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61.
62.
Summary. In this paper we again consider the rate of convergence of the conjugate gradient method. We start with a general analysis
of the conjugate gradient method for uniformly bounded solutions vectors and matrices whose eigenvalues are uniformly bounded
and positive. We show that in such cases a fixed finite number of iterations of the method gives some fixed amount of improvement
as the the size of the matrix tends to infinity. Then we specialize to the finite element (or finite difference) scheme for
the problem . We show that for some classes of function we see this same effect. For other functions we show that the gain made by performing a fixed number of iterations of the
method tends to zero as the size of the matrix tends to infinity.
Received July 9, 1998 / Published online March 16, 2000 相似文献
63.
Shlomo Margel Ella Cohen Yehudit Dolitzky Orit Sivan 《Journal of polymer science. Part A, Polymer chemistry》1992,30(6):1103-1110
The synthesis and characterization of novel surfaces composed of polyacrolein microspheres covalently bonded onto polyethylene films are described. These surfaces were prepared through a sequence of reactions carried out onto polyethylene films in order to form primary amine groups at the w position. Polyacrolein microspheres in water were then covalently bonded to these modified polyethylene surfaces. The binding between the microspheres and the modified surfaces is due to the interaction between the aldehyde groups of the microspheres and the amine groups of the modified surfaces to form the polyvalent Schiff base bonds. Fourier transform-infrared/attenuated total reflection, electron spectroscopy for chemical analysis, contact angle measurements, and scanning electron microscopy have been used for the characterization of the modified polyethylene surfaces. 相似文献
64.
Shlomo Levental 《Probability Theory and Related Fields》1988,80(1):101-118
Summary We study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type. Then we apply those results to Harris recurrent Markov chains based on some ideas of K. Athreya, P. Ney and E. Nummelin. 相似文献
65.
Shlomo Moran 《Journal of Combinatorial Theory, Series B》1984,37(2):113-141
Let V be a set of n points in Rk. Let d(V) denote the diameter of V, and l(V) denote the length of the shortest circuit which passes through all the points of V. (Such a circuit is an “optimal TSP circuit”.) lk(n) are the extremal values of l(V) defined by lk(n)=max{l(V)|V∈Vnk}, where Vnk={V|V?Rk,|V|=n, d(V)=1}. A set V∈Vnk is “longest” if l(V)=lk(n). In this paper, first some geometrical properties of longest sets in R2 are studied which are used to obtain l2(n) for small n′s, and then asymptotic bounds on lk(n) are derived. Let δ(V) denote the minimal distance between a pair of points in V, and let: δk(n)=max{δ(V)|V∈Vnk}. It is easily observed that . Hence, exists. It is shown that for all , and hence, for all . For k=2, this implies that , which generalizes an observation of Fejes-Toth that . It is also shown that . The above upper bound is used to improve related results on longest sets in k-dimensional unit cubes obtained by Few (Mathematika2 (1955), 141–144) for almost all k′s. For k=2, Few's technique is used to show that . 相似文献
66.
Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot
–1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation
, whereL is a constant. 相似文献
67.
This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency * for which the mean residence time on the line segment is a minimum. It is shown that for a random walk on a line segment of lengthL the mean residence time goes likeL
2 for largeL when *, but when =* the dependence is proportional toL. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation. 相似文献
68.
S. Shlomo Ye. A. Bogila V. M. Kolomietz A. I. Sanzhur 《Zeitschrift für Physik A Hadrons and Nuclei》1995,353(1):27-30
We present a calculation of the nuclear level density
ph(E) for a fixed number of particlesp and holesh, taking into account the energy dependence of the singleparticle level densityg(). We demonstrate the significant effects of the finite depth of the potential well (continuum effect) and the finite surface thickness of the nucleus on the value of
ph(E).Communicated by: X. Campi 相似文献
69.
Shlomo Levental 《Journal of Theoretical Probability》1989,2(3):271-287
This paper develops a method to get empirical central limit theorems for martingale differences that are uniformly bounded. The main idea is to generalize to martingales some ideas of E. Gine and J. Zinn [Ann. Prob.
12, 929–989 (1984)]. We consider two examples: An extension of a theorem of R. Dudley from i.i.d. to a certain type of Markov chain, and a uniform CLT for the baker's transformation. 相似文献
70.