Explicit inversion formulas for a subclass of integral operators with D-difference kernels on a finite interval are obtained. A case of the positive operators is treated in greater detail. An application to the inverse problem to recover canonical system from a Weyl function is given.
We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
This work represents a continuation of the studies relating to nonlinear equations, carried out by the authors. Special attention is paid to the operators with linear-fractional shifts that act on the argument of the unknown function, but also on the unknown function itself. In this work, we study homogeneous equations with such operators. The main classes of functions for which non-linear equations are considered are Hölder class real functions. Solutions of the equations have the form of infinite products or the form of infinite continued fractions; an abstract description of the solutions is also offered. The developed mathematical methods can be applied to finding the conditions of invertibility of certain operators found in modelling, as well as for the construction of their inverse operators. Subsequently, we suggest using these results for the modelling of renewable systems with elements that can be in different states: sick, healthy, immune, or vaccinated. These results can also be applied to the analysis of balance equations of the model and for finding equilibrium states of the system.
This paper presents the analogue simulation of a nonlinear liquid level system composed by two tanks; the system is controlled using the methodology of exact linearization via state feedback by cellular neural networks (CNNs). The relevance of this manuscript is to show how a block diagram representing the analogue modeling and control of a nonlinear dynamical system, can be implemented and regulated by CNNs, whose cells may contain numerical values or arithmetic and control operations. In this way the dynamical system is modeled by a set of local-interacting elements without need of a central supervisor.
Este artículo se plantea como objetivo determinar la importancia de la comunicación, del lenguaje no verbal y de la concienciación cultural en la preparación de operaciones de apoyo a la paz y en la formación militar. Para ello se analizan las competencias comunicativas y su importancia en estas operaciones, así como la interculturalidad y la comunicación no verbal. Se abordan detalladamente los elementos que implica el lenguaje no verbal. Este artículo concluye que, para desarrollar eficazmente una operación de apoyo a la paz, es necesario formar y concienciar sobre un correcto uso de la comunicación y del lenguaje no verbal atendiendo a la interculturalidad.
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