Asymptotic behaviour of iterated modified 401-1401-1401-1401-2401-2401-2transforms on some slowly convergent sequences

LetL(α, r) denote the class of complex sequences (x _n) having an asymptotic expansion of type $$x_n \sim \sum\limits_{i \ge 0} {c_i n^{ - (\alpha + ri)} } , c_0 \ne 0,\alpha > 0,r > 0.$$ We describe the asymptotic behaviour of sequences obtained by applying to (x _n) some specific modified versions of the iterated Δ² transform, the θ₂ transform and some combinations of them. In this paper, we study the particular casesr=1 andr=1/2, which are the most useful in practice. The results are also valid for sequences (S _n) whose error sequence (x _n) defined byx _n=S _n?S, S=limS _n, belongs to someL(α, r).     

227-01227-01227-01-property and normal subgroups

Summary D-property (=set of primes) in finite groups is not in general inherited by subgroups. In this paper, as evidence in favor of the following conjecture (F. Gross): (o) If a finite group G satisfies D then its normal subgroups satisfy D-property as well. the Author shows that if the D and the D-properties (=set of the primes not in ) hold together in a finite group G, then both are inherited by the normal subgroups of G. As a corollary, the characterization of the groups satisfying both the properties D and D is given in terms of the composition factors.     

区传递7-(v,k,λ)设计

具有良好传递性的区组设计是代数组合学研究的一个重要领域.1993年,Cameron和Praeger证明了不存在区传递的8-设计.因此研究区传递的7-设计的存在性是一个很重要的课题.2013年,龚罗中和刘伟俊证明了不存在指数超过5的区传递7-设计.本文在此基础上证明了不存在区长小于100的区传递7-设计.     

Singular integral operators on 53-0153-0153-01-spaces

Summary It is shown that certain singular integral operators with variable kernels leave invariant theL ^v, -spaces studied by Campanato, Stampacchia, Peetre and others. Our results extend Peetre's work on convolution operators.     

Random reals and the relation 171-1171-1171-1

It is consistent that ₁(₁,(:n))² holds in any random extension for n finite and countable.     

Eine Randwertaufgabe 191-1191-1191-1der ebenen Potentialtheorie

Ohne Zusammenfassung     

Zur konstruktion der reellen Szpiegelungsgruppe 331-1331-1331-1

Acta Mathematica Hungarica -     

On multipliers in the spaces 207-01207-01207-01

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Finally, the author wishes to express his gratefulness to Prof. P. I. Lizorkin for raising the problem and for his attention during the elaboration of the present work.