A remark on the Riemann‐Hilbert problem with a vanishing coefficient

This paper concerns the existence of nontrivial solutions of the Riemann‐Hilbert problem with a continuous coefficient whose values belong to two rays in the complex plane. Our results extend those recently obtained by E. Shargorodsky and J. F. Toland [6]. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundedness of Multilinear Operators on Herz Type Spaces： Extreme Cases

In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases.     

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。     

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     

关于多线性振荡奇异积分在加权Hardy-型空间上的一致估计

本文对一类具有光滑位相函数的多线性振荡奇异积分算子建立了一致的加权（H^1(R^n),L^1(R^n))估计及一致的加权（HKp(R^n),Kp(R^n)估计。     

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].      

Some conformally flat spin manifolds, Dirac operators and automorphic forms

In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Γ where U is a subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S¹×Sn−1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of Γ are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.