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91.
It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes
the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of
fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant
coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in
the N→∞ limit) of an
isolated
N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation.
An erratum to this article can be found at 相似文献
92.
Signed graphs for portfolio analysis in risk management 总被引:1,自引:0,他引:1
Harary Frank; Lim Meng-Hiot; Wunsch Donald C. 《IMA Journal of Management Mathematics》2002,13(3):201-210
We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable. 相似文献
93.
94.
Johan Helsing 《BIT Numerical Mathematics》2006,46(2):307-323
A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come
from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating
distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar
to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that
of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with
up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners
of otherwise similar construction, and especially so when the preconditioners are very sparse.
AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30 相似文献
95.
Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates
The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination. 相似文献
96.
97.
Modulo some natural generalizations to noncompact spaces, we show in this Letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result, i.e. the noncommutative Yang–Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fits into the rigorous framework of noncommutative geometry. 相似文献
98.
A series of low density polyethylene systems has been studied with respect to structural evolution and short-term dielectric breakdown behaviour. All materials were based upon a single polymer, that is commonly used in high voltage applications, but with different additives. In all three of these systems, multiple melting transitions were observed, as a result of molecular fractionation effects during crystallization. In the virgin polymer, a space-filling banded spherulitic morphology was found to develop at low temperatures (102 °C and below) whereas, at higher temperatures, only a few isolated axialites were observed. Inclusion of the antioxidant resulted in greatly increased nucleation densities, such that, at low temperatures, no evidence of spherulitic organisation remained. At higher temperatures, sheaf-like lamellar aggregates developed, which were much smaller and much more numerous than in the case of the virgin polymer. Further addition of dicumyl peroxide (DCP) resulted in the rapid formation of a crosslinked network at 200 °C. Some crosslinking also occurred at 150 °C, but over a much longer timescale. Where extensive crosslinking occurred prior to crystallization, the resulting gel inhibited structural development, such that only a few small, isolated sheaves were able to form at 102 °C. In view of the principal application area of this material, the breakdown strength of each of the above systems was then measured and the whole data set was analysed statistically. When structural factors were considered alongside the statistics, no clear trends emerged to indicate that either the compositional or morphological variations were reflected in the short-term electrical failure processes. 相似文献
99.
We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase. 相似文献
100.
GU Bai-Ping REN Zhong-Zhou 《理论物理通讯》2005,44(2):337-342
The Dirac optical potential for p-^14 Be elastic scattering is evaluated by the relativistic impulse approximation. Each of the real part and the imaginary part of the potential shows a pronounced “long tail” for the proton elastic scattering from halo nucleus ^14Be compared with the potentials for proton scattering from its adjacent nuclei ^12C and ^16O, which do not have halo structures.This kind of “long tail” phenomenon suggests another signature for halo nuclei. 相似文献