Lattices of dominions in quasivarieties of Abelian groups

Let M be any quasivariety of Abelian groups, (H) be the dominion of a subgroup H of a group G in M, and L_q(M) be the lattice of subquasivarieties of M. It is proved that (H ) coincides with a least normal subgroup of the group G containing H, the factor group with respect to which is in M. Conditions are specified subject to which the set L(G,H,M) = { (H) | N L_q(M)} forms a lattice under set-theoretic inclusion and the map : L_q(M) L(G,H,M) such that (N) = (H) for any quasivariety N L_q(M)is an antihomomorphism of the lattice L _q (M) onto the lattice L(G, H, M).__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 238–251, March–April, 2005.     

Pointwise hereditary majorization and some applications

A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel'sT as well as Kleene/Feferman's) is applied to systems of intuitionistic and classical arithmetic (H andH ^c) in all finite types with full induction as well as to the corresponding systems with restricted induction and^c.

Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

Blocks of orthogonal random variables and the strong law of large numbers

(X _k ),k=1,2,... — _k ² >1; (X _k ) , E(X _k X _t )=0 p k<>(p+1) (p,k,l=1, 2, ...) , , ,

On the uniqueness of canonical points in the Hobby-Rice theorem

According to the Hobby-Rice theorem for anyn-dimensional subspaceU _n ofL ₁([a, b], ) ( positive, finite, nonatomic) there exist points =s ₀x ₁x _m+1=b, where 0mn, such that

On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series

, (fz) , ,

Sharpening of Stečkin's theorem to strong approximation

. . , , : f — ,

Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics

Let _j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N()=#{j:_j^m}. It is shown that for each > 0 we have

On the preservation of periodic monotonicity

A 2-periodic continuous real functionf is said to beperiodically monotone if it has the following property: there exist numbert ₁t ₂t ₃t ₁+2 such thatf is nonincreasing fort ₁t ₂ and nondecreasing int ₂tt ₃. For any 2-periodic, integrable real functiong with ₀ ² |g(t|dt) we define

A sharp transition for the two-dimensional Ising percolation

We show that the percolation transition for the two-dimensional Ising model is sharp. Namely, we show that for every reciprocal temperature >0, there exists a critical valueh _c () of external magnetic fieldh such that the following two statements hold.

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

New covering numbers and spectral properties of operators in Banach spaces

, , , . ., . — s- , . , s- (,s- ) ; _n (T), ¦ _l (T)¦¦ ₂ (T)¦...0, T:EE .

A test of convergence of Fourier series with respect to multiplicative systems,analogous to the Jordan test

, {p _n} _n=0 (p₀=1, _n2 n2). : x f(t) V(G)

On the divergence of linear summation methods of Fourier series

[0, 1],fL(0,2),

ИНтЕгРАльНыЕ пРЕДст АВлЕНИь В тРУБЧАтых ОБлАстьх НАД пОлИЁДРАМИ И ВОпРОсы пРИБлИжЕНИ ь ФУНкцИИ

Let B ⁿ be a domain and (y), y B and arbitrary positive, continuous function. If p, s (0, +), denote byH _s, ^p (T _B ) the class of the functionsf(z)f(x+iy), holomorphic in the tube domain

Christoffel functions,orthogonal polynomials,and Nevai's conjecture for Freud weights

We obtain upper and lower bounds for Christoffel functions for Freud weights by relatively new methods, including a new way to estimate discretization of potentials. We then deduce bounds for orthogonal polynomials on thereby largely resolving a 1976 conjecture of P. Nevai. For example, let W:=e ^–Q, whereQ: is even and continuous in, Q^" is continuous in (0, ) andQ ^'>0 in (0, ), while, for someA, B,

A multielement boundary-value problem with a piecewise-smooth shift on a piecewise-Lyapunov contour for a function analytic in a domain

In an L_p-formulation (1 < p="><>) there is constructed for a function (z) analytic in a multiconnected domain with a piecewise-Lyapunov boundary a Noether theory of the boundary-value problem

Projection minima of a symmetric convex body

R ⁿ n- , : RⁿPRⁿ/ o - . —

On maximal ranges of polynomial spaces in the unit disk

Let be a domain in C, 0, and let _n ⁰ () be the set of polynomials of degreen such thatP(0)=0 andP(D), whereD denotes the unit disk. The maximal range _n is then defined to be the union of all setsP(D),P _n ⁰ (). We derive necessary and, in the case of ft convex, sufficient conditions for extremal polynomials, namely those boundaries whose ranges meet _n . As an application we solve explicitly the cases where is a half-plane or a strip-domain. This also implies a number of new inequalities, for instance, for polynomials with positive real part inD. All essential extremal polynomials found so far in the convex cases are univalent inD. This leads to the formulation of a problem. It should be mentioned that the general theory developed in this paper also works for other than polynomial spaces.Communicated by J. Milne Anderson.