Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

带有给定凸切线多边形的保形五次样条逼近

本讨论带有给定切线多边形的保形逼近问题．给出了一条与给定切线多边形相切的保形五次参数祥条曲线。     

基于改进遗传算法的布局优化子问题

本针对子问题，构造了布局子问题(关于同构布局等价类)的改进遗传算法。将该算法应用于二维布局优化子问题，数值实验表明该算法能够在很好地保持图元的邻接关系的前提下找到子问题的最优解。由于布局优化问题可分解为有限个子问题，所以利用该算法可以找到整个布局优化问题的全局最优解。     

On outer automorphism groups of coxeter groups

Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ ₁ andΠ ₂ any two bases of the root system ofW, thenΠ ₂ = ±ωΠ ₁ for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett. This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

Curvature of curvilinear 4-webs and pencils of one forms: Variation on a theorem of Poincaré, Mayrhofer and Reidemeister

A curvilinear d-web W = (F ₁ , . . . , F _d ) is a configuration of d curvilinear foliations F _i on a surface. When d = 3, Bott connections of the normal bundles of F _i extend naturally to equal affine connection, which is called Chern connection. For 3 < d, this is the case if and only if the modulus of tangents to the leaves of F _i at a point is constant. A d-web is associative if the modulus is constant and weakly associative if Chern connections of all 3-subwebs have equal curvature form. We give a geometric interpretation of the curvature form in terms of fake billiard in §2, and prove that a weakly associative d-web is associative if Chern connections of triples of the members are non flat, and then the foliations are defined by members of a pencil (projective linear family of dim 1) of 1-forms. This result completes the classification of weakly associative 4-webs initiated by Poincaré, Mayrhofer and Reidemeister for the flat case. In §4, we generalize the result for n + 2-webs of n-spaces. Received: September 23, 1996     

透镜空间L~1(p)上向量丛的示性类

本文讨论了透镜空间 L1( p)的上同调环中生成元的运算性质 ,进而利用 L1( p)的 KO -结构得到了L1( p)上任一向量丛的全 Stiefel-Whitney类     

Codes with a Certain Weight-preserving Transitive Group of Automorphisms

We determine all linear codes C containing the constant code E, for which there is a weight-preserving group of semilinear automorphisms which acts transitively on the set of nontrivial cosets of E in C. Michael Giudici - The author holds an Australian Postdoctoral Fellowship.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].