Mathematical theory of radiation

In this paper we present an informal review of our recent work whose goal is to develop a mathematical theory of the physical phenomenon of emission and absorption of radiation by systems of nonrelativistic matter such as atoms and molecules. Dedicated to Larry Horwitz on the occasion of his 65th birthday. Research supported by DFS 288 and by NSF Phy 90-10433A02. Research supported by SNF. Research supported by NSERC Grant NA 7901.     

An efficient catalytic system for cyclocarbonylation of terpenes into lactones

Three different kinds of representative monoterpenic alcohol are involved in the palladium‐catalysed cyclocarbonylation reaction. Lactone formation is shown to occur when cyclic ( 1 ), tertiary ( 3 ) and primary allylic alcohol ( 7 ) functions are reacted, in the presence of CO with [HPd(SnCl₃)L₂] as the active catalytic species. Good yields and selectivities can easily be reached for isopulegol ( 1 ), and dihydromyrcenol ( 3 ). However, more modest results are obtained for the functionalization of geraniol into the original lactone ( 9 ). This lactone can be largely favoured by using a basic chelating diphosphine ligand such as 1,4‐bis(diphenylphosphino)butane. Copyright © 2005 John Wiley & Sons, Ltd.     

Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions

In this paper, a new class of Runge–Kutta methods is introduced. Some basic properties of this subgroup of algebraically stable methods are presented and a complete parametric representation is given. Necessary and sufficient order conditions for lower order methods as well as sufficient order conditions for higher order methods are derived yielding a significantly reduced number of conditions when compared with general Runge–Kutta methods. Design examples conclude this paper.     

Rudimentary Languages and Second-Order Logic

The aim of this paper is to point out the equivalence between three notions respectively issued from recursion theory, computational complexity and finite model theory. One the one hand, the rudimentary languages are known to be characterized by the linear hierarchy. On the other hand, this complexity class can be proved to correspond to monadic second-order logic with addition. Our viewpoint sheds some new light on the close connection between these domains: We bring together the two extremal notions by providing a direct logical characterization of rudimentary languages and a representation result of second-order logic into these languages. We use natural arithmetical tools, and our proofs contain no ingredient from computational complexity.     

转镜式高速扫描相机时间分辨率的测定

 介绍了产生时间分辨率的原因，测量时间分辨率在高速摄影中的作用，前人曾做过的工作，时间分辨率测定的难点；着重介绍了新的测量方法，给出了实际测定的结果。结果表明，对于GSJ型相机，时间分辨率可达8.6 ns，测量的均方根误差为1.1 ns。     

On the possibility of phase transitions in dusty plasma structures in a glow discharge under the action of a magnetic field

The melting of a dusty plasma structure formed in a stratum of a glow discharge caused by application of a magnetic field and its subsequent increase is studied. The images of two-dimensional cross sections of dusty plasma structures previously obtained by the authors are considered. To identify the phase, the correlation functions are calculated and visual comparison with the space lattices of ideal crystals is performed. It is found that, under the conditions of the previous study of the authors, as the magnetic field increases, the phase state of the dusty structure changes from an anisotropic liquidlike (liquid-ice) state to a disordered one. There is a tendency to a change in the type of the space lattice of the structure.     

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric group algebras. Moreover, its primitive elements are exactly the Lie elements which lie in the symmetric group algebras.