共查询到20条相似文献,搜索用时 15 毫秒
2.
A sequence A of positive integers having the property that no element \(a_i \in A\) divides the sum \(a_j+a_k\) of two larger elements is said to have ‘Property P’. We construct an infinite set \(S\subset \mathbb {N}\) having Property P with counting function \(S(x)\gg \frac{\sqrt{x}}{\sqrt{\log x}(\log \log x )^2(\log \log \log x)^2}\). This improves on an example given by Erd?s and Sárközy with a lower bound on the counting function of order \(\frac{\sqrt{x}}{\log x}\). 相似文献
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Periodica Mathematica Hungarica - 相似文献
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We establish that if ? is a countable field of characteristic p, U is a unitary action of ?? on a Hilbert space ?, and P is an essential idempotent ultrafilter on ?, then for every polynomial r: ? → ?? with r(0) = 0 one has $$P - {\lim _g}{U_{r(g)}}f = {P_r}f{\rm{ weakly,}}$$ , where P r is the projection onto the closed subspace $${H_r} = \{ f \in H:{\{ {U_{r(g)}}f\} _{g \in F}}{\text{ is precompact in the strong topology\} }}{\text{.}}$$ . We then derive combinatorial consequences of this result, including results for sufficiently large finite fields. 相似文献
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László Mérai 《Periodica Mathematica Hungarica》2014,68(1):77-91
In this paper we study the irregularities of distribution of subsets of integer vectors relative to higher dimensional arithmetic progressions. In particular we give one-sided estimate of the discrepancies of subsets of d-dimensional cubes, i.e. we show that these discrepancies have both large positive and small negative values. 相似文献
6.
《纯粹数学与应用数学》1992,(1)
In the short note, we shall give a negative answer of a question which israised in[1]. 相似文献
7.
Igor E. Shparlinski 《Czechoslovak Mathematical Journal》2018,68(4):1067-1077
We consider function field analogues of the conjecture of Gy?ry, Sárközy and Stewart (1996) on the greatest prime divisor of the product (ab+1)(ac+1)(bc+1) for distinct positive integers a, b and c. In particular, we show that, under some natural conditions on rational functions F,G,H ∈ ?(X), the number of distinct zeros and poles of the shifted products FH +1 and GH +1 grows linearly with degH if degH > max{deg F, degG}. We also obtain a version of this result for rational functions over a finite field. 相似文献
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J?rg Winkelmann 《Mathematische Zeitschrift》2011,267(1-2):9-13
We show: if a bounded domain in a Stein space covers a compact complex space, it must be smooth. This give a negative answer to a question of Kollár. 相似文献
10.
Zoltán Füredi 《Combinatorica》1991,11(1):75-79
Let L
k
be the graph formed by the lowest three levels of the Boolean lattice B
k
, i.e.,V(L
k
)={0, 1,...,k, 12, 13,..., (k–1)k} and 0is connected toi for all 1ik, andij is connected toi andj (1i<jk).It is proved that if a graph G overn vertices has at leastk
3/2
n
3/2 edges, then it contains a copy of L
k
.Research supported in part by the Hungarian National Science Foundation under Grant No. 1812 相似文献
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In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented. 相似文献
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A theorem of Lovász asserts that (H)/*(H)r/2 for everyr-partite hypergraphH (where and * denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V
1, ...,V
k
) of the vertex set and a partitionp
1+...+p
k
ofr such that |eV
i
|p
i
r/2 for every edgee and every 1ik. Moreover, strict inequality holds whenr>2, and in this form the bound is tight. The investigation of the ratio /* is extended to some other classes of hypergraphs, defined by conditions of similar flavour. Upper bounds on this ratio are obtained fork-colourable, stronglyk-colourable and (what we call)k-partitionable hypergraphs.Supported by grant HL28438 at MIPG, University of Pennsylvania, and by the fund for the promotion of research at the Technion.This author's research was supported by the fund for the promotion of research at the Technion. 相似文献
16.
Dragan Djurčić Ljubiša D.R. Kočinac Mališa R. Žižović 《Applied Mathematics Letters》2012,25(10):1296-1298
We prove that certain classes of sequences of positive real numbers satisfy some selection principles related to a special kind of convergence. 相似文献
17.
Y. -K. Song 《Acta Mathematica Hungarica》2007,115(4):315-318
The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelöf in X and B is weakly almost Lindelöf in Y, but A × B is not weakly almost Lindelöf in X × Y. 相似文献
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《Discrete Mathematics》2002,231(1-3):251-256