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Axioms, Volume 7, Issue 4 (December 2018)

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Displaying articles 1-26
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Open AccessArticle A Metric for Finite Power Multisets of Positive Real Numbers Based on Minimal Matching
Received: 17 September 2018 / Revised: 2 December 2018 / Accepted: 12 December 2018 / Published: 14 December 2018
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Abstract
In this article, we show how to define a metric on the finite power multisets of positive real numbers. The metric, based on the minimal matching, consists of two parts: the matched part and the mismatched part. We also give some concrete applications [...] Read more.
In this article, we show how to define a metric on the finite power multisets of positive real numbers. The metric, based on the minimal matching, consists of two parts: the matched part and the mismatched part. We also give some concrete applications and examples to demonstrate the validity of this metric. Full article
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Open AccessArticle Diffeomorphisms with Shadowable Measures
Received: 8 November 2018 / Accepted: 5 December 2018 / Published: 7 December 2018
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Abstract
In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the C1-interior of the set [...] Read more.
In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the C 1 -interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity. Full article
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
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Open AccessArticle Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives
Received: 4 November 2018 / Revised: 25 November 2018 / Accepted: 28 November 2018 / Published: 1 December 2018
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Abstract
We introduce the concept of regional enlarged observability for fractional evolution differential equations involving Riemann–Liouville derivatives. The Hilbert Uniqueness Method (HUM) is used to reconstruct the initial state between two prescribed functions, in an interested subregion of the whole domain, without the knowledge [...] Read more.
We introduce the concept of regional enlarged observability for fractional evolution differential equations involving Riemann–Liouville derivatives. The Hilbert Uniqueness Method (HUM) is used to reconstruct the initial state between two prescribed functions, in an interested subregion of the whole domain, without the knowledge of the state. Full article
(This article belongs to the Special Issue Fractional Differential Equations)
Open AccessReview Stability Issues for Selected Stochastic Evolutionary Problems: A Review
Received: 1 May 2018 / Revised: 13 November 2018 / Accepted: 21 November 2018 / Published: 1 December 2018
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Abstract
We review some recent contributions of the authors regarding the numerical approximation of stochastic problems, mostly based on stochastic differential equations modeling random damped oscillators and stochastic Volterra integral equations. The paper focuses on the analysis of selected stability issues, i.e., the preservation [...] Read more.
We review some recent contributions of the authors regarding the numerical approximation of stochastic problems, mostly based on stochastic differential equations modeling random damped oscillators and stochastic Volterra integral equations. The paper focuses on the analysis of selected stability issues, i.e., the preservation of the long-term character of stochastic oscillators over discretized dynamics and the analysis of mean-square and asymptotic stability properties of ϑ -methods for Volterra integral equations. Full article
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Open AccessArticle Special Types of Locally Conformal Closed G2-Structures
Received: 30 October 2018 / Revised: 23 November 2018 / Accepted: 23 November 2018 / Published: 28 November 2018
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Abstract
Motivated by known results in locally conformal symplectic geometry, we study different classes of G2-structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G2-structures on simply connected [...] Read more.
Motivated by known results in locally conformal symplectic geometry, we study different classes of G 2 -structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G 2 -structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G 2 -structures. Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
Open AccessArticle A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem
Received: 16 September 2018 / Revised: 13 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
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Abstract
We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional [...] Read more.
We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included. Full article
(This article belongs to the Special Issue Applications of Differential Equations and Dynamical Systems)
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Open AccessArticle Exponentially Harmonic Maps into Spheres
Received: 29 October 2018 / Revised: 16 November 2018 / Accepted: 18 November 2018 / Published: 22 November 2018
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Abstract
We study smooth exponentially harmonic maps from a compact, connected, orientable Riemannian manifold M into a sphere SmRm+1. Given a codimension two totally geodesic submanifold ΣSm, we show that every nonconstant exponentially [...] Read more.
We study smooth exponentially harmonic maps from a compact, connected, orientable Riemannian manifold M into a sphere S m R m + 1 . Given a codimension two totally geodesic submanifold Σ S m , we show that every nonconstant exponentially harmonic map ϕ : M S m either meets or links Σ . If H 1 ( M , Z ) = 0 then ϕ ( M ) Σ . Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
Open AccessArticle Extended Partial Sb-Metric Spaces
Received: 18 October 2018 / Revised: 17 November 2018 / Accepted: 18 November 2018 / Published: 21 November 2018
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Abstract
In this paper, we introduce the concept of extended partial Sb-metric spaces, which is a generalization of the extended Sb-metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric [...] Read more.
In this paper, we introduce the concept of extended partial S b -metric spaces, which is a generalization of the extended S b -metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric spaces generalize many results in the literature. Moreover, we prove some fixed point theorems under some different contractions, and some examples are given to illustrate our results. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
Open AccessArticle Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets
Received: 31 July 2018 / Revised: 21 October 2018 / Accepted: 5 November 2018 / Published: 16 November 2018
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Abstract
We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets having the following “selective” compactness property: For [...] Read more.
We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets having the following “selective” compactness property: For each free ultrafilter p on the set N of natural numbers and every sequence ( U n ) of non-empty open subsets of G, one can choose a point x n U n for all n N in such a way that the resulting sequence ( x n ) has a p-limit in G; that is, { n N : x n V } p for every neighbourhood V of x in G. In particular, G is selectively pseudocompact (strongly pseudocompact) but not selectively sequentially pseudocompact. This answers a question of Dorantes-Aldama and the first listed author. The group G above is not pseudo- ω -bounded either. Furthermore, we show that the free precompact Boolean group of a topological sum i I X i , where each space X i is either maximal or discrete, contains no infinite separable pseudocompact subsets. Full article
(This article belongs to the collection Topological Groups) Printed Edition available
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Open AccessArticle Unification Theories: Examples and Applications
Received: 24 October 2018 / Revised: 13 November 2018 / Accepted: 13 November 2018 / Published: 16 November 2018
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Abstract
We consider several unification problems in mathematics. We refer to transcendental numbers. Furthermore, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
Open AccessArticle Equicontinuity, Expansivity, and Shadowing for Linear Operators
Received: 22 September 2018 / Revised: 9 November 2018 / Accepted: 11 November 2018 / Published: 15 November 2018
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Abstract
We prove that a linear operator of a complex Banach space has a shadowable point if and only if it has the shadowing property. In addition, every equicontinuous linear operator does not have the shadowing property and its spectrum is contained in the [...] Read more.
We prove that a linear operator of a complex Banach space has a shadowable point if and only if it has the shadowing property. In addition, every equicontinuous linear operator does not have the shadowing property and its spectrum is contained in the unit circle. Finally, we prove that if a linear operator is expansive and has the shadowing property, then the origin is the only nonwandering point. Full article
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
Open AccessArticle Application of Neutrosophic Soft Sets to K-Algebras
Received: 1 October 2018 / Revised: 2 November 2018 / Accepted: 2 November 2018 / Published: 12 November 2018
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Abstract
Neutrosophic sets and soft sets are two different mathematical tools for representing vagueness and uncertainty. We apply these models in combination to study vagueness and uncertainty in K-algebras. We introduce the notion of single-valued neutrosophic soft (SNS) K-algebras and investigate some [...] Read more.
Neutrosophic sets and soft sets are two different mathematical tools for representing vagueness and uncertainty. We apply these models in combination to study vagueness and uncertainty in K-algebras. We introduce the notion of single-valued neutrosophic soft (SNS) K-algebras and investigate some of their properties. We establish the notion of ( , q ) -single-valued neutrosophic soft K-algebras and describe some of their related properties. We also illustrate the concepts with numerical examples. Full article
(This article belongs to the Special Issue Neutrosophic Topology)
Open AccessEditorial Mathematical Analysis and Applications
Received: 7 November 2018 / Accepted: 7 November 2018 / Published: 12 November 2018
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Abstract
Website: http://www.math.uvic.ca/faculty/harimsri/ [...] Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications) Printed Edition available
Open AccessArticle The Generalized Schur Algorithm and Some Applications
Received: 2 October 2018 / Revised: 5 November 2018 / Accepted: 7 November 2018 / Published: 9 November 2018
Cited by 1 | Viewed by 612 | PDF Full-text (361 KB) | HTML Full-text | XML Full-text
Abstract
The generalized Schur algorithm is a powerful tool allowing to compute classical decompositions of matrices, such as the QR and LU factorizations. When applied to matrices with particular structures, the generalized Schur algorithm computes these factorizations with a complexity of one [...] Read more.
The generalized Schur algorithm is a powerful tool allowing to compute classical decompositions of matrices, such as the Q R and L U factorizations. When applied to matrices with particular structures, the generalized Schur algorithm computes these factorizations with a complexity of one order of magnitude less than that of classical algorithms based on Householder or elementary transformations. In this manuscript, we describe the main features of the generalized Schur algorithm. We show that it helps to prove some theoretical properties of the R factor of the Q R factorization of some structured matrices, such as symmetric positive definite Toeplitz and Sylvester matrices, that can hardly be proven using classical linear algebra tools. Moreover, we propose a fast implementation of the generalized Schur algorithm for computing the rank of Sylvester matrices, arising in a number of applications. Finally, we propose a generalized Schur based algorithm for computing the null-space of polynomial matrices. Full article
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Open AccessArticle On the Fixed-Circle Problem and Khan Type Contractions
Received: 18 October 2018 / Revised: 31 October 2018 / Accepted: 5 November 2018 / Published: 8 November 2018
Cited by 1 | Viewed by 357 | PDF Full-text (240 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of FC-Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the [...] Read more.
In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of F C -Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the common fixed-circle problem. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
Open AccessArticle Extending Characters of Fixed Point Algebras
Received: 13 October 2018 / Revised: 2 November 2018 / Accepted: 5 November 2018 / Published: 7 November 2018
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Abstract
A dynamical system is a triple (A,G,α) consisting of a unital locally convex algebra A, a topological group G, and a group homomorphism α:GAut(A) that induces a continuous [...] Read more.
A dynamical system is a triple ( A , G , α ) consisting of a unital locally convex algebra A, a topological group G, and a group homomorphism α : G Aut ( A ) that induces a continuous action of G on A. Furthermore, a unital locally convex algebra A is called a continuous inverse algebra, or CIA for short, if its group of units A × is open in A and the inversion map ι : A × A × , a a 1 is continuous at 1 A . Given a dynamical system ( A , G , α ) with a complete commutative CIA A and a compact group G, we show that each character of the corresponding fixed point algebra can be extended to a character of A. Full article
(This article belongs to the collection Topological Groups) Printed Edition available
Open AccessArticle Consistency Properties for Fuzzy Choice Functions: An Analysis with the Łukasiewicz T-Norm
Received: 10 August 2018 / Revised: 22 October 2018 / Accepted: 25 October 2018 / Published: 29 October 2018
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Abstract
We focus on the relationships among some consistency axioms in the framework of fuzzy choice functions. In order to help disclose the role of the t-norm in existing analyses, we start to study the situation that arises when we replace the standard t-norm [...] Read more.
We focus on the relationships among some consistency axioms in the framework of fuzzy choice functions. In order to help disclose the role of the t-norm in existing analyses, we start to study the situation that arises when we replace the standard t-norm with other t-norms. Our results allow us to conclude that unless we impose further structure on the domain of application for the choices, the use of the Łukasiewicz t-norm as a replacement for the standard t-norm does not guarantee a better performance. Full article
Open AccessArticle A Note on the Topological Group c0
Received: 28 September 2018 / Revised: 22 October 2018 / Accepted: 24 October 2018 / Published: 29 October 2018
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Abstract
A well-known result of Ferri and Galindo asserts that the topological group c0 is not reflexively representable and the algebra WAP(c0) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if [...] Read more.
A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions. Full article
(This article belongs to the collection Topological Groups) Printed Edition available
Open AccessArticle On the Shape Differentiability of Objectives: A Lagrangian Approach and the Brinkman Problem
Received: 26 September 2018 / Revised: 23 October 2018 / Accepted: 25 October 2018 / Published: 27 October 2018
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Abstract
This paper establishes the shape derivative of geometry-dependent objective functions for use in constrained variational problems. Using a Lagrangian approach, our differentiablity result is based on the theorem of Delfour–Zolésio on directional derivatives with respect to a parameter of shape perturbation. As the [...] Read more.
This paper establishes the shape derivative of geometry-dependent objective functions for use in constrained variational problems. Using a Lagrangian approach, our differentiablity result is based on the theorem of Delfour–Zolésio on directional derivatives with respect to a parameter of shape perturbation. As the key issue of the paper, we analyze the bijection under the kinematic transport of geometries that is needed for function spaces and feasible sets involved in variational problems. Our abstract theoretical result is applied to the Brinkman flow problem under incompressibility and mixed Dirichlet–Neumann boundary conditions, and provides an analytic formula of the shape derivative based on the velocity method. Full article
(This article belongs to the Special Issue Applications of Differential Equations and Dynamical Systems)
Open AccessReview Selective Survey on Spaces of Closed Subgroups of Topological Groups
Received: 8 October 2018 / Revised: 24 October 2018 / Accepted: 24 October 2018 / Published: 26 October 2018
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Abstract
We survey different topologizations of the set S(G) of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics. [...] Read more.
We survey different topologizations of the set S ( G ) of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics. Full article
(This article belongs to the collection Topological Groups) Printed Edition available
Open AccessArticle Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces
Received: 18 September 2018 / Revised: 14 October 2018 / Accepted: 15 October 2018 / Published: 25 October 2018
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Abstract
The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty (α,ψ,ϕ)-quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show [...] Read more.
The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II)
Open AccessArticle On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model
Received: 18 September 2018 / Revised: 13 October 2018 / Accepted: 17 October 2018 / Published: 19 October 2018
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Abstract
Tickysim is a clock tick-based simulator for the inter-chip interconnection network of the SpiNNaker architecture. Network devices such as arbiters, routers, and packet generators store, read, and write forward data through fixed-length FIFO buffers. At each clock tick, every component executes a “read” [...] Read more.
Tickysim is a clock tick-based simulator for the inter-chip interconnection network of the SpiNNaker architecture. Network devices such as arbiters, routers, and packet generators store, read, and write forward data through fixed-length FIFO buffers. At each clock tick, every component executes a “read” phase followed by a “write” phase. The structures of any finite graph which represents numerical quantities are known as topological indices. In this paper, we compute degree-based topological indices of the Tickysim SpiNNaker Model ( T S M ) sheet. Full article
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Open AccessArticle The Role of Spin(9) in Octonionic Geometry
Received: 20 September 2018 / Revised: 4 October 2018 / Accepted: 6 October 2018 / Published: 12 October 2018
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Abstract
Starting from the 2001 Thomas Friedrich’s work on Spin(9), we review some interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical [...] Read more.
Starting from the 2001 Thomas Friedrich’s work on Spin ( 9 ) , we review some interactions between Spin ( 9 ) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin ( 9 ) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin ( 9 ) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin ( 9 ) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley–Rosenfeld planes and to three series of Grassmannians. Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
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Open AccessArticle New Bell–Sheffer Polynomial Sets
Received: 20 July 2018 / Accepted: 2 October 2018 / Published: 8 October 2018
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Abstract
In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results [...] Read more.
In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results by Dattoli and Ben Cheikh on the monomiality principle, showing the possibility to derive explicitly the main properties of Sheffer polynomial families starting from the basic elements of their generating functions. The introduction of iterated exponential and logarithmic functions allows to construct new sets of Bell–Sheffer polynomials which exhibit an iterative character of the obtained shift operators and differential equations. In this context, it is possible, for every integer r, to define polynomials of higher type, which are linked to the higher order Bell-exponential and logarithmic numbers introduced in preceding papers. Connections with integer sequences appearing in Combinatorial analysis are also mentioned. Naturally, the considered technique can also be used in similar frameworks, where the iteration of exponential and logarithmic functions appear. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications) Printed Edition available
Open AccessArticle A New Efficient Method for the Numerical Solution of Linear Time-Dependent Partial Differential Equations
Received: 5 August 2018 / Revised: 21 September 2018 / Accepted: 28 September 2018 / Published: 1 October 2018
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Abstract
This paper presents a new efficient method for the numerical solution of a linear time-dependent partial differential equation. The proposed technique includes the collocation method with Legendre wavelets for spatial discretization and the three-step Taylor method for time discretization. This procedure is third-order [...] Read more.
This paper presents a new efficient method for the numerical solution of a linear time-dependent partial differential equation. The proposed technique includes the collocation method with Legendre wavelets for spatial discretization and the three-step Taylor method for time discretization. This procedure is third-order accurate in time. A comparative study between the proposed method and the one-step wavelet collocation method is provided. In order to verify the stability of these methods, asymptotic stability analysis is employed. Numerical illustrations are investigated to show the reliability and efficiency of the proposed method. An important property of the presented method is that unlike the one-step wavelet collocation method, it is not necessary to choose a small time step to achieve stability. Full article
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
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Open AccessArticle Periodically Forced Nonlinear Oscillatory Acoustic Vacuum
Received: 31 July 2018 / Revised: 14 September 2018 / Accepted: 19 September 2018 / Published: 22 September 2018
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Abstract
In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced system. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications) Printed Edition available
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