Axioms, Volume 7, Issue 4

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 application...

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 $C^1$ -...

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 pape...

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 prescr...

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 c...

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 regula...

We study smooth exponentially harmonic maps from a compact, connected, orientable Riemannian manifold M into a sphere $S^m\subset {\mathbb{R}}^{m+1}$ . Given a codimension two totally geodesic submanifold $\Sigma \subset S^m$ , we show that ev...

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 pr...

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.

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 h...

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...

Website: http://www.math.uvic.ca/faculty/harimsri/ [...]

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 neutrosop...

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...

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 t...

A dynamical system is a triple $(A,G,\alpha )$ consisting of a unital locally convex algebra A, a topological group G, and a group homomorphism $\alpha :G\to Aut\left(A\right)$ that induces a continuous action of G on A. Furthermore,...

A well-known result of Ferri and Galindo asserts that the topological group $c_0$ is not reflexively representable and the algebra WAP $\left(c_0\right)$ of weakly almost periodic functions does not separate points and closed subsets. However, it...

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-...

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 dir...

We survey different topologizations of the set $\mathcal{S}\left(G\right)$ of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics.

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty $(\alpha ,\psi ,\varphi )$ -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an appli...

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....

Starting from the 2001 Thomas Friedrich’s work on $\mathrm{Spin}\left(9\right)$ , we review some interactions between $\mathrm{Spin}\left(9\right)$ and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the $\mathrm{Spin}(9$...

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 prece...

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-ste...

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.