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Belitskii, G. R.
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Gasanenko, V. A.
New exact relations are proved for the sojourn probability of a Wiener process between two time-de-pendent boundaries. The proof is based on the investigation of the heat-conduction equation in the domain determined by these functions-boundaries. The relations are given in the form of series.
Pichugov, S. A.
We investigate the behavior of the best approximation of compressions of functions by trigonometric polynomials in the spaceLp, p<1.
Tikhonenko, N. Ya.
Ordynskaya, Z. P.
Lopotko, O. V.
We obtain an integral representation of even functions of two variables for which the kernel [k1(x + y) + k2(x − y)], x, y ∈ R2, is positive definite.
Motornyi, V. P.
For functionsf(x) representable by an integral operator of a special form, we investigate the behavior of the second difference Δ
h2f(x)=f(x+h)-2f(x)+f(x-h),h>0, depending on the location of a pointx on the segment [0,1].
Tavallaee, H. A.; Nikmehr, M. J.; Pazoki, M.
We introduce the concept of weak α-skew Armendariz ideals and investigate their properties. Moreover, we prove that I is a weak α-skew Armendariz ideal if and only if I[x] is a weak α-skew Armendariz ideal. As a consequence, we show that R is a weak α-skew Armendariz ring if and only if R[x] is a weak α-skew Armendariz ring.
Leonenko, N. N.
Sojourn measures of vector-valued Gaussian random fields are studied under the condition of strong dependence. It is proved that the presence of strong dependence among components of a random field leads to a change of normalization and a change of the limiting distribution of the sojourn measures in domains with moving boundaries.
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