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.     

A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

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。     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.     

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     

Quantification of trace elements in human serum fractions by liquid chromatography and inductively coupled plasma mass spectrometry

On‐line coupling of LC and ICP‐MS has been used for fractionation and detection of species of Cu, Fe, I, Se and Zn in human serum. It has been shown that anion exchange chromatography provided better separation capability (both intra‐ and inter‐element) than size‐exclusion chromatography. The mobile phases for ion exchange chromatography consisted of Tris–HNO₃ buffer and ammonium salt (nitrate, acetate or formate). Formate was found to be the best mobile phase counter ion, enabling good chromatographic separation, and is acceptable for mass spectrometry too. The quantitative evaluation of element concentrations adhering to individual fractions was performed by the peak area normalization method. The repeatability of results ranged from 3 to 15% (depending on the element concentration level) and represented the main part of the result uncertainty. The accuracy of Cu and Zn fraction determinations was confirmed by comparison with the isotope dilution technique. Copyright © 2006 John Wiley & Sons, Ltd.     

新疆野生黑加仑与马林果实的营养成分分析

通过对新疆野生黑加仑和野生马林的脂肪油，8种微量元素，17种氨基酸以及维生素C的含量进行测定得出：黑加仑脂肪油含量为17．9％，马林的脂肪油含量为22．3％，其中，黑加仑脂肪油中，r－亚麻酸的含量为19．02％，而马林中，其含量为9．40％，黑加仑中K，Na,Ca,Cu,Zn,Fe的含量比马林中的含量高，而Mn,Mg元素的含量却比马林含量低；马林的维生素C含量为16．22mg/g，黑加仑的含量为108mg/g，黑加仑的氨基酸的总量为1．63％，马林为1．14％。     

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].