Ural Mathematical Journal (UMJ)
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A REMARK AND AN IMPROVED VERSION ON RECENT RESULTS CONCERNING RATIONAL FUNCTIONS
Get PDFThis paper extends as a lemma an auxiliary result obtained by Singh and Chanam. Using it, we prove a refinement of the Turán-type inequality for rational functions obtained recently by Akhter et al. Next, using examples, we discuss the result of Mir et al
GROWTH OF POLYNOMIALS GENERATED BY LINEARLY INDEPENDENT SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS IN TERMS OF ITERATED ORDER
Get PDFIn this article, we have studied some properties of the growth and oscillation of polynomials generated by linearly independent solutions of the second order linear differential equation where is a meromorphic function. Here we extend and improve some of the previous results of Z. Latreuch and B. Belaïdi (2013), M.A. Abdellaouia and B. Belaïdi (2020) and others in terms of iterated order and iterated exponent of convergence
A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS
Get PDFPerfect Italian Domination is a type of vertex domination which can also be viewed as a graph labelling problem. The vertices of a graph are labelled by 0, 1 or 2 in such a way that a vertex labelled 0 should have a neighbourhood with exactly two vertices in it labelled 1 each or with exactly one vertex labelled 2. The remaining vertices in the neighbourhood of the vertex labelled 0 should be all 0's. The minimum sum of all labels of the graph G satisfying these conditions is called its Perfect Italian domination number. We study the behaviour of graph complements and how the Perfect Italian Domination number varies between a graph and its complement. The Nordhaus–Gaddum type inequalities in the Perfect Italian Domination number are also discussed
AN INTRODUCTION TO THE INDEPENDENT TOPOLOGICAL STRUCTURE GENERATED BY FUZZY SOFT -OPEN SETS
No full textIn this study, we propose a new generalized fuzzy soft open set, namely the fuzzy soft -open set. Notably, the newly defined fuzzy soft -open set is a special type of fuzzy soft-pre-open set. Additionally, a diagram (Fig. 3) is used to show how fuzzy soft -open sets are related to various existing stronger and weaker forms of fuzzy soft-open sets. The main focus of this paper is on the autonomous topological structure produced by fuzzy soft -open sets. Furthermore, we introduce the concepts of fuzzy soft -interior and -closure operators, which provide another way to define fuzzy soft -topology. Finally, we introduce and explore fuzzy soft -continuity as the application of the defined notions in this regard
APPROXIMATION OF ONE CLASS OF SMOOTH FUNCTIONS BY ANOTHER CLASS OF SMOOTHER FUNCTIONS ON THE AXIS
Get PDFThis paper investigates the problem of best and best linear approximation in the space of functions on the real axis with bounded Fourier transform. The study focuses on approximating the class of functions whose derivatives of order have variation bounded by 1 by the class of functions whose th-order derivative (. This problem is related to Stechkin's problem and the corresponding sharp Kolmogorov inequality, both previously studied by the author. Stechkin's problem concerns the best approximation in the uniform norm on the real axis of th-order differentiation operators by bounded linear operators from to , considered on the class of functions whose Fourier transform of the th-order derivative () is summable
A TWO-STAGE METHOD FOR SOLVING A NONLINEAR ILL-POSED OPERATOR EQUATION AND ITS APPLICATION TO THE INVERSE PROBLEM OF THERMAL SOUNDING OF THE ATMOSPHERE
Get PDFThe inverse problem of reconstructing the vertical profiles of CO in the atmosphere by IR spectra of the solar light transmission is investigated. To solve this problem, we propose a two-stage method. At the first stage, we use the modified Tikhonov method. At the second stage, to approximate a solution of the regularized equation, we apply a nonlinear analogue of the modified steepest descent method. The convergence theorem is formulated and the results of numerical experiments for retrieving the concentration of carbon dioxide in the atmosphere from measured spectra are discussed
ASYMPTOTIC BEHAVIOR FOR THE LOTKA–VOLTERRA EQUATION WITH DISPLACEMENTS AND DIFFUSION
Get PDFIn this paper, we consider the Lotka–Volterra equation with displacements and diffusion, that is transport-diffusion system describing the evolution of prey and predator populations with their displacements and their diffusion, in a periodic domain in . It is shown that the solution to this equation and its logarithm are globally bounded, and that, when the solution converges to the stationary solution in mean value, it converges uniformly with respect to the time variable as well as the space variable. These results are obtained by using -estimate of the well-known Lyapunov functional, and, in particular, an estimate of the point-wise growth of the solution by means of the application of the fundamental solution of the heat equation
THE IMPACT OF TOXICANTS IN THE MARINE THREE ECOLOGICAL FOOD-CHAIN ENVIRONMENT: A MATHEMATICAL APPROACH
Get PDFTo explore the impact of toxicants on a marine ecological food chain system consisting of three species, this work develops and analyzes a non-linear mathematical model. The model consists of five state variables: phytoplankton, zooplankton, fish, environmental toxicant, and organismal toxicant. We have incorporated the Monod-Haldane functional response as a predation function for each species. Using the Jacobian matrix, the stability analysis was conducted, and necessary constraints were obtained for the system's local and global stability. Hopf bifurcation analysis was performed for carrying capacity () and the rate of decrease in the growth rate of phytoplankton due to the presence of toxicants (). Also, phase portraits are presented for different parameters of the model. In addition, numerical simulations are executed using MATLAB to prove theoretical findings and explore the impact of parameter variation on ecological species behavior
ON OBSERVABILITY CONTROL FOR DIFFERENTIAL EQUATIONS
Get PDFWe consider a controlled linear differential equation with constraints as in the author's previous paper. The controller's goal is to displace an initial state of to a specified final state . An observer, unaware of the system's state vector, attempts to determine by analyzing the vector , which is linked to . Using , the observer constructs a set of possible values for . When specific constraints are used for the controls (or disturbances, from the observer's opinion), this set becomes an ellipsoid, characterized by a set of differential equations. The controller, in turn, aims to achieve its own objectives while simultaneously generating the most challenging signals for the observer. Unlike the previous article of the author not scalar, but two-criterion control observation problem is considered here. It is solved in functional spaces in two ways, without passing to sampling of a system. The solution boils down to determination of finite-dimensional parameters of optimal control from the system of linear algebraic equations. As the third option the problem can be solved also by sampling, but then the solution turns out piecewise-constant. We explore an example to illustrate these concepts
EQUILIBRIUM TRAJECTORIES FOR CONTROL SYSTEMS WITH HETEROGENEOUS DYNAMICS
Get PDFThe paper considers the construction of equilibrium in bimatrix games with heterogeneous dynamics of players' interaction. Heterogeneity of dynamics is connected with difference in maximal rates of the participants. In such a formulation, the switching curves of players' controls are represented by fractional rational functions and are constructed on the basis of N.N. Krasovskii's guaranteed strategies using elements of L.S. Pontryagin's maximum principle. Equilibrium trajectories are generated within the framework of the concept of the dynamic Nash equilibrium introduced by A.F. Kleimenov and are obtained by pasting together the characteristics of the Hamilton-Jacobi equations expressed as exponential functions. The sensitivity analysis is carried out for the shapes of control switching curves with respect to the proportions of players' maximal rates. The comparative analysis is implemented for the values of players' payoffs calculated on equilibrium trajectories of the dynamic game