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41.
For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller–Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg–Martin's (white noise initial velocity) and Carraro–Duchon's Lévy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases. 相似文献
42.
43.
Jean-Pierre Changeux Alain Connes M. B. DeBevoise Jean Petitot Mark Anspach 《Mathematical Intelligencer》2005,27(4):48-56
Conclusion The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It
re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge
and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between
a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception
that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities.
It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book
is to cast a spotlight on this confrontation. 相似文献
44.
Pierre Antoine Grillet 《Semigroup Forum》1995,50(1):317-326
An explicit upper bound is given for the number of commutative semigroups withn elements. 相似文献
45.
Pierre Antoine Grillet 《Semigroup Forum》2007,74(1):41-54
New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen
existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the
multiplication table in detail and provide a numerical profile with which it can be compared to other rows. 相似文献
46.
A general framework is developed to treat inverse problems with parameters that are random fields. It involves a sampling
method that exploits the sensitivity derivatives of the control variable with respect to the random parameters. As the sensitivity
derivatives are computed only at the mean values of the relevant parameters, the related extra cost of the present method
is a fraction of the total cost of the Monte Carlo method. The effectiveness of the method is demonstrated on an example problem
governed by the Burgers equation with random viscosity. It is specifically shown that this method is two orders of magnitude
more efficient compared to the conventional Monte Carlo method. In other words, for a given number of samples, the present
method yields two orders of magnitude higher accuracy than its conventional counterpart. 相似文献
47.
48.
Jean E. Taylor 《Discrete and Computational Geometry》1991,6(1):225-262
We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number
of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS.
The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford
University, where this paper was extensively rewritten, are gratefully acknowledged. 相似文献
49.
Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained. 相似文献
50.
The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and 13C NMR allows an accurate measure of the ee. 相似文献