De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。     

Arithmetic Hodge Structure and Nonvanishing of the Cycle Class of 0-Cycles

We construct 0-cycles on a self-product of a curve whose cycle classes are linearly independent in the extension group of arithmetic Hodge structure. This is an extended version of Theorem 4.5 of Asakura's contribution to CMR Lecture Notes Ser. 24 ((2000), pp. 133–154).     

A graph theory approach to subcontracting, machine duplication and intercell moves in cellular manufacturing

We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance.     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

超立方体的Laplace矩阵的谱

本文解决了超立方体的Laplace矩阵的谱问题．n维超立方体Q。的Laplace矩阵L（Q）的谱specL（Qn）。[0 2 4…2n Cn^0 Cn^1 Cn^2 … Cn^n],．其中2t（t=0，1，2，…，n）为L（Qn）的n＋1个不同的特征值，二项式系数Cn为特征值2t的重数．     

Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi

We study the asymptotic expansion of the first Dirichlet eigenvalue of certain families of triangles and of rhombi as a singular limit is approached. In certain cases, which include isosceles and right triangles, we obtain the exact value of all the coefficients of the unbounded terms in the asymptotic expansion as the angle opening approaches zero, plus the constant term and estimates on the remainder. For rhombi and other triangle families such as isosceles triangles where now the angle opening approaches π, we have the first two terms plus bounds on the remainder. These results are based on new upper and lower bounds for these domains whose asymptotic expansions coincide up to the orders mentioned. Apart from being accurate near the singular limits considered, our lower bounds for the rhombus improve upon the bound by Hooker and Protter for angles up to approximately 22° and in the range (31°,54°). These results also show that the asymptotic expansion around the degenerate case of the isosceles triangle with vanishing angle opening depends on the path used to approach it.