Gamova N.A., Girina A.N., Spiridonova E.V.
THE PERIODIZATION OF A.N. KOLMOGOROV AS THE BASIS OF IDEAS ABOUT THE HISTORY OF THE DEVELOPMENT OF MATHEMATICAL SCIENCE ^{[№ 4 ' 2023]}
The periodization of the development of mathematical science was proposed by A.N. Kolmogorov. He identifies four periods in the development of mathematics. The basis of periodization includes assessment of the content, level of achievements and features of mathematical research: its most important methods, results, ideas. Particular attention is paid to the development of probability theory structured according to Kolmogorov periods. The prerequisites for the formation of probability theory began to appear during the second millennium BC — the first period. During the period of accumulation of knowledge (before 600 BC), the concept of “chance” — the main concept in the science in question – began to develop. Until the third period, the concept was invariably associated with the philosophical category “fate,” that is, a certain predetermined process, which contradicts modern ideas about chance. Probability Theory received its unofficial name precisely from the period of elementary mathematics (before the 15–16th centuries) — the second period. The next period was called by Kolmogorov “Mathematics of Variables” (XVII–XVIII centuries). Since the beginning of the period of modern mathematics (since the 19th century), random variables and the patterns associated with them have come to the fore in probability theory. This is due to the general scientific growth in the 19th century. The main problems that arose by the end of the third period are being solved: all the basic concepts, rules for their application, and theorems are clearly defined. By the beginning of the 20th century — the fourth period–there was a need to formalize the acquired knowledge. Andrei Nikolaevich built a system based on modern and already developed by that time set theory and measure theory. The periodization of the development of mathematical science, proposed by A.N. Kolmogorov, with the rapid progress of mathematical knowledge and the emergence of information technologies in the future may require adjustments to the last stage of development of the history of mathematics or will lead to the emergence of a new stage of periodization.

Ivashkina G.A., Spiridonova E.V.
THE PROBLEM WITH SHIFT FOR A SPECIAL AREA ^{[№ 9 ' 2013]}
Problem with shift for generalized Tricomi equation is considered in a special area, bounded normal curve Г with endpoints A (0, 0) and B (1, 0), which lies in the upper half, a ray emanating from the point B and going in the direction of Oх, and feature АС: . Proved that the solution exists and is unique.

Polkunov Yu.G., Spiridonova E.V.
THE MAHTEMATICA MODEL OF UNWEDGING MATERIAL WITH DIFFERENT LENGTH OF THE BASIC AND GAPING CRACK ^{[№ 9 ' 2010]}
The article represents the numerical solution of the task of the development of the wedging crack in the undivided material with different length of the basic and gaping crack. Solution of problem was achieved by the torn-tape system displacement.

Polkunov Yu.G., Spiridonova E.V.
MATHEMATICAL MODEL OF BRITTLE FAILURE OF GEOMATERIALS IN A MIXED POSING ^{[№ 4 ' 2010]}
The authors of the article presents correlation which determine the relation between tensions and biases with coefficients of stress intensity of the first and second type and describe the mechanism of rupture forming at the mixed type of crack loading.

Polkunov Yu.G., Spiridonova E.V.
CALCULUS OF APPROXIMATIONS OF CRITERIA OF CRACK GROWTH IN MIXED PROBLEMS OF ELASSTICITY THEORY ^{[№ 11 ' 2008]}
The article covers development of calculus of approximations to solve mixed tasks of elasticity theory to determine stress intensity factors for cracks on the edges of which displacement and intensity factors are set.

Polkunov Yu.G., Spiridonova E.V.
MATHEMATICAL MODELING OF ELASTIC PLANE DESTRUCTION WITH HALF-INFINITE CROSSCUTS WITH YAWNING CRACKS ^{[№ 5 ' 2008]}
This article is devoted to attachment working out of disruptive deflections method for coefficient determination of the first and second types voltage intensity for half-infinite crosscuts of elastic plane to banks of which the normal variable and shearing deflection with yawning cracks are attached.

Polkunov Yu.G., Spiridonova E.V.
MODELING OF WEDGE CRACK DEVELOPMENT IN DEFECTIVE MATERIAL ^{[№ 9 ' 2007]}
This article is devoted to working out of criteria of wedge cracks development in plane. Dependences of the first type tensions intension coefficient to physical-mechanical features of material, loading length and distance till inclined crack are determined in this article. Adequacy of modeling results is proved with analytical researches.