On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems

Summary In recent years, a group of inverse iteration type algorithms have been developed for solving nonlinear elliptic eigenvalue problems in plasma physics [4]. Although these algorithms have been very successful in practice, no satisfactory theoretical justification of convergence has been available. The present paper fills this gap and proves for a large class of such problems and a simple version of such algorithms that linear convergence to a local maximum of a certain potential is obtained.This work was supported by the Deutsche Forschungsgemeinschaft, SFB 72 an der Universität Bonn     

On a “lack of memory” property

For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0]<P [Y<X]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless property relative to a continuous variable. Research partially supported by NRC of Canada grants #A8057 and #T0500. Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia.     

On nearly pseudocompact spaces

A completely regular space X is called nearly pseudocompact if υX?X is dense in βX?X, where βX is the Stone-?ech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X₁, X₂ such that Int X₁ is locally compact, no points of X₂ has a closed realcompact neighborhood, and $\text{Int(X}{}_1\text{?X}{}_2\text{)=?}$. It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact.     

The Ackermann function. a theoretical,computational, and formula manipulative study

Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is investigated.Results from tests with the Ackermann function of recursive procedure implementations in ALGOL-60, ALGOL W, PL/I and SIMULA-67 on IBM 360/75 and CD 6600 are given.A SYMBAL formula manipulating program, that automatically solves recurrence relations for the first members of the function class and for the number of calls needed in their straightforward computation, is given.The Ackermann rating of programming languages is discussed.     

Comments of the paper, “stochastic integral equations applied to telecommunications traffic without delay”

Let F be a univariate distribution with negative expectation, and let M denote the distribution of the positive maxima of a random walk generated by a sequence of independent observations from F. We consider the Laplace transforms of 1?F(x) and 1?M(x). A relation between the transforms yields some known results on the moments and the regularly varying properties of the two distributions.     

C60与聚乙烯咔唑（PVK）键合物和共混物在紫外激光作用下的碳笼增强融合

用飞行时间质谱测量３０８ｎｍ激光熔蚀Ｃ６０化学修饰的聚乙烯咔唑（Ｃ６０－ＰＶＫ）与Ｃ６０／聚乙烯咔唑共混物（Ｃ６０／ＰＶＫ）的产物分布，分析了正负离子质谱，发现明显的碳笼融合现象。比较分析了融合过程的增强机理，认为Ｃ６０与ＰＶＫ间的化学键合以及电荷转移络合分别在Ｃ６０－ＰＶＫ键合物和Ｃ６０／ＰＶＫ共混物的富勒烯融合过程中起了重要作用。     

On Subsets with Small Product in Torsion-Free Groups

G be a nonabelian torsion-free group. Let C be a finite generating subset of G such that . We prove that, for all subsets B of G with , we have . In particular, a finite subset X with cardinality satisfies the inequality if and only if there are elements , such that the following two conditions hold: (i) . (ii) where . Received: October 13, 1997/Revised: Revised August 18, 1998     

A hierarchy of approximate models for the Maxwell equations

Summary. In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter where is the characteristic velocity associated with the physical problem and is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models. Received May 18, 1995