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Axioms
Number of Followers: 1 Open Access journal ISSN (Online) 2075-1680 Published by MDPI [246 journals] |
- Axioms, Vol. 11, Pages 660: Social Simulation Model of the Spread and
Prevention of the Omicron SARS-CoV-2 Variant
Authors: Ya Su, Lihu Pan, Huimin Yan, Guoyou Zhang, Rui Zhang
First page: 660
Abstract: The enhanced virulence and infectiousness of the Omicron variant of SARS-CoV-2 is having more significant impacts on certain socioeconomic areas, and rapidly suppressing the spread of the epidemic remains a priority for maintaining public health security throughout the world. Thus, we applied multi-agent modeling theory to create a social simulation model of Omicron variant transmission and prevention and control in order to analyze the virus transmission status in complex urban systems and its changing trends under different interventions. By considering the six municipal districts under the jurisdiction of Taiyuan City as examples, we developed state transition rules between five types of resident agents, mobility and contact behavior rules, and rules for patient admission behavior by hospital agents. We then conducted multi-scenario simulation experiments based on single measures of pharmacological and non-pharmacological interventions under non-governmental control as well as multiple interventions in combination to evaluate the effects of different measures on rapidly suppressing the spread of the epidemic. The experimental results demonstrated the utility of the model and the multi-agent modeling method effectively analyzed the transmission trends for the Omicron variant, thereby allowing a comprehensive diagnosis of the future urban epidemic situation and providing an important scientific basis for exploring more accurate normalized prevention and control measures.
Citation: Axioms
PubDate: 2022-11-22
DOI: 10.3390/axioms11120660
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 661: Wave Patterns inside Transparent Scatterers
Authors: Youzi He, Hongyu Liu, Xianchao Wang
First page: 661
Abstract: It may happen that under a certain wave interrogation, a medium scatterer produces no scattering. In such a case, the scattering field is trapped inside the scatterer and forms a certain interior resonant mode. We are concerned with the behavior of the wave propagation inside a transparent scatterer. It turns out that the study can be boiled down to analyzing the interior transmission eigenvalue problem. For isotropic mediums, it is shown in a series of recent works that the transmission eigenfunctions possess rich patterns. In this paper, we show that those spectral patterns also hold for anisotropic mediums.
Citation: Axioms
PubDate: 2022-11-22
DOI: 10.3390/axioms11120661
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 662: Some New Generalized Inequalities of Hardy
Type Involving Several Functions on Time Scale Nabla Calculus
Authors: A. I. Saied, Ghada ALNemer, Mohammed Zakarya, Clemente Cesarano, Haytham M. Rezk
First page: 662
Abstract: In this article, we establish several new generalized Hardy-type inequalities involving several functions on time-scale nabla calculus. Furthermore, we derive some new multidimensional Hardy-type inequalities on time scales nabla calculus. The main results are proved by applying Minkowski’s inequality, Jensen’s inequality and Arithmetic Mean–Geometric Mean inequality. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, the results which are essentially new.
Citation: Axioms
PubDate: 2022-11-22
DOI: 10.3390/axioms11120662
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 663: Sketch-Based Retrieval Approach Using
Artificial Intelligence Algorithms for Deep Vision Feature Extraction
Authors: Eman S. Sabry, Salah Elagooz, Fathi E. Abd El-Samie, Walid El-Shafai, Nirmeen A. El-Bahnasawy, Ghada El-Banby, Naglaa F. Soliman, Sudhakar Sengan, Rabie A. Ramadan
First page: 663
Abstract: Since the onset of civilization, sketches have been used to portray our visual world, and they continue to do so in many different disciplines today. As in specific government agencies, establishing similarities between sketches is a crucial aspect of gathering forensic evidence in crimes, in addition to satisfying the user’s subjective requirements in searching and browsing for specific sorts of images (i.e., clip art images), especially with the proliferation of smartphones with touchscreens. With such a kind of search, quickly and effectively drawing and retrieving sketches from databases can occasionally be challenging, when using keywords or categories. Drawing some simple forms and searching for the image in that way could be simpler in some situations than attempting to put the vision into words, which is not always possible. Modern techniques, such as Content-Based Image Retrieval (CBIR), may offer a more useful solution. The key engine of such techniques that poses various challenges might be dealt with using effective visual feature representation. Object edge feature detectors are commonly used to extract features from different image sorts. However, they are inconvenient as they consume time due to their complexity in computation. In addition, they are complicated to implement with real-time responses. Therefore, assessing and identifying alternative solutions from the vast array of methods is essential. Scale Invariant Feature Transform (SIFT) is a typical solution that has been used by most prevalent research studies. Even for learning-based methods, SIFT is frequently used for comparison and assessment. However, SIFT has several downsides. Hence, this research is directed to the utilization of handcrafted-feature-based Oriented FAST and Rotated BRIEF (ORB) to capture visual features of sketched images to overcome SIFT limitations on small datasets. However, handcrafted-feature-based algorithms are generally unsuitable for large-scale sets of images. Efficient sketched image retrieval is achieved based on content and separation of the features of the black line drawings from the background into precisely-defined variables. Each variable is encoded as a distinct dimension in this disentangled representation. For representation of sketched images, this paper presents a Sketch-Based Image Retrieval (SBIR) system, which uses the information-maximizing GAN (InfoGAN) model. The establishment of such a retrieval system is based on features acquired by the unsupervised learning InfoGAN model to satisfy users’ expectations for large-scale datasets. The challenges with the matching and retrieval systems of such kinds of images develop when drawing clarity declines. Finally, the ORB-based matching system is introduced and compared to the SIFT-based system. Additionally, the InfoGAN-based system is compared with state-of-the-art solutions, including SIFT, ORB, and Convolutional Neural Network (CNN).
Citation: Axioms
PubDate: 2022-11-22
DOI: 10.3390/axioms11120663
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 664: A Selective Portfolio Management Algorithm
with Off-Policy Reinforcement Learning Using Dirichlet Distribution
Authors: Hyunjun Yang, Hyeonjun Park, Kyungjae Lee
First page: 664
Abstract: Existing methods in portfolio management deterministically produce an optimal portfolio. However, according to modern portfolio theory, there exists a trade-off between a portfolio’s expected returns and risks. Therefore, the optimal portfolio does not exist definitively, but several exist, and using only one deterministic portfolio is disadvantageous for risk management. We proposed Dirichlet Distribution Trader (DDT), an algorithm that calculates multiple optimal portfolios by taking Dirichlet Distribution as a policy. The DDT algorithm makes several optimal portfolios according to risk levels. In addition, by obtaining the pi value from the distribution and applying importance sampling to off-policy learning, the sample is used efficiently. Furthermore, the architecture of our model is scalable because the feed-forward of information between portfolio stocks occurs independently. This means that even if untrained stocks are added to the portfolio, the optimal weight can be adjusted. We also conducted three experiments. In the scalability experiment, it was shown that the DDT extended model, which is trained with only three stocks, had little difference in performance from the DDT model that learned all the stocks in the portfolio. In an experiment comparing the off-policy algorithm and the on-policy algorithm, it was shown that the off-policy algorithm had good performance regardless of the stock price trend. In an experiment comparing investment results according to risk level, it was shown that a higher return or a better Sharpe ratio could be obtained through risk control.
Citation: Axioms
PubDate: 2022-11-23
DOI: 10.3390/axioms11120664
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 665: A Novel Approach for the Approximate Solution
of Wave Problems in Multi-Dimensional Orders with Computational
Applications
Authors: Muhammad Nadeem, Ali Akgül, Liliana Guran, Monica-Felicia Bota
First page: 665
Abstract: The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform (AIT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach.
Citation: Axioms
PubDate: 2022-11-24
DOI: 10.3390/axioms11120665
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 666: Extending Normality: A Case of Unit
Distribution Generated from the Moments of the Standard Normal
Distribution
Authors: Miguel S. Concha-Aracena, Leonardo Barrios-Blanco, David Elal-Olivero, Paulo Henrique Ferreira da Silva, Diego Carvalho do Nascimento
First page: 666
Abstract: This paper presents an important theorem, which shows that, heading from the moments of the standard normal distribution, one can generate density functions originating a family of models. Additionally, we discussed that different random variable domains are achieved with transformations. For instance, we adopted the moment of order two, from the proposed theorem, and transformed it, which enabled us to exemplify this class as a unit distribution. We named it as Alpha-Unit (AU) distribution, which contains a single positive parameter α (AU(α)∈[0,1]). We presented its properties and demonstrated two estimation methods for the α parameter, the maximum likelihood estimator (MLE) and uniformly minimum-variance unbiased estimator (UMVUE) methods. In order to analyze the statistical consistency of the estimators, a Monte Carlo simulation study was carried out, in which the robustness was demonstrated. As a real-world application, we adopted two sets of unit data, the first regarding the dynamics of Chilean inflation in the post-military period, and the other one regarding the daily maximum relative humidity of the air in the Atacama Desert. In both cases presented, the AU model is competitive, whenever the data present a range greater than 0.4 and extremely heavy asymmetric tail. We compared our model with other commonly used unit models, such as the beta, Kumaraswamy, logit-normal, simplex, unit-half-normal, and unit-Lindley distributions.
Citation: Axioms
PubDate: 2022-11-24
DOI: 10.3390/axioms11120666
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 667: Fractional Dynamical Behavior of an Elastic
Magneto Piezo Oscillator including Non-Ideal Motor Excitation
Authors: Ribeiro, Balthazar, Lenz, Felix, Litak, Tusset
First page: 667
Abstract: In this work, we analyzed the nonlinear fractional dynamics in the equations of motion of a bar coupled to support under the effect of a potential described by two equally spaced magnetic poles. We also considered Bouc–Wen damping in the equations of motion. For external force vibrations, we considered an equation of a non-ideal motor based on the parameters that related the interaction between the oscillation and the excitation source. With such considerations, we explored the influence of the fractional derivative operator parameter on the average power generated by the device and the dynamic behavior to determine the chaotic and periodic regions. We use Bifurcation Diagrams, Test 0–1, Phase Portrait, and Poincaré Maps. As a conclusion, we established a set of parameters for the fractional differential equations to obtain higher average powers and the periodicity windows that corroborate the establishment of energetic orbits for energy harvesting.
Citation: Axioms
PubDate: 2022-11-24
DOI: 10.3390/axioms11120667
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 668: Risk Analysis of Green Supply Chain Using a
Hybrid Multi-Criteria Decision Model: Evidence from Laptop Manufacturer
Industry
Authors: I-Fei Chen, Pi-Ying Kuo, Ruey-Chyn Tsaur, Santanu Sarkar, Shih-Chun Huang
First page: 668
Abstract: Green supply chain management has become enormously significant over the last two decades. Traditional supply chain risk management is inept at dealing with the intangible criteria related to environmental issues. Contrary to most of the previous research, which emphasized risks in merely one or two phases of the green supply chain, this study provides a systematic checklist of the cradle-to-grave approach to risk identification and prioritization using a hybrid method. Based on a world-leading Taiwanese laptop manufacturer, we first identified the risk factors of the green supply chain with respect to the components and subcomponents of Risk Priority Numbers (RPN) on the Failure Mode and Effects Analysis (FMEA). Second, we used the Analytic Network Process (ANP) to derive the relative weights of the subcomponents of RPN. Third, we combined grey relational analysis and ANP weights to derive the relative importance of each risk criterion in each risk factor in the green supply chain. The empirical results verified that our proposed method can be applied to the laptop manufacturing industry and found industry-specific green risk criteria in each factor. Therefore, following this, enterprises can control the possible risks for continuous improvement in their green activities.
Citation: Axioms
PubDate: 2022-11-24
DOI: 10.3390/axioms11120668
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 669: Comparison of Systemic Financial Risks in the
US before and after the COVID-19 Outbreak—A Copula–GARCH with
CES Approach
Authors: Ji Ma, Xiaoqing Li, Jianxu Liu, Jiande Cui, Mingzhi Zhang, Songsak Sriboonchitta
First page: 669
Abstract: The analysis and prediction of systemic financial risks in the US during the COVID-19 pandemic is of great significance to the stability of financial markets in the US and even the world. This paper aims to predict the systemic financial risk in the US before and during the COVID-19 pandemic by using copula–GJR–GARCH models with component expected shortfall (CES), and also identify systemically important financial institutions (SIFIs) for the two comparative periods. The empirical results show that the overall systemic financial risk increased after the outbreak of the COVID-19 pandemic, especially in the first half of the year. We predicted four extreme risks that were basically successful in capturing the high risks in the US financial markets. Second, we identified the SIFIs, and depository banks made the greatest contribution to systemic risk from four financial groups. Third, after the outbreak of the epidemic, the share of Broker–Dealer and Other Institutions in the overall systemic risk has apparently increased. Finally, we recommend that the US financial regulators should consider macro-prudential guidance for major financial institutions, and we should pay more attention to Broker–Dealers, thereby improving the financial stability of the US and the global financial markets.
Citation: Axioms
PubDate: 2022-11-25
DOI: 10.3390/axioms11120669
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 670: Set Theory, Dynamism, and the Event:
Reinjecting Time into the Foundations of Mathematics
Authors: Said Mikki
First page: 670
Abstract: This article concentrates on exploring the relevance of the postmodernist concept of the event to mathematical philosophy and the foundations of mathematics. In both the scientific and philosophical study of nature, and particularly event ontology, we find that space and dynamism are fundamental. However, whether based on set theory or category theory, modern mathematics faces conceptual and philosophical difficulties when the temporal is intentionally invoked as a key aspect of that intrinsic dynamism so characteristic of mathematical being, physical becoming, process, and thought. We present a multidisciplinary investigation targeting a diverse audience including mathematicians, scientists, and philosophers who are interested in exploring alternative modes of doing mathematics or using mathematics to approach nature. Our aim is to understand both the formal character and the philosophy of time as realized through a radical mode of thinking that goes beyond the spatial in mathematics. In particular, we suggest the need to transcend the purely geometrical view altogether in future foundational research in both mathematics and mathematical philosophy. We reexamine these issues at a fundamental and comprehensive level, where a detailed exposition and critique of both modern set theories and theories of space is outlined, with emphasis on how the philosophy of Idealism has been permeating much of old and new mathematics. Furthermore, toward the end of the article, we explore some possible constructive directions in mathematical ontology by providing new proposals on how to develop a fragment of mathematics for the description of dynamic events.
Citation: Axioms
PubDate: 2022-11-25
DOI: 10.3390/axioms11120670
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 671: Higher-Order Jacobsthal–Lucas
Quaternions
Authors: Mine Uysal, Engin Özkan
First page: 671
Abstract: In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties. We give Binet’s formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, and exponential generating functions of the higher-order Jacobsthal–Lucas quaternions. We also give some relations between higher-order Jacobsthal and Jacobsthal–Lucas quaternions.
Citation: Axioms
PubDate: 2022-11-25
DOI: 10.3390/axioms11120671
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 672: A Procedure for Constructing the Solution of a
Nonlinear Fredholm Integro-Differential Equation of Second Order
Authors: Gama, Gama
First page: 672
Abstract: In this work, a large class of integro-differential equations, arising from the description of heat transfer problems, is considered, particularly the nonlinear equations. We propose a procedure for constructing their solution in a very simple and reliable way in which the only needed tool is the same one employed to solve a linear second-order ordinary differential equation, subject to Robin boundary conditions. Proofs of the convergence, existence, and uniqueness are presented. Some special cases are simulated to illustrate the proposed tools.
Citation: Axioms
PubDate: 2022-11-26
DOI: 10.3390/axioms11120672
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 673: Nearly Sasakian Manifolds of Constant Type
Authors: Aligadzhi Rustanov
First page: 673
Abstract: The article deals with nearly Sasakian manifolds of a constant type. It is proved that the almost Hermitian structure induced on the integral manifolds of the maximum dimension of the first fundamental distribution of the nearly Sasakian manifold is a nearly Kähler manifold. It is proved that the class of nearly Sasakian manifolds of the zero constant type coincides with the class of Sasakian manifolds. The concept of constancy of the type of an almost contact metric manifold is introduced through its Nijenhuis tensor, and the criterion of constancy of the type of an almost contact metric manifold is proved. The coincidence of both concepts of type constancy for the nearly Sasakian manifold is proved. It is proved that the almost Hermitian structure induced on the integral manifolds of the maximum dimension of the first fundamental distribution of the almost contact metric manifold of the zero constant type is the Hermitian structure.
Citation: Axioms
PubDate: 2022-11-26
DOI: 10.3390/axioms11120673
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 674: Text Data Analysis Using Generalized Linear
Mixed Model and Bayesian Visualization
Authors: Sunghae Jun
First page: 674
Abstract: Many parts of big data, such as web documents, online posts, papers, patents, and articles, are in text form. So, the analysis of text data in the big data domain is an important task. Many methods based on statistics or machine learning algorithms have been studied for text data analysis. Most of them were analytical methods based on the generalized linear model (GLM). For the GLM, text data analysis is performed based on the assumption of the error included in the given data and follows the Gaussian distribution. However, the GLM has shown limitations in the analysis of text data, including data sparseness. This is because the preprocessed text data has a zero-inflated problem. To solve this problem, we proposed a text data analysis using the generalized linear mixed model (GLMM) and Bayesian visualization. Therefore, the objective of our study is to propose the use of GLMM to overcome the limitations of the conventional GLM in the analysis of text data with a zero-inflated problem. The GLMM uses various probability distributions as well as Gaussian for error terms and considers the difference between observations by clustering. We also use Bayesian visualization to find meaningful associations between keywords. Lastly, we carried out the analysis of text data searched from real domains and provided the analytical results to show the performance and validity of our proposed method.
Citation: Axioms
PubDate: 2022-11-26
DOI: 10.3390/axioms11120674
Issue No: Vol. 11, No. 12 (2022)
- Axioms, Vol. 11, Pages 579: Dynamical Analysis and Finite-Time
Synchronization for a Chaotic System with Hidden Attractor and Surface
Equilibrium
Authors: Runhao Zhang, Xiaojian Xi, Huaigu Tian, Zhen Wang
First page: 579
Abstract: In this paper, a chaotic system with surface equilibrium and a hidden attractor was studied, and the dynamical behavior, synchronization scheme and circuit application of the system were analyzed. Firstly, the stability analysis and dynamic behavior of the system were carried out (the type of attractor, bifurcation, Poincaré section, Lyapunov exponents spectrum and complexity). Secondly, the finite-time synchronization observer was designed according to the finite-time stability theorem to achieve the synchronization of the finite-time master–slave systems, and the error system asymptotically approached zero. Finally, the existence and practicability of the original system were proven through the implementation of the circuit system, and through using an appropriate control circuit to realize the synchronization of chaotic master–slave systems.
Citation: Axioms
PubDate: 2022-10-22
DOI: 10.3390/axioms11110579
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 580: Hybrid Fuzzy Contraction Theorems with Their
Role in Integral Inclusions
Authors: Faryad Ali, Mohammed Shehu Shagari, Akbar Azam
First page: 580
Abstract: The focus of this paper is to establish a new concept of b-hybrid fuzzy contraction regarding the study of fuzzy fixed-point theorems in the setting of b-metric spaces. This idea harmonizes and refines several well-known results in the direction of point-valued, multivalued, and fuzzy-set-valued maps in the comparable literature. To attract new researchers to this field, some important results are shown to be corollaries. Moreover, a result is presented to establish sufficient conditions for the existence of solutions of integral inclusion of Fredholm type. Lastly, illustrations are presented to validate the suppositions of the given theorems.
Citation: Axioms
PubDate: 2022-10-22
DOI: 10.3390/axioms11110580
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 581: Prediction of the Share of Solar Power in
China Based on FGM (1,1) Model
Authors: Yuhan Li, Shuya Wang, Wei Dai, Liusan Wu
First page: 581
Abstract: In recent years, fossil energy reserves have decreased year by year, and the development and use of renewable energy has attracted great attention of governments all over the world. China continues to promote the high-quality development of renewable energy such as solar power generation. Accurate prediction of the share of solar power in China is beneficial to implementing the goals of carbon peaking and carbon neutralization. According to the website of China’s National Bureau of statistics, the earliest annual data of China’s solar power generation is 2017, which leads to there being very few data on the share of China’s solar power generation. Therefore, the prediction accuracy of most prediction methods is low, and the advantages of the grey prediction model are shown. Based on the share of solar power in China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r using the Particle Swarm Optimization (PSO) algorithm, and predicts the share of solar power in China in the next few years. r = 0.3858 and MAPE = 0.20% were obtained by calculation of the model. The prediction results show that the share of solar power generation in China will increase year by year, and it will reach about 4.2301% by 2030. In addition, it is found that the share of China’s solar power generation in 2021 is 2.1520%, and the predicted value is 2.1906%. It can be seen that the prediction error is small. Finally, the limitations and future research directions are elucidated. The prediction results presented in this paper will help to guide the development of solar power generation in China, and are of great significance in speeding up the pace of energy structural adjustment, accelerating the construction of a clean, low-carbon, safe and efficient energy system, and promoting sustainable development.
Citation: Axioms
PubDate: 2022-10-22
DOI: 10.3390/axioms11110581
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 582: First Passage Analysis in a Queue with State
Dependent Vacations
Authors: Jewgeni H. Dshalalow, Ryan T. White
First page: 582
Abstract: This paper deals with a single-server queue where the server goes on maintenance when the queue is exhausted. Initially, the maintenance time is fixed by deterministic or random number T. However, during server’s absence, customers are screened by a dispatcher who estimates his service times based on his needs. According to these estimates, the dispatcher shortens server’s maintenance time and as the result the server returns earlier than planned. Upon server’s return, if there are not enough customers waiting (under the N-Policy), the server rests and then resumes his service. At first, the input and service are general. We then prove a necessary and sufficient condition for a simple linear dependence between server’s absence time (including his rest) and the number of waiting customers. It turns out that the input must be (marked) Poisson. We use fluctuation and semi-regenerative analyses (previously established and embellished in our past work) to obtain explicit formulas for server’s return time and the queue length, both with discrete and continuous time parameter. We then dedicate an entire section to related control problems including the determination of the optimal T-value. We also support our tractable formulas with many numerical examples and validate our results by simulation.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110582
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 583: Boundedness of Riesz Potential Operator on
Grand Herz-Morrey Spaces
Authors: Babar Sultan, Fatima Azmi, Mehvish Sultan, Mazhar Mehmood, Nabil Mlaiki
First page: 583
Abstract: In this paper, we introduce grand Herz–Morrey spaces with variable exponent and prove the boundedness of Riesz potential operators in these spaces.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110583
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 584: Mutant Number Laws and Infinite Divisibility
Authors: Anthony G. Pakes
First page: 584
Abstract: Concepts of infinitely divisible distributions are reviewed and applied to mutant number distributions derived from the Lea-Coulson and other models which describe the Luria-Delbrück fluctuation test. A key finding is that mutant number distributions arising from a generalised Lea-Coulson model for which normal cell growth is non-decreasing are unimodal. An integral criterion is given which separates the cases of a mode at the origin, or not.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110584
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 585: The General Analytic Expression of a Harvested
Logistic Model with Slowly Varying Coefficients
Authors: Fahad M. Alharbi
First page: 585
Abstract: The harvested logistic model with a slow variation in coefficients has been considered. Two cases, which depend on the harvest rate, were identified. The first one is when the harvest is subcritical, where the population evolves to an equilibrium. The other is supercritical harvesting, where the population decreases to zero at finite times. The single analytic approximate expression, which is capable of describing both harvesting cases, is readily and explicitly obtained using the multi-time scaling method together with the perturbation approach. This solution fits for a wide range of coefficient values. In addition, such an expression is validated by utilizing numerical computations, which are obtained by using the fourth-order Runge–Kutta technique. Finally, the comparison shows a very good agreement between the two methods.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110585
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 586: Variational Iteration Method for Solving
Fractional Integro-Differential Equations with Conformable
Differointegration
Authors: Mondher Damak, Zaid Amer Mohammed
First page: 586
Abstract: Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When the differentiation or integration operators or both are of fractional order, the integral equation in this case is called a multidimensional fractional integro-differential equation. Such equations are difficult to solve analytically; therefore, as the main objective of this paper, an approximate method—which is the variational iteration method—will be used to solve this type of equation with conformable fractional-order derivatives and integrals. First, we drive the iterative sequence of approximate solutions using the proposed method, and then, under certain conditions over the kernel of the integro-differential equation, prove its convergence to the exact solution. Two illustrative examples, linear and nonlinear, are given, and their approximated solutions are simulated using computer programs in order to verify from the reliability and applicability of the proposed method.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110586
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 587: Testing Multivariate Normality Based on
t-Representative Points
Authors: Jiajuan Liang, Ping He, Jun Yang
First page: 587
Abstract: Testing multivariate normality is an ever-lasting interest in the goodness-of-fit area since the classical Pearson’s chi-squared test. Among the numerous approaches in the construction of tests for multivariate normality, normal characterization is one of the common approaches, which can be divided into the necessary and sufficient characterization and necessary-only characterization. We construct a test for multivariate normality by combining the necessary-only characterization and the idea of statistical representative points in this paper. The main idea is to transform a high-dimensional sample into a one-dimensional one through the necessary normal characterization and then employ the representative-point-based Pearson’s chi-squared test. A limited Monte Carlo study shows a considerable power improvement of the representative-point-based chi-square test over the traditional one. An illustrative example is given to show the supplemental function of the new test when used together with existing ones in the literature.
Citation: Axioms
PubDate: 2022-10-24
DOI: 10.3390/axioms11110587
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 588: Trapezoidal Intuitionistic Fuzzy Power
Heronian Aggregation Operator and Its Applications to Multiple-Attribute
Group Decision-Making
Authors: Jeevaraj Selvaraj, Prakash Gatiyala, Sarfaraz Hashemkhani Zolfani
First page: 588
Abstract: Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.
Citation: Axioms
PubDate: 2022-10-25
DOI: 10.3390/axioms11110588
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 589: Entanglement Dynamics Governed by
Time-Dependent Quantum Generators
Authors: Artur Czerwinski
First page: 589
Abstract: In the article, we investigate entanglement dynamics defined by time-dependent linear generators. We consider multilevel quantum systems coupled to an environment that induces decoherence and dissipation, such that the relaxation rates depend on time. By applying the condition of partial commutativity, one can precisely describe the dynamics of selected subsystems. More specifically, we investigate the dynamics of entangled states. The concurrence is used to quantify the amount of two-qubit entanglement in the time domain. The framework appears to be an efficient tool for investigating quantum evolution of entangled states driven by time-local generators. In particular, non-Markovian effects can be included to observe the restoration of entanglement in time.
Citation: Axioms
PubDate: 2022-10-25
DOI: 10.3390/axioms11110589
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 590: Geometric Study of 2D-Wave Equations in View
of K-Symbol Airy Functions
Authors: Samir B. Hadid, Rabha W. Ibrahim
First page: 590
Abstract: The notion of k-symbol special functions has recently been introduced. This new concept offers many interesting geometric properties for these special functions including logarithmic convexity. The aim of the present paper is to exploit essentially two-dimensional wave propagation in the earth-ionosphere wave path using k-symbol Airy functions (KAFs) in the open unit disk. It is shown that the standard wave-mode working formula may be determined by orthogonality considerations without the use of intricate justifications of the complex plane. By taking into account the symmetry-convex depiction of the KAFs, the formula combination is derived.
Citation: Axioms
PubDate: 2022-10-26
DOI: 10.3390/axioms11110590
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 591: The Laplace Transform of Composed Functions
and Bivariate Bell Polynomials
Authors: Diego Caratelli, Rekha Srivastava, Paolo Emilio Ricci
First page: 591
Abstract: The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell’s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica©, are given proving the effectiveness of the proposed method. In the Appendix, a table of the first few bivariate Bell polynomials is also reported.
Citation: Axioms
PubDate: 2022-10-26
DOI: 10.3390/axioms11110591
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 592: Optimal Location of Exit Doors for Efficient
Evacuation of Crowds at Gathering Places
Authors: Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Carmen Rodríguez, Miguel E. Vázquez-Méndez
First page: 592
Abstract: This work deals with the optimal design for the location of the exit doors at meeting places (such as sports centers, public squares, street markets, transport stations, etc.) to guarantee a safer emergency evacuation in events of a sporting, social, entertainment or religious type. This problem is stated as an optimal control problem of nonlinear partial differential equations, where the state system is a reformulation of the Hughes model (coupling the eikonal equation for a density-weighted walking velocity of pedestrians and the continuity equation for conservation of the pedestrian density), the control is the location of the exit doors at the domain boundary (subject to several geometric constraints), and the cost function is related to the evacuation rate. We provide a full numerical algorithm for solving the problem (a finite element technique for the discretization and a gradient-free procedure for the optimization), and show several numerical results for a realistic case.
Citation: Axioms
PubDate: 2022-10-26
DOI: 10.3390/axioms11110592
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 593: Pseudo Overlap Functions, Fuzzy Implications
and Pseudo Grouping Functions with Applications
Authors: Xiaohong Zhang, Rong Liang, Humberto Bustince, Benjamin Bedregal, Javier Fernandez, Mengyuan Li, Qiqi Ou
First page: 593
Abstract: Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.
Citation: Axioms
PubDate: 2022-10-26
DOI: 10.3390/axioms11110593
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 594: Conformal η-Ricci Solitons on Riemannian
Submersions under Canonical Variation
Authors: Mohd. Danish Siddiqi, Ali Hussain Alkhaldi, Meraj Ali Khan, Aliya Naaz Siddiqui
First page: 594
Abstract: This research article endeavors to discuss the attributes of Riemannian submersions under the canonical variation in terms of the conformal η-Ricci soliton and gradient conformal η-Ricci soliton with a potential vector field ζ. Additionally, we estimate the various conditions for which the target manifold of Riemannian submersion under the canonical variation is a conformal η-Ricci soliton with a Killing vector field and a φ(Ric)-vector field. Moreover, we deduce the generalized Liouville equation for Riemannian submersion under the canonical variation satisfying by a last multiplier Ψ of the vertical potential vector field ζ and show that the base manifold of Riemanian submersion under canonical variation is an η Einstein for gradient conformal η-Ricci soliton with a scalar concircular field γ on base manifold. Finally, we illustrate an example of Riemannian submersions between Riemannian manifolds, which verify our results.
Citation: Axioms
PubDate: 2022-10-27
DOI: 10.3390/axioms11110594
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 595: Applications of the q-Derivative Operator to
New Families of Bi-Univalent Functions Related to the Legendre Polynomials
Authors: Ying Cheng, Rekha Srivastava, Jin-Lin Liu
First page: 595
Abstract: By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained. The results derived in this article are shown to extend and generalize those in some earlier works.
Citation: Axioms
PubDate: 2022-10-27
DOI: 10.3390/axioms11110595
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 596: Regularity and Decay of Global Solutions for
the Generalized Benney-Lin Equation Posed on Bounded Intervals and on a
Half-Line
Authors: Nikolai A. Larkin
First page: 596
Abstract: Initial-boundary value problems for the generalized Benney-Lin equation posed on bounded intervals and on the right half-line were considered. The existence and uniqueness of global regular solutions on arbitrary intervals as well as their exponential decay for small solutions and for a special choice of a bounded interval have been established.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110596
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 597: Hyperbolic B-Spline Function-Based
Authors: Mohammad Tamsir, Mutum Zico Meetei, Ahmed H. Msmali
First page: 597
Abstract: We propose a differential quadrature method (DQM) based on cubic hyperbolic B-spline basis functions for computing 3D wave equations. This method converts the problem into a system of ODEs. We use an optimum five-stage and order four SSP Runge-Kutta (SSPRK-(5,4)) scheme to solve the obtained system of ODEs. The matrix stability analysis is also investigated. The accuracy and efficiency of the proposed method are demonstrated via three numerical examples. It has been found that the proposed method gives more accurate results than the existing methods. The main purpose of this work is to present an accurate, economically easy-to-implement, and stable technique for solving hyperbolic partial differential equations.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110597
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 598: Combinatorial Interpretation of Numbers in the
Generalized Padovan Sequence and Some of Its Extensions
Authors: Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino
First page: 598
Abstract: There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach. Thus, mathematical theorems are introduced that refer to the study of the Padovan combinatorial model and some of its extensions, namely Tridovan, Tetradovan and its generalization (Z-dovan). Finally, we obtained a generalization of the Padovan combinatorial model, which was the main result of this research.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110598
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 599: Strategic Alliances for Sustainable
Development: An Application of DEA and Grey Theory Models in the Coal
Mining Sector
Authors: Chia-Nan Wang, Hoang-Phu Nguyen, Yen-Hui Wang, Nhat-Luong Nhieu
First page: 599
Abstract: Sustainable development is a global trend and an economic priority for many governments. Although new energies can be considered good investments in green growth, they may lead to financial barriers to developing countries. The purpose of the study concentrates on an alternative solution that increases the efficiency performance of current fossil energy industries. The study has combined two models of Data Envelopment Analysis (DEA) and Grey Theory in determining inefficient units to propose potential strategic alliances for sustainable development in the Vietnam Coal industry. Besides considering inputs and outputs in the models, the location of coal mines is also a key indicator in recommending good alliances. The results show that the collaborations between the Cao Son coal mine and the Coc Sau coal mine, and between the Nui Beo coal mine and the Vang Danh coal mine, bring the best improvement for sustainable development. The study suggests detailed strategies in action that enterprises and policymakers can refer to, to apply in practice.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110599
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 600: Development of the Generalized
Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its
Application in Hierarchical MCDM
Authors: Debasmita Banerjee, Debashree Guha, Radko Mesiar, Juliet Karmakar Mondol
First page: 600
Abstract: In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110600
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 601: Selection of Business Process Modeling Tool
with the Application of Fuzzy DEMATEL and TOPSIS Method
Authors: Jin, Jin, Huo
First page: 601
Abstract: The business process modeling tool selection problem has a significant impact on the overall performance of enterprise business process modeling, which will directly affect the development of enterprise information systems. Apart from that, the process to select the business process modeling tool from all alternatives is a Multi-Criteria Decision Making (MCDM) problem. This paper develops a methodology based on the hybrid fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method to help companies select the optimal business process modeling tool, where the business process modeling process is more efficient, economic and safe. The proposed method has the following state-of-the-art contributions and features: (1) the latest application of the MCDM methodology to the field of BPM tool selection, (2) addressing the direct and indirect impact between criteria in the selection of BPM tools, and (3) considering the hybrid fuzzy (uncertainty) decision-making issue in the BPM tool selection process. Meanwhile, the mathematical formula in TOPSIS can be regarded as a formula for solving a symmetric problem. The hybrid fuzzy DEMATEL method is used to obtain the weight for the criteria to be considered in the BPM tool selection process, and the TOPSIS method is used to obtain the final business process modeling tool.
Citation: Axioms
PubDate: 2022-10-28
DOI: 10.3390/axioms11110601
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 602: Some New Integral Inequalities Involving
Fractional Operator with Applications to Probability Density Functions and
Special Means
Authors: Bibhakar Kodamasingh, Soubhagya Kumar Sahoo, Wajid Ali Shaikh, Kamsing Nonlaopon, Sotiris K. Ntouyas, Muhammad Tariq
First page: 602
Abstract: Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R−L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers.
Citation: Axioms
PubDate: 2022-10-29
DOI: 10.3390/axioms11110602
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 603: A Fractional-Order SIR-C Cyber Rumor
Propagation Prediction Model with a Clarification Mechanism
Authors: Linna Li, Yuze Li, Jianke Zhang
First page: 603
Abstract: As communication continues to develop, the high freedom and low cost of the communication network environment also make rumors spread more rapidly. If rumors are not clarified and controlled in time, it is very easy to trigger mass panic and undermine social stability. Therefore, it is important to establish an efficient model for rumor propagation. In this paper, the impact of rumor clarifiers on the spread of rumors is considered and fractional order differentiation is introduced to solve the problem that traditional models do not take into account the "anomalous propagation" characteristics of information. A fractional-order Susceptible-Infected-Removal-Clarify (SIR-C) rumor propagation prediction model featuring the clarification mechanism is proposed. The existence and asymptotic stability conditions of the rumor-free equilibrium point (RFEP) E0; the boundary equilibrium points (BEPs) E1 and E2 are also given. Finally, the stability conditions and practical cases are verified by numerical simulations. The experimental results confirm the analysis of the theoretical study and the model fits well with the real-world case data with just minor deviations. As a result, the model can play a positive and effective role in rumor propagation prediction.
Citation: Axioms
PubDate: 2022-10-29
DOI: 10.3390/axioms11110603
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 604: Enhanced Lot Acceptance Testing Based on
Defect Counts and Posterior Odds Ratios
Authors: Arturo J. Fernández
First page: 604
Abstract: Optimal defects-per-unit test plans based on posterior odds ratios are developed for the disposition of product lots. The number of nonconformities per unit is modeled by the Conway–Maxwell–Poisson distribution rather than the typical Poisson model. In essence, a submitted batch is conforming if its posterior acceptability is sufficiently large. First, a useful approximation of the optimal test plan is derived in closed form using the asymptotic normality of the log ratio. A mixed-integer nonlinear programming problem is then solved via Monte Carlo simulation to find the smallest number of inspected items per lot and the maximum tolerable posterior odds ratio. The methodology is applied to the manufacturing of paper and glass. The suggested sampling plan for lot sentencing provides the specified protections to both manufacturers and customers and minimizes the needed sample size. In terms of inspection effort and accuracy, the proposed approach is virtually an advantageous extension of the classical frequentist perspective. In many practical cases, it yields more precise assessments of the current consumer and producer risks, as well as more realistic decision rules.
Citation: Axioms
PubDate: 2022-10-29
DOI: 10.3390/axioms11110604
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 605: A Probe into a (2 + 1)-Dimensional Combined
Cosmological Model in f(R,T) Gravity
Authors: Safiqul Islam, Muhammad Aamir, Irina Radinschi, Dwiptendra Bandyopadhyay
First page: 605
Abstract: This research is an extension of our earlier published (2+1) dimensional cosmological models in f(R,T) gravity with \(\text{Λ}\)(R, T) (IOP Conf. Ser. J. Phys. Conf. Ser. 2019, 1258, 012026). A different class of cosmological space model is studied under modified theories of f(R,T) gravity, where the cosmological constant \(\text{Λ}\) is expressed as a function of the Ricci scalar R and the trace of the stress-energy momentum tensor T. We call such a model as “\(\text{Λ}\)(R, T) gravity”. Such a specific form of \(\text{Λ}\)(R, T) has been defined in the dust as well as in the perfect fluid case. We intend to search for a combined model that satisfies the equation of state for dark energy matter or quintessence matter or perfect matter fluid. Some geometric and intrinsic physical properties of the model are also described. The energy conditions, pressure and density are discussed both when \(\text{Λ}\) = \(\text{Λ}\)(r) is a function of the radial parameter r, as well as when \(\text{Λ}\) is zero. We study the effective mass function and also the gravitational redshift function, both of which are found to be positive as per the latest observations. The cosmological model is studied in f(R,T) modified theory of gravity, where the gravitational Lagrangian is expressed both in terms of the Ricci scalar R and the trace of the stress-energy tensor T. The equation of state parameter is discussed in terms of ω corresponding to the three cases mentioned above. The behaviour of the cosmological constant is separately examined in the presence of quintessence matter, dark energy matter and perfect fluid matter.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110605
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 606: Amoud Class for Hazard-Based and Odds-Based
Regression Models: Application to Oncology Studies
Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, Huda M. Alshanbari, Abdal-Aziz H. El-Bagoury
First page: 606
Abstract: The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using a structure resembling the general class of hazard-based regression models, with the addition that the baseline odds function is multiplied by a link function. The class is broad enough to cover a number of widely used models, including the proportional hazard model, the general hazard model, the proportional odds model, the general odds model, the accelerated hazards model, the accelerated odds model, and the accelerated failure time model, as well as combinations of these. The proposed class incorporates the analysis of crossing survival curves. Based on a versatile parametric distribution (generalized log-logistic) for the baseline hazard, we introduced a technique for applying these various hazard-based and odds-based regression models. This distribution allows us to cover the most common hazard rate shapes in practice (decreasing, constant, increasing, unimodal, and reversible unimodal), and various common survival distributions (Weibull, Burr-XII, log-logistic, exponential) are its special cases. The proposed model has good inferential features, and it performs well when different information criteria and likelihood ratio tests are used to select hazard-based and odds-based regression models. The proposed model’s utility is demonstrated by an application to a right-censored lifetime dataset with crossing survival curves.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110606
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 607: A Method for Analyzing the Performance Impact
of Imbalanced Binary Data on Machine Learning Models
Authors: Ming Zheng, Fei Wang, Xiaowen Hu, Yuhao Miao, Huo Cao, Mingjing Tang
First page: 607
Abstract: Machine learning models may not be able to effectively learn and predict from imbalanced data in the fields of machine learning and data mining. This study proposed a method for analyzing the performance impact of imbalanced binary data on machine learning models. It systematically analyzes 1. the relationship between varying performance in machine learning models and imbalance rate (IR); 2. the performance stability of machine learning models on imbalanced binary data. In the proposed method, the imbalanced data augmentation algorithms are first designed to obtain the imbalanced dataset with gradually varying IR. Then, in order to obtain more objective classification results, the evaluation metric AFG, arithmetic mean of area under the receiver operating characteristic curve (AUC), F-measure and G-mean are used to evaluate the classification performance of machine learning models. Finally, based on AFG and coefficient of variation (CV), the performance stability evaluation method of machine learning models is proposed. Experiments of eight widely used machine learning models on 48 different imbalanced datasets demonstrate that the classification performance of machine learning models decreases with the increase of IR on the same imbalanced data. Meanwhile, the classification performances of LR, DT and SVC are unstable, while GNB, BNB, KNN, RF and GBDT are relatively stable and not susceptible to imbalanced data. In particular, the BNB has the most stable classification performance. The Friedman and Nemenyi post hoc statistical tests also confirmed this result. The SMOTE method is used in oversampling-based imbalanced data augmentation, and determining whether other oversampling methods can obtain consistent results needs further research. In the future, an imbalanced data augmentation algorithm based on undersampling and hybrid sampling should be used to analyze the performance impact of imbalanced binary data on machine learning models.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110607
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 608: Swirling Flow of Chemically Reactive
Viscoelastic Oldroyd-B Fluid through Porous Medium with a Convected
Boundary Condition Featuring the Thermophoresis Particle Deposition and
Soret–Dufour Effects
Authors: Abeer Al Elaiw, Abdul Hafeez, Asma Khalid, Muneerah AL Nuwairan
First page: 608
Abstract: In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110608
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 609: Generalized Mathematical Model of Brinkman
Fluid with Viscoelastic Properties: Case over a Sphere Embedded in Porous
Media
Authors: Siti Farah Haryatie Mohd Kanafiah, Abdul Rahman Mohd Kasim, Syazwani Mohd Zokri
First page: 609
Abstract: The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110609
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 610: Evaluating Global Container Shipping
Companies: A Novel Approach to Investigating Both Qualitative and
Quantitative Criteria for Sustainable Development
Authors: Chia-Nan Wang, Thanh-Tuan Dang, Ngoc-Ai-Thy Nguyen, Chien-Chang Chou, Hsien-Pin Hsu, Le-Thanh-Hieu Dang
First page: 610
Abstract: The COVID-19 pandemic has implications for the container shipping industry and global supply chains. Measuring the efficiency of major international container shipping companies (CSCs) is an important issue that helps them make strategic decisions to improve performance, especially in the context that all businesses and governments are adapting to build back better the post-pandemic world. This paper develops a new integrated approach using both a qualitative assessment tool and a performance assessment tool as a systematic and flexible framework for evaluating the container shipping industry. This new methodology is implemented in two phases to consider both qualitative and quantitative criteria for assessing the performance of CSCs based on efficiency. In the first phase, qualitative performance evaluation is performed using spherical fuzzy analytical hierarchical process (AHP-SF) to find criteria weights and then the grey complex proportional assessment methodology (COPRAS-G) is used to find the ranking of CSCs. Qualitative variables are converted into a quantitative variable for use in the data envelopment analysis (DEA) model as an output called an output variable called expert-based qualitative performance (EQP). Then, DEA is performed to identify efficient and inefficient CSCs with the EQP variable and other quantitative parameters (i.e., capacity, lifting, expenses, revenue, and CO2 emissions). The efficiency of 14 major global CSCs is empirically evaluated, and the scores for CSCs’ efficiency in all dimensions are measured and examined. The results show that the average cargo efficiency of the CSCs is lower than their eco-efficiency performance, revealing the operational disruption caused by the pandemic. Moreover, by identifying efficient and inefficient CSCs, our findings provide practical implications for decision-makers in the maritime field and assist in modifying applicable policies and strategies to achieve sustainable performance.
Citation: Axioms
PubDate: 2022-11-01
DOI: 10.3390/axioms11110610
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 611: Existence Solutions for Implicit Fractional
Relaxation Differential Equations with Impulsive Delay Boundary Conditions
Authors: Varaporn Wattanakejorn, Panjaiyan Karthikeyann, Sadhasivam Poornima, Kulandhaivel Karthikeyan, Thanin Sitthiwirattham
First page: 611
Abstract: The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive implicit delay differential equations with boundary conditions. Some findings are established by applying the Banach contraction mapping principle and the Schauder fixed-point theorem. An example is provided that illustrates the theoretical results.
Citation: Axioms
PubDate: 2022-11-02
DOI: 10.3390/axioms11110611
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 612: New Robust Estimators for Handling
Multicollinearity and Outliers in the Poisson Model: Methods, Simulation
and Applications
Authors: Issam Dawoud, Fuad A. Awwad, Elsayed Tag Eldin, Mohamed R. Abonazel
First page: 612
Abstract: The Poisson maximum likelihood (PML) is used to estimate the coefficients of the Poisson regression model (PRM). Since the resulting estimators are sensitive to outliers, different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PML estimator is sensitive to multicollinearity. Therefore, several biased Poisson estimators have been provided to cope with this problem, such as the Poisson ridge estimator, Poisson Liu estimator, Poisson Kibria–Lukman estimator, and Poisson modified Kibria–Lukman estimator. Despite different Poisson biased regression estimators being proposed, there has been no analysis of the robust version of these estimators to deal with the two above-mentioned problems simultaneously, except for the robust Poisson ridge regression estimator, which we have extended by proposing three new robust Poisson one-parameter regression estimators, namely, the robust Poisson Liu (RPL), the robust Poisson Kibria–Lukman (RPKL), and the robust Poisson modified Kibria–Lukman (RPMKL). Theoretical comparisons and Monte Carlo simulations were conducted to show the proposed performance compared with the other estimators. The simulation results indicated that the proposed RPL, RPKL, and RPMKL estimators outperformed the other estimators in different scenarios, in cases where both problems existed. Finally, we analyzed two real datasets to confirm the results.
Citation: Axioms
PubDate: 2022-11-03
DOI: 10.3390/axioms11110612
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 613: Joint Approximation of Analytic Functions by
Shifts of the Riemann Zeta-Function Twisted by the Gram Function II
Authors: Antanas Laurinčikas
First page: 613
Abstract: Let tτ be a solution to the equation θ(t)=(τ−1)π, τ>0, where θ(t) is the increment of the argument of the function π−s/2Γ(s/2) along the segment connecting points s=1/2 and s=1/2+it. tτ is called the Gram function. In the paper, we consider the approximation of collections of analytic functions by shifts of the Riemann zeta-function (ζ(s+itτα1),…,ζ(s+itταr)), where α1,…,αr are different positive numbers, in the interval [T,T+H] with H=o(T), T→∞, and obtain the positivity of the density of the set of such shifts. Moreover, a similar result is obtained for shifts of a certain absolutely convergent Dirichlet series connected to ζ(s). Finally, an example of the approximation of analytic functions by a composition of the above shifts is given.
Citation: Axioms
PubDate: 2022-11-04
DOI: 10.3390/axioms11110613
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 614: Diabetic Retinopathy Progression Prediction
Using a Deep Learning Model
Authors: Hanan A. Hosni Mahmoud
First page: 614
Abstract: Diabetes is an illness that happens with a high level of glucose in the body, and can harm the retina, causing permanent loss vision or diabetic retinopathy. The fundus oculi method comprises detecting the eyes to perform a pathology test. In this research, we implement a method to predict the progress of diabetic retinopathy. There is a research gap that exists for the detection of diabetic retinopathy progression employing deep learning models. Therefore, in this research, we introduce a recurrent CNN (R-CNN) model to detect upcoming visual field inspections to predict diabetic retinopathy progression. A benchmark dataset of 7000 eyes from healthy and diabetic retinopathy progress cases over the years are utilized in this research. Approximately 80% of ocular cases from the dataset is utilized for the training stage, 10% of cases are used for validation, and 10% are used for testing. Six successive visual field tests are used as input and the seventh test is compared with the output of the R-CNN. The precision of the R-CNN is compared with the regression model and the Hidden Markov (HMM) method. The average prediction precision of the R-CNN is considerably greater than both regression and HMM. In the pointwise classification, R-CNN depicts the least classification mean square error among the compared models in most of the tests. Also, R-CNN is found to be the minimum model affected by the deterioration of reliability and diabetic retinopathy severity. Correctly predicting a progressive visual field test with the R-CNN model can aid physicians in making decisions concerning diabetic retinopathy.
Citation: Axioms
PubDate: 2022-11-04
DOI: 10.3390/axioms11110614
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 615: Mathematical Fuzzy Logic in the Emerging
Fields of Engineering, Finance, and Computer Sciences
Authors: Amit K. Shukla
First page: 615
Abstract: With more than 50 years of literature, fuzzy logic has gradually progressed from an emerging field to a developed research domain, incorporating the sub-domain of mathematical fuzzy logic (MFL) [...]
Citation: Axioms
PubDate: 2022-11-05
DOI: 10.3390/axioms11110615
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 616: Hermite–Hadamard’s Integral
Inequalities of (α,s)-GA- and (α,s,m)-GA-Convex Functions
Authors: Jing-Yu Wang, Hong-Ping Yin, Wen-Long Sun, Bai-Ni Guo
First page: 616
Abstract: In this paper, the authors propose the notions of (α,s)-geometric-arithmetically convex functions and (α,s,m)-geometric-arithmetically convex functions, while they establish some new integral inequalities of the Hermite–Hadamard type for (α,s)-geometric-arithmetically convex functions and for (α,s,m)-geometric-arithmetically convex functions.
Citation: Axioms
PubDate: 2022-11-06
DOI: 10.3390/axioms11110616
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 617: Operator Jensen’s Inequality for
Operator Superquadratic Functions
Authors: Mohammad W. Alomari, Christophe Chesneau, Ahmad Al-Khasawneh
First page: 617
Abstract: In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for positive operators is thus deduced. A Jensen-type inequality is proved. Equivalent statements of a non-commutative version of Jensen’s inequality for operator superquadratic function are also established. Finally, several trace inequalities for superquadratic functions (in the ordinary sense) are provided as well.
Citation: Axioms
PubDate: 2022-11-06
DOI: 10.3390/axioms11110617
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 618: New Fractional Integral Inequalities
Pertaining to Caputo–Fabrizio and Generalized
Riemann–Liouville Fractional Integral Operators
Authors: Muhammad Tariq, Omar Mutab Alsalami, Asif Ali Shaikh, Kamsing Nonlaopon, Sotiris K. Ntouyas
First page: 618
Abstract: Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary generations because of their applications in various branches of science. In this paper, we concentrate on establishing Hermite–Hadamard and Pachpatte-type integral inequalities with the aid of two different fractional operators. In particular, we acknowledge the critical Hermite–Hadamard and related inequalities for n-polynomial s-type convex functions and n-polynomial s-type harmonically convex functions. We practice these inequalities to consider the Caputo–Fabrizio and the k-Riemann–Liouville fractional integrals. Several special cases of our main results are also presented in the form of corollaries and remarks. Our study offers a better perception of integral inequalities involving fractional operators.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110618
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 619: Copula Dynamic Conditional Correlation and
Functional Principal Component Analysis of COVID-19 Mortality in the
United States
Authors: Jong-Min Kim
First page: 619
Abstract: This paper shows a visual analysis and the dependence relationships of COVID-19 mortality data in 50 states plus Washington, D.C., from January 2020 to 1 September 2022. Since the mortality data are severely skewed and highly dispersed, a traditional linear model is not suitable for the data. As such, we use a Gaussian copula marginal regression (GCMR) model and vine copula-based quantile regression to analyze the COVID-19 mortality data. For a visual analysis of the COVID-19 mortality data, a functional principal component analysis (FPCA), graphical model, and copula dynamic conditional correlation (copula-DCC) are applied. The visual from the graphical model shows five COVID-19 mortality equivalence groups in the US, and the results of the FPCA visualize the COVID-19 daily mortality time trends for 50 states plus Washington, D.C. The GCMR model investigates the COVID-19 daily mortality relationship between four major states and the rest of the states in the US. The copula-DCC models investigate the time-trend dependence relationship between the COVID-19 daily mortality data of four major states.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110619
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 620: Hybrid Deep Learning Algorithm for Forecasting
SARS-CoV-2 Daily Infections and Death Cases
Authors: Alqahtani, Abotaleb, Kadi, Makarovskikh, Potoroko, Alakkari, Badr
First page: 620
Abstract: The prediction of new cases of infection is crucial for authorities to get ready for early handling of the virus spread. Methodology Analysis and forecasting of epidemic patterns in new SARS-CoV-2 positive patients are presented in this research using a hybrid deep learning algorithm. The hybrid deep learning method is employed for improving the parameters of long short-term memory (LSTM). To evaluate the effectiveness of the proposed methodology, a dataset was collected based on the recorded cases in the Russian Federation and Chelyabinsk region between 22 January 2020 and 23 August 2022. In addition, five regression models were included in the conducted experiments to show the effectiveness and superiority of the proposed approach. The achieved results show that the proposed approach could reduce the mean square error (RMSE), relative root mean square error (RRMSE), mean absolute error (MAE), coefficient of determination (R Square), coefficient of correlation (R), and mean bias error (MBE) when compared with the five base models. The achieved results confirm the effectiveness, superiority, and significance of the proposed approach in predicting the infection cases of SARS-CoV-2.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110620
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 621: Fixed Point Results for a Family of
Interpolative F-Contractions in b-Metric Spaces
Authors: Nabanita Konwar, Pradip Debnath
First page: 621
Abstract: In this paper, we introduce a new generalized concept, namely, extended interpolative Cirić–Reich–Rus-type F-contraction in b-metric space. In addition, we put forward the notion of interpolative Kannan-type F-contractions. Fixed point results for these new interpolative contraction mappings are established, and non-trivial examples involving finite and infinite sets are provided to validate the results.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110621
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 622: Some New Integral Inequalities for Generalized
Preinvex Functions in Interval-Valued Settings
Authors: Muhammad Bilal Khan, Jorge E. Macías-Díaz, Mohamed S. Soliman, Muhammad Aslam Noor
First page: 622
Abstract: In recent years, there has been a significant amount of research on the extension of convex functions which are known as preinvex functions. In this paper, we have used this approach to generalize the preinvex interval-valued function in terms of (£1,£2)-preinvex interval-valued functions because of its extraordinary applications in both pure and applied mathematics. The idea of (£1,£2) -preinvex interval-valued functions is explained in this work. By using the Riemann integral operator, we obtain Hermite-Hadamard and Fejér-type inequalities for (£1,£2) -preinvex interval-valued functions. To discuss the validity of our main results, we provide non-trivial examples. Some exceptional cases have been discussed that can be seen as applications of main outcomes.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110622
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 623: Analysis and Design of Robust Controller for
Polynomial Fractional Differential Systems Using Sum of Squares
Authors: Hassan Yaghoubi, Assef Zare, Roohallah Alizadehsani
First page: 623
Abstract: This paper discusses the robust stability and stabilization of polynomial fractional differential (PFD) systems with a Caputo derivative using the sum of squares. In addition, it presents a novel method of stability and stabilization for PFD systems. It demonstrates the feasibility of designing problems that cannot be represented in LMIs (linear matrix inequalities). First, sufficient conditions of stability are expressed for the PFD equation system. Based on the results, the fractional differential system is Mittag–Leffler stable when there is a polynomial function to satisfy the inequality conditions. These functions are obtained from the sum of the square (SOS) approach. The result presents a valuable method to select the Lyapunov function for the stability of PFD systems. Then, robust Mittag–Leffler stability conditions were able to demonstrate better convergence performance compared to asymptotic stabilization and a robust controller design for a PFD equation system with unknown system parameters, and design performance based on a polynomial state feedback controller for PFD-controlled systems. Finally, simulation results indicate the effectiveness of the proposed theorems.
Citation: Axioms
PubDate: 2022-11-07
DOI: 10.3390/axioms11110623
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 624: Tempered Fractional Trapezium Inequalities
Authors: Miguel Vivas-Cortez, Muhammad Uzair Awan, Muhammad Ubaid Ullah, Sadia Talib, Muhammad Aslam Noor, Khalida Inayat Noor
First page: 624
Abstract: The main objective of this paper is to derive some new fractional analogs of trapezium-like inequalities essentially using the class of preinvex functions and the concepts of tempered fractional integrals. We discuss some special cases that show that our results are unifying. In order to demonstrate the significance of our results, we present some applications to means. To check the validity of our results, we also give some numerical examples.
Citation: Axioms
PubDate: 2022-11-08
DOI: 10.3390/axioms11110624
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 625: Global Existence of Bounded Solutions for
Eyring–Powell Flow in a Semi-Infinite Rectangular Conduct
Authors: Saeed ur Rahman, Jose Luis Diaz Palencia, Nomaq Tariq, Pablo Salgado Sánchez, Julian Roa Gonzalez
First page: 625
Abstract: The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial velocity profiles (u10,u20) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u10,u20)∈L2(Ω), Ω=[0,L]×[0,H]×(0,∞). Afterward, the results are extended for (u10,u20)∈Lp(Ω), p>2. Lastly, the existence criteria are obtained when (u10,u20)∈H1(Ω). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids.
Citation: Axioms
PubDate: 2022-11-08
DOI: 10.3390/axioms11110625
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 626: Representations, Translations and Reductions
for Ternary Semihypergroups
Authors: Anak Nongmanee, Sorasak Leeratanavalee
First page: 626
Abstract: The concept of ternary semihypergroups can be considered as a natural generalization of arbitrary ternary semigroups. In fact, each ternary semigroup can be constructed to a ternary semihypergroup. In this article, we investigate some interesting algebraic properties of ternary semihypergroups induced by semihypergroups. Then, we extend the well-known result on group theory and semigroup theory, the so-called Cayley’s theorem, to study on ternary semihypergroups. This leads us to construct the ternary semihypergroups of all multivalued full binary functions. In particular, we investigate that each element of a ternary semihypergroup induced by a semihypergroup can be represented by a multivalued full binary function. Moreover, we introduce the concept of translations for ternary semihypergroups which can be considered as a generalization of translations on ternary semigrgoups. Then, we construct ternary semihypergroups of all multivalued full functions and ternary semihypergroups via translations. So, some interesting algebraic properties are investigated. At the last section, we discover that there are ternary semihypergroups satisfying some significant conditions which can be reduced to semihypergroups. Furthermore, ternary semihypergroups with another one condition can be reduced to idempotent semihypergroups.
Citation: Axioms
PubDate: 2022-11-08
DOI: 10.3390/axioms11110626
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 627: Local Grey Predictor Based on Cubic Polynomial
Realization for Market Clearing Price Prediction
Authors: Akash Saxena, Adel Fahad Alrasheedi, Khalid Abdulaziz Alnowibet, Ahmad M. Alshamrani, Shalini Shekhawat, Ali Wagdy Mohamed
First page: 627
Abstract: With the development of restructured power markets, the profit-making competitive business environment has emerged. With the help of different advanced technologies, generating companies are taking decisions regarding trading electricity with imperfect information about marketing operating conditions. The forecasting of the market clearing price (MCP) is a potential issue in these markets. Early information on the MCP can be a proven beneficial tool for accumulating profit. In this work, a local grey prediction model based on a cubic polynomial function is presented to estimate the MCP with the help of historical data. The mathematical framework of this grey model was established and evaluated for different market conditions and databases. The comparison between traditional grey models and some advanced grey models reveals that the proposed model yields accurate results.
Citation: Axioms
PubDate: 2022-11-08
DOI: 10.3390/axioms11110627
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 628: On Solvability for Some Classes of System of
Non-Linear Integral Equations in Two Dimensions via Measure of
Non-Compactness
Authors: Rakesh Kumar, Shubham Kumar, Mohammad Sajid, Bhupander Singh
First page: 628
Abstract: In this paper, we present some results of coupled fixed points for the system of non-linear integral equations in Banach space. Our results enlarge the results of newer papers. Additionally, we prove the applicability of those results to the solvability of the system of non-linear integral equations. Finally, we give an example to validate the applicability of our results.
Citation: Axioms
PubDate: 2022-11-09
DOI: 10.3390/axioms11110628
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 629: Certain Geometric Properties of the
Fox–Wright Functions
Authors: Anish Kumar, Saiful R. Mondal, Sourav Das
First page: 629
Abstract: The primary objective of this study is to establish necessary conditions so that the normalized Fox–Wright functions possess certain geometric properties, such as convexity and pre-starlikeness. In addition, we present a linear operator associated with the Fox–Wright functions and discuss its k-uniform convexity and k-uniform starlikeness. Furthermore, some sufficient conditions were obtained so that this function belongs to the Hardy spaces. The results of this work are presumably new and illustrated by several consequences, remarks, and examples.
Citation: Axioms
PubDate: 2022-11-09
DOI: 10.3390/axioms11110629
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 630: Existence Results for an m-Point Mixed
Fractional-Order Problem at Resonance on the Half-Line
Authors: Ogbu F. Imaga, Samuel A. Iyase, Peter O. Ogunniyi
First page: 630
Abstract: This work considers the existence of solutions for a mixed fractional-order boundary value problem at resonance on the half-line. The Mawhin’s coincidence degree theory will be used to prove existence results when the dimension of the kernel of the linear fractional differential operator is equal to two. An example is given to demonstrate the main result obtained.
Citation: Axioms
PubDate: 2022-11-09
DOI: 10.3390/axioms11110630
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 631: Some Inequalities for Certain p-Valent
Functions Connected with the Combination Binomial Series and Confluent
Hypergeometric Function
Authors: Sheza M. El-Deeb, Adriana Cătaş
First page: 631
Abstract: The present paper deals with a new differential operator denoted by Fp,tδ,n,b,c,m,β, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introduced operator is defined by making use of a linear combination of the binomial series and confluent hypergeometric function. In addition, by using special values of the parameters, we establish certain results concretized in specific corollaries, which provide useful inequalities. Studying these properties by using various types of operators is a technique that is widely used.
Citation: Axioms
PubDate: 2022-11-10
DOI: 10.3390/axioms11110631
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 632: A Malware Propagation Model Considering
Conformity Psychology in Social Networks
Authors: Qingyi Zhu, Yuhang Liu, Xuhang Luo, Kefei Cheng
First page: 632
Abstract: At present, malware is still a major security threat to computer networks. However, only a fraction of users with some security consciousness take security measures to protect computers on their own initiative, and others who know the current situation through social networks usually follow suit. This phenomenon is referred to as conformity psychology. It is obvious that more users will take countermeasures to prevent computers from being infected if the malware spreads to a certain extent. This paper proposes a deterministic nonlinear SEIQR propagation model to investigate the impact of conformity psychology on malware propagation. Both the local and global stabilities of malware-free equilibrium are proven while the existence and local stability of endemic equilibrium is proven by using the central manifold theory. Additionally, some numerical examples and simulation experiments based on two network datasets are performed to verify the theoretical analysis results. Finally, the sensitivity analysis of system parameters is carried out.
Citation: Axioms
PubDate: 2022-11-10
DOI: 10.3390/axioms11110632
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 633: Solving Biharmonic Equations with Tri-Cubic C1
Splines on Unstructured Hex Meshes
Authors: Jeremy Youngquist, Jörg Peters
First page: 633
Abstract: Unstructured hex meshes are partitions of three spaces into boxes that can include irregular edges, where n≠4 boxes meet along an edge, and irregular points, where the box arrangement is not consistent with a tensor-product grid. A new class of tri-cubic C1 splines is evaluated as a tool for solving elliptic higher-order partial differential equations over unstructured hex meshes. Convergence rates for four levels of refinement are computed for an implementation of the isogeometric Galerkin approach applied to Poisson’s equation and the biharmonic equation. The ratios of error are contrasted and superior to an implementation of Catmull-Clark solids. For the trivariate Poisson problem on irregularly partitioned domains, the reduction by 24 in the L2 norm is consistent with the optimal convergence on a regular grid, whereas the convergence rate for Catmull-Clark solids is measured as O(h3). The tri-cubic splines in the isogeometric framework correctly solve the trivariate biharmonic equation, but the convergence rate in the irregular case is lower than O(h4). An optimal reduction of 24 is observed when the functions on the C1 geometry are relaxed to be C0.
Citation: Axioms
PubDate: 2022-11-10
DOI: 10.3390/axioms11110633
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 634: Multiterm Impulsive Caputo–Hadamard Type
Differential Equations of Fractional Variable Order
Authors: Amar Benkerrouche, Mohammed Said Souid, Gani Stamov, Ivanka Stamova
First page: 634
Abstract: In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted.
Citation: Axioms
PubDate: 2022-11-10
DOI: 10.3390/axioms11110634
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 635: Strong Players and Stable Coalition Structures
in PMAS Profit Game
Authors: Ana Meca, Greys Sošić
First page: 635
Abstract: In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions.
Citation: Axioms
PubDate: 2022-11-10
DOI: 10.3390/axioms11110635
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 636: Non-Canonical Functional Differential Equation
of Fourth-Order: New Monotonic Properties and Their Applications in
Oscillation Theory
Authors: Amany Nabih, Clemente Cesarano, Osama Moaaz, Mona Anis, Elmetwally M. Elabbasy
First page: 636
Abstract: In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. Then, we find iterative criteria that exclude the existence of these positive decreasing solutions. Using these new criteria and based on the comparison and Riccati substitution methods, we create sufficient conditions to ensure that all solutions of the studied equation oscillate. In addition to having many applications in various scientific domains, the study of the oscillatory and non-oscillatory features of differential equation solutions is a theoretically rich field with many intriguing issues. Finally, we show the importance of the results by applying them to special cases of the studied equation.
Citation: Axioms
PubDate: 2022-11-12
DOI: 10.3390/axioms11110636
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 637: Analytic Approximate Solution in the
Authors: Victor Orlov, Magomedyusuf Gasanov
First page: 637
Abstract: The paper considers a class of nonlinear differential equations which are not solvable in quadratures in general case. The author’s technology for solving such equations contains six problems. In this article, the solution to one of these problems is given, a real area in which it is possible to calculate an analytical approximate solution in the case of an approximate value of a moving singular point is obtained. Obtained results are based on the application of elements of differential calculus in finding estimates for the approximate solution error. Theoretical provisions are confirmed by numerical calculations, which characterize their reliability.
Citation: Axioms
PubDate: 2022-11-12
DOI: 10.3390/axioms11110637
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 638: The Λ-Fractional Hydrocephalus
Model
Authors: Anastasios K. Lazopoulos, Dimitrios Karaoulanis, Kostantinos A. Lazopoulos
First page: 638
Abstract: Infant hydrocephalus is a clinically abnormal clinical state with an accumulation of fluid in cavities (ventricles) deep within the brain. Hence, pressure is increased inside the skull. The ventricles widen due to the excess fluid applying pressure upon the (parenchyma) brain tissues. The infant brain tissue is described by a biomechanics model as a hyperelastic, Λ-fractional viscoelastic material, trying to describe the various conditions developing hydrocephalus. Λ-fractional continuum mechanics is applied with time variables due to viscosity and space fractional variables due to porosity. The simultaneous influence of both the viscosity and porosity of the membrane material (parenchyma) increases the cerebrospinal fluid’s pressure, causing the fluid’s accumulation in the brain.
Citation: Axioms
PubDate: 2022-11-12
DOI: 10.3390/axioms11110638
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 639: Towards Optimal Robustness of Network
Controllability by Nested-Edge Rectification
Authors: Zhuoran Yu, Junfeng Nie, Junli Li
First page: 639
Abstract: When a network is attacked, the network controllability decreases and the network is at risk of collapse. A network with good controllability robustness can better maintain its own controllability while under attack to provide time for network recovery. In order to explore how to build a network with optimal controllability robustness, an exhaustive search with adding edges was executed on a given set of small-sized networks. By exhaustive search, we mean: (1) All possible ways of adding edges, except self-loops, were considered and calculated at the time of adding each edge. (2) All possible node removal sequences were taken into account. The nested ring structure (NRS) was obtained from the result of the exhaustive search. NRS has a backbone ring, and the remaining edges of each node point to the nearest nodes along the direction of the backbone ring’s edges. The NRS satisfies an empirically necessary condition (ENC) and has great ability to resist random attacks. Therefore, nested edge rectifcation (NER) was designed to optimize the network for controllability robustness by constructing NRS in networks. NER was compared with the random edge rectification (RER) strategy and the unconstrained rewiring (UCR) strategy on synthetic networks and real-world networks by simulation. The simulation results show that NER can better improve the robustness of network’s controllability, and NER can also quickly improve the initial network controllability for networks with more than one driver node. In addition, as NER is executed, NRS gains more edges in the network, so the network has better controllability robustness. NER will be helpful for network model design or network optimization in future.
Citation: Axioms
PubDate: 2022-11-13
DOI: 10.3390/axioms11110639
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 640: Optical Solitons in Fiber Bragg Gratings with
Dispersive Reflectivity Having Five Nonlinear Forms of Refractive Index
Authors: Ming-Yue Wang, Anjan Biswas, Yakup Yıldırım, Hashim M. Alshehri, Luminita Moraru, Simona Moldovanu
First page: 640
Abstract: This paper implements the trial equation approach to retrieve cubic–quartic optical solitons in fiber Bragg gratings with the aid of the trial equation methodology. Five forms of nonlinear refractive index structures are considered. They are the Kerr law, the parabolic law, the polynomial law, the quadratic–cubic law, and the parabolic nonlocal law. Dark and singular soliton solutions are recovered along with Jacobi’s elliptic functions with an appropriate modulus of ellipticity.
Citation: Axioms
PubDate: 2022-11-13
DOI: 10.3390/axioms11110640
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 641: On h-Quasi-Hemi-Slant Riemannian Maps
Authors: Mohd Bilal, Sushil Kumar, Rajendra Prasad, Abdul Haseeb, Sumeet Kumar
First page: 641
Abstract: In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
Citation: Axioms
PubDate: 2022-11-14
DOI: 10.3390/axioms11110641
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 642: Solving Time-Fractional Partial Differential
Equation Using Chebyshev Cardinal Functions
Authors: Haifa Bin Jebreen, Carlo Cattani
First page: 642
Abstract: We propose a numerical scheme based on the Galerkin method for solving the time-fractional partial differential equations. To this end, after introducing the Chebyshev cardinal functions (CCFs), using the relation between fractional integral and derivative, we represent the Caputo fractional derivative based on these bases and obtain an operational matrix. Applying the Galerkin method and using the operational matrix for the Caputo fractional derivative, the desired equation reduces to a system of linear algebraic equations. By solving this system, the unknown solution is obtained. The convergence analysis for this method is investigated, and some numerical simulations show the accuracy and ability of the technique.
Citation: Axioms
PubDate: 2022-11-14
DOI: 10.3390/axioms11110642
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 643: Hilbert’s Double Series Theorem’s
Extensions via the Mathieu Series Approach
Authors: Tibor Pogány
First page: 643
Abstract: The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively investigated non-homogeneous kernel, which mutually covers the homogeneous kernel cases as well. Particularly, novel Hilbert’s double series inequality results are presented, which include the upper bounds built exclusively with non-weighted ℓp–norms. The main mathematical tools are the integral expression of Mathieu (a, λ)-series, the Hölder inequality and a generalization of the double series theorem by Yang.
Citation: Axioms
PubDate: 2022-11-14
DOI: 10.3390/axioms11110643
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 644: On Some New Dynamic Inequalities Involving
C-Monotonic Functions on Time Scales
Authors: Ghada AlNemer, A. I. Saied, A. M. Hassan, Clemente Cesarano, Haytham M. Rezk, Mohammed Zakarya
First page: 644
Abstract: In this paper, we establish some new dynamic inequalities involving C-monotonic functions with C≥1, on time scales. As a special case of our results when C=1, we obtain the inequalities involving increasing or decreasing functions (where for C=1, the 1-decreasing function is decreasing and the 1-increasing function is increasing). The main results are proved by applying the properties of C-monotonic functions and the chain rule formula on time scales. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, to the best of the authors’ knowledge, the results are essentially new.
Citation: Axioms
PubDate: 2022-11-15
DOI: 10.3390/axioms11110644
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 645: Hidden Dynamics and Hybrid Synchronization of
Fractional-Order Memristive Systems
Authors: Haipeng Jiang, Lizhou Zhuang, Cheng Chen, Zuolei Wang
First page: 645
Abstract: A fractional-order memristive system without equilibrium is addressed. Hidden attractors in the proposed system are discussed and the coexistence of a hidden attractor is found. Via theoretical analysis, the hybrid synchronization of the proposed system with partial controllers is investigated using fractional stability theory. Numerical simulation verifies the validity of the hybrid synchronization scheme.
Citation: Axioms
PubDate: 2022-11-15
DOI: 10.3390/axioms11110645
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 646: Modelling Coronavirus and Larvae Pyrausta
Data: A Discrete Binomial Exponential II Distribution with Properties,
Classical and Bayesian Estimation
Authors: Mohamed S. Eliwa, Abhishek Tyagi, Bader Almohaimeed, Mahmoud El-Morshedy
First page: 646
Abstract: In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are derived. The shape of the failure rate function is increasing. Moreover, the proposed model is appropriate for modelling equi-, over- and under-dispersed data. The parameter estimation through the classical point of view has been done using the method of maximum likelihood, whereas, in the Bayesian framework, assuming independent beta priors of model parameters, the Metropolis–Hastings algorithm within Gibbs sampler is used to obtain sample-based Bayes estimates of the unknown parameters of the proposed model. A detailed simulation study is carried out to examine the outcomes of maximum likelihood and Bayesian estimators. Finally, two distinctive real data sets are analyzed using the proposed model. These applications showed the flexibility of the new distribution.
Citation: Axioms
PubDate: 2022-11-16
DOI: 10.3390/axioms11110646
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 647: Justification of Direct Scheme for Asymptotic
Solving Three-Tempo Linear-Quadratic Control Problems under Weak Nonlinear
Perturbations
Authors: Galina Kurina, Margarita Kalashnikova
First page: 647
Abstract: The paper deals with an application of the direct scheme method, consisting of immediately substituting a postulated asymptotic solution into a problem condition and determining a series of control problems for finding asymptotics terms, for asymptotics construction of a solution of a weakly nonlinearly perturbed linear-quadratic optimal control problem with three-tempo state variables. For the first time, explicit formulas for linear-quadratic optimal control problems, from which all terms of the asymptotic expansion are found, are justified, and the estimates of the proximity between the asymptotic and exact solutions are proved for the control, state trajectory, and minimized functional. Non-increasing of the minimized functional, if a next approximation to the optimal control is used, following from the proposed algorithm of the asymptotics construction, is also established.
Citation: Axioms
PubDate: 2022-11-16
DOI: 10.3390/axioms11110647
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 648: Optimality Conditions and Dualities for Robust
Efficient Solutions of Uncertain Set-Valued Optimization with Set-Order
Relations
Authors: Yuwen Zhai, Qilin Wang, Tian Tang
First page: 648
Abstract: In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on. By the new subdifferential and its properties, we establish a necessary and sufficient optimality condition of set-based robust efficient solutions for the uncertain set-valued optimization problem. We also introduce a Wolfe type dual problem of the uncertain set-valued optimization problem. Finally, we establish the robust weak duality theorem and the robust strong duality theorem between the uncertain set-valued optimization problem and its robust dual problem. Several main results extend to the corresponding ones in the literature.
Citation: Axioms
PubDate: 2022-11-16
DOI: 10.3390/axioms11110648
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 649: Probing the Oscillatory Behavior of Internet
Game Addiction via Diffusion PDE Model
Authors: Kaihong Zhao
First page: 649
Abstract: We establish a non-linear diffusion partial differential equation (PDE) model to depict the dynamic mechanism of Internet gaming disorder (IGD). By constructing appropriate super- and sub-solutions and applying Schauder’s fixed point theorem and continuation method, we study the existence and asymptotic stability of traveling wave solutions to probe into the oscillating behavior of IGD. An example is numerically simulated to examine the correctness of our outcomes.
Citation: Axioms
PubDate: 2022-11-16
DOI: 10.3390/axioms11110649
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 650: Six-Dimensional Space with Symmetric Signature
and Some Properties of Elementary Particles
Authors: Nikolay Popov, Ivan Matveev
First page: 650
Abstract: The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, and hypercharge, are expressed through the symmetries of this space. The symmetries are brought out by the various representation of the metric in E3,3 with the aid of spinors and hyperbolic complex numbers. The properties of the metric allow predicting the number of quarks equal to 18. The violation of strong conservation laws in weak interactions is treated through compactifying the three-dimensional temporal subspace at the subparticle scale into single-dimensional time at bigger scales, which reduces symmetry from the spherical to axial type.
Citation: Axioms
PubDate: 2022-11-17
DOI: 10.3390/axioms11110650
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 651: Computational Framework of the SVIR Epidemic
Model with a Non-Linear Saturation Incidence Rate
Authors: Attaullah Attaullah, Adil Khurshaid, Zeeshan Zeeshan, Sultan Alyobi, Mansour F. Yassen, Din Prathumwan
First page: 651
Abstract: In this study, we developed an autonomous non-linear epidemic model for the transmission dynamics of susceptible, vaccinated, infected, and recovered individuals (SVIR model) with non-linear saturation incidence and vaccination rates. The non-linear saturation incidence rate significantly reduces the death ratio of infected individuals by increasing human immunity. We discuss a detailed explanation of the model equilibrium, its basic reproduction number R0, local stability, and global stability. The disease-free equilibrium is observed to be stable if R0<1, while the endemic equilibrium exists and the disease exists permanently in the population if R0>1. To approximate the solution of the model, the well-known Runge–Kutta (RK4) methodology is utilized. The implications of numerous parameters on the population dynamics of susceptible, vaccinated, infected, and recovered individuals are addressed. We discovered that increasing the value of the disease-included death rate ψ has a negative impact on those affected, while it has a positive impact on other populations. Furthermore, the value of interaction between vaccinated and infected λ2 has a decreasing impact on vulnerable and vaccinated people, while increasing in other populations. On the other hand, the model is solved using Euler and Euler-modified techniques, and the results are compared numerically and graphically. The quantitative computations demonstrate that the RK4 method provides very precise solutions compared to the other approaches. The results show that the suggested SVIR model that approximates the solution method is accurate and useful.
Citation: Axioms
PubDate: 2022-11-17
DOI: 10.3390/axioms11110651
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 652: New Subclasses of Bi-Univalent Functions with
Respect to the Symmetric Points Defined by Bernoulli Polynomials
Authors: Mucahit Buyankara, Murat Çağlar, Luminiţa-Ioana Cotîrlă
First page: 652
Abstract: In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z∈C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 and Fekete–Szegö inequalities a3−μa22 for these new subclasses.
Citation: Axioms
PubDate: 2022-11-17
DOI: 10.3390/axioms11110652
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 653: Application of the Averaging Method to the
Optimal Control Problem of Non-Linear Differential Inclusions on the
Finite Interval
Authors: Tetiana Zhuk, Nina Kasimova, Anton Ryzhov
First page: 653
Abstract: In this paper, we use the averaging method to find an approximate solution for the optimal control of non-linear differential inclusions with fast-oscillating coefficients on a finite time interval.
Citation: Axioms
PubDate: 2022-11-17
DOI: 10.3390/axioms11110653
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 654: Fractional Clique Collocation Technique for
Numerical Simulations of Fractional-Order Brusselator Chemical Model
Authors: Mohammad Izadi, Hari Mohan Srivastava
First page: 654
Abstract: The primary focus of this research study is in the development of an effective hybrid matrix method to solve a class of nonlinear systems of equations of fractional order arising in the modeling of autocatalytic chemical reaction problems. The fractional operator is considered in the sense of Liouville–Caputo. The proposed approach relies on the combination of the quasi-linearization technique and the spectral collocation strategy based on generalized clique bases. The main feature of the hybrid approach is that it converts the governing nonlinear fractional-order systems into a linear algebraic system of equations, which is solved in each iteration. In a weighted L2 norm, we prove the error and convergence analysis of the proposed algorithm. By using various model parameters in the numerical examples, we show the computational efficacy as well as the accuracy of our approach. Comparisons with existing available schemes show the high accuracy and robustness of the designed hybrid matrix collocation technique.
Citation: Axioms
PubDate: 2022-11-18
DOI: 10.3390/axioms11110654
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 655: Certain New Class of Analytic Functions
Defined by Using a Fractional Derivative and Mittag-Leffler Functions
Authors: Mohammad Faisal Khan, Shahid Khan, Saqib Hussain, Maslina Darus, Khaled Matarneh
First page: 655
Abstract: Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag–Leffler functions to formulate and arrange a new operator of fractional calculus. We define a new class of normalized analytic functions by means of a newly defined fractional operator and discuss some of its interesting geometric properties in open unit disk.
Citation: Axioms
PubDate: 2022-11-18
DOI: 10.3390/axioms11110655
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 656: A Unified Asymptotic Theory of Supersonic,
Transonic, and Hypersonic Far Fields
Authors: Lung-Jieh Yang, Chao-Kang Feng
First page: 656
Abstract: The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such a problem with far fields was solved by W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This far field small disturbance theory is reexamined in this study first by using asymptotic expansion theory. A systematic approach is adopted to obtain the nonlinear Burgers’ equation for supersonic far fields. We also use the similarity method to solve this boundary value problem (BVP) of the inviscid Burgers’ equation and obtain the nonlinear flow patterns, including the jump condition for the shock wave. Secondly, the transonic and hypersonic far field equations were obtained from the supersonic Burgers’ equation by stretching the coordinate in the y direction and considering an expansion of the freestream Mach number in terms of the transonic and hypersonic similarity parameters. The mathematical structures of the far fields of the supersonic, transonic, and hypersonic flows are unified to be the same. The similar far field flow patterns including the shock positions of a parabolic airfoil for the supersonic, transonic, and hypersonic flow regimes are exemplified and discussed.
Citation: Axioms
PubDate: 2022-11-19
DOI: 10.3390/axioms11110656
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 657: Computation of the Deuteron Mass and Force
Unification via the Rotating Lepton Model
Authors: Constantinos G. Vayenas, Dimitrios Grigoriou, Dionysios Tsousis, Konstantinos Parisis, Elias C. Aifantis
First page: 657
Abstract: The rotating lepton model (RLM), which is a 2D Bohr-type model of three gravitating rotating neutrinos, combining Newton’s gravitational law, special relativity, and the de Broglie equation of quantum mechanics, and which has already been used to model successfully quarks and the strong force in several hadrons, has been extended to 3D and to six rotating neutrinos located at the vertices of a normal triangular octahedron in order to compute the Lorentz factors, gamma, of the six neutrinos and, thus, to compute the total energy and mass of the deuteron, which is the lightest nucleus. The computation includes no adjustable parameters, and the computed deuteron mass agrees within 0.05% with the experimental mass value. This very good agreement suggests that, similarly to the strong force in hadrons, the nuclear force in nuclei can also be modeled as relativistic gravity. This implies that, via the combination of special relativity and quantum mechanics, the Newtonian gravity gets unified with the strong force, including the residual strong force.
Citation: Axioms
PubDate: 2022-11-20
DOI: 10.3390/axioms11110657
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 658: Hypercomplex Systems and Non-Gaussian
Stochastic Solutions with Some Numerical Simulation of χ-Wick-Type (2
1)-D C-KdV Equations+
Authors: Mohammed Zakarya, Mahmoud A. Abd-Rabo, Ghada AlNemer
First page: 658
Abstract: In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, Hermite transform (HT), and technicality via the F-expansion procedure. By means of the direct connection between the theory of hypercomplex systems (HCS) and white noise analysis (WNA), we establish non-Gaussian white noise (NGWN) by studying stochastic partial differential equations (PDEs) with NG-parameters. So, by using the F-expansion method we present multiples of exact and stochastic families from variable coefficients of travelling wave and stochastic NG-functional solutions of (2 + 1)-D C-KdV equations. These solutions are Jacobi elliptic functions (JEF), trigonometric,and hyperbolic forms, respectively.
Citation: Axioms
PubDate: 2022-11-21
DOI: 10.3390/axioms11110658
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 659: Multi-Criteria Group Decision-Making Models in
a Multi-Choice Environment
Authors: Qazi Shoeb Ahmad, Mohammad Faisal Khan, Naeem Ahmad
First page: 659
Abstract: The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the option to select values from several comparison scales. The MCBWM technique has been shown to be better. Presenting the options for which an optimal solution has been found simplifies the calculation and establishes the ideal weight values. This study proposes two different mathematical programming models for solving multi-criteria decision-making problems having multiple decision-makers. The two methods are proposed considering the multi-choice uncertainty assumption in pairwise criteria comparisons. Additionally, it considers the best–worst method as the base model. The multi-choice uncertainty is applied to determine the best choice out of multiple choices. It gives a real-life scenario to the decision-making problems. Although there are many other forms of uncertainty, such as fuzzy, intuitionistic fuzzy, neutrosophic, probabilistic, etc., it focuses on choices instead of ambiguity in terms of the probabilistic or fuzzy nature of parameters. The parameter considered as multi-choice is the pairwise comparison. These parameters are handled by applying the Lagrange interpolating polynomial method. The proposed models are novel in terms of their mathematical structure and group decision-making approach. The models are formulated and further validated by solving numerical examples. It provides a framework for solving mcdm problems where the weightage to the decision-makers is also incorporated. The CR values for all the models of example 1 and 2, and the case study has been found acceptable.
Citation: Axioms
PubDate: 2022-11-21
DOI: 10.3390/axioms11110659
Issue No: Vol. 11, No. 11 (2022)
- Axioms, Vol. 11, Pages 575: Stability and Hopf Bifurcation Analysis of a
Stage-Structured Predator–Prey Model with Delay
Authors: Xueyong Zhou
First page: 575
Abstract: In this work, a Lotka–Volterra type predator–prey system with time delay and stage structure for the predators is proposed and analyzed. By using the permanence theory for infinite dimensional system, we get that the system is permanent if some conditions are satisfied. The local and global stability of the positive equilibrium is presented. The existence of Hopf bifurcation around the positive equilibrium is observed. Further, by using the normal form theory and center manifold approach, we derive the explicit formulas determining the stability of bifurcating periodic solutions and the direction of Hopf bifurcation. Numerical simulations are carried out by Matlab software to explain the theoretical results. We find that combined time delay and stage structure can affect the dynamical behavior of the system.
Citation: Axioms
PubDate: 2022-10-20
DOI: 10.3390/axioms11100575
Issue No: Vol. 11, No. 10 (2022)
- Axioms, Vol. 11, Pages 576: Extended Gevrey Regularity via Weight Matrices
Authors: Nenad Teofanov, Filip Tomić
First page: 576
Abstract: The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces Gt(U) and the space of smooth functions C∞(U). The first approach in the style of Komatsu is based on the properties of two parameter sequences Mp=pτpσ, τ>0, σ>1. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space than the one obtained as the inductive limit of extended Gevrey classes.
Citation: Axioms
PubDate: 2022-10-21
DOI: 10.3390/axioms11100576
Issue No: Vol. 11, No. 10 (2022)
- Axioms, Vol. 11, Pages 577: Stability Analysis of a Patchy
Predator–Prey Model with Fear Effect
Authors: Tingting Liu, Lijuan Chen
First page: 577
Abstract: In this paper, a predator–prey model with fear effect and dispersal is proposed. Assume that only the prey migrates at a constant rate between patches and the migration of prey on each patch is faster than the time scale of local predator–prey interaction. Using two time scales, an aggregation system of total prey density for two patches is constructed. Mathematical analysis shows that there may exist a trivial, a boundary and a unique positive equilibrium point. Under certain conditions, the corresponding unique equilibrium point is global asymptotically stable. The impact of the fear effect on the system is also investigated, i.e., the predator density decreases when the amount of fear effect increases. Moreover, dispersal has a great impact on the persistence of the predator and the prey. Numerical experiments are also presented to verify the feasibility of our conclusion.
Citation: Axioms
PubDate: 2022-10-21
DOI: 10.3390/axioms11100577
Issue No: Vol. 11, No. 10 (2022)
- Axioms, Vol. 11, Pages 578: A Computational Approach to a Model for HIV
and the Immune System Interaction
Authors: Attaullah Attaullah, Zeeshan, Muhammad Tufail Khan, Sultan Alyobi, Mansour F. Yassen, Din Prathumwan
First page: 578
Abstract: This study deals with the numerical solution of the human immunodeficiency virus (HIV) infection model, which is a significant problem for global public health. Acquired immunodeficiency syndrome (AIDS) is a communicable disease, and HIV is the causative agent for AIDS, which damages the ability of the body to fight against disease and easily usual innocuous infections attack the body. On entering the body, HIV infects a large amount of CD4+ T-cells and disturbs the supply rate of these cells from the thymus. Herein, we consider the model with variable source terms in which the production of these cells is a monotonically decreasing function of viral load. Based on the reproduction number, we describe the stability of free equilibrium. The continuous Galerkin–Petrov method, in particular the cGP(2)-method, is implemented to determine the numerical solutions of the model. The influence of different parameters on the population dynamics of healthy/infected CD4+ T-cells and free HIV particles are examined, and the results are presented graphically. On the other hand, the model is solved using the fourth-order Runge–Kutta method, and briefly, the RK4-method, and the results of the proposed schemes are compared with those obtained from other classical schemes such as the Bessel collocation method (BCM), Laplace Adomian decomposition method (LADM), perturbation iteration algorithm (PIA), modified variational iteration method (MVIM), differential transform method (DTM), and exponential Galerkin method (EGM), numerically. Furthermore, absolute errors relative to the RK4 method are computed to describe the accuracy of the proposed scheme. It is presented that the cGP(2)-method gains accurate results at larger time step sizes in comparison with the results of the aforementioned methods. The numerical and graphical comparison reveals that the proposed scheme yields more accurate results relative to other traditional schemes from the literature.
Citation: Axioms
PubDate: 2022-10-21
DOI: 10.3390/axioms11100578
Issue No: Vol. 11, No. 10 (2022)