Diffusive properties of motion on a bumpy plane

We report on experiments studying the statistical properties of the motion of balls on a bumpy surface. This motion is found to be diffusive. In the direction of the mean flow, the coefficient of diffusion is found to attain a constant value, independent of the size of the ball and the inclination angle. The diffusion transverse to the mean flow is characterized by a coefficient which decreases with the inclination of the plane, and scales with the size of moving ball. Received: 13 March 1997 / Revised: 10 December 1997 / Accepted: 17 February 1998     

Computability of String Functions Over Algebraic Structures Armin Hemmerling

We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a BSS-like manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper.     

New experimental studies on the quaternary fission of <Superscript>233, 235</Superscript>U(n<Subscript>th</Subscript>, f ) and <Superscript>252</Superscript>Cf (sf )

Experiments have been performed for studying quaternary fission (QF) in spontaneous fission of ²⁵²Cf, on the one hand, and for the neutron-induced fission reactions ^{233, 235}U(n_th, f ), on the other hand. In this higher-multiplicity fission mode, by definition, four charged products appear in the final state. In other words, as a generalization of the ternary-fission process, not only one but two light charged particles (LCPs) are accompanying the splitting of an actinide nucleus into the customary pair of fission fragments. In the two sets of measurements, which have used quite different approaches, the yields of several QF reactions with α-particles and tritons as the LCPs have been determined and the corresponding kinetic-energy distributions of the α-particles measured. The QF process can appear in two basically different ways: i) the simultaneous creation of two LCPs in the act of fission (“true” QF) and ii) via a fast sequential decay of a single but particle-unstable LCP in common ternary fission (“pseudo” QF). Experimentally the two varieties of QF have been distinguished by exploiting the different patterns of angular correlations between the two outgoing LCPs. The experiments described in the present paper are the first to demonstrate that both types of reactions, true and pseudo QF, occur with quite comparable probabilities. As a new result also, the kinetic-energy distributions related to the two processes have been shown to be significantly different. For all QF reactions which could be explored, the yields for ²⁵²Cf(sf) were found to be roughly by an order of magnitude larger than the yields found in the ²³³U(n_th, f ) and ²³⁵U(n_th, f ) reactions. An interesting by-product has been the measurement of yields of excited LCPs which allows to deduce nuclear temperatures at scission by comparison to the respective yields in the ground state.     

Review: Experiments in Fundamental Physics Scheduled and in Development for the ISS

This is a review of those experiments in the area of Fundamental Physics that are either approved by ESA and NASA, or are currently under development, which are to be performed in the microgravity environment of the International Space Station. These experiments cover the physics of liquid Helium (SUE, BEST, MISTE, DYNAMX, and EXACT), ultrastable atomic clocks (PHARAO, PARCS, RACE), ultrastable microwave resonators (SUMO), and particle detectors (AMS and EUSO). The scientific goals are to study more precisely the universality properties of liquid Helium under microgravity conditions, to establish better time standards and to test the universality of the gravitational red shift, to make more precise tests of the constancy of the speed of light, and to measure the particle content in space directly without disturbances from the Earth's inner atmosphere.     

一般退化时滞微分系统解的存在性及通解

研究退化时滞系统Ex（t）=Ax（t）＋Bx（t-1）＋f（t）（t≥0），x（t）=（t)-1≤t≤0），其中E、A、B∈Rm×n，x（t）∈Rn，f（t）∈Rm．给出了上述系统解的存在性条件及通解表达式．     

浙江教育会考略

浙江教育会是清末民初的一个涵盖会省的民间教育团体。尽管共活动时间不长，但在研究新教育、传播新文化、新观念等方面，做了不少的工作，在浙江教育的近代化中起过极其重要的作用。     

线性方程组Ax=b的反问题的一般解

给出了线性方程组Ax=b的反问题在n阶矩阵类中解的一般形式．     

New results on general observers for nonlinear systems

In this paper, we establish that detectability is a necessary condition for the existence ofgeneral observers (asymptotic or exponential) for nonlinear systems. Using this necessary condition, we show that there does not exist any general observer (asymptotic or exponential), for nonlinear systems with real parametric uncertainty, if the state equilibrium does not change with the parameter values and if the plant output function is purely a function of the state. Next, using center manifold theory, we derive necessary and sufficient conditions for the existence of general exponential observers for Lyapunov stable nonlinear systems. As an application of this result, we show that for the existence of general exponential observers for Lyapunov stable nonlinear systems, the dimension of the state of the general exponential observer should not be less than the number of critical eigenvalues of the linearization matrix of the state dynamics of the plant.     

ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

§1. Introduction Let q ≥3 be a positive integer. For any integers m, n and k , we de?ne the generalk-th Kloosterman sums S(m,n,k,χ;q) as follows: q …     

General linear methods with external stages of different orders

The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. In this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna.The work of the first author was supported by the National Science Foundation under grant NSF DMS-9208048. The work of the second author was supported by the Italian Consiglio Nazionale delle Richerche.