共查询到10条相似文献，搜索用时 93 毫秒
1.
E.G. Coffman Jr. George S. Lueker Joel Spencer Peter M. Winkler 《Probability Theory and Related Fields》2001,120(4):585-599
A random rectangle is the product of two independent random intervals, each being the interval between two random points
drawn independently and uniformly from [0,1]. We prove that te number C
n
of items in a maximum cardinality disjoint subset of n random rectangles satisfies
where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that, for some absolute constat K,
Finally, for a certain distribution of random cubes we show that for some absolute constant K, the number Q
n
of items in a maximum cardinality disjoint subset of the cubes satisies
Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001 相似文献
2.
Kentaro Hirata 《Potential Analysis》2009,30(2):165-177
In an unbounded domain Ω in ℝ
n
(n ≥ 2) with a compact boundary or Ω = ℝ
n
, we investigate the existence of limits at infinity of positive superharmonic functions u on Ω satisfying a nonlinear inequality like as
where Δ is the Laplacian and c > 0 and p > 0 are constants. The result is applicable to positive solutions of semilinear elliptic equations of Matukuma type.
This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 19740062), Japan Society for the Promotion
of Science. 相似文献
3.
Dominique Barbolosi 《Monatshefte für Mathematik》1999,28(4):189-200
For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)
In this paper, we first point out that for all , ( has no limit for for almost all , proving more precisely that: For all , one has for almost all
相似文献
4.
It is well known that the recurrence relations
are periodic, in the sense that they define periodic sequences for all choices of the initial data, and lead to sequences
with periods 2, 5 and 8, respectively. In this paper we determine all periodic recursions of the form
where are complex numbers, are non-zero and . We find that, apart from the three recursions listed above, only
lead to periodic sequences (with periods 6 and 8). The non-periodicity of (R) when (or and ) depends on the connection between (R) and the recurrence relations
and
We investigate these recursions together with the related
Each of (A), (B), and (C) leads to periodic sequences if k = 1 (with periods 6, 5, and 9, respectively). Also, for k = 2, (B) leads to periodicity with period 8. However, no other cases give rise to periodicity. We also prove that every real
sequence satisfying any of (A), (B), and (C) must be bounded. As a consequence, we find that for an arbitrary k, every rational sequence satisfying any of (A), (B), and (C) must be periodic.
(Received 27 June 2000; in revised form 5 January 2001) 相似文献
5.
Summary. We prove a functional central limit theorem for stationary random sequences given by the transformations
on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale
differences with values in a separable Hilbert space of square integrable functions.
Received: 11 March 1997 / In revised form: 1 December 1997This research was supported by the Deutsche Forschungsgemeinschaft
and the Russian Foundation for Basic Research, grant 96-01-00096. The second author was also partially supported by INTAS,
grant 94-4194. 相似文献
6.
In this paper we completely solve the family of Thue equations
where is an integral parameter. In particular, for , the only solutions are the trivial ones with x = 0 or y = 0. The result is achieved by sharpening the estimates of part I of the paper and by solving Thue equations with the method of Bilu and Hanrot. 相似文献
7.
In this paper we completely solve the family of Thue equations
where is an integral parameter. In particular, for , the only solutions are the trivial ones with x = 0 or y = 0. The result is achieved by sharpening the estimates of part I of the paper and by solving Thue equations with the method of Bilu and Hanrot.
(Received 25 January 2000; in revised form 10 April 2000) 相似文献
8.
Dominique Barbolosi 《Monatshefte für Mathematik》1999,128(3):189-200
For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)
In this paper, we first point out that for all , ( has no limit for for almost all , proving more precisely that: For all , one has for almost all
Then we prove mainly the more precise result: For all , the sequence has no subsequence which converges almost everywhere.
(Re?u le 4 mai 1998; en forme révisée le 25 février 1999) 相似文献
9.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
10.
Horst Alzer 《Monatshefte für Mathematik》2000,131(3):179-188
A classical inequality for Euler’s gamma function states that
for all and with . We prove the following extension of this result. Let be the weighted power mean of of order r. The inequality
holds for all and with if and only if
(Received 3 April 2000; in revised form 26 June 2000) 相似文献