25 articles in this issue
V.F. Babenko,G.S. Zhiganova
We obtain sharp inequalities of Jackson type for the best approximations of functions in L2(Rm)L_2(\mathbb{R}^m) by means of partial sums of wavelet series in case of multidimensional analogues of Shannon-Kotelnikov wavelets.
V.F. Babenko,A.A. Ligun,O.M. Shumeiko
We propose the method to construct high-frequency and low-frequency analysing and restoring filters for digital processing of multidimensional signals.
V.F. Babenko,D.S. Skorokhodov
We solved the problem about the best interval quadrature formula on the class WrFW^r F of differentiable periodic functions with arbitrary permutation-invariant set FF of derivatives of order rr. We proved that the formula with equal coefficients and nn n... see more
V.F. Babenko,M.S. Churilova
We obtain new inequalities for fractional Marchaud derivatives of functions defined on the whole real domain, in integral metric (1?p<81 \leqslant p ); for p=1p = 1 we establish the sharpness of obtained inequalities.
S.V. Babenko,V.I. Ruban
We investigate the interrelations between the error of one method of curve approximation and the error of the best approximation.
V.Ye. Belozerov,V.S. Chernyshenko,S.V. Chernyshenko
We obtain new sufficient conditions of asymptotic stability on solution cone of the set of usual uniform quadratic differential equations. For non-uniform quadratic sets (with non-zero linear part) we give the conditions of boundedness of solutions. We de... see more
Ye.Yu. Bovdui,V.L. Velik?n
We obtain two-sided bounds, and, in some cases, exact values as well, for interpolational spreads of subspaces of Hermitian splines in the space of continuous functions with uniform metric.
L.G. Bojtsun,A.I. Khaliuzova
We establish sufficient conditions for summability of integrals with multiplier by |¯W,p(y)|k|\overline{W}, p(y)|_k, k?1k \geqslant 1, method.
S.B. Vakarchuk,M.B. Vakarchuk
For classes of 2p2\pi-periodic functions of two discrete variables, defined on grid set sq,p\sigma_{q,p}, we found exact values of Kolmogorov and linear quasiwidths of classes Wr,p(l2q,p)W^{r,p}(l^2_{q,p}) in l2q,pl^2_{q,p} space.
S.V. Goncharov,V.P. Motornyi
We establish the order of growth of modified Lebesgue constants of Fourier-Jacobi sums in Lp,wL_{p,w} spaces.
Ye.V. Derets
We found the error of interval quadrature formula of rectangles for the class of functions with given convex majorant of integral modulus of continuity of second derivative.
V.G. Doronin,A.A. Ligun
We conducted the research of sharp inequalities of Jackson type in L2L_2 space for approximation by entire functions of exponential type.
D.A. Kovtoniuk
We show that, if homeomorphism ff of domain D?RnD \subset \mathbb{R}^n, n?2n \geqslant 2, is a hyper Q-homeomorphism with Q?L1locQ \in L_{loc}^1, then f?ACLf \in ACL. As a consequence, such homeomorphism has partial derivatives almost everywhere and appro... see more
V.A. Kofanov,V.Ye. Miropolskii
We obtain new sharp inequality of Kolmogorov type for differentiable periodic functions x?L31x \in L_1^3.
K.S. Mordak
We consider the criterion of existence of exact irreducible representations of finite groups and construct the algorithm that allows to verify it by means of computer algebra system GAP.
B.I. Peleshenko
We prove theorems on boundedness of operators of weak type (f0,?0,f1,?1)(\varphi_0, \psi_0, \varphi_1, \psi_1) from Lorentz space ?f,a(Rn)\Lambda_{\varphi,a}(\mathbb{R}^n) to ?f,b(Rn)\Lambda_{\varphi,b}(\mathbb{R}^n) in “limit” cases, when one of function... see more
R.R. Salimov
We study the problem of continuation on boundary of the so-called Q-homeomorphisms between domains in metric spaces with measures. We obtain conditions for function Q(x) and domain boundary, under which any homeomorphism allows continuous continuation on ... see more
Ye.A. Sevostianov
We study mappings with finite distortion in Rn\mathbb{R}^n, n?2n \geqslant 2. For the classes of mappings with branching that satisfy modal inequalities we obtain the set of theorems on removal of isolated singularities.
V.M. Traktynska
We obtain the criterion of the best approximant for multivariable functions in Lp1,…pnL_{p_1,\ldots p_n} space.
R.M. Trigub
We study the following problem: describe all linear differential operators with constant coefficients that are majorated by given operators of the same form.
N.A. Turbai
We consider extension of important characteristics of finite solvable PT-groups to the class of periodic locally solvable FC-groups.
A.V. Tushev
We find characteristic subgroup of soluble torsion-free group of finite rank, whose structure determines sufficient conditions of existence of exact irreducible representations of the group over locally finite field.
V.A. Chupordia
We consider RG-moduli A, in which R=Z, and group G is a finite-finitary group with some constraints.
P.I. Kogut,T.N. Rudyanova
We study boundary properties of one class of periodic functions as e?0\varepsilon \rightarrow 0, where e\varepsilon is a period of periodically perforated domain. We show that their weak limit is the homothetic mean value of such functions.