共查询到20条相似文献，搜索用时 31 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.
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
3.
Jie Wu 《Monatshefte für Mathematik》2002,135(1):69-81
We prove that under the Riemann hypothesis one has for any ,
This improves a result of Zhai and Cao, which requires 11/30 in place of 221/608.
Received 28 May 2001 相似文献
4.
In this paper we establish an asymptotic formula for the sum
when y is large compared to x1/2 log x.
Received: 27 January 2005 相似文献
5.
Xiaojing Yang 《Archiv der Mathematik》2005,85(5):460-469
In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator
is discussed, where α, β are positive constants satisfying
for some ω ∈R+ /Q, h(t) ∈L∞ [0, 2π ] is 2π-periodic, x±=max {±x, 0 }.
Received: 23 September 2004 相似文献
6.
7.
Krzysztof Fraączek 《Monatshefte für Mathematik》2000,131(4):279-307
In this paper we introduce the notion of degree for C
1-cocycles over irrational rotations on the circle with values in the group SU(2). It is shown that if a C
1-cocycle over an irrational rotation by α has nonzero degree, then the skew product
is not ergodic and the group of essential values of ϕ is equal to the maximal Abelian subgroup of SU(2). Moreover, if ϕ is of class C
2 (with some additional assumptions) the Lebesgue component in the spectrum of the skew product has countable multiplicity.
Possible values of degree are discussed, too.
(Received 8 February 2000; in revised form 26 September 2000) 相似文献
8.
We are concerned with the existence of radial solutions for the following Neumann problem
where Ω is an exterior domain in ℝ
N
, denotes the normal interior derivative on ∂Ω and g satisfies certain assumptions.
Received: 26 May 1999 / Revised version: 2 April 2001 相似文献
9.
We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space WN,2([0, ∞); e−x) and the Sobolev-Legendre space WN,2([−1, 1]) with respect to the Sobolev-Laguerre inner product
and with respect to the Sobolev-Legendre inner product
respectively, where a0 = 1, ak ≥0, 1 ≤k ≤N −1, γ > 0, and N ≥1 is an integer. 相似文献
10.
Aleksandar Ivić 《Archiv der Mathematik》2008,90(5):412-419
If
denotes the error term in the classical Rankin-Selberg problem, then it is proved that
where Δ1(x) = ∫
x
0 Δ(u)du. The latter bound is, up to ‘ɛ’, best possible.
Received: 8 February 2007 相似文献
11.
L. Olsen 《Monatshefte für Mathematik》2003,140(4):335-350
Let be a subshift modelled by a strongly connected graph, and let
denote the shift. For n , let
be the nth empirical measure, i.e.
where
x
denotes the Dirac measure at x and
denotes the family of probability measures on . We consider continuous deformations of L
n
, i.e. pairs
where X is a metric vector space and
is continuous with respect to the weak topology on
. For a sequence (x
n
)
n
in X, we write
for the set of accumulation points of (x
n
)
n
. Assume that T and U are subsets of X, and define
In previous work we computed the Hausdorff dimension of the sets (T,U). In this paper we prove that these sets are dimensionless, i.e. if t denotes the Hausdorff dimension of (T,U) and h is a dimension function of the form h(r) = r
t
L(t) where L is a slowly varying function, then
provided that
. In particular,
or
. This implies that various sets of divergence points associated with different multifractal spectra (e.g. local dimensions, local entropies, local Lyapunov exponents, ergodic averages) are dimensionless. 相似文献
12.
Aleksandar Ivić 《Monatshefte für Mathematik》2005,145(1):35-46
Let P(n) denote the largest prime factor of an integer n (2), and let N (x) denote the number of natural numbers n such that 2 n x, and n does not divide P(n)!. We prove that
where (u) is the Dickman-de Bruijn function. In terms of elementary functions we have
thereby sharpening and correcting recent results of K. Ford and J.-M. De Koninck and N. Doyon. 相似文献
13.
Micciancio 《Discrete and Computational Geometry》2003,29(1):133-138
Abstract. We prove that the best way to reduce the volume of the n -dimensional unit cube by a linear transformation that maps each of the main vertices
to a point within distance ɛ <
from
is to shorten all edges by a factor (1-ɛ) . In particular, the minimal volume of such an almost cubic parallelepiped is (1-ɛ)
n
. This problem naturally arises in the construction of lattice-based one-way functions with worst-case/ average-case connection. 相似文献
14.
Lewin 《Semigroup Forum》2008,66(1):43-62
Abstract. Given a set A and a function
, we study the set of all functions
that are continuous for all topologies for which f continuous.
We prove that in a sense to be made precise in the text, for any essentially infinitary function f , any non-constant such g equals f
n
, for some n∈ N. We also prove a similar result for the clone of n -ary functions from
. 相似文献
15.
WUSHAOPING YANGHAITAO 《高校应用数学学报(英文版)》1998,13(3):251-262
Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x f(t,x)=0 are given by means of variational methods, where the function -1/2a（t）|s|^2∫^t0f（t,s）ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t 1 t a（t）dt= ∞,VI∈R^1.A resonance case as well as a noncompact case is discussed too. 相似文献
16.
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
17.
Fabienne Castell 《Probability Theory and Related Fields》2001,121(4):492-524
We prove a homogenization result for system of semilinear parabolic PDEs of the type
where V and a are random ergodic fields. We extend to the random case, results of Buckdahn, Hu & Peng [4] for periodic structures. The
same method involving stability results is applied. Our main tool is an L
p
estimate for the gradient of the solution of the auxiliary problems. The same type of resultsis obtained for systems of semilinear
elliptic PDEs.
Received: 26 September 2000 / Revised version: 22 March 2001 / Published online: 15 October 2001 相似文献
18.
Let be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field B
H
defined by
where are independent copies of B
0
H
. In this paper, the existence and joint continuity of the local times of B
H
are established.
Received: 2 October 2001 / Revised version: 7 January 2002 / Published online: 22 August 2002 相似文献
19.
Abstract. Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth
surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called
-subdivision , has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix 2I ,
-subdivision is based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points.
This paper concerns the problem of achieving maximal sum rule orders for stationary
-subdivision schemes with given mask support, which is important because the sum rule order characterizes the order of the
polynomial reproduction, and provides an upper bound on the Sobolev smoothness of the surface. We study both interpolating
and approximating schemes for a natural family of symmetric mask support sets related to squares of sidelength 2n in Z
2
, and obtain exact formulas for the maximal sum rule order for arbitrary n . For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit
family of schemes based on repeated averaging [15].
In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of
interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in
size by using symmetries. From this, we construct some new examples of smooth (C
2
,C
3
) interpolating
-subdivision schemes with maximal sum rule order and symmetric masks. The construction of associated dual schemes is also
discussed. 相似文献
20.
Viorel Barbu Aurel Răşcanu Gianmario Tessitore 《Applied Mathematics and Optimization》2003,47(2):97-120
Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat
equation (with Dirichlet boundary conditions in the bounded domain D
⊂ R
d
and multiplicative noise):
and for the corresponding backward dual equation:
We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward
equation.
\par 相似文献