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81.
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
82.
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
83.
Pogliani L 《Journal of computational chemistry》2003,24(9):1097-1109
The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model. 相似文献
84.
Bholanath Mandal 《International journal of quantum chemistry》2005,103(2):140-148
A graph theoretical procedure for obtaining eigenvalues of linear chains and cycles having alternant vertex weights (h1, h2, h1, h2, h1, h2, …) and the same edge weight (k) have been developed. The eigenvalues of some complicated graphs, such as graphs of linear polyacenes, methylene‐substituted linear polyacenes and cylindrical polyacene strips, stack graphs, and reciprocal graphs have been shown to be generated in closed analytical forms by this procedure. Many such graphs represent chemically important molecules or radicals. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
85.
Teobald Kupka Roman Wrzalik Gra
yna Pasterna Karol Pasterny 《Journal of Molecular Structure》2002,616(1-3):17-32
The results of extended MO calculations using density functional theory (DFT) approximation supported by experimental Raman, 1H and 13C NMR studies on thiophene are reported. Raman spectra of liquid thiophene were re-examined and the performance of a hybrid B3PW91 density functional was compared with the ab initio restricted Hartree–Fock (RHF) method. With the basis sets of the 6-311++G** quality, the DFT calculated bond lengths, dipole moments and harmonic vibrations were predicted in a very good agreement with available experimental data.
Additionally, the results on thiophene were extended by calculations on 3-methylthiophene and selenophene. In this case, a significant change in geometry and charge distribution in thiophene ring due to a methyl group substituent or replacement of sulphur by selene atom was observed.
A linear correlation between the predicted harmonic vibrational frequencies (scaled using SQM method) and experimental ones for thiophene, selenophene and 3-methylthiophene was shown. The theoretically calculated spectra have satisfactorily reproduced the available experimental spectra for thiophene and selenophene. 相似文献
86.
Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004). 相似文献
87.
Suppose k 1 ,<, k m and n are positive integers such that k 1 + … + k m h n . We characterize those k i × k i Hermitian matrices A i , i = 1, < , m that can appear as diagonal blocks of an n × n Hermitian matrix C with prescribed eigenvalues. The characterization will be given in terms of the eigenvalues of C and A i , i = 1, <, m . Our results extend those of Thompson and Freede, Horn, Fan and Pall. 相似文献
88.
In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of n-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface tensors, whereas the other algorithm is based on noisy measurements of a finite number of harmonic intrinsic volumes. The derived stability results ensure consistency of the two algorithms. Examples that illustrate the feasibility of the algorithms are presented. 相似文献
89.
90.
Luis Escauriaza 《偏微分方程通讯》2013,38(5-6):821-845
It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds. 相似文献