A problem has been identified related to deformations of aircraft structures operating in the extreme north and orbital objects in near-earth orbits under conditions of cyclic alternating temperature loads. The formulation of the problem of studying the deformations of materials of structures operating under conditions of cyclic alternating temperature loads using the theories of cyclic strength, low-cycle fatigue and crack resistance is presented. It is assumed that at 16 revolutions of an orbital object around the Earth (the number of temperature loading cycles n ≥ 1,2105 ), cracking occurs or the size of existing cracks increases to a critical size from low-cycle fatigue. Linear deformations of the body material of the International Space Station are determined, taking into account heating from solar radiation and cooling, while in the shadow of the Earth. A hypothesis has been put forward that, under conditions of cyclic temperature loads, the maximum effect on the material endurance is exerted by the calculated ones: the amplitude of the stress cycle, the maximum stress of the cycle and the range of stress fluctuations in the cycle, both separately and jointly. Comparative analysis of the results of calculating the stresses under cyclic temperature loading according to 3 hypotheses showed that the values of the calculated stresses are the closest to the maximum cycle stress or to the cycle stress amplitude.
New two-sided bounds are proposed for the ruin probability in the classical risk process.In the present paper new two-sided bounds are proposed for the ruin probability in the classical risk process. These bounds are based on the Pollaczek-Khinchin-Beekman formula for the ruin probability, representation of the compound geometric distribution as a compound mixed Poisson law and Berry-Esseen-type bounds for the normal approximation to compound Poisson distributions. The obtained results complement (and improve) the known bounds (see, for example, [2,5]).For the sake of convenience, without loss of generality assume that all the random variables and processes are defined on the same probability space.Consider the classical risk processHere, u > 0 is the initial surplus of the insurance company, c > 0 is the constant rate of the premiums arrival, claims X 1 , X 2 , . . . arrive according to the Poisson process N (t) with intensity Λ > 0, and are assumed to be independent and identically distributed non-negative random variables with common distribution function F (x). Moreover, the process N (t) is assumed to be independent of the sequence X 1 , X 2 , . . .. For definiteness, let 0 k=1 X k = 0. Denote
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