共查询到20条相似文献,搜索用时 843 毫秒
1.
Jason Fulman 《Annals of Combinatorics》2006,10(3):319-332
Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent,
identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of
a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
Received March 11, 2005 相似文献
2.
Simona Rota Nodari 《Annales Henri Poincare》2010,10(7):1377-1393
The aim of this work is to prove by a perturbation method the existence of solutions of the coupled Einstein–Dirac equations
for a static, spherically symmetric system of two fermions in a singlet spinor state. We relate the solutions of our equations
to those of the nonlinear Choquard equation and we show that the nondegenerate solution of Choquard’s equation generates solutions
of the Einstein–Dirac equations. 相似文献
3.
A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation
flux through the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates.
It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the
event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price’s law for the collapse of a self-gravitating
scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled
Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large
data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.’s in 2 independent variables. The technique
is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we
feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of
the first author concerning the internal structure of charged black holes, which had assumed the validity of Price’s law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real
scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou’s
C0-formulation, the conjecture is proven to be false. 相似文献
4.
S. A. Sergeev 《Differential Equations》2009,45(10):1514-1525
We seek the optimal boundary control of vibrations of a spherical layer in the spherically symmetric case. This paper continues
the series of papers by V.A. Il’in and his students and, unlike the previous papers, uses a more general control optimality
criterion. We obtain closed formulas for the controls; these formulas are consistent with Il’in’s earlier results. 相似文献
5.
Sourav Chatterjee 《Probability Theory and Related Fields》2007,138(1-2):305-321
We introduce a version of Stein’s method for proving concentration and moment inequalities in problems with dependence. Simple
illustrative examples from combinatorics, physics, and mathematical statistics are provided.
相似文献
6.
In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras. 相似文献
7.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
8.
M. C. Nucci 《Theoretical and Mathematical Physics》2007,151(3):851-862
In addition to the reduction method, we present a novel application of Jacobi’s last multiplier for finding Lie symmetries
of ordinary differential equations algorithmically. These methods and Lie symmetries allow unveiling the hidden linearity
of certain nonlinear equations that are relevant in physics. We consider the Einstein-Yang-Mills equations and Calogero’s
many-body problem in the plane as examples.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 495–509, June, 2007. 相似文献
9.
Dominique Fourdrinier William E. Strawderman Martin T. Wells 《Annals of the Institute of Statistical Mathematics》2006,58(1):73-92
In this article we consider estimating a location parameter of a spherically symmetric distribution under restrictions on
the parameter. First we consider a general theory for estimation on polyhedral cones which includes examples such as ordered
parameters and general linear inequality restrictions. Next, we extend the theory to cones with piecewise smooth boundaries.
Finally we consider shrinkage toward a closed convex set K where one has vague prior information that θ is in K but where θ is not restricted to be in K. In this latter case we give estimators which improve on the usual unbiased estimator while in the restricted parameter case
we give estimators which improve on the projection onto the cone of the unbiased estimator. The class of estimators is somewhat
non-standard as the nature of the constraint set may preclude weakly differentiable shrinkage functions. The technique of
proof is novel in the sense that we first deduce the improvement results for the normal location problem and then extend them
to the general spherically symmetric case by combining arguments about uniform distributions on the spheres, conditioning
and completeness. 相似文献
10.
Joseph Zaks 《Israel Journal of Mathematics》1971,10(2):244-251
We prove the analogue of Eberhard’s Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture
of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.
This research was supported by the National Research Council of Canada Grant A-3999. 相似文献
11.
A. F. Voronin 《Siberian Mathematical Journal》2011,52(1):41-53
We propose a method for determining the partial indices of matrix functions with some symmetries. It rests on the canonical
factorization criteria of the author’s previous articles. We show that the method is efficient for the symmetric classes of
matrix functions: unitary, hermitian, orthogonal, circular, symmetric, and others. We apply one of our results on the partial
indices of Hermitian matrix functions and find effective well-posedness conditions for a generalized scalar Riemann problem
(the Markushevich problem). 相似文献
12.
Chuanming Zong 《Monatshefte für Mathematik》2002,42(2):247-255
In this article we study the simultaneous packing and covering constants of two-dimensional centrally symmetric convex domains. Besides an identity result between translative case and lattice case and a general upper bound, exact values for some special domains are determined. Similar to Mahler and Reinhardt’s result about packing densities, we show that the simultaneous packing and covering constant of an octagon is larger than that of a circle. 相似文献
13.
Recent advances in Stein’s lemma imply that under elliptically symmetric distributions all rational investors will select a portfolio which lies on Markowitz’ mean–variance efficient frontier. This paper describes extensions to Stein’s lemma for the case when a random vector has the multivariate extended skew-Student distribution. Under this distribution, rational investors will select a portfolio which lies on a single mean–variance–skewness efficient hyper-surface. The same hyper-surface arises under a broad class of models in which returns are defined by the convolution of a multivariate elliptically symmetric distribution and a multivariate distribution of non-negative random variables. Efficient portfolios on the efficient surface may be computed using quadratic programming. 相似文献
14.
Éric Gaudron 《manuscripta mathematica》2009,130(2):159-182
A Siegel’s lemma provides an explicit upper bound for a non-zero vector of minimal height in a finite dimensional vector spaces
over a number field. This article explains how to obtain Siegel’s lemmas for which the minimal vectors do not belong to a
finite union of vector subspaces (Siegel’s lemmas with conditions). The proofs mix classical results of adelic geometry of numbers and an adelic variant of a theorem of Henk about the number
of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. 相似文献
15.
Extreme properties of quermassintegrals of convex bodies 总被引:3,自引:0,他引:3
In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the
well-known Aleksandrov’ s projection theorem and Loomis-Whitney’ s inequality, respectively. Applying these two theorems,
we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the
perturbation element of a convex body, and prove an extreme property of it. 相似文献
16.
We define dynamical models on the q-Minkowski space algebra (which is a particular case of the Reflection Equation Algebra) as deformations (quantizations) of dynamical models with rotational symmetries, and we find their integrals. In particular, we introduce a q-analog of the Runge-Lenz vector and a q-analog of the dynamics in space-time with a spherically symmetric metric. 相似文献
17.
Chuanming Zong 《Monatshefte für Mathematik》2002,134(3):247-255
In this article we study the simultaneous packing and covering constants of two-dimensional centrally symmetric convex domains.
Besides an identity result between translative case and lattice case and a general upper bound, exact values for some special
domains are determined. Similar to Mahler and Reinhardt’s result about packing densities, we show that the simultaneous packing
and covering constant of an octagon is larger than that of a circle.
(Received 17 January 2001; in revised form 13 July 2001) 相似文献
18.
David W. Barnette 《Israel Journal of Mathematics》1971,9(3):290-298
Steinitz’ theorem states that a graph is the graph of a 3-dimensional convex polytope if and only if it is planar and 3-connected.
Grünbaum has shown that Steinitz’ proof can be modified to characterize the graphs of polytopes that are centrally symmetric
or have a plane of symmetry. We show how to modify Steinitz’ proof to take care of the remaining involutory case—polytopes
that are symmetric about a line.
Research supported by NSF Grant GP-3470. 相似文献
19.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,55(2):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
20.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,47(10):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献