Search Results

You are looking at 1 - 10 of 27 items for :

  • "subsequences" x
  • Refine by Access: All Content x
Clear All

Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

Open access

Abstract  

Let χ be a primitive multiplicative character modulo an integer m ≥ 1. Using some classical bounds of character sums, we estimate the average value of the character sums with subsequence sums
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$T_m (\mathcal{S},\chi ) = \sum\nolimits_{\mathcal{I} \subseteq \{ 1, \ldots ,N\} } {\chi (\sum\nolimits_{i \in \mathcal{I}} {s_i } )}$$ \end{document}
taken over all N-element sequences S = (s 1, …, s N) of integer elements in a given interval [K + 1, K + L]. In particular, we show that T m (S, χ) is small on average over all such sequences. We apply it to estimating the number of perfect squares in subsequence sums in almost all sequences.
Restricted access

Abstract  

The concepts of subsequence and rearrangement of double sequence are used to present multidimensional analogues of the following core questions. If x is a bounded real sequence and A is a matrix summability method, under what conditions does there exist y, a subsequence (rearrangement) of x such that each number t in the core of x is a limit point of Ay?

Restricted access
Acta Mathematica Hungarica
Authors:
Rui Chi
,
Shuyan Ding
,
Weidong Gao
,
Alfred Geroldinger
, and
Wolfgang A. Schmid

Summary For a finite abelian group G, we investigate the invariant  s(G) (resp.  the invariant  s0(G)) which is defined as the smallest integer l ? N such that every sequence S in G of length |S| = l has a subsequence T with sum zero and length |T|= exp(G) (resp. length |T|=0 mod exp(G)).

Restricted access

Abstract  

Numerical series
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop \Sigma \limits_{n = 0}^\infty u_n$$ \end{document}
with partial sumss n are studied under the assumption that a subsequence
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\{ {S_{n_k } } \right\}_{k = 0}^\infty$$ \end{document}
of the partial sums is convergent. Then a sequence {η k } is chosen, by means of which a majorant of the termsu n is constructed. Conditions on {n k } and {η k } are found which imply the (C, 1)-summability of the series∑ u n (Theorem 1). In the meanwhile, it is proved that the (C, 1)-means in Theorem 1 cannot be replaced by (C, α)-means, if 0<α<1 (Theorem 2). On the other hand, if the assumption in Theorem 1 is not satisfied, then in certain cases the series∑ u n preserves the property of (C, 1)-summability (Theorems 4 and 5), while in other cases it is not summable even by Abel means (Theorems 3 and 6).
Restricted access
Acta Mathematica Hungarica
Authors:
Alfred Geroldinger
,
David J. Grynkiewicz
, and
Wolfgang A. Schmid

Mathematical Society . [3] Chi , R. , Ding , S. , Gao , W. , Geroldinger , A. , Schmid , W. A. 2005 On zero-sum subsequences of restricted size. IV Acta Math. Hungar. 107 337 – 344 10

Restricted access