Characterization of modules of finite projective dimension over complete intersections

Let be a finitely generated module over a local complete intersection of characteristic . The property that has finite projective dimension can be characterized by the vanishing of for some and for some .

     

Brownian intersection local times: Exponential moments and law of large masses

Consider independent Brownian motions in , each running up to its first exit time from an open domain , and their intersection local time as a measure on . We give a sharp criterion for the finiteness of exponential moments,

where are nonnegative, bounded functions with compact support in . We also derive a law of large numbers for intersection local time conditioned to have large total mass.

     

Structural features responsible for GFPuv and S147P-GFP’s improved fluorescence

Green fluorescent protein (GFP) is used as a biological marker. It is a protein in the jellyfish, Aequorea victorea, which is found in the cold Pacific Northwest. Mature GFP, i.e. fully fluorescent GFP, is most efficiently formed at temperatures well below 37 °C. The GFPuv (F99S/M153T/V163A) and S147P-GFP mutants mature more efficiently at room temperature than wild-type GFP, and therefore result in increased fluorescence at room temperature. Computational methods have been used to examine whether the low-energy precyclized forms of these improved GFP-mutants are preorganized so that they can more efficiently form the chromophore than the wild-type and S65T-GFP. All mutations examined (S147P, F99S, M153T, V163A and F99S/M153T/V163A) more efficiently preorganize the immature precyclized forms of GFP for chromophore formation than immature wild-type GFP. It has been proposed that Arg96 is involved in chromophore formation. Our calculations suggest that the M153T and V163A mutations in GFPuv maybe partially responsible for the increased maturation efficiency observed in GFPuv because they improve the Arg96–Tyr66 interaction. The same is true for the S147P mutation in S147P-GFP.     

Busemann-Petty问题的对偶均质积分形式

本文主要建立了凸体几何中Busemann-Petty问题的一个对偶均质积分形式,并将Funk截面定理推广到了对偶均质积分形式．     

Best Approximation and Perturbation Property in Hilbert Spaces

We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.The authors thank the referees for valuable suggestions.K.F. Ng - This author was partially supported by Grant A0324638 from the National Natural Science Foundation of China and Grants (2001) 01GY051-66 and SZD0406 from Sichuan Province. Y.R. He -This author was supported by a Direct Grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong.     

剩余交和一般剩余交的几个性质

本文给出了剩余交和一般剩余交的几个性质，主要讨论了剩余交的ＧＣＭ性和在形变下的变化情况，并讨论了一般剩余交的ＧＣＭ性，ＣＭ性和可光滑性等．     

On the Hardness of Computing Intersection,Union and Minkowski Sum of Polytopes

For polytopes P ₁,P ₂⊂ℝ ^d , we consider the intersection P ₁∩P ₂, the convex hull of the union CH(P ₁∪P ₂), and the Minkowski sum P ₁+P ₂. For the Minkowski sum, we prove that enumerating the facets of P ₁+P ₂ is NP-hard if P ₁ and P ₂ are specified by facets, or if P ₁ is specified by vertices and P ₂ is a polyhedral cone specified by facets. For the intersection, we prove that computing the facets or the vertices of the intersection of two polytopes is NP-hard if one of them is given by vertices and the other by facets. Also, computing the vertices of the intersection of two polytopes given by vertices is shown to be NP-hard. Analogous results for computing the convex hull of the union of two polytopes follow from polar duality. All of the hardness results are established by showing that the appropriate decision version, for each of these problems, is NP-complete.     

On the probability distribution of data at points in real complete intersection varieties

We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations.     

Limiting -subgradient characterizations of constrained best approximation

In this paper, we show that the strong conical hull intersection property (CHIP) completely characterizes the best approximation to any x in a Hilbert space X from the set

K:=C∩{xX:-g(x)S},