Research of strengthening process of machines details surfaces by treatment spark digits

Розраховано математичне сподівання площі зміцненої поверхні деталі шляхом обробки імпульсами одиничних іскрових розрядів, яке залежить від кількості розрядів та їх площі. Досліджено залежність частки зміцненої поверхні від кількості імпульсів розряду при різних значеннях їх площі та від величини площі одиничного розряду при дії різною кількістю розрядів. Аналіз отриманих результатів свідчить про необхідність урахування площі одиничного іскрового розряду та їх кількості при розробленні технології зміцнення деталей машин.The mathematical hope of area of the fixed detail surface is calculated by treatment of high spark bits impulses, which depends on the amount of digits and their area. Dependence of part of the fixed surface is investigational on the amount of impulses of digit at the different values of their area and from the size of area of high bit at the action of digits a different amount. An analysis of investigated results testifies to the necessity of account of area of high bit and their amount at development of technology of strengthening of details of machines

Existence of diffusive processes with the given local characteristics

The results which concern to existence of diffusive processes with the given local characteristics (vector of drift, operator of diffusion) are considered in the article. The processes are examined in separable Hilbert space. Some properties of such processes (equivalence of measures, connection with stochastic differential equations) are also considered

Existence of diffusive processes with the given local characteristics

The results which concern to existence of diffusive processes with the given local characteristics (vector of drift, operator of diffusion) are considered in the article. The processes are examined in separable Hilbert space. Some properties of such processes (equivalence of measures, connection with stochastic differential equations) are also considered

On the number of crossings of some levels by a sequence of diffusion processes

The limit behavior of the number of crossings of some sequence of levels by the following sequence of random variables $xi_n(0)$, $xi_nleft(frac{1}{m}ight)$,..., $xi_nleft(frac{N}{m}ight)$, as the integers $n$, $m$, $N$ are increasing to infinity in some consistent way, is investigated, where $(xi_n(t))_{tge0}$ for $n=1,2,dots$ is a diffusion process on a real line $mathbb{R}$ with its local characteristics (that is, drift and diffusion coefficients) $(a_n(x))_{xinmathbb{R}}$ and $(b_n(x))_{xinmathbb{R}}$ given by $a_n(x)=na(nx)$, $b_n(x)=b(nx)$ for $xinmathbb{R}$ and $n=1,2,dots$ with some fixed functions $(a(x))_{xinmathbb{R}}$ and $(b(x))_{xinmathbb{R}}$