Necessary and Sufficient Conditions for the Solvability of Inverse Problem for a Class of Dirac Operators

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvabilty of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given.Comment: 19 page

The Levinson-Type Formula for a class of Sturm-Liouville Equation

The boundary value problem $$-{\psi}''+q(x)\psi={\lambda}^2 \psi, \quad 0<x<\infty,$$ $${\psi}'(0)-(\alpha_{0}+\alpha_{1}\lambda){\psi}(0)=0$$ is considered, where $\lambda$ is a spectral parameter, $q(x)$ is real-valued function such that \begin{equation*} \int\limits_{0}^{\infty}(1+x)|q(x)|dx<\infty \end{equation*} with $\alpha_{0}, \alpha_{1}\geq0$ ( $\alpha_{0},\alpha_{1}\in \mathbb{R}$). In this paper, for the above-mentioned boundary value problem, the scattering data is considered and the characteristics properties (such as continuity of the scattering function $S(\lambda)$ and giving the Levinson-type formula) of this data are studied.{\small \bf Keywords. }{Scattering data, scattering function, Gelfand-Levitan-Marchenko equation, Levinson-type formula.

THE CURRENT STATUS OF THE DEVELOPMENT OF A PERFORMANCE MANAGEMENT SYSTEM AND THE APPLICABILITY OF ITS BASIC METHODS IN MUNICIPAL ADMINISTRATIONS

The existing approaches to the management of municipal entities, the methods of planning used are explored. The main problems and constraints of development of the efficiency management system are singled out. A number of administrations of municipalities of the Moscow region have been surveyed on the use of methods for planning and managing the implementation of development programs. It was concluded that there is a lack of awareness and a weak nature of the use of well-known and well-proven methods in business. The main recommendations for the development of a methodological framework for the development and implementation of economic programs of municipal administrations and, in particular, for a more extensive application of modern tools for performance management have been formulated

THE TASKS OF IMPROVING THE MANAGEMENT SYSTEM OF PROGRAMMES AND PROJECTS IMPLEMENTATION IN MUNICIPAL ADMINISTRATIONS

In the article problems of control systems of municipal authorities are considered. Problems of improvement of control systems of processes of implementation of programs and projects of development of business in administrations of municipal educations are developed and proved. It is defined that development of the system of management of processes of implementation of programs and projects at the municipal level is necessary. The author noted that the possibility of high efficiency and effectiveness of system development and monitoring of execution of programs and projects of support of small business in municipal unit can be carried out by means of application of concepts of system of the balanced indicators, process and project management