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101.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
102.
F. den Hollander 《Journal of statistical physics》1994,75(5-6):891-918
Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on 2 that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California. 相似文献
103.
Todor Todorov 《Transactions of the American Mathematical Society》1996,348(2):673-689
We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.
104.
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25. 相似文献
105.
The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion. 相似文献
106.
A. G. Schlijper 《Journal of statistical physics》1985,40(1-2):1-27
A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf
n on the free energy per lattice sitef and thatf
n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states. 相似文献
107.
Rate constants for the reaction of ethyl bromoacetate with three series of substituted naphthoate ions have been measured
in an acetone-water mixture (90% v/v). Using σ
p
values rate constants at 30o correlate well with the Hammett equation yielding ρ=−0.54, −0.19 and −0.25 for (4,1−), (6,1−) and (6,2−) series, respectively.
Comparison of these ρ values with those of the reaction of phenacyl bromide reveals the failure of the reactivity-selectivity
principle RSP in these reactions. Failure of RSP has been explained in terms of isoselective temperature. 相似文献
108.
Torrent-Sucarrat M Luis JM Solà M 《Chemistry (Weinheim an der Bergstrasse, Germany)》2005,11(20):6024-6031
The vibrational motions that disobey the minimum polarizability principle (MPP) in pi-conjugated molecules are distortions of the equilibrium geometry that produce a reduction in the polarizability due to the localization of pi electrons. For aromatic species, this electronic localization is responsible for the subsequent reduction in the aromaticity of the system. In the present work, we diagonalize the Hessian matrix of the polarizability with respect to the vibrational nontotally symmetric normal coordinates, to calculate the nontotally symmetric distortions that produce the maximum breakdown of the MPP in a series of twenty polycyclic aromatic hydrocarbons. It is shown that the nuclear displacements that break the MPP have larger components in those rings that possess the highest local aromaticity. Thus, these vibrational motions can be used as an indicator of local aromaticity. 相似文献
109.
On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation 总被引:1,自引:0,他引:1
Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts. 相似文献
110.