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Axioms, Volume 9, Issue 3 (September 2020) – 24 articles

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Open AccessArticle
Fractional Singular Differential Systems of Lane–Emden Type: Existence and Uniqueness of Solutions
Axioms 2020, 9(3), 95; https://doi.org/10.3390/axioms9030095 - 02 Aug 2020
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Abstract
A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution [...] Read more.
A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
Open AccessArticle
Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers
Axioms 2020, 9(3), 94; https://doi.org/10.3390/axioms9030094 - 01 Aug 2020
Viewed by 170
Abstract
We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures [...] Read more.
We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-Kähler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5C6C12 of Chinea-González classification. Full article
(This article belongs to the Special Issue Pseudo-Riemannian Metrics and Applications)
Open AccessArticle
On the Triple Lauricella–Horn–Karlsson q-Hypergeometric Functions
Axioms 2020, 9(3), 93; https://doi.org/10.3390/axioms9030093 - 31 Jul 2020
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Abstract
The Horn–Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are [...] Read more.
The Horn–Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are replaced by Ward q-additions. Mostly referring to Krishna Srivastava 1956, we give q-integral representations for these functions. Full article
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Open AccessArticle
A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty
Axioms 2020, 9(3), 92; https://doi.org/10.3390/axioms9030092 (registering DOI) - 30 Jul 2020
Viewed by 147
Abstract
A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order [...] Read more.
A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples. Full article
(This article belongs to the Special Issue Isogeometric Analysis Theory and Applications)
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Open AccessArticle
Feedback Diagram Application for the Generation and Solution of Linear Differential Equations Solvable by Quadrature
Axioms 2020, 9(3), 91; https://doi.org/10.3390/axioms9030091 - 29 Jul 2020
Viewed by 151
Abstract
A novel method for generating and providing quadrature solutions to families of linear, second-order, ordinary differential equations is presented in this paper. It is based upon a comparison of control system feedback diagrams—one representing the system and equation under study and a second [...] Read more.
A novel method for generating and providing quadrature solutions to families of linear, second-order, ordinary differential equations is presented in this paper. It is based upon a comparison of control system feedback diagrams—one representing the system and equation under study and a second equalized to it and providing solutions. The resulting Riccati equation connection between them is utilized to generate and solve groups of equations parameterized by arbitrary functions and constants. This method also leads to a formal solution mechanism for all second-order linear differential equations involving an infinite series of integrals of each equation’s Schwarzian derivative. The practicality of this mechanism is strongly dependent on the series rates of and allowed regions for convergence. The feedback diagram method developed is shown to be equivalent to a comparable method based on the differential equation’s normal form and another relying upon the grouping of terms for a reduction of the equation order, but augmenting their results. Applications are also made to the Helmholtz equation. Full article
(This article belongs to the collection Mathematical Analysis and Applications)
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Open AccessArticle
Stochastic Process Emerged from Lattice Fermion Systems by Repeated Measurements and Long-Time Limit
Axioms 2020, 9(3), 90; https://doi.org/10.3390/axioms9030090 - 29 Jul 2020
Viewed by 150
Abstract
It is known that, in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the ‘Quantum Zeno Effect’. This is the phenomena that, if one performs the measurements M times asking whether the system is in the same [...] Read more.
It is known that, in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the ‘Quantum Zeno Effect’. This is the phenomena that, if one performs the measurements M times asking whether the system is in the same state as the one at the initial time until the fixed measurement time t, then survival probability tends to 1 by taking the limit M. This is the case for fixed measurement time t. It is known that, if one takes measurement time infinite at appropriate scaling, the ‘Quantum Zeno Effect’ does not occur and the effect of Hamiltonian dynamics emerges. In the present paper, we consider the long time repeated measurements and the dynamics of quantum many body systems in the scaling where the effect of measurements and dynamics are balanced. We show that the stochastic process, called the symmetric simple exclusion process (SSEP), is obtained from the repeated and long time measurements of configuration of particles in finite lattice fermion systems. The emerging stochastic process is independent of potential and interaction of the underlying Hamiltonian of the system. Full article
(This article belongs to the Special Issue Quantum Information, Foundations and Measurement)
Open AccessArticle
The Modified Helmholtz Equation on a Regular Hexagon—The Symmetric Dirichlet Problem
Axioms 2020, 9(3), 89; https://doi.org/10.3390/axioms9030089 - 28 Jul 2020
Viewed by 151
Abstract
Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by the same function on [...] Read more.
Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by the same function on each side of the hexagon. We show that if this function is odd, then this problem can be solved in closed form; numerical verification is also provided. Full article
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Open AccessArticle
Reconstruction of Piecewise Smooth Multivariate Functions from Fourier Data
Axioms 2020, 9(3), 88; https://doi.org/10.3390/axioms9030088 - 24 Jul 2020
Viewed by 212
Abstract
In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving [...] Read more.
In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Padé-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
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Open AccessArticle
Commutative Topological Semigroups Embedded into Topological Abelian Groups
Axioms 2020, 9(3), 87; https://doi.org/10.3390/axioms9030087 - 24 Jul 2020
Viewed by 241
Abstract
In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological [...] Read more.
In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity. Full article
(This article belongs to the Special Issue Topological Algebra)
Open AccessArticle
On the Regularized Asymptotics of a Solution to the Cauchy Problem in the Presence of a Weak Turning Point of the Limit Operator
Axioms 2020, 9(3), 86; https://doi.org/10.3390/axioms9030086 - 23 Jul 2020
Viewed by 210
Abstract
An asymptotic solution of the linear Cauchy problem in the presence of a "weak" turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given [...] Read more.
An asymptotic solution of the linear Cauchy problem in the presence of a "weak" turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given for ε that characterize the behavior of singularities for ϵ 0 . The asymptotic convergence of a regularized series is proven. The results are illustrated by an example. Bibliography: six titles. Full article
Open AccessArticle
Hybrid Ideals of BCK/BCI-Algebras
Axioms 2020, 9(3), 85; https://doi.org/10.3390/axioms9030085 - 23 Jul 2020
Viewed by 177
Abstract
The notion of hybrid ideals in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characterizations of hybrid ideals are considered. Based [...] Read more.
The notion of hybrid ideals in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characterizations of hybrid ideals are considered. Based on a hybrid structure, properties of special sets are investigated, and conditions for the special sets to be ideals are displayed. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
Open AccessArticle
Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic
Axioms 2020, 9(3), 84; https://doi.org/10.3390/axioms9030084 - 21 Jul 2020
Viewed by 181
Abstract
Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given [...] Read more.
Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults. Full article
(This article belongs to the Special Issue Deductive Systems)
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Open AccessArticle
Eigenfunction Families and Solution Bounds for Multiplicatively Advanced Differential Equations
Axioms 2020, 9(3), 83; https://doi.org/10.3390/axioms9030083 - 21 Jul 2020
Viewed by 208
Abstract
A family of Schwartz functions W ( t ) are interpreted as eigensolutions of MADEs in the sense that W ( δ ) ( t ) = E W ( q γ t ) where the eigenvalue E R is independent of [...] Read more.
A family of Schwartz functions W ( t ) are interpreted as eigensolutions of MADEs in the sense that W ( δ ) ( t ) = E W ( q γ t ) where the eigenvalue E R is independent of the advancing parameter q > 1 . The parameters δ , γ N are characteristics of the MADE. Some issues, which are related to corresponding q-advanced PDEs, are also explored. In the limit that q 1 + we show convergence of MADE eigenfunctions to solutions of ODEs, which involve only simple exponentials and trigonometric functions. The limit eigenfunctions ( q = 1 + ) are not Schwartz, thus convergence is only uniform in t R on compact sets. An asymptotic analysis is provided for MADEs which indicates how to extend solutions in a neighborhood of the origin t = 0 . Finally, an expanded table of Fourier transforms is provided that includes Schwartz solutions to MADEs. Full article
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Open AccessArticle
Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays
Axioms 2020, 9(3), 82; https://doi.org/10.3390/axioms9030082 - 18 Jul 2020
Viewed by 228
Abstract
An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, [...] Read more.
An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use. Full article
(This article belongs to the Special Issue Iterative Processes for Nonlinear Problems with Applications)
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Open AccessArticle
On Smoothness of the Solution to the Abel Equation in Terms of the Jacobi Series Coefficients
Axioms 2020, 9(3), 81; https://doi.org/10.3390/axioms9030081 - 17 Jul 2020
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Abstract
In this paper, we continue our study of the Abel equation with the right-hand side belonging to the Lebesgue weighted space. We have improved the previously known result— the existence and uniqueness theorem formulated in terms of the Jacoby series coefficients that gives [...] Read more.
In this paper, we continue our study of the Abel equation with the right-hand side belonging to the Lebesgue weighted space. We have improved the previously known result— the existence and uniqueness theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity to find and classify a solution by virtue of an asymptotic of some relation containing the Jacobi series coefficients of the right-hand side. The main results are the following—the conditions imposed on the parameters, under which the Abel equation has a unique solution represented by the series, are formulated; the relationship between the values of the parameters and the solution smoothness is established. The independence between one of the parameters and the smoothness of the solution is proved. Full article
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
Open AccessArticle
On the Uniqueness Classes of Solutions of Boundary Value Problems for Third-Order Equations of the Pseudo-Elliptic Type
Axioms 2020, 9(3), 80; https://doi.org/10.3390/axioms9030080 - 16 Jul 2020
Viewed by 169
Abstract
The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this [...] Read more.
The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this estimate, the uniqueness theorems were obtained for solutions of the first boundary value problem for third order equations in unlimited domains. The energy estimates are illustrated on two examples. Full article
Open AccessArticle
Anti-Intuitionistic Fuzzy Soft a-Ideals Applied to BCI-Algebras
Axioms 2020, 9(3), 79; https://doi.org/10.3390/axioms9030079 - 08 Jul 2020
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Abstract
The notion of anti-intuitionistic fuzzy soft a-ideals of B C I -algebras is introduced and several related properties are investigated. Furthermore, the operations, namely; AND, extended intersection, restricted intersection, and union on anti-intuitionistic fuzzy soft a-ideals are discussed. Finally, characterizations of anti-intuitionistic fuzzy [...] Read more.
The notion of anti-intuitionistic fuzzy soft a-ideals of B C I -algebras is introduced and several related properties are investigated. Furthermore, the operations, namely; AND, extended intersection, restricted intersection, and union on anti-intuitionistic fuzzy soft a-ideals are discussed. Finally, characterizations of anti-intuitionistic fuzzy soft a-ideals of B C I -algebras are given. Full article
(This article belongs to the Special Issue Softcomputing: Theories and Applications)
Open AccessArticle
On t-Conorm Based Fuzzy (Pseudo)metrics
Axioms 2020, 9(3), 78; https://doi.org/10.3390/axioms9030078 - 08 Jul 2020
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Abstract
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare [...] Read more.
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
Open AccessArticle
Facility Location Selection for B-Schools in Indian Context: A Multi-Criteria Group Decision Based Analysis
Axioms 2020, 9(3), 77; https://doi.org/10.3390/axioms9030077 - 08 Jul 2020
Viewed by 194
Abstract
Facility location is one of the critical strategic decisions for any organization. It not only carries the organization’s identity but also connects the point of origin and point of consumption. In the case of higher educational institutions, specifically B-Schools, location is one of [...] Read more.
Facility location is one of the critical strategic decisions for any organization. It not only carries the organization’s identity but also connects the point of origin and point of consumption. In the case of higher educational institutions, specifically B-Schools, location is one of the primary concerns for potential students and their parents while selecting an institution for pursuing higher education. There has been a plethora of research conducted to investigate the factors influencing the B-School selection decision-making. However, location as a standalone factor has not been widely studied. This paper aims to explore various location selection criteria from the viewpoint of the candidates who aspire to enroll in B-Schools. We apply an integrated group decision-making framework of pivot pairwise relative criteria importance assessment (PIPRECIA), and level-based weight assessment LBWA is used wherein a group of student counselors, admission executives, and educators from India has participated. The factors which influence the location decision are identified through qualitative opinion analysis. The results show that connectivity and commutation are the dominant issues. Full article
(This article belongs to the Special Issue Softcomputing: Theories and Applications)
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Open AccessArticle
Mindfulness Model Using Polariton Oscillation in Plasmonic Circuit for Human Performance Management
Axioms 2020, 9(3), 76; https://doi.org/10.3390/axioms9030076 - 08 Jul 2020
Viewed by 258
Abstract
We have proposed that human life is formed on a space and time function relationship basis, which is distorted after fertilization in the ovum, from which growth is generated by a space–time distortion against the universe’s gravity. A space–time distortion’s reduction can be [...] Read more.
We have proposed that human life is formed on a space and time function relationship basis, which is distorted after fertilization in the ovum, from which growth is generated by a space–time distortion against the universe’s gravity. A space–time distortion’s reduction can be managed by space and time separation, which is known as mindfulness. A space–time distortion in human cells is configured by a polariton traveling in a gold grating film, which can be employed to investigate mindfulness characteristics. Mindfulness is the steady state of the time function of energy after the separation. Energy levels of mindfulness based on polariton aspects are categorized by a quantum number (n), which can be reduced to be a two-level system called Rabi oscillation by a successive filtering method. We have assumed a cell space–time distortion can reduce to reach the original state, which is the stopping state. Mindfulness with a certain frequency energy level of n = 2 was achieved. Several techniques in the practice of mindfulness based on successive filtering called meditation are given and explained, where the required levels of the mindfulness state can be achieved. The criteria of the proposed method are a low energy level (n) and high frequency (f) outputs, which can apply to having a working performance improvement. Full article
(This article belongs to the collection Mathematical Analysis and Applications)
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Open AccessArticle
On the Periodicity of General Class of Difference Equations
Axioms 2020, 9(3), 75; https://doi.org/10.3390/axioms9030075 - 01 Jul 2020
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Abstract
In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this [...] Read more.
In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method. Full article
Open AccessArticle
Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations
Axioms 2020, 9(3), 74; https://doi.org/10.3390/axioms9030074 - 01 Jul 2020
Viewed by 256
Abstract
We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics [...] Read more.
We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method. Full article
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Approximating Functions of Positive Compact Operators by Using Bell Polynomials
Axioms 2020, 9(3), 73; https://doi.org/10.3390/axioms9030073 - 30 Jun 2020
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Abstract
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value [...] Read more.
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
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Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles
Axioms 2020, 9(3), 72; https://doi.org/10.3390/axioms9030072 - 30 Jun 2020
Viewed by 207
Abstract
In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base [...] Read more.
In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics). Full article
(This article belongs to the Special Issue Pseudo-Riemannian Metrics and Applications)
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