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971.
Franz Merkl 《Probability Theory and Related Fields》2003,126(3):307-338
This article describes the almost sure infinite volume asymptotics of the ground state energy of random Schr?dinger operators
with scaled Gibbsian potentials. The random potential is obtained by distributing soft obstacles according to an infinite
volume grand canonical tempered Gibbs measure with a superstable pair interaction. There is no restriction on the strength
of the pair interaction: it may be taken, e.g., at a critical point. The potential is scaled with the box size in a critical
way, i.e. the scale is determined by the typical size of large deviations in the Gibbsian cloud. The almost sure infinite
volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles
involving only thermodynamic quantities. The qualitative behaviour of the ground state energy asymptotics is analysed: Depending
on the dimension and on the H?lder exponents of the free energy density, it is identified which cases lead to a phase transition
of the asymptotic behaviour of the ground state energy.
Received: 24 June 2002 / Revised version: 17 February 2003
Published online: 12 May 2003
Mathematics Subject Classification (2000): Primary 82B44; Secondary 60K35
Key words or phrases: Gibbs measure – H?lder exponents – Random Schr?dinger operator – Ground state – Large deviations 相似文献
972.
Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the
replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information
entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information. 相似文献
973.
Xiaoming Wang 《纯数学与应用数学通讯》2004,57(10):1265-1282
We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh‐Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer. © 2003 Wiley Periodicals, Inc. 相似文献
974.
We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995). 相似文献
975.
The Schlesinger equations S
(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation
of the general Schlesinger equations S
(n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates. 相似文献
976.
Alina Constantinescu 《Applications of Mathematics》2007,52(4):321-326
In one if his paper Luo transformed the problem of sum-fuzzy rationality into artificial learning procedure and gave an algorithm
which used the learning rule of perception. This paper extends the Luo method for finding a sum-fuzzy implementation of a
choice function and offers an algorithm based on the artificial learning procedure with fixed fraction. We also present a
concrete example which uses this algorithm. 相似文献
977.
The generalized independent set (GIS) problem was first introduced by Hochbaum and Pathria (Forest Sci 43(4), 544–554, 1997) and independently explored in greater detail by Hochbaum (Manage Sci 50(6), 709–123, 2004). This problem, with applications in forest management and a variety of related areas, is a generalization of the classical maximum independent set problem. In this paper we highlight a natural, nonlinear formulation for the problem that is an attractive alternative to the linear model found in the literature. The effectiveness of this alternative formulation is demonstrated by computational experience on test problems of varying size and density, disclosing a dramatic reduction in the time to obtain optimal and near optimal solutions and an ability to solve much larger problems. 相似文献
978.
Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported
spline-wavelets with minimum support and their derivatives. It is shown that with the alternating signs removed, all these
sequences are totally positive. On the other hand, truncations of the reciprocal Euler-Frobenius polynomials lead to finite
sequences for orthogonal wavelet decompositions. For this purpose, sharp estimates are given in terms of the exact reconstruction
of these approximate decomposed components.
Research supported by NSF Grant DMS 89-0-01345 and ARO Contract No. DAAL 03-90-G-0091. 相似文献
979.
980.
Wei-Min Wang 《Communications in Mathematical Physics》1995,172(2):401-425
We study the asymptotics for the density of states of the magnetic Schrödinger operator with a random potential. By using the methods of effective Hamiltonian, complex dilation and complex translation, we obtain in the large magnetic field limit, the asymptotic expansion for the density of states measure considered as a distribution. 相似文献