Jack van Lint (1932-2004): A survey of his scientific work

When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations.     

Density functional theory investigation of the structure of SO2 and SO3 on Cu(1 1 1) and Ni(1 1 1)

Density functional theory (DFT) slab calculations, mainly using the generalised gradient approximation, have been used to investigate the minimum energy structures of molecular SO₂ and SO₃ on Cu(1 1 1) and Ni(1 1 1) surfaces. On Ni(1 1 1) the optimal local adsorption structures are in close agreement with experimental results for both molecular species obtained using the X-ray standing wavefield technique, although for adsorbed SO₂ the energetic difference between two alternative lateral positions of the lying-down molecule on the surface is marginally significant. On Cu(1 1 1) the results for adsorbed SO₂, in particular, were sensitive to the DFT functional used in the calculations, but in all cases failed to reproduce the experimentally-established preference for adsorption with the molecular plane perpendicular to the surface. This result is discussed in the context of previously published DFT results for these species adsorbed on Cu(1 0 0). The optimal geometry found for SO₃ on Cu(1 1 1) is similar to that on Ni(1 1 1), providing agreement with experiment regarding the molecular orientation but not the adsorption site.     

Existence and multiplicity of solutions for a nonlinear Neumann problem

We consider a Neumann problem of the type -εΔu+F ^′(u(x))=0 in an open bounded subset Ω of R ⁿ , where F is a real function which has exactly k maximum points. Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them. Received: October 30, 1999 Published online: December 19, 2001     

One-Parameter Fixed-Point Theory and Gradient Flows of Closed 1-Forms

We use the one-parameter fixed-point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a completed simplicial chain complex of the universal cover of M.     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

钐(Ⅱ)类卡宾CH_3SmCH_2X(X=Cl、Br和Ⅰ)促进乙烯环丙烷化反应途径的理论研究(英文)

用密度泛函B3LYP方法研究了过渡金属钐类卡宾与乙烯的环丙烷化反应的机理。对三种不同的钐的SS试剂CH_3SmCH_2X(其中X=Cl、Br和Ⅰ)分别和CH_2CH_2反应的各反应物、中间体、过渡态和产物构型的全部结构几何参数进行了优化,用内禀反应坐标(IRC)计算和频率分析方法,对过渡态进行了验证。结果表明：CH_3SmCH_2X(其中X=Cl、Br和Ⅰ)与CH_2CH_2环丙烷化反应按亚甲基转移通道(通道A)和卡宾金属化通道(通道B)都可以进行,与锂类卡宾的反应机理相同,只是按亚甲基转移通道(通道A)进行反应较容易一些,而且此反应在较低的温度下就可以发生。     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

市场竞争与国有企业所有权安排

改进了张维迎对地区间竞争与国有企业民营化的分析,给出了经营者的剩余索取份额对竞争性的连续依赖关系:国有企业若要降低成本,就必须参与市场竞争,随着市场竞争的加强,国有企业经营者的剩余索取份额应该逐渐增大,而当市场竞争水平超过某一阈值,国有企业经营者拥有全部剩余索取权是最优的.     

On the Evaluation of Uncertain Courses of Action

We consider the problem of decision making under uncertainty. The fuzzy measure is introduced as a general way of representing available information about the uncertainty. It is noted that generally in uncertain environments the problem of comparing alternative courses of action is difficult because of the multiplicity of possible outcomes for any action. One approach is to convert this multiplicity of possible of outcomes associated with an alternative into a single value using a valuation function. We describe various ways of providing a valuation function when the uncertainty is represented using a fuzzy measure. We then specialize these valuation functions to the cases of probabilistic and possibilistic uncertainty.     

Quintessence and Dark Matter Created by Weyl–Dirac Geometry

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,⁽³¹⁾ provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.