共查询到20条相似文献，搜索用时 687 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.
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
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3.
Alexander D. Wentzell 《Probability Theory and Related Fields》1999,113(2):255-271
. For a certain class of families of stochastic processes ηε(t), 0≤t≤T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(ηε[0,T]) are proved of the form
where w
0 is a Wiener process starting from 0, with variance σ2 per unit time, A
i
are linear differential operators acting on functionals, and m=1 or 2. Some intricate differentiability conditions are imposed on the functional.
Received: 12 September 1995 / Revised version: 6 April 1998 相似文献
4.
Let B
0,B
1, ⋯ ,B
n
be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time
where 0<b
i
≤ 1, 1 ≤i≤n. In particular, we have ?τ3=∞ and ?τ5<∞. Various generalizations are also studied.
Received: 10 January 2000 / Revised version: 12 January 2001 /?Published online: 14 June 2001 相似文献
5.
Suppose that {R n } n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers
where a is a nonzero algebraic number and b, c, and d are integers with c ⩾ 1 and d ⩾ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions. 相似文献
6.
Yu. Baryshnikov 《Probability Theory and Related Fields》2001,119(2):256-274
Consider the process D
k
, k = 1,2,…, given by
B
i
being independent standard Brownian motions. This process describes the limiting behavior “near the edge” in queues in series,
totally asymmetric exclusion processes or oriented percolation. The problem of finding the distribution of D. was posed in [GW]. The main result of this paper is that the process D. has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from Gaussian
Unitary Ensemble.
Received: 17 November 1999 / Revised version: 4 April 2000 / Published online: 24 January 2000 相似文献
7.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
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8.
Let K be a field of characteristic 0 and let p, q, G 0 , G 1 , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G n (x)) n=0 ∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G n (x) = G m (P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set
相似文献
9.
Olivier Teulié 《Monatshefte für Mathematik》2002,116(3):313-324
In this paper, we prove that if β1,…, β n are p-adic numbers belonging to an algebraic number field K of degree n + 1 over Q such that 1, β1,…,β n are linearly independent over Z, there exist infinitely many sets of integers (q 0,…, q n ), with q 0 ≠ 0 and
with H = H(q 0,…, q n ). Therefore, these numbers satisfy the p-adic Littlewood conjecture. To obtain this result, we are using, as in the real case by Peck [2], the structure of a group of units of K. The essential argument to obtain the exponent 1/(n-1) (the same as in the real case) is the use of the p-adic logarithm. We also prove that with the same hypothesis, the inequalities
have no integer solution (q 0,…, q n ) with q 0 ≠ 0, if ɛ > 0 is small enough. 相似文献
10.
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
11.
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
12.
We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of
the classical Fejér-Jackson inequality: For all integers n ⩾ 2 and real numbers x ∈ (0,π) we have
with the best possible constant factor α = 1. This improves an inequality due to Turán.
Received February 12, 2002
Published online April 4, 2003 相似文献
13.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
14.
Any solution of the functional equation
where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed
reflected Brownian motion. Similarly any solution of
behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an α,β-doubly perturbed Brownian
motion. We complete some recent investigations by showing that for all permissible values of the parameters α, α and β respectively,
these equations have pathwise unique solutions, and these are adapted to the filtration of B.
Received: 7 November 1997 / Revised version: 13 July 1998 相似文献
15.
Hydrodynamic large scale limit for the Ginzburg-Landau ∇φ interface model was established in [6]. As its next stage this
paper studies the corresponding large deviation problem. The dynamic rate functional is given by
for h=h(t,θ),t∈[0,T],θ∈?
d
, where σ=σ(u) is the surface tension for mean tilt u∈ℝ
d
. Our main tool is H
−1-method expoited by Landim and Yau [9]. The relationship to the rate functional obtained under the static situation by Deuschel
et al. [3] is also discussed.
Received: 22 February 2000 / Revised version: 19 October 2000 / Published online: 5 June 2001 相似文献
16.
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
17.
Let {X
n
,n ≥ 1} be a sequence of i.i.d. random variables. Let M
n
and m
n
denote the first and the second largest maxima. Assume that there are normalizing sequences a
n
> 0, b
n
and a nondegenerate limit distribution G, such that . Assume also that {d
k
,k ≥ 1} are positive weights obeying some mild conditions. Then for x > y we have
when G(y) > 0 (and to zero when G(y) = 0).
相似文献
18.
John S. Caughman 《Graphs and Combinatorics》1998,14(4):321-343
Let Y=(X,{R
i
}0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A
0, A
1,…, A
D
of the associate matrices, and Q-polynomial with respect to the ordering E
0, E
1,…,E
D
of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv).
(i)
(ii) D is even, and
(iii) θ*
0>θ0, and
(iv) θ*
0>θ0, D is odd, and
Received: February 13, 1996 / Revised: October 16, 1996 相似文献
19.
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
20.
In this paper we prove a stochastic representation for solutions of the evolution equation
where L
∗ is the formal adjoint of a second order elliptic differential operator L, with smooth coefficients, corresponding to the infinitesimal generator of a finite dimensional diffusion (X
t
). Given ψ
0 = ψ, a distribution with compact support, this representation has the form ψ
t
= E(Y
t
(ψ)) where the process (Y
t
(ψ)) is the solution of a stochastic partial differential equation connected with the stochastic differential equation for (X
t
) via Ito’s formula.
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