К оценке хаусдорфова отклонения выпуклых многоугольников в R2 от их геометрической разности с кругами

We study a problem concerning the estimation of the Hausdorff deviation of convex polygons in R2 from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space Rn are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in Rn in their geometric difference with closed balls in Rn are presented in the works of L.S. Pontryagin, his staff and colleagues. These estimates are very important in deriving an estimate for the mismatch of the alternating Pontryagin's integral in linear differential games of pursuit and alternating sums. Similar estimates turn out to be useful in deriving an estimate for the mismatch of the attainability sets of nonlinear control systems in Rn and the sets approximating them. The paper considers a specific convex heptagon in R2. To study the geometry of this heptagon, we introduce the concept of a wedge in R2. On the basis of this notion, we obtain an upper bound for the Hausdorff deviation of a heptagon from its geometric difference with the disc in R2 of sufficiently small radius. © 2020 Udmurt State University. All rights reserved

On one addition to evaluation by L.S. Pontryagin of the geometric difference of sets in a plane

In this paper, two generalizations of convex sets on the plane are considered. The first generalization is the concept of the α-sets. These sets allow for the existence of several projections onto them from an arbitrary point on the plane. However, these projections should be visible from this point at an angle not exceeding α. The second generalization is related to the definition of a convex set according to which the segment connecting the two points of the convex set is also inside it. We consider central symmetric sets for which this statement holds only for two points lying on the opposite sides of some given line. For these two types of nonconvex sets, the problem of finding the maximum area subset is considered. The solution to this problem can be useful for finding suboptimal solutions to optimization problems and, in particular, linear programming. A generalization of the Pontryagin estimate for the geometric difference of an α-set and a ball is proved. In addition, as a corollary, the statement that the α-set in the plane necessarily contains a nonzero point with integer coordinates if its area exceeds a certain critical value is given. This corollary is one of generalizations of the Minkowski theorem for nonconvex sets. © 2019 Udmurt State University. All rights reserved.Russian Foundation for Basic Research, RFBR: 18–01– 00264, 18–31–00018Government Council on Grants, Russian FederationFunding. The study of the first and the third authors was funded by RFBR, project number 18–01– 00264. The study of the second author was funded by RFBR, project number 18–31–00018. The work was funded by Act 211 of the Government of the Russian Federation, contract number 02.A03.21.0006

"Water supply and drain" Manual

This manual provides lectures and guidance material for performing eight laboratory works, two homework tasks as well as test questions for defending laboratory works, test questions and tasks for module control on the discipline "Water supply and drain". Intended for students of specialty 6.060101 "Civil Engineering"

REINFORCED CONCRETE AND STONE STRUCTURES

Книга висвітлює особливості методів розрахунку, конструювання і експериментального дослідження залізобетонних та кам’яних конструкцій, особливості методів розрахунку конструкцій при будівництві аеропортів. Наукова монографія може бути корисною для науково-педагогічних працівників і інженерів, докторантів, аспірантів і студентів технічних вузів, які будуть навчатися за спеціальністю 192 «Будівництво та цивільна інженерія» та всім, хто цікавиться проектуванням і будівництвом аеропортів. Більш детальна бібліографічна інформація щодо книги знаходиться у Німецькій Національній Бібліотеці ФРН у містах Берлін, Лейпциг та Франкфурт на Майні

SOME ASPECTS OF NSC OLIMPIYSKIY VARIANT DESIGNING ON THE BASE OF MODERN TECHNOLOGIES

Different approaches to choosing of roofing structural decisions over the modern grandstands were analyzed. Some variants of stadium roofing were considered. Expediency of taking into account the geometrical non-linearity at calculation of guy systems and membrane covering were proved

SOME ASPECTS OF NSC OLIMPIYSKIY VARIANT DESIGNING ON THE BASE OF MODERN TECHNOLOGIES

Different approaches to choosing of roofing structural decisions over the modern grandstands were analyzed. Some variants of stadium roofing were considered. Expediency of taking into account the geometrical non-linearity at calculation of guy systems and membrane covering were proved

Terraforming of Mars planet

The main task is the terraforming of Mars planet. Nowadays it's a veru important task, because there are a lot of problems om the planet Earth, which deals with the exhaustions of natural resources. The solution is in the colonizing, building and transport formation on Mars planet. After researching with a help of Nasa devices, scientist could develop different ideas about constructions and transport inventions for new planet of human

Terraforming of Mars planet

The main task is the terraforming of Mars planet. Nowadays it's a veru important task, because there are a lot of problems om the planet Earth, which deals with the exhaustions of natural resources. The solution is in the colonizing, building and transport formation on Mars planet. After researching with a help of Nasa devices, scientist could develop different ideas about constructions and transport inventions for new planet of human

REINFORCED CONCRETE AND STONE STRUCTURES

Книга висвітлює особливості методів розрахунку, конструювання і експериментального дослідження залізобетонних та кам’яних конструкцій, особливості методів розрахунку конструкцій при будівництві аеропортів. Наукова монографія може бути корисною для науково-педагогічних працівників і інженерів, докторантів, аспірантів і студентів технічних вузів, які будуть навчатися за спеціальністю 192 «Будівництво та цивільна інженерія» та всім, хто цікавиться проектуванням і будівництвом аеропортів. Більш детальна бібліографічна інформація щодо книги знаходиться у Німецькій Національній Бібліотеці ФРН у містах Берлін, Лейпциг та Франкфурт на Майні

"Water supply and drain" Manual

This manual provides lectures and guidance material for performing eight laboratory works, two homework tasks as well as test questions for defending laboratory works, test questions and tasks for module control on the discipline "Water supply and drain". Intended for students of specialty 6.060101 "Civil Engineering"