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Axioms
Number of Followers: 1 Open Access journal ISSN (Online) 2075-1680 Published by MDPI [238 journals] |
- Axioms, Vol. 10, Pages 237: Series with Commuting Terms in Topologized
Semigroups
Authors: Alberto Castejón, Eusebio Corbacho, Vaja Tarieladze
First page: 237
Abstract: We show that the following general version of the Riemann–Dirichlet theorem is true: if every rearrangement of a series with pairwise commuting terms in a Hausdorff topologized semigroup converges, then its sum range is a singleton.
Citation: Axioms
PubDate: 2021-09-24
DOI: 10.3390/axioms10040237
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 238: Global Stability Condition for the
Disease-Free Equilibrium Point of Fractional Epidemiological Models
Authors: Ricardo Almeida, Natália Martins, Cristiana J. Silva
First page: 238
Abstract: In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.
Citation: Axioms
PubDate: 2021-09-25
DOI: 10.3390/axioms10040238
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 239: Revisiting a Classic Identity That Implies the
Rogers–Ramanujan Identities II
Authors: Hei-Chi Chan
First page: 239
Abstract: We give a new proof of an identity due to Ramanujan. From this identity, he deduced the famous Rogers–Ramanujan identities. We prove this identity by establishing a simple recursion Jk=qkJk−1, where q <1. This is a sequel to our recent work.
Citation: Axioms
PubDate: 2021-09-27
DOI: 10.3390/axioms10040239
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 240: Characterization of Wave Fronts of
Ultradistributions Using Directional Short-Time Fourier Transform
Authors: Sanja Atanasova, Snježana Maksimović, Stevan Pilipović
First page: 240
Abstract: In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.
Citation: Axioms
PubDate: 2021-09-28
DOI: 10.3390/axioms10040240
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 241: Wilson Bases and Ultradistributions
Authors: Nenad Teofanov
First page: 241
Abstract: We provide a characterization of the Gelfand–Shilov-type spaces of test functions and their dual spaces of tempered ultradistributions by means of Wilson bases of exponential decay. We offer two different proofs and extend known results to the Roumieu case.
Citation: Axioms
PubDate: 2021-09-28
DOI: 10.3390/axioms10040241
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 242: Can You Hear the Shape of a Market'
Geometric Arbitrage and Spectral Theory
Authors: Simone Farinelli, Hideyuki Takada
First page: 242
Abstract: Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”. The cash flow bundle is the associated vector bundle. The zero eigenspace of its connection Laplacian parameterizes all risk-neutral measures equivalent to the statistical one. A market satisfies the No-Free-Lunch-with-Vanishing-Risk (NFLVR) condition if and only if 0 is in the discrete spectrum of the Laplacian. The Jarrow–Protter–Shimbo theory of asset bubbles and their classification and decomposition extend to markets not satisfying the NFLVR. Euler’s characteristic of the asset nominal space and non-vanishing of the homology group of the cash flow bundle are both topological obstructions to NFLVR.
Citation: Axioms
PubDate: 2021-09-28
DOI: 10.3390/axioms10040242
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 243: Estimation Algorithm for a Hybrid PDE–ODE
Model Inspired by Immunocompetent Cancer-on-Chip Experiment
Authors: Gabriella Bretti, Adele De Ninno, Roberto Natalini, Daniele Peri, Nicole Roselli
First page: 243
Abstract: The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a “digital twin” of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE–ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.
Citation: Axioms
PubDate: 2021-09-28
DOI: 10.3390/axioms10040243
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 244: Hyperreal Delta Functions as a New General
Tool for Modeling Systems with Infinitely High Densities
Authors: Marcoen J. T. F. Cabbolet
First page: 244
Abstract: In general, the state of a system in which a physical quantity such as mass is distributed over space can be modeled by a function that represents the density distribution. The purpose of this paper is to introduce special functions that can be applied when in the system to be modeled, where the quantity is distributed over isolated points. For that matter, the expanded real numbers are introduced as an ordered subring of the hyperreal number field that does not contain any infinitesimals, and hyperreal delta functions are defined as special functions from the real numbers to the expanded real numbers satisfying the condition that (i) the support is a singleton, and (ii) the integral over the reals is a nonzero real number. These newly defined hyperreal delta functions, and tensor products thereof, then provide a general tool, applicable for the mathematical modeling of physical systems in which infinitely high densities occur.
Citation: Axioms
PubDate: 2021-09-29
DOI: 10.3390/axioms10040244
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 245: A Single-Valued Neutrosophic Extension of the
EDAS Method
Authors: Dragiša Stanujkić, Darjan Karabašević, Gabrijela Popović, Dragan Pamučar, Željko Stević, Edmundas Kazimieras Zavadskas, Florentin Smarandache
First page: 245
Abstract: This manuscript aims to propose a new extension of the EDAS method, adapted for usage with single-valued neutrosophic numbers. By using single-valued neutrosophic numbers, the EDAS method can be more efficient for solving complex problems whose solution requires assessment and prediction, because truth- and falsity-membership functions can be used for expressing the level of satisfaction and dissatisfaction about an attitude. In addition, the indeterminacy-membership function can be used to point out the reliability of the information given with truth- and falsity-membership functions. Thus, the proposed extension of the EDAS method allows the use of a smaller number of complex evaluation criteria. The suitability and applicability of the proposed approach are presented through three illustrative examples.
Citation: Axioms
PubDate: 2021-09-29
DOI: 10.3390/axioms10040245
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 246: Criteria for the Oscillation of Solutions to
Linear Second-Order Delay Differential Equation with a Damping Term
Authors: Osama Moaaz, Elmetwally M. E. Elabbasy, Jan Awrejcewicz, Aml Abdelnaser
First page: 246
Abstract: The aim of this work is to present new oscillation results for a class of second-order delay differential equations with damping term. The new criterion of oscillation depends on improving the asymptotic properties of the positive solutions of the studied equation by using an iterative technique. Our results extend some of the results recently published in the literature.
Citation: Axioms
PubDate: 2021-09-30
DOI: 10.3390/axioms10040246
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 247: Axiomatic Characterizations of a Proportional
Influence Measure for Sequential Projects with Imperfect Reliability
Authors: Andries van Beek, Peter Borm, Marieke Quant
First page: 247
Abstract: We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If, in a certain task group, a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.
Citation: Axioms
PubDate: 2021-09-30
DOI: 10.3390/axioms10040247
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 248: Accelerated Modified Tseng’s Extragradient
Method for Solving Variational Inequality Problems in Hilbert Spaces
Authors: Godwin Amechi Okeke, Mujahid Abbas, Manuel De la Sen, Hira Iqbal
First page: 248
Abstract: The aim of this paper is to propose a new iterative algorithm to approximate the solution for a variational inequality problem in real Hilbert spaces. A strong convergence result for the above problem is established under certain mild conditions. Our proposed method requires the computation of only one projection onto the feasible set in each iteration. Some numerical examples are presented to support that our proposed method performs better than some known comparable methods for solving variational inequality problems.
Citation: Axioms
PubDate: 2021-10-01
DOI: 10.3390/axioms10040248
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 249: Applications of Optimal Spline Approximations
for the Solution of Nonlinear Time-Fractional Initial Value Problems
Authors: Enza Pellegrino, Francesca Pitolli
First page: 249
Abstract: Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods to solve such problems. In this respect, collocation methods are particularly attractive for their ability to deal with the nonlocal behavior of the fractional derivative. Among the variety of collocation methods, methods based on spline approximations are preferable since the approximations can be represented by local bases, thereby reducing the computational load. In this paper, we use a collocation method based on spline quasi-interpolant operators to solve nonlinear time-fractional initial value problems. The numerical tests we performed show that the method has good approximation properties.
Citation: Axioms
PubDate: 2021-10-02
DOI: 10.3390/axioms10040249
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 250: Powers of Elliptic Scator Numbers
Authors: Manuel Fernandez-Guasti
First page: 250
Abstract: Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1 + 1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called Victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1 + 2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1 + 2 dimensions.
Citation: Axioms
PubDate: 2021-10-07
DOI: 10.3390/axioms10040250
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 251: Near-Common Fixed Point Result in Cone
Interval b-Metric Spaces over Banach Algebras
Authors: Muhammad Sarwar, Ziaul Islam, Hijaz Ahmad, Hüseyin Işık, Samad Noeiaghdam
First page: 251
Abstract: In this article, we proposed the concept of cone interval b-metric space over Banach algebras. Furthermore, some near-fixed point and near-common fixed point results are proved in the context of cone interval b-metric space and normed interval spaces for self-mappings under different types of generalized contractions. An example is presented to validate our main outcome.
Citation: Axioms
PubDate: 2021-10-09
DOI: 10.3390/axioms10040251
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 252: Existence of Mild Solutions for Multi-Term
Time-Fractional Random Integro-Differential Equations with Random
Carathéodory Conditions
Authors: Amadou Diop, Wei-Shih Du
First page: 252
Abstract: In this paper, we investigate the existence of mild solutions to a multi-term fractional integro-differential equation with random effects. Our results are mainly relied upon stochastic analysis, Mönch’s fixed point theorem combined with a random fixed point theorem with stochastic domain, measure of noncompactness and resolvent family theory. Under the condition that the nonlinear term is of Carathéodory type and satisfies some weakly compactness condition, we establish the existence of random mild solutions. A nontrivial example illustrating our main result is also given.
Citation: Axioms
PubDate: 2021-10-12
DOI: 10.3390/axioms10040252
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 253: Using Free Mathematical Software in
Engineering Classes
Authors: Víctor Gayoso Martínez, Luis Hernández Encinas, Agustín Martín Muñoz, Araceli Queiruga Dios
First page: 253
Abstract: There are many computational applications and engines used in mathematics, with some of the best-known arguably being Maple, Mathematica, MATLAB, and Mathcad. However, although they are very complete and powerful, they demand the use of commercial licences, which can be a problem for some education institutions or in cases where students desire to use the software on an unlimited number of devices or to access it from several of them simultaneously. In this contribution, we show how GeoGebra, WolframAlpha, Python, and SageMath can be applied to the teaching of different mathematical courses in engineering studies, as they are some of the most interesting representatives of free (and mostly open source) mathematical software. As the best way to show a topic in mathematics is by providing examples, this article explains how to make calculations for some of the main topics associated with Calculus, Algebra, and Coding theories. In addition to this, we provide some results associated with the usage of Mathematica in different graded activities. Moreover, the comparison between the results from students that use Mathematica and students that participate in a “traditional” course, solving problems and attending to master classes, is shown.
Citation: Axioms
PubDate: 2021-10-12
DOI: 10.3390/axioms10040253
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 254: Oscillation of Repeated Max-Weighted Power
Mean Compositions of Fuzzy Matrices
Authors: Jun-Lin Lin, Laksamee Khomnotai, Hsin-Chieh Liu
First page: 254
Abstract: In the literature, the powers of a square fuzzy matrix with respect to the max-weighted power mean composition have been shown to always converge. This study considers the max-weighted power mean composition for a sequence of fuzzy matrices. It reveals that the repeated compositions of a sequence of n fuzzy matrices oscillate among n fuzzy matrices once the number of compositions exceeds a certain threshold. The previous finding can be considered as a special case of this study with n = 1.
Citation: Axioms
PubDate: 2021-10-13
DOI: 10.3390/axioms10040254
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 255: On Some Fractional Integral Inequalities
Involving Caputo–Fabrizio Integral Operator
Authors: Vaijanath L. Chinchane, Asha B. Nale, Satish K. Panchal, Christophe Chesneau
First page: 255
Abstract: In this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral. Moreover, several fractional integral inequalities for extended Chebyshev functional by considering the Caputo–Fabrizio fractional integral operator are discussed. In addition, we obtain fractional integral inequalities for three positive functions involving the same operator.
Citation: Axioms
PubDate: 2021-10-14
DOI: 10.3390/axioms10040255
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 256: Structure of Iso-Symmetric Operators
Authors: Bhagwati Prashad Duggal, In-Hyoun Kim
First page: 256
Abstract: For a Hilbert space operator T∈B(H), let LT and RT∈B(B(H)) denote, respectively, the operators of left multiplication and right multiplication by T. For positive integers m and n, let ▵T∗,Tm(I)=(LT∗RT−I)m(I) and δT∗,Tn(I)=(LT∗−RT)m(I). The operator T is said to be (m,n)-isosymmetric if ▵T∗,TmδT∗,Tn(I)=0. Power bounded (m,n)-isosymmetric operators T∈B(H) have an upper triangular matrix representation T=T1T30T2∈B(H1⊕H2) such that T1∈B(H1) is a C0.-operator which satisfies δT1∗,T1n(I H1)=0 and T2∈B(H2) is a C1.-operator which satisfies AT2=(Vu⊕Vb) H2A, A=limt→∞T2∗tT2t, Vu is a unitary and Vb is a bilateral shift. If, in particular, T is cohyponormal, then T is the direct sum of a unitary with a C00-contraction.
Citation: Axioms
PubDate: 2021-10-14
DOI: 10.3390/axioms10040256
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 257: Forecasting Economic Growth of the Group of
Seven via Fractional-Order Gradient Descent Approach
Authors: Xiaoling Wang, Michal Fečkan, JinRong Wang
First page: 257
Abstract: This paper establishes a model of economic growth for all the G7 countries from 1973 to 2016, in which the gross domestic product (GDP) is related to land area, arable land, population, school attendance, gross capital formation, exports of goods and services, general government, final consumer spending and broad money. The fractional-order gradient descent and integer-order gradient descent are used to estimate the model parameters to fit the GDP and forecast GDP from 2017 to 2019. The results show that the convergence rate of the fractional-order gradient descent is faster and has a better fitting accuracy and prediction effect.
Citation: Axioms
PubDate: 2021-10-15
DOI: 10.3390/axioms10040257
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 258: Nonlinear EHD Instability of Two-Superposed
Walters’ B Fluids Moving through Porous Media
Authors: Ji-Huan He, Galal M. Moatimid, Aya Sayed
First page: 258
Abstract: The current work examines the application of the viscous potential flow to the Kelvin-Helmholtz instability (KHI) of a planar interface between two visco-elastic Walters’ B fluids. The fluids are fully saturated in porous media in the presence of heat and mass transfer across the interface. Additionally, the structure is pervaded via a uniform, normal electrical field in the absence of superficial charges. The nonlinear scheme basically depends on analyzing the linear principal equation of motion, and then applying the appropriate nonlinear boundary-conditions. The current organization creates a nonlinear characteristic equation describing the amplitude performance of the surface waves. The classical Routh–Hrutwitz theory is employed to judge the linear stability criteria. Once more, the implication of the multiple time scale with the aid of Taylor theory yields a Ginzburg–Landau equation, which controls the nonlinear stability criteria. Furthermore, the Poincaré–Lindstedt technique is implemented to achieve an analytic estimated bounded solution for the surface deflection. Many special cases draw upon appropriate data selections. Finally, all theoretical findings are numerically confirmed in such a way that ensures the effectiveness of various physical parameters.
Citation: Axioms
PubDate: 2021-10-18
DOI: 10.3390/axioms10040258
Issue No: Vol. 10, No. 4 (2021)
- Axioms, Vol. 10, Pages 159: Popularity Prediction of Online Contents via
Cascade Graph and Temporal Information
Authors: Yingdan Shang, Bin Zhou, Ye Wang, Aiping Li, Kai Chen, Yichen Song, Changjian Lin
First page: 159
Abstract: Predicting the popularity of online content is an important task for content recommendation, social influence prediction and so on. Recent deep learning models generally utilize graph neural networks to model the complex relationship between information cascade graph and future popularity, and have shown better prediction results compared with traditional methods. However, existing models adopt simple graph pooling strategies, e.g., summation or average, which prone to generate inefficient cascade graph representation and lead to unsatisfactory prediction results. Meanwhile, they often overlook the temporal information in the diffusion process which has been proved to be a salient predictor for popularity prediction. To focus attention on the important users and exclude noises caused by other less relevant users when generating cascade graph representation, we learn the importance coefficient of users and adopt sample mechanism in graph pooling process. In order to capture the temporal features in the diffusion process, we incorporate the inter-infection duration time information into our model by using LSTM neural network. The results show that temporal information rather than cascade graph information is a better predictor for popularity. The experimental results on real datasets show that our model significantly improves the prediction accuracy compared with other state-of-the-art methods.
Citation: Axioms
PubDate: 2021-07-23
DOI: 10.3390/axioms10030159
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 160: Properties of Certain Multivalent Analytic
Functions Associated with the Lemniscate of Bernoulli
Authors: Likai Liu, Jin-Lin Liu
First page: 160
Abstract: Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.
Citation: Axioms
PubDate: 2021-07-26
DOI: 10.3390/axioms10030160
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 161: Semilocal Convergence of the Extension of
Chun’s Method
Authors: Alicia Cordero, Javier G. Maimó, Eulalia Martínez, Juan R. Torregrosa, María P. Vassileva
First page: 161
Abstract: In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Fréchet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results.
Citation: Axioms
PubDate: 2021-07-26
DOI: 10.3390/axioms10030161
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 162: Critical Indices and Self-Similar Power
Transform
Authors: Simon Gluzman
First page: 162
Abstract: “Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea that the critical index by itself should be optimized through the parameters of power transform to be calculated from the minimal sensitivity (derivative) optimization condition. The critical index is a product of the algebraic self-similar renormalization which contributes to the expressions the set of control parameters typical to the algebraic self-similar renormalization, and of the power transform which corrects them even further. The parameter of power transformation is, in a nutshell, the multiplier connecting the critical exponent and the correction-to-scaling exponent. We mostly study the minimal model of critical phenomena based on expansions with only two coefficients and critical points. The optimization appears to bring quite accurate, uniquely defined results given by simple formulas. Many important cases of critical phenomena are covered by the simple formula. For the longer series, the optimization condition possesses multiple solutions, and additional constraints should be applied. In particular, we constrain the sought solution by requiring it to be the best in prediction of the coefficients not employed in its construction. In principle, the error/measure of such prediction can be optimized by itself, with respect to the parameter of power transform. Methods of calculation based on optimized power-transformed factors are applied and results presented for critical indices of several key models of conductivity and viscosity of random media, swelling of polymers, permeability in two-dimensional channels. Several quantum mechanical problems are discussed as well.
Citation: Axioms
PubDate: 2021-07-26
DOI: 10.3390/axioms10030162
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 163: The Existence of Nontrivial Solution for a
Class of Kirchhoff-Type Equation of General Convolution Nonlinearity
without Any Growth Conditions
Authors: Li Zhou, Chuanxi Zhu
First page: 163
Abstract: In this paper, we consider the following Kirchhoff-type equation: {u∈H1(RN),−(a+b∫RN ∇u 2dx)Δu+V(x)u=(Iα∗F(u))f(u)+λg(u),inRN, where a>0, b≥0, λ>0, α∈(N−2,N), N≥3, V:RN→R is a potential function and Iα is a Riesz potential of order α∈(N−2,N). Under certain assumptions on V(x), f(u) and g(u), we prove that the equation has at least one nontrivial solution by variational methods.
Citation: Axioms
PubDate: 2021-07-27
DOI: 10.3390/axioms10030163
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 164: Rough Approximation Operators on a Complete
Orthomodular Lattice
Authors: Songsong Dai
First page: 164
Abstract: This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.
Citation: Axioms
PubDate: 2021-07-27
DOI: 10.3390/axioms10030164
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 165: A Novel Numerical Method for Solving
Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral
Equations with Zero Absolute Error
Authors: Mutaz Mohammad, Alexandre Trounev, Mohammed Alshbool
First page: 165
Abstract: In this work, a new numerical method for the fractional diffusion-wave equation and nonlinear Fredholm and Volterra integro-differential equations is proposed. The method is based on Euler wavelet approximation and matrix inversion of an M×M collocation points. The proposed equations are presented based on Caputo fractional derivative where we reduce the resulting system to a system of algebraic equations by implementing the Gaussian quadrature discretization. The reduced system is generated via the truncated Euler wavelet expansion. Several examples with known exact solutions have been solved with zero absolute error. This method is also applied to the Fredholm and Volterra nonlinear integral equations and achieves the desired absolute error of 0×10−31 for all tested examples. The new numerical scheme is exceptional in terms of its novelty, efficiency and accuracy in the field of numerical approximation.
Citation: Axioms
PubDate: 2021-07-28
DOI: 10.3390/axioms10030165
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 166: Global Stability of a Lotka-Volterra
Competition-Diffusion-Advection System with Different Positive Diffusion
Distributions
Authors: Lili Chen, Shilei Lin, Yanfeng Zhao
First page: 166
Abstract: In this paper, the problem of a Lotka–Volterra competition–diffusion–advection system between two competing biological organisms in a spatially heterogeneous environments is investigated. When two biological organisms are competing for different fundamental resources, and their advection and diffusion strategies follow different positive diffusion distributions, the functions of specific competition ability are variable. By virtue of the Lyapunov functional method, we discuss the global stability of a non-homogeneous steady-state. Furthermore, the global stability result is also obtained when one of the two organisms has no diffusion ability and is not affected by advection.
Citation: Axioms
PubDate: 2021-07-28
DOI: 10.3390/axioms10030166
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 167: Factoring Continuous Characters Defined on
Subgroups of Products of Topological Groups
Authors: Mikhail G. Tkachenko
First page: 167
Abstract: This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of paratopological groups, S be a dense subgroup of D, and χ a continuous character of S. Then one can find a finite set E⊂I and continuous characters χi of Di, for i∈E, such that χ=∏i∈Eχi∘piS, where pi:D→Di is the projection.
Citation: Axioms
PubDate: 2021-07-28
DOI: 10.3390/axioms10030167
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 168: Social Network Group Decision-Making Method
Based on Q-Rung Orthopair Fuzzy Set and Its Application in the Evaluation
of Online Teaching Quality
Authors: Yingjie Hu, Shouzhen Zeng, Llopis-Albert Carlos, Kifayat Ullah, Yuqi Yang
First page: 168
Abstract: As q-rung orthopair fuzzy set (q-ROFS) theory can effectively express complex fuzzy information, this study explores its application to social network environments and proposes a social network group decision-making (SNGDM) method based on the q-ROFS. Firstly, the q-rung orthopair fuzzy value is used to represent the trust relationships between experts in the social network, and a trust q-rung orthopair fuzzy value is defined. Secondly, considering the decreasing and multipath of trust in the process of trust propagation, this study designs a trust propagation mechanism by using its multiplication operation in the q-ROFS environment and proposes a trust q-ROFS aggregation approach. Moreover, based on the trust scores and confidence levels of experts, a new integration operator called q-rung orthopair fuzzy-induced ordered weighted average operator is proposed to fuse experts’ evaluation information. Additionally, considering the impact of consensus interaction on decision-making results, a consensus interaction model based on the q-ROF distance measure and trust relationship is proposed, including consistency measurement, identification of inconsistent expert decision-making opinions and a personalized adjustment mechanism. Finally, the SNGDM method is applied to solve the problem of evaluating online teaching quality.
Citation: Axioms
PubDate: 2021-07-28
DOI: 10.3390/axioms10030168
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 169: Application of a Generalized Secant Method to
Nonlinear Equations with Complex Roots
Authors: Avram Sidi
First page: 169
Abstract: The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.
Citation: Axioms
PubDate: 2021-07-29
DOI: 10.3390/axioms10030169
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 170: Positive Solvability for Conjugate Fractional
Differential Inclusion of (k, n − k) Type without Continuity and
Compactness
Authors: Ahmed Salem, Aeshah Al-Dosari
First page: 170
Abstract: The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.
Citation: Axioms
PubDate: 2021-07-29
DOI: 10.3390/axioms10030170
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 171: On a Non-Newtonian Calculus of Variations
Authors: Delfim F. M. Torres
First page: 171
Abstract: The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the non-Newtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (non-Newtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given.
Citation: Axioms
PubDate: 2021-07-29
DOI: 10.3390/axioms10030171
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 172: Novel Concept of Energy in Bipolar
Single-Valued Neutrosophic Graphs with Applications
Authors: Siti Nurul Fitriah Mohamad, Roslan Hasni, Florentin Smarandache, Binyamin Yusoff
First page: 172
Abstract: The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life.
Citation: Axioms
PubDate: 2021-07-29
DOI: 10.3390/axioms10030172
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 173: Correction: Bates et al. Vector Fields and
Differential Forms on the Orbit Space of a Proper Action. Axioms 2021, 10,
118
Authors: Larry Bates, Richard Cushman, Jędrzej Śniatycki
First page: 173
Abstract: There was an error in the original article [...]
Citation: Axioms
PubDate: 2021-07-30
DOI: 10.3390/axioms10030173
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 174: Sequential Riemann–Liouville and
Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled
Fractional Integral Boundary Conditions
Authors: Chanakarn Kiataramkul, Weera Yukunthorn, Sotiris K. Ntouyas, Jessada Tariboon
First page: 174
Abstract: In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.
Citation: Axioms
PubDate: 2021-07-31
DOI: 10.3390/axioms10030174
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 175: Some New Fractional Estimates of Inequalities
for LR-p-Convex Interval-Valued Functions by Means of Pseudo Order
Relation
Authors: Muhammad Bilal Khan, Pshtiwan Othman Mohammed, Muhammad Aslam Noor, Dumitru Baleanu, Juan Luis García Guirao
First page: 175
Abstract: It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis, both the inclusion relation (⊆) and pseudo order relation (≤p) are two different concepts. In this article, by using pseudo order relation, we introduce the new class of nonconvex functions known as LR-p-convex interval-valued functions (LR-p-convex-IVFs). With the help of this relation, we establish a strong relationship between LR-p-convex-IVFs and Hermite-Hadamard type inequalities (HH-type inequalities) via Katugampola fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-p-convex-IVFs and their variant forms as special cases. Useful examples that demonstrate the applicability of the theory proposed in this study are given. The concepts and techniques of this paper may be a starting point for further research in this area.
Citation: Axioms
PubDate: 2021-07-31
DOI: 10.3390/axioms10030175
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 176: The Axioms in My Understanding from Many Years
of Experience
Authors: Boyan Dimitrov
First page: 176
Abstract: This is a discussion article that should raise more questions than answers. We write our own point of view about the concept of axioms. We list several examples, mostly known to readers, and focus on examples where the axioms produce separate areas of studies and applications. The classic definitions are schematically presented since these are well known. We briefly notice how they generated various other fields of development. Set theory is, in our opinion, the fundamental for new areas of development. Our focus is on some recent axioms such as uncertainty, probability, and new concepts and results related to these fields. The emphasis is on the meaning of an undefined concept and on its measuring.
Citation: Axioms
PubDate: 2021-08-01
DOI: 10.3390/axioms10030176
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 177: Source Identification of a Chemical Incident
in an Urban Area
Authors: Francisco J. Fernández, Miguel E. Vázquez-Méndez
First page: 177
Abstract: This work deals aims to present a methodology for source identification of chemical incidents in urban areas. We propose an approximation of the problem within the framework of the optimal control theory and we provide an algorithm for its numerical resolution. Finally, we analyze the validity of the algorithm in several academic situations.
Citation: Axioms
PubDate: 2021-08-03
DOI: 10.3390/axioms10030177
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 178: A Method for Visualizing Posterior Probit
Model Uncertainty in the Early Prediction of Fraud for Sustainability
Development
Authors: Shih-Hsien Tseng, Tien Son Nguyen
First page: 178
Abstract: Corporate fraud is not only curtailed investors’ rights and privileges but also disrupts the overall market economy. For this reason, the formulation of a model that could help detect any unusual market fluctuations would be essential for investors. Thus, we propose an early warning system for predicting fraud associated with financial statements based on the Bayesian probit model while examining historical data from 1999 to 2017 with 327 businesses in Taiwan to create a visual method to aid in decision making. In this study, we utilize a parametric estimation via the Markov Chain Monte Carlo (MCMC). The result show that it can reduce over or under-confidence within the decision-making process when standard logistic regression is utilized. In addition, the Bayesian probit model in this study is found to offer more accurate calculations and not only represent the prediction value of the responses but also possible ranges of these responses via a simple plot.
Citation: Axioms
PubDate: 2021-08-04
DOI: 10.3390/axioms10030178
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 179: An Advanced Decision Making Framework via
Joint Utilization of Context-Dependent Data Envelopment Analysis and
Sentimental Messages
Authors: Hsueh-Li Huang, Sin-Jin Lin, Ming-Fu Hsu
First page: 179
Abstract: Compared to widely examined topics in the related literature, such as financial crises/difficulties in accurate prediction, studies on corporate performance forecasting are quite scarce. To fill the research gap, this study introduces an advanced decision making framework that incorporates context-dependent data envelopment analysis (CD-DEA), fuzzy robust principal component analysis (FRPCA), latent Dirichlet allocation (LDA), and stochastic gradient twin support vector machine (SGTSVM) for corporate performance forecasting. Ratio analysis with the merits of easy-to-use and intuitiveness plays an essential role in performance analysis, but it typically has one input variable and one output variable, which is unable to appropriately depict the inherent status of a corporate’s operations. To combat this, we consider CD-DEA as it can handle multiple input and multiple output variables simultaneously and yields an attainable target to analyze decision making units (DMUs) when the data present great variations. To strengthen the discriminant ability of CD-DEA, we also conduct FRPCA, and because numerical messages based on historical principles normally cannot transmit future corporate messages, we execute LDA to decompose the accounting narratives into many topics and preserve those topics that are relevant to corporate operations. Sequentially, the process matches the preserved topics with a sentimental dictionary to exploit the hidden sentiments in each topic. The analyzed data are then fed into SGTSVM to construct the forecasting model. The result herein reveals that the introduced decision making framework is a promising alternative for performance forecasting.
Citation: Axioms
PubDate: 2021-08-04
DOI: 10.3390/axioms10030179
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 180: Multicriteria Evaluation of Deep Neural
Networks for Semantic Segmentation of Mammographies
Authors: Yoshio Rubio, Oscar Montiel
First page: 180
Abstract: Breast segmentation plays a vital role in the automatic analysis of mammograms. Accurate segmentation of the breast region increments the probability of a correct diagnostic and minimizes computational cost. Traditionally, model-based approaches dominated the landscape for breast segmentation, but recent studies seem to benefit from using robust deep learning models for this task. In this work, we present an extensive evaluation of deep learning architectures for semantic segmentation of mammograms, including segmentation metrics, memory requirements, and average inference time. We used several combinations of two-stage segmentation architectures composed of a feature extraction net (VGG16 and ResNet50) and a segmentation net (FCN-8, U-Net, and PSPNet). The training examples were taken from the mini Mammographic Image Analysis Society (MIAS) database. Experimental results using the mini-MIAS database show that the best net scored a Dice similarity coefficient of 99.37% for breast boundary segmentation and 95.45% for pectoral muscle segmentation.
Citation: Axioms
PubDate: 2021-08-05
DOI: 10.3390/axioms10030180
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 181: On a Nonlinear Mixed Problem for a Parabolic
Equation with a Nonlocal Condition
Authors: Abdelkader Djerad, Ameur Memou, Ali Hameida
First page: 181
Abstract: The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.
Citation: Axioms
PubDate: 2021-08-06
DOI: 10.3390/axioms10030181
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 182: On Uniform Stability with Growth Rates of
Stochastic Skew-Evolution Semiflows in Banach Spaces
Authors: Tímea Melinda Személy Fülöp, Mihail Megan, Diana Ioana Borlea(Pătraşcu)
First page: 182
Abstract: The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure. This concept includes, as particular cases, the concepts of uniform exponential stability in mean and uniform polynomial stability in mean. Extending techniques employed in the deterministic case, we obtain variants of some results for the general cases of uniform stability in mean for stochastic skew-evolution semiflows in Banach spaces.
Citation: Axioms
PubDate: 2021-08-08
DOI: 10.3390/axioms10030182
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 183: Simulations between Network Topologies in
Networks of Evolutionary Processors
Authors: José Ángel Sánchez Martín, Victor Mitrana
First page: 183
Abstract: In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.
Citation: Axioms
PubDate: 2021-08-11
DOI: 10.3390/axioms10030183
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 184: Exponentially Convergent Galerkin Method for
Numerical Modeling of Lasing in Microcavities with Piercing Holes
Authors: Alexander O. Spiridonov, Anna I. Repina, Ilya V. Ketov, Sergey I. Solov’ev, Evgenii M. Karchevskii
First page: 184
Abstract: The paper investigates an algorithm for the numerical solution of a parametric eigenvalue problem for the Helmholtz equation on the plane specially tailored for the accurate mathematical modeling of lasing modes of microring lasers. The original problem is reduced to a nonlinear eigenvalue problem for a system of Muller boundary integral equations. For the numerical solution of the obtained problem, we use a trigonometric Galerkin method, prove its convergence, and derive error estimates in the eigenvalue and eigenfunction approximation. Previous numerical experiments have shown that the method converges exponentially. In the current paper, we prove that if the generalized eigenfunctions are analytic, then the approximate eigenvalues and eigenfunctions exponentially converge to the exact ones as the number of basis functions increases. To demonstrate the practical effectiveness of the algorithm, we find geometrical characteristics of microring lasers that provide a significant increase in the directivity of lasing emission, while maintaining low lasing thresholds.
Citation: Axioms
PubDate: 2021-08-11
DOI: 10.3390/axioms10030184
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 185: Spherical Linear Diophantine Fuzzy Soft Rough
Sets with Multi-Criteria Decision Making
Authors: Masooma Raza Hashmi, Syeda Tayyba Tehrim, Muhammad Riaz, Dragan Pamucar, Goran Cirovic
First page: 185
Abstract: Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.
Citation: Axioms
PubDate: 2021-08-13
DOI: 10.3390/axioms10030185
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 186: The Fourth Fundamental Form IV of Dini-Type
Helicoidal Hypersurface in the Four Dimensional Euclidean Space
Authors: Erhan Güler
First page: 186
Abstract: We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space E4. We find the Gauss map of helicoidal hypersurface in E4. We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix IV of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects.
Citation: Axioms
PubDate: 2021-08-16
DOI: 10.3390/axioms10030186
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 187: An Extension of Beta Function by Using
Wiman’s Function
Authors: Rahul Goyal, Shaher Momani, Praveen Agarwal, Michael Th. Rassias
First page: 187
Abstract: The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.
Citation: Axioms
PubDate: 2021-08-16
DOI: 10.3390/axioms10030187
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 188: Analysis on Controllability Results for
Wellposedness of Impulsive Functional Abstract Second-Order Differential
Equation with State-Dependent Delay
Authors: Kulandhivel Karthikeyan, Dhatchinamoorthy Tamizharasan, Dimplekumar N. Chalishajar
First page: 188
Abstract: The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation.
Citation: Axioms
PubDate: 2021-08-16
DOI: 10.3390/axioms10030188
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 189: Reinitializing Sea Surface Temperature in the
Ensemble Intermediate Coupled Model for Improved Forecasts
Authors: Sittisak Injan, Angkool Wangwongchai, Usa Humphries, Amir Khan, Abdullahi Yusuf
First page: 189
Abstract: The Ensemble Intermediate Coupled Model (EICM) is a model used for studying the El Niño-Southern Oscillation (ENSO) phenomenon in the Pacific Ocean, which is anomalies in the Sea Surface Temperature (SST) are observed. This research aims to implement Cressman to improve SST forecasts. The simulation considers two cases in this work: the control case and the Cressman initialized case. These cases are simulations using different inputs where the two inputs differ in terms of their resolution and data source. The Cressman method is used to initialize the model with an analysis product based on satellite data and in situ data such as ships, buoys, and Argo floats, with a resolution of 0.25 × 0.25 degrees. The results of this inclusion are the Cressman Initialized Ensemble Intermediate Coupled Model (CIEICM). Forecasting of the sea surface temperature anomalies was conducted using both the EICM and the CIEICM. The results show that the calculation of SST field from the CIEICM was more accurate than that from the EICM. The forecast using the CIEICM initialization with the higher-resolution satellite-based analysis at a 6-month lead time improved the root mean square deviation to 0.794 from 0.808 and the correlation coefficient to 0.630 from 0.611, compared the control model that was directly initialized with the low-resolution in-situ-based analysis.
Citation: Axioms
PubDate: 2021-08-17
DOI: 10.3390/axioms10030189
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 190: Advances in the Theory of Compact Groups and
Pro-Lie Groups in the Last Quarter Century
Authors: Karl H. Hofmann, Sidney A. Morris
First page: 190
Abstract: This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century. It begins with developments in the 18th and 19th centuries. Next is from Hilbert’s Fifth Problem in 1900 to its solution in 1952 by Montgomery, Zippin, and Gleason and Yamabe’s important structure theorem on almost connected locally compact groups. This half century included profound contributions by Weyl and Peter, Haar, Pontryagin, van Kampen, Weil, and Iwasawa. The focus in the last quarter century has been structure theory, largely resulting from extending Lie Theory to compact groups and then to pro-Lie groups, which are projective limits of finite-dimensional Lie groups. The category of pro-Lie groups is the smallest complete category containing Lie groups and includes all compact groups, locally compact abelian groups, and connected locally compact groups. Amongst the structure theorems is that each almost connected pro-Lie group G is homeomorphic to RI×C for a suitable set I and some compact subgroup C. Finally, there is a perfect generalization to compact groups G of the age-old natural duality of the group algebra R[G] of a finite group G to its representation algebra R(G,R), via the natural duality of the topological vector space RI to the vector space R(I), for any set I, thus opening a new approach to the Hochschild-Tannaka duality of compact groups.
Citation: Axioms
PubDate: 2021-08-17
DOI: 10.3390/axioms10030190
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 191: Periodic Property and Instability of a
Rotating Pendulum System
Authors: Ji-Huan He, Tarek S. Amer, Shimaa Elnaggar, Abdallah A. Galal
First page: 191
Abstract: The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.
Citation: Axioms
PubDate: 2021-08-18
DOI: 10.3390/axioms10030191
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 192: Oscillation and Asymptotic Properties of
Differential Equations of Third-Order
Authors: R. Elayaraja, V. Ganesan, Omar Bazighifan, Clemente Cesarano
First page: 192
Abstract: The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.
Citation: Axioms
PubDate: 2021-08-18
DOI: 10.3390/axioms10030192
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 193: The Representation of D-Invariant Polynomial
Subspaces Based on Symmetric Cartesian Tensors
Authors: Xue Jiang, Kai Cui
First page: 193
Abstract: Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D-invariant polynomial subspace Pn in terms of Cartesian tensors, where Pn is a subspace with a maximal total degree equal to n,n≥1. For an arbitrary homogeneous polynomial p(k) of total degree k in Pn, p(k) can be rewritten as the inner products of a kth order symmetric Cartesian tensor and k column vectors of indeterminates. We show that p(k) can be determined by all polynomials of a total degree one in Pn. Namely, if we treat all linear polynomials on the basis of Pn as a column vector, then this vector can be written as a product of a coefficient matrix A(1) and a column vector of indeterminates; our main result shows that the kth order symmetric Cartesian tensor corresponds to p(k) is a product of some so-called relational matrices and A(1).
Citation: Axioms
PubDate: 2021-08-19
DOI: 10.3390/axioms10030193
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 194: Differential Evolution with Shadowed and
General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal
Design of Fuzzy Controllers
Authors: Patricia Ochoa, Oscar Castillo, Patricia Melin, José Soria
First page: 194
Abstract: This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.
Citation: Axioms
PubDate: 2021-08-19
DOI: 10.3390/axioms10030194
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 195: Global Directed Dynamic Behaviors of a
Lotka-Volterra Competition-Diffusion-Advection System
Authors: Lili Chen, Shilei Lin, Yanfeng Zhao
First page: 195
Abstract: This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments. The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards a positive distribution. By virtue of the principal eigenvalue theory, the linear stability of the co-existing steady state is established. Furthermore, the classification of dynamical behaviors is shown by utilizing the monotone dynamical system theory. This work can be seen as a further development of a competition-diffusion system.
Citation: Axioms
PubDate: 2021-08-20
DOI: 10.3390/axioms10030195
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 196: An Improved Tikhonov-Regularized Variable
Projection Algorithm for Separable Nonlinear Least Squares
Authors: Hua Guo, Guolin Liu, Luyao Wang
First page: 196
Abstract: In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.
Citation: Axioms
PubDate: 2021-08-22
DOI: 10.3390/axioms10030196
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 197: Bounded Perturbation Resilience of Two
Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility
Problem
Authors: Yingying Li, Yaxuan Zhang
First page: 197
Abstract: In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.
Citation: Axioms
PubDate: 2021-08-23
DOI: 10.3390/axioms10030197
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 198: Closure System and Its Semantics
Authors: Yinbin Lei, Jun Zhang
First page: 198
Abstract: It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or derived-set operator (or dually, co-derived-set operator). It is also known that a topological closure operator (and dually, a topological interior operator) can be weakened into generalized closure (interior) systems. What about boundary operator, exterior operator, and derived-set (and co-derived-set) operator in the weakened systems' Our paper completely answers this question by showing that the above six set operators can all be weakened (from their topological counterparts) in an appropriate way such that their inter-relationships remain essentially the same as in topological systems. Moreover, we show that the semantics of an interior point, an exterior point, a boundary point, an accumulation point, a co-accumulation point, an isolated point, a repelling point, etc. with respect to a given set, can be extended to an arbitrary subset system simply by treating the subset system as a base of a generalized interior system (and hence its dual, a generalized closure system). This allows us to extend topological semantics, namely the characterization of points with respect to an arbitrary set, in terms of both its spatial relations (interior, exterior, or boundary) and its dynamic convergence of any sequence (accumulation, co-accumulation, and isolation), to much weakened systems and hence with wider applicability. Examples from the theory of matroid and of Knowledge/Learning Spaces are used as an illustration.
Citation: Axioms
PubDate: 2021-08-23
DOI: 10.3390/axioms10030198
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 199: Random Walk Analysis in a Reliability System
under Constant Degradation and Random Shocks
Authors: Jewgeni H. Dshalalow, Ryan T. White
First page: 199
Abstract: In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.
Citation: Axioms
PubDate: 2021-08-23
DOI: 10.3390/axioms10030199
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 200: Improved Block-Pulse Functions for Numerical
Solution of Mixed Volterra-Fredholm Integral Equations
Authors: Ji-Huan He, Mahmoud H. Taha, Mohamed A. Ramadan, Galal M. Moatimid
First page: 200
Abstract: The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a linear system of algebraic equations through the use of IBPFs in addition to the operational matrix of integration. Typically, the classical alterations have enhanced the time taken by the computer program to solve the system of algebraic equations. The current modification works perfectly and has improved the efficiency over the regular block–pulse basis functions (BPF). Additionally, the paper handles the uniqueness plus the convergence theorems of the solution. Numerical examples have been presented to illustrate the efficiency as well as the accuracy of the method. Furthermore, tables and graphs are used to show and confirm how the method is highly efficient.
Citation: Axioms
PubDate: 2021-08-24
DOI: 10.3390/axioms10030200
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 201: On Self-Aggregations of Min-Subgroups
Authors: Carlos Bejines, Sergio Ardanza-Trevijano, Jorge Elorza
First page: 201
Abstract: Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.
Citation: Axioms
PubDate: 2021-08-24
DOI: 10.3390/axioms10030201
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 202: Numerical Solution for Singular Boundary Value
Problems Using a Pair of Hybrid Nyström Techniques
Authors: Mufutau Ajani Rufai, Higinio Ramos
First page: 202
Abstract: This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.
Citation: Axioms
PubDate: 2021-08-25
DOI: 10.3390/axioms10030202
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 203: The Soliton Solutions for Some Nonlinear
Fractional Differential Equations with Beta-Derivative
Authors: Erdoğan Mehmet Özkan, Ayten Özkan
First page: 203
Abstract: Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.
Citation: Axioms
PubDate: 2021-08-26
DOI: 10.3390/axioms10030203
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 204: How Containment Can Effectively Suppress the
Outbreak of COVID-19: A Mathematical Modeling
Authors: Bootan Rahman, Sarbaz H. A. Khoshnaw, Grace O. Agaba, Fahad Al Basir
First page: 204
Abstract: In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown practices in response to containment policies. Local stability and basic reproduction numbers are analyzed. Local sensitivity indices of the parameters of the proposed model are calculated, using the non-normalization, half-normalization, and full-normalization techniques. Numerical investigations show that the dynamics of the system depend on the model parameters. The infection transmission rate (as a function of the lockdown parameter) for both reported and unreported symptomatic infected peoples is a significant parameter in spreading the infection. A nationwide public lockdown decreases the number of infected cases and stops the pandemic’s peak from occurring. The results obtained from this study are beneficial worldwide for developing different COVID-19 management programs.
Citation: Axioms
PubDate: 2021-08-28
DOI: 10.3390/axioms10030204
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 205: New Necessary Conditions for the
Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
Authors: Aníbal Coronel, Fernando Huancas, Alex Tello, Marko Rojas-Medar
First page: 205
Abstract: We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.
Citation: Axioms
PubDate: 2021-08-29
DOI: 10.3390/axioms10030205
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 206: Approximation of Directional Step Derivative
of Complex-Valued Functions Using a Generalized Quaternion System
Authors: Ji-Eun Kim
First page: 206
Abstract: The step derivative of a complex function can be defined with various methods. The step direction defines a basis that is distinct from that of a complex number; the derivative can then be treated by using Taylor series expansion in this direction. In this study, we define step derivatives based on complex numbers and quaternions that are orthogonal to the complex basis while simultaneously being distinct from it. Considering previous studies, the step derivative defined using quaternions was insufficient for applying the properties of quaternions by setting a quaternion basis distinct from the complex basis or setting the step direction to which only a part of the quaternion basis was applied. Therefore, in this study, we examine the definition of quaternions and define the step derivative in the direction of a generalized quaternion basis including a complex basis. We find that the step derivative based on the definition of a quaternion has a relative error in some domains; however, it can be used as a substitute derivative in specific domains.
Citation: Axioms
PubDate: 2021-08-30
DOI: 10.3390/axioms10030206
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 207: A Parametric Type of Cauchy Polynomials with
Higher Level
Authors: Takao Komatsu
First page: 207
Abstract: There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials. A parametric type of Cauchy numbers with level 3 is its analogue. In this paper, as an analogue of a parametric type of Bernoulli polynomials with level 3 and its extension, we introduce a parametric type of Cauchy polynomials with a higher level. We present their characteristic and combinatorial properties. By using recursions, we show some determinant expressions.
Citation: Axioms
PubDate: 2021-08-30
DOI: 10.3390/axioms10030207
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 208: Selection of Logistics Service Provider for
the E-Commerce Companies in Pakistan Based on Integrated GRA-TOPSIS
Approach
Authors: Muhammad Hamza Naseem, Jiaqi Yang, Ziquan Xiang
First page: 208
Abstract: Recently, the demand for third-party logistics providers has become extremely relevant and the key subject for businesses to enhance their service quality and minimize logistics costs. The key success factor for an e-commerce business is product delivery, and the third-party logistics service provider is responsible for that. Each 3PLP has its own business characteristics, meaning it is important to select the most suitable logistics provider for the e-commerce business. This study uses a combination of grey relational analysis (GRA) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, assisting decision makers in choosing the best logistics service provider for their e-business. A case study of an e-commerce company based in Faisalabad, Pakistan, was selected to demonstrate the steps of the proposed methods. In this process, seven criteria of logistics suppliers were considered, and then the best alternatives among four logistics provider companies were selected using the proposed method.
Citation: Axioms
PubDate: 2021-08-30
DOI: 10.3390/axioms10030208
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 209: θ*-Weak Contractions and Discontinuity at the
Fixed Point with Applications to Matrix and Integral Equations
Authors: Atiya Perveen, Waleed M. Alfaqih, Salvatore Sessa, Mohammad Imdad
First page: 209
Abstract: In this paper, the notion of θ*-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.
Citation: Axioms
PubDate: 2021-08-31
DOI: 10.3390/axioms10030209
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 210: Qualitative and Quantitative Analyses of
COVID-19 Dynamics
Authors: Taye Samuel Faniran, Leontine Nkague Nkamba, Thomas Timothee Manga
First page: 210
Abstract: COVID-19 is a highly contagious disease which has spread across the world. A deterministic model that considers an important component of individuals with vertically transmitted underlying diseases (high-risk susceptible individuals), rather than the general public, is formulated in this paper. We also consider key parameters that are concerned with the disease. An epidemiological threshold, R0, is computed using next-generation matrix approach. This is used to establish the existence and global stability of equilibria. We identify the most sensitive parameters which effectively contribute to change the disease dynamics with the help of sensitivity analysis. Our results reveal that increasing contact tracing of the exposed individuals who are tested for COVID-19 and hospitalizing them, largely has a negative impact on R0. Results further reveal that transmission rate between low-risk/high-risk susceptible individuals and symptomatic infectious individuals β and incubation rate of the exposed individuals σ have positive impact on R0. Numerical simulations show that there are fewer high-risk susceptible individuals than the general public when R0<1. This may be due to the fact that high-risk susceptible individuals may prove a bit more difficult to control than the low-risk susceptible individuals as a result of inherited underlying diseases present in them. We thus conclude that high level of tracing and hospitalizing the exposed individuals, as well as adherence to standard precautions and wearing appropriate Personal Protective Equipment (PPE) while handling emergency cases, are needed to flatten the epidemic curve.
Citation: Axioms
PubDate: 2021-08-31
DOI: 10.3390/axioms10030210
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 211: Numerical Algorithms for Computing an
Arbitrary Singular Value of a Tensor Sum
Authors: Asuka Ohashi, Tomohiro Sogabe
First page: 211
Abstract: We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.
Citation: Axioms
PubDate: 2021-08-31
DOI: 10.3390/axioms10030211
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 212: (ρ,η,μ)-Interpolative Kannan
Contractions I
Authors: Yaé Ulrich Gaba, Hassen Aydi, Nabil Mlaiki
First page: 212
Abstract: We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.
Citation: Axioms
PubDate: 2021-09-03
DOI: 10.3390/axioms10030212
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 213: De Moivre’s and Euler Formulas for
Matrices of Hybrid Numbers
Authors: Mücahit Akbıyık, Seda Yamaç Akbıyık, Emel Karaca, Fatih Yılmaz
First page: 213
Abstract: It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted the attention of many scientists. At this paper, we provide the Euler’s and De Moivre’s formulas for the 4×4 matrices associated with hybrid numbers by using trigonometric identities. Also, we give the roots of the matrices of hybrid numbers. Moreover, we give some illustrative examples to support the main formulas.
Citation: Axioms
PubDate: 2021-09-06
DOI: 10.3390/axioms10030213
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 214: Location of Urban Logistics Spaces (ULS) for
Two-Echelon Distribution Systems
Authors: José Ruiz-Meza, Karen Meza-Peralta, Jairo R. Montoya-Torres, Jesus Gonzalez-Feliu
First page: 214
Abstract: The main concern in city logistics is the need to optimize the movement of goods in urban contexts, and to minimize the multiple costs inherent in logistics operations. Inspired by an application in a medium-sized city in Latin America, this paper develops a bi-objective mixed linear integer programming (MILP) model to locate different types of urban logistics spaces (ULS) for the configuration of a two-echelon urban distribution system. The objective functions seek to minimize the costs associated with distance traveled and relocation, in addition to the costs of violation of time windows. This model considers heterogeneous transport, speed assignment, and time windows. For experimental evaluation, two operational scenarios are considered, and Pareto frontiers are obtained to identify the efficient non-dominated solutions to select the most feasible ones from such a set. A case study of a distribution company of goods for supermarkets in the city of Barranquilla, Colombia, is also used to validate the proposed model. These solutions allow decision-makers to define the configuration of ULS networks for urban product delivery.
Citation: Axioms
PubDate: 2021-09-07
DOI: 10.3390/axioms10030214
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 215: Image Encryption and Decryption System through
a Hybrid Approach Using the Jigsaw Transform and Langton’s Ant Applied
to Retinal Fundus Images
Authors: Andrés Romero-Arellano, Ernesto Moya-Albor, Jorge Brieva, Ivan Cruz-Aceves, Juan Gabriel Avina-Cervantes, Martha Alicia Hernandez-Gonzalez, Luis Miguel Lopez-Montero
First page: 215
Abstract: In this work, a new medical image encryption/decryption algorithm was proposed. It is based on three main parts: the Jigsaw transform, Langton’s ant, and a novel way to add deterministic noise. The Jigsaw transform was used to hide visual information effectively, whereas Langton’s ant and the deterministic noise algorithm give a reliable and secure approach. As a case study, the proposal was applied to high-resolution retinal fundus images, where a zero mean square error was obtained between the original and decrypted image. The method performance has been proven through several testing methods, such as statistical analysis (histograms and correlation distributions), entropy computation, keyspace assessment, robustness to differential attack, and key sensitivity analysis, showing in each one a high security level. In addition, the method was compared against other works showing a competitive performance and highlighting with a large keyspace (>1×101,134,190.38). Besides, the method has demonstrated adequate handling of high-resolution images, obtaining entropy values between 7.999988 and 7.999989, an average Number of Pixel Change Rate (NPCR) of 99.5796%±0.000674, and a mean Uniform Average Change Intensity (UACI) of 33.4469%±0.00229. In addition, when there is a small change in the key, the method does not give additional information to decrypt the image.
Citation: Axioms
PubDate: 2021-09-07
DOI: 10.3390/axioms10030215
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 216: A Dynamic Model of Multiple Time-Delay
Interactions between the Virus-Infected Cells and Body’s Immune System
with Autoimmune Diseases
Authors: Hoang Pham
First page: 216
Abstract: The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.
Citation: Axioms
PubDate: 2021-09-07
DOI: 10.3390/axioms10030216
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 217: Normed Spaces Which Are Not Mackey Groups
Authors: Saak Gabriyelyan
First page: 217
Abstract: It is well known that every normed (even quasibarrelled) space is a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give the first examples of normed spaces which are not Mackey groups.
Citation: Axioms
PubDate: 2021-09-08
DOI: 10.3390/axioms10030217
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 218: Calculations on Matrix Transformations
Involving an Infinite Tridiagonal Matrix
Authors: Ali Fares, Ali Ayad, Bruno de Malafosse
First page: 218
Abstract: Given any sequence z=znn≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=ynn≥1 such that y/z=yn/znn≥1∈E; in particular, sz0 denotes the set of all sequences y such that y/z tends to zero. Here, we consider the infinite tridiagonal matrix Br,s,t˜, obtained from the triangle Br,s,t, by deleting its first row. Then we determine the sets of all positive sequences a=ann≥1 such that EaBr,s,t˜⊂Ea, where E=ℓ∞, c0, or c. These results extend some recent results.
Citation: Axioms
PubDate: 2021-09-08
DOI: 10.3390/axioms10030218
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 219: A Family of the r-Associated Stirling Numbers
of the Second Kind and Generalized Bernoulli Polynomials
Authors: Paolo Emilio Ricci, Rekha Srivastava, Pierpaolo Natalini
First page: 219
Abstract: In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials. Herein, we use the Blissard umbral approach and the familiar Bell polynomials. Links with available literature on this subject are also pointed out. The extension to the bivariate case is discussed.
Citation: Axioms
PubDate: 2021-09-09
DOI: 10.3390/axioms10030219
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 220: Inequalities on General Lp-Mixed Chord
Integral Difference
Authors: Hongying Xiao, Weidong Wang, Zhaofeng Li
First page: 220
Abstract: In this article, we introduce the concept of general Lp-mixed chord integral difference of star bodies. Further, we establish the Brunn–Minkowski type, Aleksandrov–Fenchel type and cyclic inequalities for the Lp-mixed chord integral difference.
Citation: Axioms
PubDate: 2021-09-10
DOI: 10.3390/axioms10030220
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 221: Strictly Convex Banach Algebras
Authors: David Yost
First page: 221
Abstract: We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C∗-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there.
Citation: Axioms
PubDate: 2021-09-11
DOI: 10.3390/axioms10030221
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 222: Periodic Third-Order Problems with a Parameter
Authors: Feliz Minhós, Nuno Oliveira
First page: 222
Abstract: This work concerns with the solvability of third-order periodic fully problems with a weighted parameter, where the nonlinearity must verify only a local monotone condition and no periodic, coercivity or super or sublinearity restrictions are assumed, as usual in the literature. The arguments are based on a new type of lower and upper solutions method, not necessarily well ordered. A Nagumo growth condition and Leray–Schauder’s topological degree theory are the existence tools. Only the existence of solution is studied here and it will remain open the discussion on the non-existence and the multiplicity of solutions. Last section contains a nonlinear third-order differential model for periodic catatonic phenomena, depending on biological and/or chemical parameters.
Citation: Axioms
PubDate: 2021-09-11
DOI: 10.3390/axioms10030222
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 223: On New Generalizations of Hermite-Hadamard
Type Inequalities via Atangana-Baleanu Fractional Integral Operators
Authors: Erhan Set, Ahmet Ocak Akdemir, Ali Karaoǧlan, Thabet Abdeljawad, Wasfi Shatanawi
First page: 223
Abstract: Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.
Citation: Axioms
PubDate: 2021-09-12
DOI: 10.3390/axioms10030223
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 224: Error Compensation of Strapdown Inertial
Navigation System for the Boom-Type Roadheader under Complex Vibration
Authors: Yang Shen, Pengjiang Wang, Weixiong Zheng, Xiaodong Ji, Hai Jiang, Miao Wu
First page: 224
Abstract: The strapdown inertial navigation system can provide the navigation information for the boom-type roadheader in the unmanned roadway tunneling working face of the coal mine. However, the complex vibration caused by the cutting process of the boom-type roadheader may result in significant errors of its attitude and position measured by the strapdown inertial navigation system. Thus, an error compensation method based on the vibration characteristics of the roadheader is proposed in this paper. In order to further analyze the angular and linear vibration of the fuselage, as the main vibration sources of the roadheader, the dynamic model of the roadheader is formulated based on the cutting load. Following that, multiple sub-samples compensation algorithms for the coning and sculling errors are constructed. Simulation experiments were carried out under different subsample compensation algorithms, different coal and rock characteristics, and different types of roadheader. The experimental results show that the proposed error compensation algorithm can eliminate the effect of the angular and linear vibration on the measurement accuracy. The coning and sculling error of the strapdown inertial navigation system can reduce at least 52.21% and 42.89%, respectively. Finally, a strapdown inertial navigation error compensation accuracy experiment system is built, and the validity and superiority of the method proposed in this paper are verified through calculation and analysis of the data collected on the actual tunneling work face.
Citation: Axioms
PubDate: 2021-09-14
DOI: 10.3390/axioms10030224
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 225: An Expository Lecture of María Jesús Chasco
on Some Applications of Fubini’s Theorem
Authors: Alberto Castejón, María Jesús Chasco, Eusebio Corbacho, Virgilio Rodríguez de Miguel
First page: 225
Abstract: The usefulness of Fubini’s theorem as a measurement instrument is clearly understood from its multiple applications in Analysis, Convex Geometry, Statistics or Number Theory. This article is an expository paper based on a master class given by the second author at the University of Vigo and is devoted to presenting some Applications of Fubini’s theorem. In the first part, we present Brunn–Minkowski’s and Isoperimetric inequalities. The second part is devoted to the estimations of volumes of sections of balls in Rn.
Citation: Axioms
PubDate: 2021-09-14
DOI: 10.3390/axioms10030225
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 226: Closed-Form Solutions of Linear Ordinary
Differential Equations with General Boundary Conditions
Authors: Efthimios Providas, Stefanos Zaoutsos, Ioannis Faraslis
First page: 226
Abstract: This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.
Citation: Axioms
PubDate: 2021-09-14
DOI: 10.3390/axioms10030226
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 227: Chaotic Dynamics by Some Quadratic Jerk
Systems
Authors: Mei Liu, Bo Sang, Ning Wang, Irfan Ahmad
First page: 227
Abstract: This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.
Citation: Axioms
PubDate: 2021-09-14
DOI: 10.3390/axioms10030227
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 228: Mathematical Modeling and Forecasting of
COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo
Sense with Power-Law
Authors: Mdi Begum Jeelani, Abeer S. Alnahdi, Mohammed S. Abdo, Mansour A. Abdulwasaa, Kamal Shah, Hanan A. Wahash
First page: 228
Abstract: This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.
Citation: Axioms
PubDate: 2021-09-15
DOI: 10.3390/axioms10030228
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 229: Statistical Riemann and Lebesgue Integrable
Sequence of Functions with Korovkin-Type Approximation Theorems
Authors: Hari Mohan Srivastava, Bidu Bhusan Jena, Susanta Kumar Paikray
First page: 229
Abstract: In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.
Citation: Axioms
PubDate: 2021-09-16
DOI: 10.3390/axioms10030229
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 230: The Approximate and Analytic Solutions of the
Time-Fractional Intermediate Diffusion Wave Equation Associated with the
Fokker–Planck Operator and Applications
Authors: Entsar A. Abdel-Rehim
First page: 230
Abstract: In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the three-term time-fractional equation. The explicit expressions for the Green function G3(t) of the three-term time-fractional wave equation with constant coefficients is also studied for two physical and biological models. The explicit analytic solutions, for the two studied models, are expressed in terms of the Weber, hypergeometric, exponential, and Mittag–Leffler functions. The relation to the diffusion equation is given. The asymptotic behaviors of the Mittag–Leffler function, the hypergeometric function 1F1, and the exponential functions are compared numerically. The Grünwald–Letnikov scheme is used to derive the approximate difference schemes of the Caputo time-fractional operator and the Feller–Riesz space-fractional operator. The explicit difference scheme is numerically studied, and the simulations of the approximate solutions are plotted for different values of the fractional orders.
Citation: Axioms
PubDate: 2021-09-17
DOI: 10.3390/axioms10030230
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 231: Fixed Point Results for Frum-Ketkov Type
Contractions in b-Metric Spaces
Authors: Cristian Chifu, Erdal Karapınar, Gabriela Petrusel
First page: 231
Abstract: The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.
Citation: Axioms
PubDate: 2021-09-18
DOI: 10.3390/axioms10030231
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 232: Two Forms of An Inverse Operator to the
Generalized Bessel Potential
Authors: Akhmed Dzhabrailov, Yuri Luchko, Elina Shishkina
First page: 232
Abstract: In this paper, we treat a convolution-type operator called the generalized Bessel potential. Our main result is the derivation of two different forms of its inversion. The first inversion is provided in terms of an approximative inverse operator using the method of an improving multiplier. The second one employs the regularization technique for the divergent integrals in the form of the appropriate segments of the Taylor–Delsarte series.
Citation: Axioms
PubDate: 2021-09-18
DOI: 10.3390/axioms10030232
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 233: On r-Noncommuting Graph of Finite Rings
Authors: Rajat Kanti Nath, Monalisha Sharma, Parama Dutta, Yilun Shang
First page: 233
Abstract: Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is a simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and only if [x,y]≠r and [x,y]≠−r. In this paper, we obtain expressions for vertex degrees and show that ΓRr is neither a regular graph nor a lollipop graph if R is noncommutative. We characterize finite noncommutative rings such that ΓRr is a tree, in particular a star graph. It is also shown that ΓR1r and ΓR2ψ(r) are isomorphic if R1 and R2 are two isoclinic rings with isoclinism (ϕ,ψ). Further, we consider the induced subgraph ΔRr of ΓRr (induced by the non-central elements of R) and obtain results on clique number and diameter of ΔRr along with certain characterizations of finite noncommutative rings such that ΔRr is n-regular for some positive integer n. As applications of our results, we characterize certain finite noncommutative rings such that their noncommuting graphs are n-regular for n≤6.
Citation: Axioms
PubDate: 2021-09-19
DOI: 10.3390/axioms10030233
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 234: On Solvability Conditions for a Certain
Conjugation Problem
Authors: Vladimir Vasilyev, Nikolai Eberlein
First page: 234
Abstract: We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.
Citation: Axioms
PubDate: 2021-09-20
DOI: 10.3390/axioms10030234
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 235: Integral Characterizations for Uniform
Stability with Growth Rates in Banach Spaces
Authors: Rovana Boruga (Toma), Mihail Megan, Daniela Maria-Magdalena Toth
First page: 235
Abstract: The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be uniform h- stable. As particular cases of this notion, we obtain four characterizations for uniform exponential stability and two characterizations for uniform polynomial stability.
Citation: Axioms
PubDate: 2021-09-21
DOI: 10.3390/axioms10030235
Issue No: Vol. 10, No. 3 (2021)
- Axioms, Vol. 10, Pages 236: Mellin Transform of Logarithm and Quotient
Authors: Robert Reynolds, Allan Stauffer
First page: 236
Abstract: A class of definite integrals involving a quotient function with a reducible polynomial, logarithm and nested logarithm functions are derived with a possible connection to contact problems for a wedge. The derivations are expressed in terms of the Lerch function. Special cases are also derived in terms fundamental constants. The majority of the results in this work are new.
Citation: Axioms
PubDate: 2021-09-21
DOI: 10.3390/axioms10030236
Issue No: Vol. 10, No. 3 (2021)