Mathematics, Volume 5, Issue 4

The characteristic polynomial (ChP) has found its use in the characterization of chemical compounds since Hückel’s method of molecular orbitals. In order to discriminate the atoms of different elements and different bonds, an extension of the classic...

The article is devoted to reflexive Müntz spaces $M_{\Lambda ,p}$...

In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains. We show that the product of generator matrices of codes over the rings mod a and mod b produces gen...

The notions of hyperfuzzy ideals in $BCK/BCI$ -algebras are introduced, and related properties are investigated. Characterizations of hyperfuzzy ideals are established. Relations between hyperfuzzy ideals and hyperfuzzy subalgebras are dis...

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when ${\mathcal{R}}_0$ , th...

We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matr...

We prove the generalized Hyers–Ulam stability of a mean value type functional equation $f\left(x\right)-g\left(y\right)=(x-y)h(x+y)$ by applying a method originated from fixed point theory.

We apply the reproducing kernel method and group preserving scheme for investigating the Lane–Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These ap...

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the...

In this paper, we construct a free semicircular family induced by $\left|\mathbb{Z}\right|$ -many mutually-orthogonal projections, and construct Banach ∗-probabili...

The classical Lagrange-d’Alembert principle had a decisive influence on formation of modern analytical mechanics which culminated in modern Hamilton and Poisson mechanics. Being mainly interested in the geometric interpretation of this principle, we...

The high gain free electron laser (FEL) equation is a Volterra type integro-differential equation amenable for analytical solutions in a limited number of cases. In this note, a novel technique, based on an expansion employing a family of two variabl...

In this paper, we introduce a generalization of a bipolar fuzzy (BF) subsemigroup, namely, a $({\alpha }_1,{\alpha }_2;{\beta }_1,{\beta }_2)$ -BF subsemigroup. The notions of $({\alpha }_1,{\alpha }_2;{\beta }_1,{\beta }_2)$ -BF quasi(generalized bi-, bi-) ideals are...

In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to...

Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective. One famous e...

Semi-arid ecosystems made up of patterned vegetation, for instance, are thought to be highly sensitive. This highlights the importance of understanding the dynamics of the formation of vegetation patterns. The most renowned mathematical model describ...

One major concern of channel engineering in nanotransistors is the coupling of the conduction channel to the source/drain contacts. In a number of previous publications, we have developed a semiempirical quantum model in quantitative agreement with t...

With fractional differential equations (FDEs) rising in popularity and methods for solving them still being developed, approximations to solutions of fractional initial value problems (IVPs) have great applications in related fields. This paper prove...

We study an edge irregular reflexive k-labelling for the generalized friendship graphs, also known as flowers (a symmetric collection of cycles meeting at a common vertex), and determine the exact value of the reflexive edge strength for several subf...

We consider a generalized Langevin equation with regularized Prabhakar derivative operator. We analyze the mean square displacement, time-dependent diffusion coefficient and velocity autocorrelation function. We further introduce the so-called temper...

In this work, we aim to formalize the inception of representative bubbles giving the condition under which they may arise. We will find that representative bubbles may start at any time, depending on the definition of a behavioral component. This res...

Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to eff...

The particular solutions of inhomogeneous differential equations with polynomial coefficients in terms of the Green’s function are obtained in the framework of distribution theory. In particular, discussions are given on Kummer’s and the hypergeometr...

This paper studies fractional differential equations (FDEs) with mixed fractional derivatives. Existence, uniqueness, stability, and asymptotic results are derived.

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate...

Let S be a polynomial ring in n variables over a field K of any characteristic. Given a strongly stable submodule M of a finitely generated graded free S-module F, we propose a method for constructing a standard Borel-fixed submodule $\tilde{M}$ of F...

This study introduces a procedure to obtain all interpolating functions, $y=f\left(x\right)$ , subject to linear constraints on the function and its derivatives defined at specified values. The paper first shows how to express these interpolating func...

Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are comp...

Compartmental epidemic models are intriguing in the sense that the generic model may explain different kinds of infectious diseases with minor modifications. However, there may exist some ailments that may not fit the generic capsule. Amoebiasis is o...

The paper contributes to stabilization problems of linear systems subject to time-varying delays. Drawing upon small gain criteria and robust analysis techniques, upper and lower bounds on the largest allowable time-varying delay are developed by usi...

The Radial Basis Function (RBF) method has been considered an important meshfree tool for numerical solutions of Partial Differential Equations (PDEs). For various situations, RBF with infinitely differentiable functions can provide accurate results...

In this paper, we prove the stability of the following functional equation ${\sum }_{i=0}^n{}_n{C}_i{(-1)}^{n-i}f(ix+y)-n!f\left(x\right)=0$ on a restricted domain by employing the direct method in the sense of Hyers.

We consider the Gauss–Manin differential equations for hypergeometric integrals associated with a family of weighted arrangements of hyperplanes moving parallel to themselves. We reduce these equations modulo a prime integer p and construct polynomia...

The position vector field is the most elementary and natural geometric object on a Euclidean submanifold. The position vector field plays important roles in physics, in particular in mechanics. For instance, in any equation of motion, the position ve...

In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation ${\partial }_{t}u-\mathrm{div}a(x,t,\nabla u)+{\lambda (|u|}^{p(x,t)-2}u)=0\mathrm{in}{\Omega }_T,$ where $\lambda \ge 0$ and ${\partial }_{t}u$ denot...

Cancer is a disease of unregulated cell growth that is estimated to kill over 600,000 people in the United States in 2017 according to the National Institute of Health. While there are several therapies to treat cancer, tumor resistance to these ther...

This study shows how to obtain least-squares solutions to initial value problems (IVPs), boundary value problems (BVPs), and multi-value problems (MVPs) for nonhomogeneous linear differential equations (DEs) with nonconstant coefficients of any order...

This paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is shown. The appr...