Approximation characteristics for diagonal operators in different computational settings

First we study several extremal problems on minimax, and prove that they are equivalent. Then we connect this result with the exact values of some approximation characteristics of diagonal operators in different settings, such as the best n-term approximation, the linear average and stochastic n-widths, and the Kolmogorov and linear n-widths. Most of these exact values were known before, but in terms of equivalence of these extremal problems, we present a unified approach to give them a direct proof.     

Randomization of Sharkovskii-type theorems

We formulate an abstract scheme for the randomization of Shar- kovskii-type theorems via transformation to the deterministic case. In particular, Sharkovskii-type theorems for scalar differential equations can be randomized in this way. A random version of the standard Sharkovskii theorem is presented explicitly. Many remarks, comments and illustrating examples are supplied.

     

Optimal stopping for extremal processes

For an extremal process (Z_t)_t the optimal stopping problem for X_t = f(Z_t)?g(t) gives the continuous time analogue of the optimal stopping problem for max{Y₁,…,Y_k}?c_k where Y₁, Y₂,… are i.i.d. For the continuous time problem we derive optimal stopping times in explicit form and also show that the optimal stopping boundary is the limit of the optimal stopping boundaries for suitably standardized discrete problems.     

关于Cn中积分表示的拓广问题

指出文［４］所得的结果只是Ｌｅｒａｙ公式和Ｃａｕｃｈｙ－Ｆａｎｔａｐｐｉｅ公式的特殊情况。     

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

In this paper hierarchical Bayes and empirical Bayes results are used to obtain confidence intervals of the population means in the case of real problems. This is achieved by approximating the posterior distribution with a Pearson distribution. In the first example hierarchical Bayes confidence intervals for the Efron and Morris (1975, J. Amer. Statist. Assoc., 70, 311–319) baseball data are obtained. The same methods are used in the second example to obtain confidence intervals of treatment effects as well as the difference between treatment effects in an analysis of variance experiment. In the third example hierarchical Bayes intervals of treatment effects are obtained and compared with normal approximations in the unequal variance case.Financially supported by the CSIR and the University of the Orange Free State, Central Research Fund.     

Inference for earthquake models: A self-correcting model

Questions of asymptotic inference are discussed for a point process model in which the conditional intensity function increases monotonically between events and drops by determined (nonrandom) amounts after each event. Parameter estimates are shown to be consistent and, except under the null hypothesis of a Poisson process, normally distributed. Under the null hypothesis, however, the Hessian matrix is not asymptotically constant, and the limiting distribution of the likelihood ratio statistics is not χ², but has a form related to that of the Cramer-von Mises ω² statistic for the test of goodness of fit.     

Asymptotics of solutions for sub critical non‐convective type equations

We study the Cauchy problem for non‐linear dissipative evolution equations (1) where ?? is the linear pseudodifferential operator and the non‐linearity is a quadratic pseudodifferential operator (2) û ≡ ?_x→ξ u is the Fourier transformation. We consider non‐convective type non‐linearity, that is we suppose that a(t,0,y) ≠ 0. Let the initial data , are sufficiently small and have a non‐zero total mass , where is the weighted Sobolev space. Then we give the main term of the large time asymptotics of solutions in the sub critical case. Copyright © 2004 John Wiley & Sons, Ltd.     

一类齐三次系统的全局结构

本文讨论了一类齐三次系统的全局结构，并给出了它们的系数条件．     

Analysis theory of random energy of train derailment in wind

Based on the analysis theory of random energy of train derailment, an analysis theory of random energy of train derailment in wind is suggested. Two methods are proposed -the time domain method and the frequency domain method of analysis theory of random energy of train derailment in wind. The curves of σ pw -v under various wind speeds are obtained through the computation. The original curve of σ p -v is expanded, which turns the analysis theory of random energy of train derailment into the all-weather theory. Train derailment condition has been established under wind action. The first and second criterions of train derailment have been proposed in light of wind action. The analysis of train derailment cases at home or abroad is made, in- cluding the first analysis of Xinjiang train derailment case encountered 13-level of gale, which explained the inevitability of train derailment. The analysis theory of random energy of train derailment in wind shows its validity and accuracy. The input energy σ pw of the transverse vibration of train-track(bridge)-wind system is linked to train speed. With the establishment of the analysis theory of random energy of train derailment in wind, It is likely to initiate an all-weather speed limit map for a train or any high-speed train.