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101.
András Telcs 《Journal of Theoretical Probability》1995,8(1):77-96
This paper continues the study of exponentsd(x), d
(x), d
R
(x) andd
(x) for graphG; and the nearest neighbor random walk {X
n
}
nN
onG, if the starting pointX
0=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e
,e
R
,e
are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph. 相似文献
102.
Tamás F. Móri 《Journal of Theoretical Probability》1995,8(1):139-164
Considering an infinite string of i.i.d. random letters drawn from a finite alphabet we define the cover timeW
n
as the number of random letters needed until each pattern of lenghtn appears at least once as a substring. Sharp weak and a.s. limit results onW
n
are known in the symmetric case, i.e., when the random letters are uniformly distributed over the alphabet. In this paper we determine the limit distribution ofW
n
in the nonsymmetric case asn. Generalizations in terms of point processes are also proved.Dedicated to Endre Csáki on his 60th birthday. 相似文献
103.
We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one. 相似文献
104.
F. B. Shepherd 《Mathematical Programming》1994,64(1-3):295-323
A 0, 1 matrixA isnear-perfect if the integer hull of the polyhedron {x0: Ax
} can be obtained by adding one extra (rank) constraint. We show that in general, such matrices arise as the cliquenode incidence matrices of graphs. We give a colouring-like characterization of the corresponding class of near-perfect graphs which shows that one need only check integrality of a certain linear program for each 0, 1, 2-valued objective function. This in contrast with perfect matrices where it is sufficient to check 0, 1-valued objective functions. We also make the following conjecture: a graph is near-perfect if and only if sequentially lifting any rank inequality associated with a minimally imperfect graph results in the rank inequality for the whole graph. We show that the conjecture is implied by the Strong Perfect Graph Conjecture. (It is also shown to hold for graphs with no stable set of size eleven.) Our results are used to strengthen (and give a new proof of) a theorem of Padberg. This results in a new characterization of minimally imperfect graphs: a graph is minimally imperfect if and only if both the graph and its complement are near-perfect.The research has partially been done when the author visited Mathematic Centrum, CWI, Amsterdam, The Netherlands. 相似文献
105.
It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs. 相似文献
106.
We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value. 相似文献
107.
QI Yuanhua GUAN Daren & LIU Chengbu . Institute of Theoretical Chemistry Shandong University Jinan China . School of Physics Microelectronics Shandong University Jinan China 《中国科学B辑(英文版)》2006,49(6):492-498
The density functional theory (DFT) combining with the non-equilibrium Green functions (NEGF) method is applied to the study of the electronic transport properties for a Di-thiol-benzene (DTB) molecule coupled to two Au(111) surfaces. The dependence of the transport properties on the bias, the coupling geometry of the molecule-electrode interface, and the intermolecular interaction are examined in detail. The results show that the existence of the hydrogen atom at the end of the DTB molecule would significantly decrease the transmission coefficients, and then the differential conductance (dI/dV). By changing the position of the DTB molecule located between two electrodes a maximum value of calculated current is observed. It is also found that the intermolecular interaction will strongly influence the transport properties of the system studied. 相似文献
108.
The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature
with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems. 相似文献
109.
Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs
and
, related by a chemical transformation
, the reaction graph
is determined using a maximal common subgraph defined for vertex mapping
. A binary operation defined for graphs constructed over the same vertex set enables us to decompose the reaction graph
into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at
and ending at
corresponds to a breakdown of the transformation
into a sequence of intermediates. 相似文献
110.
Garavelli M Ruggeri F Ogliaro F Bearpark MJ Bernardi F Olivucci M Robb MA 《Journal of computational chemistry》2003,24(11):1357-1363
MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted. 相似文献