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In this document, we present a novel approach for approximating analytical solutions to differential equations, referred to as the Polynomial Approximation on Subintervals (PAS) method. We demonstrate the method's effectiveness when applied to optimal control problems. To begin, the original optimal control problem is transformed into a variational problem. Subsequently, we solve the corresponding Euler-Lagrange Equation and obtain an approximate analytical solution utilizing the innovative PAS method. To evaluate its performance, we provide a numerical example that includes a comparative analysis between the outcomes obtained with PAS and those achieved by other researchers who employed various approximation techniques. [ABSTRACT FROM AUTHOR]

This paper deals with few spectral properties for elements from a fuzzy normed algebra. It is introduced the definition of the spectral radius of an element from the fuzzy normed linear space (X, N, Λ) and some basic properties of it are shown. More precisely, we will prove that almost all the properties of this spectrum from some particular case of locally convex spaces are also true for this setup. [ABSTRACT FROM AUTHOR]

In this paper, we study the mathematical model associated to an economic growth process with logistic population, CES utility function and delay. We have that the model is described by dynamical system of differential functions equations have the steady state. This steady state exhibits the Hopf bifurcation. [ABSTRACT FROM AUTHOR]

In this paper we consider a version of the Ramsey growth model in finite and continuous time, with the bounded consumption. This model of Ramsey leads to an optimal control problem. We prove an existence theorem of the optimal solution for this optimal control problem. [ABSTRACT FROM AUTHOR]

Signal processing methods cannot be circumscribed to existing models but require some extensions of mathematical theories (operator theory, functional analysis) to enable the widening of more general spaces or the modelling using more general functions but with fewer properties satisfying theorems used in similar frameworks. In this context, one can expand the Hilbert space L2 to a locally convex space, sequentially complete, extension required in terms of types of data that must be processed. Hence, there is a need to obtain some equivalent theorems which can characterize operators endowed with a certain type of limitation. In this paper, a study on such equivalent conditions for T (where T is a multiplier on a locally convex algebra A which has a closed range) is performed. [ABSTRACT FROM AUTHOR]