Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

?*-extensions of tori, higher chow groups and applications to incidence equivalence relations for algebraic cycles

LetX be a smooth projective variety over an algebraically closed fieldk. We repeat Bloch's construction of aG _m -biextension (torseur)E over CH _hom ^p (X)×CH _hom ^q (X) forp+q=dim(X)+1. First we show that in characteristic zeroE comes via pullback from the Poincaré biextension over the corresponding product of intermediate Jacobians which has been conjectured by Bloch and Murre. Then the relations betweenE and various equivalence relations for algebraic cycles are studied. In particular we reprove Murre's theorem stating that Griffiths' conjecture holds for codimension 2 cycles, i.e. every 2-codimensional cycle which is algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.     

On quadratic forms of height two and a theorem of Wadsworth

Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .

     

关于凸规划对偶模型的讨论

修正了文[1]中的错误,在其基础上讨论了凸规划的Lagrange对偶,Subgradient对偶及Wolfe对偶等四种对偶模型之间的关系,给出了它们之间等价的条件.     

离散式任意充磁角度Halbach永磁电机解析模型研究

Halbach电机因其自身优势在新型船舶推进、海洋洋流发电等方面受到广泛关注. 本文在假设铁磁材料线性和定子内表面光滑的条件下, 通过将任意充磁角度Halbach阵列等效为两组90° Halbach(或180° Halbach)阵列的矢量合成, 提出了一种分析离散式任意充磁角度Halbach永磁电机气隙磁场的解析方法; 通过对电机中磁标量势的傅里叶级数进行计算, 推导出了最简单的90° Halbach永磁电机在极坐标系下的气隙磁密表达式, 并在此基础上, 给出了任意充磁角度Halbach电机永磁体磁化强度在一个极下的表达式, 进而得出任意充磁角度Halbach电机气隙磁密的分布, 并分析了气隙磁密与电机极对数、永磁体厚度和充磁角度间的关系. 最后通过有限元和试验结果验证了本文方法的正确性. 关键词： 离散式Halbach电机 任意充磁角度 矢量等效 解析模型     

两种χ2形式的等价性

通过矩阵计算证明了两种χ2形式的等价性,同时讨论了最小化估计值的有偏性. 利用简化的R值测量定量地检验了等价性的结论.     

Half Exact Functors Associated with Cotorsion Pairs on Exact Categories

In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394, 245–284 (2013)”, we introduced the notion o     

广义相对论的几个问题

介绍了爱因斯坦如何建立广义相对论,以及人们应该如何理解这一关于时间、空间和引力的理论.     

Smooth equivalence of differential equations and linear automorphisms

For systems of ordinary differential equations admitting linear automorphisms, we consider the problems of smooth equivalence and linearization preserving these automorphisms. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 567–578, October, 1999.