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## Invariant vector fields and linear equations on the sphere

### Ukrainian Mathematical Journal (1989-03-01) 41: 264-268 , March 01, 1989

## On certain exact relations for sojourn probabilities of a wiener process

### Ukrainian Mathematical Journal (1999-06-01) 51: 942-947 , June 01, 1999

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.

## Approximation of compressions of periodic functions in the spaceL p,p<1

### Ukrainian Mathematical Journal (1995-12-01) 47: 1953-1957 , December 01, 1995

We investigate the behavior of the best approximation of compressions of functions by trigonometric polynomials in the space*L*_{p}, p<1.

## Approximate solution of two-element boundary-value problems with a shift

### Ukrainian Mathematical Journal (1977-01-01) 29: 58-67 , January 01, 1977

## The dichotomy of solutions of nonlinear systems of differential equations with lag

### Ukrainian Mathematical Journal (1978-05-01) 30: 306-310 , May 01, 1978

## Naum Il'ich Akhiezer (on his seventieth birthday)

### Ukrainian Mathematical Journal (1971-05-01) 23: 305-306 , May 01, 1971

## Integral representation of even positive-definite functions of two variables

### Ukrainian Mathematical Journal (2011-11-01) 63: 981-992 , November 01, 2011

We obtain an integral representation of even functions of two variables for which the kernel [*k*_{1}(*x* + *y*) + *k*_{2}(*x* − *y*)], *x*, *y* ∈ *R*^{2}, is positive definite.

## Approximation of fractional-order integrals by algebraic polynomials. I

### Ukrainian Mathematical Journal (1999-05-01) 51: 672-683 , May 01, 1999

For functions*f(x)* representable by an integral operator of a special form, we investigate the behavior of the second difference Δ
_{h}^{2}*f*(*x*)=*f*(*x*+*h*)-2*f*(*x*)+*f*(*x*-*h*),*h*>0, depending on the location of a point*x* on the segment [0,1].

## Weak α-skew Armendariz ideals

### Ukrainian Mathematical Journal (2012-08-01) 64: 456-469 , August 01, 2012

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.

## Limiting theorems for sojourn measures in domains of vector-valued Gaussian random fields

### Ukrainian Mathematical Journal (1990-05-01) 42: 554-561 , May 01, 1990

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.