An extension of the pairing theory between divergence-measure fields and BV functions

In this paper we introduce a nonlinear version of the notion of Anzellotti's pairing between divergence-measure vector fields and functions of bounded variation, motivated by possible applications to evolutionary quasilinear problems. As a consequence of our analysis, we prove a generalized Gauss–Green formula.     

系统数值优化方法的研究与应用

大系统具有结构复杂、功能综合、因素众多等特点,相应的规划和决策问题的求解是非常困难的。我们针对大系统工程规划和决策的特点,结合运筹学的原理,提出了大系统数值优化概念,建立了优化模型,给出了优化问题的求解方法;并选择了中石油的DS-1油田作为应用实例,进行了油田采油工程数值优化,取得了很好的效果。为一般的复杂工程系统的规划和决策提供了一个新方法。     

Elliptic curves of rank 1 satisfying the 3-part of the Birch and Swinnerton–Dyer conjecture

Let E be an elliptic curve over Q of conductor N and K be an imaginary quadratic field, where all prime divisors of N split. If the analytic rank of E over K is equal to 1, then the Gross and Zagier formula for the value of the derivative of the L-function of E over K, when combined with the Birch and Swinnerton–Dyer conjecture, gives a conjectural formula for the order of the Shafarevich–Tate group of E over K. In this paper, we show that there are infinitely many elliptic curves E such that for a positive proportion of imaginary quadratic fields K, the 3-part of the conjectural formula is true.     

Imaginary quadratic function fields

In Bautista-Ancona and Diaz-Vargas (2006) [B-D] a characterization and complete listing is given of the imaginary quadratic extensions K of k(x), where k is a finite field, in which the ideal class group has exponent two and the infinite prime of k(x) ramifies. The objective of this work is to give a characterization and list of these kind of extensions but now considering the case in which the infinite prime of k(x) is inert in K. Thus, we get all the imaginary quadratic extensions of k(x), in which the ideal class group has exponent two.     

Concentration inequalities for random fields via coupling

We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.      

数域Q(P_1~(1/2),…,P_t~(1/2))(t≥4)的类数为偶数

设t≥4,ｐ１,…,ｐｔ为不同的模４余１的素数,本文证明了数域P1~(1/2),…,Pt~(1/2)的类数为偶数．     

Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R ^d is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L ^p -properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit.