共查询到20条相似文献，搜索用时 328 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.
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
3.
We prove that the G?del incompleteness theorem holds for a weak arithmetic T = IΔ0 + Ω2 in the form
where Cons
H
(T) is an arithmetic formula expressing the consistency of T with respect to the Herbrand notion of provability.
Received: 22 September 1997 / Revised version: 27 March 2000 /?Published online: 15 June 2001 相似文献
4.
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
5.
C. Bahadoran 《Probability Theory and Related Fields》1998,110(3):287-331
Summary. We prove hydrodynamical limit for spatially heterogeneous, asymmetric simple exclusion processes on Z
d
. The jump rate of particles depends on the macroscopic position x through some nonnegative, smooth velocity profile α(x). Hydrodynamics are described by the entropy solution to a spatially heterogeneous conservation law of the form
To derive this result, we prove an alternative characterization of entropy solutions involving stationary solutions, and work
with macroscopically stationary states rather than the unknown stationary measures of the process. The method can be extended
to spatially heterogeneous, asymmetric misanthrope processes with slow birth and death.
Received: 11 November 1996/In revised form: 10 October 1997 相似文献
6.
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
7.
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
8.
Djairo G. de Figueiredo Ireneo Peral Julio D. Rossi 《Annali di Matematica Pura ed Applicata》2008,187(3):531-545
In this paper we look for existence results for nontrivial solutions to the system,
with Dirichlet boundary conditions, u = v = 0 on and α, β < N. We find the existence of a critical hyperbola in the (p,q) plane (depending on α, β and N) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking theorem).
I. Peral was partially supported by project MTM2004-02223 of MEC, Spain. J. D. Rossi partially supported by Universidad de
Buenos Aires (grant TX066), ANPCyT and Fundacion Antorchas. 相似文献
9.
The central limit theorem for Markov chains with normal transition operators, started at a point 总被引：2，自引：0，他引：2
The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov
chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point,
almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains
whose transition operator is normal.
Received: 28 March 2000 / Revised version: 25 July 2000 /?Published online: 15 February 2001 相似文献
10.
11.
elements of some (finite) poset , write for the probability that precedes in a random (uniform) linear extension of . For define
where the infimum is over all choices of and distinct .
Addressing an issue raised by Fishburn [6], we give the first nontrivial lower bounds on the function . This is part of a more general geometric result, the exact determination of the function
where the infimum is over chosen uniformly from some compact convex subset of a Euclidean space.
These results are mainly based on the Brunn–Minkowski Theorem and a theorem of Keith Ball [1], which allow us to reduce to
a 2-dimensional version of the problem.
Received: October 6, 1997 相似文献
12.
José Carlos Sierra 《Mathematische Zeitschrift》2009,262(3):517-525
Let E be a globally generated vector bundle of rank e ≥ 2 over a reduced irreducible projective variety X of dimension n defined over an algebraically closed field of characteristic zero. Let L := det(E). If deg(E) := deg(L) = L
n
> 0 and E is not isomorphic to , we obtain a sharp bound
on the degree of E, proving also that deg(L) = h
0(X, L) − n if equality holds. As an application, we obtain a Del Pezzo–Bertini type theorem on varieties of minimal degree for subvarieties
of Grassmannians, as well as a bound on the sectional genus for subvarieties of degree at most N + 1.
Research partially supported by the Spanish MCYT project MTM2006-04785 and by the program “Profesores de la UCM en el extranjero.
Convocatoria 2006”. 相似文献
13.
Equations with two time scales (refinement equations or dilation equations) are central to wavelet theory. Several applications
also include an inhomogeneous forcing term F(t). We develop here a part of the existence theory for the inhomogeneous refinement
equation
where a (k) is a finite sequence and F is a compactly supported distribution on ℝ.
The existence of compactly supported distributional solutions to an inhomogeneous refinement equation is characterized in
terms of conditions on the pair (a, F).
To have Lp solutions from F ∈ Lp(ℝ), we construct by the cascade algorithm a sequence of functions φ0 ∈ Lp(ℝ) from a compactly supported initial function ℝ as
A necessary and sufficient condition for the sequence {φn} to converge in Lp(ℝ)(1 ≤ p ≤ ∞) is given by the p-norm joint spectral radius of two matrices derived from the mask a. A convexity property
of the p-norm joint spectral radius (1 ≤ p ≤ ∞) is presented.
Finally, the general theory is applied to some examples and multiple refinable functions.
Acknowledgements and Notes. Research supported in part by Research Grants Council and City University of Hong Kong under Grants #9040281, 9030562, 7000741. 相似文献
14.
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
15.
Michael Fuchs 《Monatshefte für Mathematik》2003,139(3):177-203
In [7], LeVeque proved a central limit theorem for the number of solutions p,q of
subject to the conditions
where x [0,1] and f satisfies certain assumptions. The case d = 1 was considerably improved a few years later by Philipp [8]. We give a common extension of both results by proving almost sure and distribution type invariance principles. Our results entail several corollaries, e.g. a functional central limit theorem and a Strassens type version of the iterated logarithm law.Received December 28, 2001; in revised form July 31, 2002
Published online April 4, 2003 相似文献
16.
Chong Li Shujie Li Zhaoli Liu 《Calculus of Variations and Partial Differential Equations》2008,32(2):237-251
In this paper we study the jumping nonlinear problem
together with its energy functional
Convexity and concavity of J
(b,a)(u) in the case where Ky Fan’s minimax theorem does not directly work is studied, existence of type (II) regions is verified,
and unique solvability of the problem
is investigated.
Chong Li was supported by NSFC(10601058), NSFC(10471098), NSFC(10571096), and TYF(10526027)
Shujie Li was supported by NSFC(10471098) and NSFB(KZ200610028015)
Zhaoli Liu was supported by NSFC(10571123), NSFB(KZ200610028015), and PHR(IHLB). 相似文献
17.
Jeff Kahn 《Combinatorica》2000,20(3):339-391
Dedicated to the memory of Paul Erdős, both for his pioneering discovery of normality in unexpected places, and for his questions,
some of which led (eventually) to the present work.
For a simple graph G, let be the size of a matching drawn uniformly at random from the set of all matchings of G. Motivated by work of C. Godsil [11], we give, for a sequence and , several necessary and sufficient conditions for asymptotic normality of the distribution of , for instance
(where
E
and is the size of a largest matching in ). In particular this gives asymptotic normality for any sequence of regular graphs (of positive degree) or graphs with perfect
matchings. When tends to a finite limit, a sufficient (and probably necessary) condition is given for to be asymptotically Poisson.
The material presented here suggests numerous related questions, some of which are discussed in the last section of the paper.
Received April 9, 1999/Revised December 6, 1999 相似文献
18.
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
19.
Let β
0=0.308443… denote the Littlewood-Salem-Izumi number, i.e., the unique solution of the equation
In this paper it is proved that if a
0≥a
1≥⋅⋅⋅≥a
n
>0 and
, k≥1 then for all θ∈(0,π)
and furthermore, the number β
0 is best possible in the sense that for any β∈(0,β
0)
where the coefficients c
k
(β) are defined as
Results for the sine sums are obtained as well.
These results generalize and sharpen the well known trigonometric inequalities of Vietoris.
This research was supported by a grant from the Australian Research Council. The second author was also supported in part
by the NSERC Canada under grant G121211001. The third author was also supported in part by the NSFC of China under grant 10471010. 相似文献
20.
Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献