新经典MHD效应与内扭曲模本征方程

本文从一简化的新经典ＭＨＤ方程组出发，利用气球模表示及多尺度近似等方法，在ｑ＝１磁面附近的过渡层内导出了包含新经典ＭＨＤ效应的内扭曲模本征方程。与从前相关工作的比较表明，新经典ＭＨＤ效应对通常采用的磁流体或电阻磁流体内扭曲模本征方程，均产生十分重要的修正。     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

ＡＭＯＤＥＬＦＯＲＷＨＩＴＥＮＯＩＳＥＡＮＡＬＹＳＩＳＩＮＰ－ＡＤＩＣＮＵＭＢＥＲＦＩＥＬＤＳ（黄志远）￥ＡｎｄｒｅｗＫｈｒｅｎｎｉｋｏｖ（ＭｏｓｃｏｗＩｎｓｔ．ｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，１０３４９８，Ｚｅｌｅｎｏｇｒａｄ，Ｋ－...     

On Fourier transform of generalized Brownian functionals

Let $\text{(L}{}^2\text{)}{}_{\mathrm{<mtext>B</mtext><mtext>?</mtext>}}{}^{\mathrm{?}}$ and $\text{(L}{}^2\text{)}{}_{\mathrm{<mtext>b</mtext><mtext>?</mtext>}}{}^{\mathrm{?}}$ be the spaces of generalized Brownian functionals of the white noises ? and ?, respectively. A Fourier transform from $\text{(L}{}^2\text{)}{}_{\mathrm{<mtext>B</mtext><mtext>?</mtext>}}{}^{\mathrm{?}}$ into $\text{(L}{}^2\text{)}{}_{\mathrm{<mtext>b</mtext><mtext>?</mtext>}}{}^{\mathrm{?}}$ is defined by ??(?) = ∫$\text{S}$¹: exp[?i ∫_$\text{R}$?(t) ?(t) dt]: ${}_{\mathrm{<mtext>b</mtext><mtext>?</mtext>}}\text{?(}\text{B}\text{?}\text{) dμ(}\text{B}\text{?}$), where : :${}_{\mathrm{<mtext>b</mtext><mtext>?</mtext>}}$ denotes the renormalization with respect to ? and μ is the standard Gaussian measure on the space $\text{S}$¹ of tempered distributions. It is proved that the Fourier transform carries ?(t)-differentiation into multiplication by i?(t). The integral representation and the action of?? as a generalized Brownian functional are obtained. Some examples of Fourier transform are given.     

An extension and analysis of the Shu-Osher representation of Runge-Kutta methods

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is total-variation-diminishing (TVD). Much attention has been paid to these representations in the literature.

In general, a Shu-Osher representation of a given Runge-Kutta method is not unique. Therefore, of special importance are representations of a given method which are best possible with regard to the stepsize condition that can be derived from them.

Several basic questions are still open, notably regarding the following issues: (1) the formulation of a simple and general strategy for finding a best possible Shu-Osher representation for any given Runge-Kutta method; (2) the question of whether the TVD property of a given Runge-Kutta method can still be guaranteed when the stepsize condition, corresponding to a best possible Shu-Osher representation of the method, is violated; (3) the generalization of the Shu-Osher approach to general (possibly implicit) Runge-Kutta methods.

In this paper we give an extension and analysis of the original Shu-Osher representation, by means of which the above questions can be settled. Moreover, we clarify analogous questions regarding properties which are referred to, in the literature, by the terms monotonicity and strong-stability-preserving (SSP).

     

Nonlinear Commutation Relations: Representations by Point-Supported Operators

We present a class of non-Lie commutation relations admitting representations by point-supported operators (i.e., by operators whose integral kernels are generalized point-supported functions). For such relations we construct all operator-irreducible representations (up to equivalence). Each representation is realized by point-supported operators in the Hilbert space of antiholomorphic functions. We show that the reproducing kernels of these spaces can be represented via hypergeometric series and the theta function, as well as via their modifications. We construct coherent states that intertwine abstract representations with irreducible representations.     

The Magnus representation of the Torelli group

In this paper we consider the Magnus representation of the Torelli group. We prove that it is not faithful by showing a non-trivial element in the kernel of this representaion.

     

Efficient parallel exponentiation in using normal basis representations

Von zur Gathen proposed an efficient parallel exponentiation algorithm in finite fields using normal basis representations. In this paper we present a processor-efficient parallel exponentiation algorithm in GF(qⁿ) which improves upon von zur Gathen's algorithm. We also show that exponentiation in GF(qⁿ) can be done in O((log₂n)²/log_qn) time using n/(log₂n)² processors. Hence we get a processor-time bound of O(n/log_qn), which matches the best known sequential algorithm. Finally, we present an efficient on-line processor assignment scheme which was missing in von zur Gathen's algorithm.     

SL(2,R)上的Fourier变换的渐近性质的注记

该文借助于犛犔（２，犚）上李代数及其万有包络代数讨论了犛犔（２，犚）上函数的Ｆｏｕｒｉｅｒ变换在无穷远处下降的阶与函数的光滑性的关系，我们得到的结论较［６］中的结论好，并由此得到犆２犮（犌）中的Ｐｌａｎｃｈｅｒｅｌ定理．     

Sensitivity Analysis of M-Estimates of Nonlinear Regression Model: Influence of Data Subsets

Asymptotic representations of the difference of M-estimators of the parameters of nonlinear regression model for the full data and for the subsample of data are given for the following three situation: i) fix number of points excluded from data, ii) increasing number, however asymptotically negligible part of data excluded, and finally iii) asymptotically fix portion of data excluded. Asymptotic normality of the difference of estimators (for the two latter cases) is proved.