direct product is an important graph product. This paper mainly focuses on the super connectedness of the direct product of graphs and cycles. The connectivity of G, denoted by

κ (G)

, is the size of a minimum vertex set

S \subseteq V (G)

such that

G - S

is not connected or has only one vertex. The graph G is said to be super connected, simply super-

κ

, if every minimum vertex cut is the neighborhood of a vertex with minimum degree. The direct product of two graphs G and H, denoted by

G \times H

, is the graph with vertex set

V (G \times H) = V (G) \times V (H)

and edge set

E (G \times H) = {(u_{1}, v_{1}) (u_{2}, v_{2}) | u_{1} u_{2} \in E (G), v_{1} v_{2} \in E (H)}

. In this paper, we give some sufficient conditions for the direct product

G \times C_{n}

to be super connected, where

C_{n}

is the cycle on n vertices. Furthermore, those sufficient conditions are the best possible. Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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19 pages, 11264 KiB

Open AccessArticle

Interval Type-3 Fuzzy Control for Automated Tuning of Image Quality in Televisions

by Oscar Castillo, Juan R. Castro and Patricia Melin

Axioms 2022, 11(6), 276; https://doi.org/10.3390/axioms11060276 - 9 Jun 2022

Cited by 26 | Viewed by 2743

Abstract

In this article, an intelligent system utilizing type-3 fuzzy logic for automated image quality tuning in televisions is presented. The tuning problem can be formulated as controlling the television imaging system to achieve the requirements of production quality. Previously, the tuning process has [...] Read more.

In this article, an intelligent system utilizing type-3 fuzzy logic for automated image quality tuning in televisions is presented. The tuning problem can be formulated as controlling the television imaging system to achieve the requirements of production quality. Previously, the tuning process has been carried out by experts, by manually adjusting the television imaging system on production lines to meet the quality control standards. In this approach, interval type-3 fuzzy logic is utilized with the goal of automating the tuning of televisions manufactured on production lines. An interval type-3 fuzzy approach for image tuning is proposed, so that the best image quality is obtained and, in this way, meet quality requirements. A system based on type-3 fuzzy control is implemented with good simulation results. The validation of the type-3 fuzzy approach is made by comparing the results with human experts on the process of electrical tuning of televisions. The key contribution is the utilization of type-3 fuzzy in the image tuning application, which has not been reported previously in the literature. Full article

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

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15 pages, 330 KiB

Open AccessArticle

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

by Jingqian Wang and Xiaohong Zhang

Axioms 2022, 11(6), 275; https://doi.org/10.3390/axioms11060275 - 6 Jun 2022

Cited by 26 | Viewed by 2312

Abstract

Rough set theory provides a useful tool for data analysis, data mining and decision making. For multi-criteria decision making (MCDM), rough sets are used to obtain decision rules by reducing attributes and objects. However, different reduction methods correspond to different rules, which will [...] Read more.

Rough set theory provides a useful tool for data analysis, data mining and decision making. For multi-criteria decision making (MCDM), rough sets are used to obtain decision rules by reducing attributes and objects. However, different reduction methods correspond to different rules, which will influence the decision result. To solve this problem, we propose a novel method for MCDM based on rough sets and a fuzzy measure in this paper. Firstly, a type of non-additive measure of attributes is presented by the importance degree in rough sets, which is a fuzzy measure and called an attribute measure. Secondly, for a decision information system, the notion of the matching degree between two objects is presented under an attribute. Thirdly, based on the notions of the attribute measure and matching degree, a Choquet integral is constructed. Moreover, a novel MCDM method is presented by the Choquet integral. Finally, the presented method is compared with other methods through a numerical example, which is used to illustrate the feasibility and effectiveness of our method. Full article

(This article belongs to the Special Issue Soft Computing with Applications to Decision Making and Data Mining)

9 pages, 369 KiB

Open AccessArticle

Homogeneity of Complex Fuzzy Operations

by Bo Hu, Wei Wu and Songsong Dai

Axioms 2022, 11(6), 274; https://doi.org/10.3390/axioms11060274 - 6 Jun 2022

Viewed by 1771

Abstract

The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of [...] Read more.

The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of both rotational invariance and ratio scale invariance for complex fuzzy operations. We show that a binary function is homogeneous if and only if it is both rotationally invariant and ratio scale invariant. Moreover, we consider the simplification of the homogeneity for complex fuzzy binary operators. Full article

(This article belongs to the Special Issue Fuzzy Logic as the Foundation for Theories of Fuzzy Mathematical Structures)

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11 pages, 300 KiB

Open AccessFeature PaperArticle

Topological and Geometrical Properties of k-Symplectic Structures

by Essabab Said, Fanich El Mokhtar and Awane Azzouz

Axioms 2022, 11(6), 273; https://doi.org/10.3390/axioms11060273 - 6 Jun 2022

Cited by 1 | Viewed by 1757

Abstract

We study new geometrical and topological aspects of polarized k-symplectic manifolds. In addition, we study the De Rham cohomology groups of the k-symplectic group. In this work, we pay particular attention to the problem of the orientation of polarized k-symplectic [...] Read more.

We study new geometrical and topological aspects of polarized k-symplectic manifolds. In addition, we study the De Rham cohomology groups of the k-symplectic group. In this work, we pay particular attention to the problem of the orientation of polarized k-symplectic manifolds in a way analogous to symplectic manifolds which are all orientable. Full article

(This article belongs to the Collection Topological Groups)

7 pages, 242 KiB

Open AccessArticle

On a Class of Positive Definite Operators and Their Application in Fractional Calculus

by Temirkhan Aleroev

Axioms 2022, 11(6), 272; https://doi.org/10.3390/axioms11060272 - 5 Jun 2022

Cited by 2 | Viewed by 2050

Abstract

This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated. In particular, the positive definiteness of the studied operators is shown, which [...] Read more.

This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated. In particular, the positive definiteness of the studied operators is shown, which makes it possible to select areas in the complex plane where there are no eigenvalues of these operators. Full article

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

16 pages, 1784 KiB

Open AccessArticle

Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities

by Jianwei Hao, Jinrong Wang and Jiangfeng Han

Axioms 2022, 11(6), 271; https://doi.org/10.3390/axioms11060271 - 5 Jun 2022

Viewed by 1868

Abstract

In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued [...] Read more.

In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued pseudomonotone operators and the property of the conformable derivative. Notice that we imply some new fractional viscoelastic constitutive laws. Full article

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

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6 pages, 252 KiB

Open AccessArticle

k-Path-Connectivity of Completely Balanced Tripartite Graphs

by Pi Wang, Shasha Li and Xiaoxue Gao

Axioms 2022, 11(6), 270; https://doi.org/10.3390/axioms11060270 - 5 Jun 2022

Cited by 2 | Viewed by 1935

Abstract

For a graph

G = (V, E)

and a set

S \subseteq V (G)

of a size at least 2, a path in G is said to be an S-path if it connects all vertices of S [...] Read more.

For a graph

G = (V, E)

and a set

S \subseteq V (G)

of a size at least 2, a path in G is said to be an S-path if it connects all vertices of S. Two S-paths

P_{1}

and

P_{2}

are said to be internally disjoint if

E (P_{1}) \cap E (P_{2}) = \emptyset

and

V (P_{1}) \cap V (P_{2}) = S

; that is, they share no vertices and edges apart from S. Let

π_{G} (S)

denote the maximum number of internally disjoint S-paths in G. The k-path-connectivity

π_{k} (G)

of G is then defined as the minimum

π_{G} (S)

, where S ranges over all k-subsets of

V (G)

. In this paper, we study the k-path-connectivity of the complete balanced tripartite graph

K_{n, n, n}

and obtain

π_{k} (K_{n, n, n}) = ⌊\frac{2 n}{k - 1}⌋

for

3 \leq k \leq n .

Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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Axioms, Volume 11, Issue 6 (June 2022) – 56 articles

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