23 research outputs found
Extremal problems for the generalized heat equation and optimal recovery of its solution from inaccurate data
No full text
Linear best method for recovering the second derivatives of Hardy class functions
No full textThe linear best method for approximating the second derivatives of Hardy class functions defined in the unit circle at zero in accordance with the information about their values in a finite number of points forming a regular polygon is found. The paper is divided into three sections. The first contains the necessary concepts and results from the work of K.Yu. Osipenko. It also recalls some results obtained by S. Ya. Havinson and other authors. In the second section, the error of the best method is calculated, and the corresponding extremal functions are written out. The third proves that the linear best approximation method is unique, and its coefficients are calculated
Ismagilov Type Theorems for Linear, Gel′fand and Bernstein n-Widths
No full textAbstractUsing a variational principle for s-numbers, we obtain estimates for the linear, Gel′fand. and Bernstein n-widths. A simple proof of some results concerned with the exact values of n-widths of diagonal operators is given. We also calculate the exact values at the Bernstein n-widths for the Hardy-Sobolev classes
On some problems of optimal recovery of analytic and harmonic functions from inaccurate data
No full textAbstractWe consider some problems of optimal recovery of holomorphic and harmonic functions in the unit disc. We obtain extensions of Schwartz's Lemma and optimal formulas for numerical differentiation
Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data
No full textAbstractWe consider the problem of optimal recovery of solutions of the generalized heat equation in the unit ball. Information is given at two time instances, but inaccurate. The solution is to be constructed at some intermediate time. We provide the optimal error and present an algorithm which achieves this error level
Optimal recovery of derivatives of Hardy class functions
No full textThe paper considers the best linear method for approximating the values of derivatives of Hardy class functions in the unit circle at zero according to the information about the values of functions at a finite number of points z1,...,zn that form a regular polygon, and also the error of the best method is obtained. The introduction provides the necessary concepts and results from the papers of K.Yu. Osipenko. Some results of the studies of S.Ya. Khavinson and other authors are also mentioned here. The main section consists of two parts. In the first part of the second section, the research method is disclosed, namely, the error of the best method for approximating the derivatives at zero according to the information about the values of functions at the points z1,...,zn is calculated; the corresponding extremal function is written out. It is established that for p>1, the corresponding extremal function is unique up to a constant factor that is equal to one in modulus. For p=1, the corresponding extremal function is not unique. All such corresponding extremal functions are determined here. In the second part of the second section, it is proved that for all p (1≤p<∞), the best linear approximation method is unique, and the coefficients of the best linear recovery method are calculated. The expressions used to calculate the coefficients are greatly simplified. At the end of the paper, the obtained results are described, and possible areas for further research are indicated
Analytical assessment of current insurance as part of management of consequences of emergencies
No full textThe article examines the current state of the insurance system as a component of managing the consequences of emergencies. The researches are presented in the following areas: the insurance against accidents and fire risks and risks of natural disasters; property insurance (property, goods and agricultural products); the insurance of transport (by modes); liability insurance (by liability). So, the author made the statistical and analytical assessment of consequences of emergencies that was learned through the study of modern insurance system, which enabled to identify the complex of accounting objects in the management of consequences of emergencies
Crimean Khanate, Polish-Lithuanian Commonwealth and Russian State in 1524–1571: The Diplomatic Correspondence from the Archive of the Grand Duchy of Lithuania
No full textThe manuscript of the Czartoryskis’ Library in Krakow № 2893 contains, among other sources, the correspondence of the Crimean-Kazan Gireys with the kings of Polish Crown and Grand Duchy of Lithuania in Ruthenian translation (“prosta mowa”). The collection of letters springs from the Radziwills’ archive and can be dated back to 1524–1571 based on the reasons outlined in this article. The manuscript from the Warsaw Main Archive of the Ancient Acts (Radziwills coll., part II, № 3294) contains a part of the same correspondence, which is present in the Czartoryski manuscript № 2893. The author reinterprets the historical context of the Warsaw manuscript. The senders of the letters are Sahib-Giray (to Sigismund I, 1st: ca. 1521–1524, 2nd: June–July 1530, 3rd: September–October 1537), Safa-Giray (two letters to Sigismund I, spring or summer of 1524), Amin-Giray-Saltan (a letter to Sigismund I, September–October 1537) and Poland’s King Sigismund I the Old (to Khan Sahib-Giray at end of December 1537 or the beginning of January 1538). The latest-dated part of the Polish-Lithuanian and Crimean-Kazan correspondence in the Czartoryski manuscript contains the materials of Devlet-Giray’s diplomatic correspondence with Sigismund II Augustus, which sheds a new light on the Crimean march against the Muscovite state in 1571. These materials are contextualized and studied with respect to the new information they may provide on the history of Russian-Crimean relations (letter to Sigismund II ca. April 5, 1571 and Ardy-Berdey’s embassy ca. July 5, 1571). The author found a list of 27 towns devastated by the khan during the war against Moscow recorded in the embassy accounts of the Polish Royal Treasury at the Warsaw Archive. It was composed as a means of propaganda, but it reflects the marching route of the Crimean troops to Moscow and the ravaging of other Russian districts after Moscow had been burned on May 24, 1574
Background effects of emergencies on indicators of economic analysis of enterprise economic activity
No full textThe paper deals with the study of scientific works on the issue of formation and development of organizational and methodological regulations of accounting and analytical support of the economic activity of an enterprise in emergencies, which led to the conclusion about the complex character of the study of theory, methodology and economic analysis of enterprises in various sectors of national economy. The author studies the approaches to the nature and methods of economic analysis that resulted in the presentation of instructional techniques to the economic structure. In assessing the consequences of emergencies, it is necessary to determine their impact on the indices of economic analysis; so, there was the need to define areas resulting index changes as a result of emergency situations by identifying its components which may affect emergencies. After analyzing the data, it was found that the consequences of emergency situations affecting the indices of business analysis and can lead to changes in management decisions of internal and external users
