15 articles in this issue
R.O. Bilichenko
We obtain the best approximation of unbounded functional (Akx;f)(A^k x; f) on the class {x?D(Ar):?Arx??1}\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \} by linear bounded functionals for a normal operator AA in the Hilbert space HH (k<rk , f?Hf\in H).
S.B. Vakarchuk,M.B. Vakarchuk
On the classes of 2p2\pi-periodic functions Wa(Kß,F){\mathcal{W}}^{\alpha} (K_{\beta}, \Phi), where a,ß?(0;8)\alpha, \beta \in (0;\infty), defined by KK-functionals KßK_{\beta}, fractional derivatives of order a\alpha, and majorants F\Phi, the exact value... see more
A.Ye. Haidabura,V.A. Kofanov
We prove the equivalence theorem for additive inequalities on a finite interval. Besides, we describe a pair of constants so that the additive inequalities with that constants are valid on the whole class of functions LsL_s.
S.V. Goncharov
We show the method to expand functions being integrable with a weight on the interval, and satisfying conditions of integral Lipschitz type, on the whole line. We prove that the differential properties of such functions are kept at the expansion.
M.S. Gun'ko
We found the optimal information and the optimal method of its use to recover the convolution of n-functions on some convex and centrally-symmetric classes of 2p2\pi-periodic functions.
O.V. Zelenskiy,V.M. Darmosiuk
This paper investigates the quivers derived from finite number of exponent matrices. The authors have proved that for any natural m, there is a quiver which is derived from m pairwise non-equivalent exponent matrices.
N.V. Kalashn?kova
We study some properties of structure of the multiplicative group Z*mZ^*_m, in case when m is Mersenne prime, Fermat or Carmichael number. Using the results of these studies, we obtain properties of Mersenne primes, Fermat and Carmichael numbers.
O.D. Kostyuk,V.M. Traktyns'ka,M.Ye. Tkachenko
The questions of the characterization of the best approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterions of the best approximant in spaces L1,p2,...,pnL_{1,p_2,...,p_n} and Lp1,...,... see more
V.A. Kofanov
We prove new sharp Remez-type inequalities of various metrics for periodic functions, polynomials and splines.
O.V. Lopotko
We obtain integral representations for positive definite functions of one variable, when kernels K(x,y)K(x,y) are positive definite. The proof is based on the spectral theory of differential operators of fourth order.
N.V. Parfinovich,I.A. Shevchenko
We obtain the conditions under which the exact values of the best relative approximation of classes of periodic functions by splines coincide with the exact values of the best approximations of these classes by splines without constraints.
A.M. Pas'ko
We calculate the homology groups Hk(COn)H_k(\mathbb{C}{\Omega}_n), k=0,1,2,2n-1,2n,2n+1k = 0,1,2,2n-1,2n,2n+1. We establish that the COn\mathbb{C}{\Omega}_n space has a zero Euler characteristic.
B.I. Peleshenko,T.N. Semirenko
We obtain the necessary and sufficient conditions in terms of Fourier coefficients of 2p2\pi-periodic functions ff with absolutely convergent Fourier series, for ff to belong to the generalized Lipschitz classes H?,aCH^{\omega, \alpha}_{\mathbb{C}}, and t... see more
O.V. Polyakov
We obtain certain inequalities of Jackson type, connecting the value of the best approximation of periodic differentiable functions and the generalized modulus of continuity of the highest derivative.
V.I. Ruban,A.A. Rudenko
For discrete dynamical systems with a finite number of states, we obtain order of time complexity ascension of algorithms of their full analysis.