Abstract: The paper considers two notions of logarithmic dichotomy for discrete skew-evolution semiflows in Banach spaces. We establish the relation between them, we give a characterization for the uniform logarithmic dichotomy of Zabczyk type and a sufficient criteria for the uniform logarithmic dichotomy. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: A three-dimensional mathematical model is analyzed in order to study the labour market, with an emphasis on unemployment, employment and the number of open positions. The rate of change of new positions created by the public and private sectors depends on the historical levels of unemployment, taking into account the distributed time delay. The non-dimensional mathematical model is done and the existence of the equilibrium points is examined. The findings related to the positivity and boundedness of solutions are presented. In addition the global asymptotic stability of the positive equilibrium is provided. The theoretical results are exemplified by the numerical simulations. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: In this paper we consider a concept of uniform polynomial splitting for a discrete cocycle over a discrete semiflow in Banach spaces. We obtain some characterizations of Datko type and also in terms of Lyapunov functions. The study is made from the point of view of the invariant projectors and also strongly invariant projectors. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: We consider a Cauchy problem for a fractional differential inclusion defined by a Caputo type fractional derivative and we obtain a sufficient condition for local controllability along a reference trajectory in terms of a certain fractional variational differential inclusion associated to the initial problem. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: In this paper we present a new approach for the fuzzy quasi-b-metric spaces and we obtain some properties of these spaces. A special attention is granted to the decomposition theorems of a fuzzy quasi-b-metric into a right continuous and ascending family of quasi-b-metrics. Finally, some future lines of research are highlighted. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: In this paper we study the following problem (Problem 4.2 in, I.A. Rus, Sets with structure, mappings and fixed point property: fixed point structures, Fixed Point Theory 23, No. 2 (2022), 689-706):Let (𝒰, 𝒮, M) be a fixed point structure on (𝒰, M). We suppose that (𝒰, M) is with cartesian product. In which conditions, we have that:X,Y∈𝒮⇒X×Y∈𝒮'Some results in terms of exponential with fixed point property are also given. The basic results are illustrated by examples. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: The paper presents some characterizations for the study of dichotomy of dynamical systems. Integral characterizations of Datko type are considered for the notion of uniform dichotomy with growth rates, also called uniform h-dichotomy, for skew-evolution cocycles in Banach spaces. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: Using the notion of strict h-contraction, existence results for Ψ-asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with integral term as right side and modified argument are given. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: The aim of the present paper is to emphasize some growth concepts for the dichotomic behavior of evolution operators in Banach spaces. In fact, we approach the exponential growth, the polynomial growth and the h-growthfor both uniform and nonuniform cases. Connections between concepts are established. Majorization criteria for the uniform behaviors are given. PubDate: Sat, 24 Dec 2022 00:00:00 GMT

Abstract: In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: In this paper we show that, if that the function f : [0, ∞) → 𝔾 is operator monotone in [0, ∞) then there exist b ≥ 0 and a positive measure m on [0, ∞) such that [ f(B)-f(A) ](B-A)==b(B-A)2+∫0∞s2[ ∫01[ ((1-t)A+tB+s)-1(B-A) ]2dt ]dm(s)\matrix{ {\left[ {f\left( B \right) - f\left( A \right)} \right]\left( {B - A} \right) = } \hfill \cr { = b{{\left( {B - A} \right)}^2} + \int_0^\infty {{s^2}\left[ {\int_0^1 {{{\left[ {{{\left( {\left( {1 - t} \right)A + tB + s} \right)}^{ - 1}}\left( {B - A} \right)} \right]}^2}dt} } \right]dm\left( s \right)} } \hfill \cr } for all A, B > 0. Some necessary and sufficient conditions for the operators A, B > 0 such that the inequality f(B)B+f(A)A≥f(A)B+f(B)Af\left( B \right)B + f\left( A \right)A \ge f\left( A \right)B + f\left( B \right)Aholds for any operator monotone function f on [0, ∞) are also given. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The object of the present article is to study the notion of η-Einstein-like LP-Sasakian manifolds admitting η-Ricci soliton. Furthermore, we study the η-Ricci soliton on LP-Sasakian manifolds when the potential vector field V is point-wise collinear. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: Let 𝒜 p be the class of functions f of the form f(z)=zp+ap+1zp+1+ap+2zp+2+⋯f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + \cdots that are analytic in the open unit disk 𝕌. For f ∈ 𝒜 p, new integral and differential operator nf is considered. The object of the present paper is to discuss some interesting properties of nf and to consider some examples for our results. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The aim of this paper is to give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The aim of this paper is to study a frictional contact problem between an elastic body and a foundation. We focus on the optimal control of the model which consists of acting with a control on a portion of the boundary of the body and leading the stress tensor as close as possible to a given target. We state an optimal control problem for which we establish an existence theorem of the solution. We then introduce a sequence of regularized problems depending on a positive parameter α and we study the convergence of the sequence of the solutions when the parameter α tends to zero. Finally, an optimality condition is established for this problem. PubDate: Mon, 20 Jun 2022 00:00:00 GMT

Abstract: The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of this paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces. PubDate: Mon, 20 Jun 2022 00:00:00 GMT