THE SCHWARZIAN DERIVATIVE IN SEVERAL COMPLEX VARIABLES(II)

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CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization.     

关于多项式系数微分方程复振荡理论的两个结果

本文证明了：如果ａ_ｋ－ｊ（ｊ＝１，…，ｋ）为多项式，ｄｅｇａ_ｋ－ｊ＝ｎ_ｋ－ｊ，存在某个ａ_ｋ－s（１≤ｓ≤ｋ）满足：当１≤ｊ＜ｓ时，ｎ_ｋ－ｊ／ｊ≤ｎ_ｋ－s／ｓ；当ｓ＜ｊ≤ｋ时，ｎ_ｋ－ｊ＜ｎ_ｋ－s－（ｊ－ｓ）．如果Ｆ≠０是整函数且满足σ（Ｆ）＝β＜（ｎ_ｋ－s＋ｓ）／ｓ，那么微分方程ｆ^（ｋ）＋ａ     

优化路问题的代数方法—论动态规划（Ⅱ）

本文用同一思路求解多阶段有向图中三种优化路问题:最优路、N阶最优路及多指标Pareto优化路问题,它们都服从嘉量原理,都用同一个代数公式表达它们的嘉量,并可在同一种表格中进行计算,只是所在半域不同,以本文的方法讨论动态规划中一些离散决定型典型应用问题,其提法、建模思路以及求解过程都有可观的扩大与改善。     

Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases,the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y₂BaNi_1-xZn_xO₅. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ( T ) ∼ C /(Θ + T ) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility ( T ) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T ( T ) = C _imp 1 + T _imp / T . In the temperature range [100 mK, 1 K] the experimental data are well fitted by T ( T ) = A ln( T / T _c ), where T _c increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility ( T ) which suggests the existence of antiferromagnetic correlations at very low temperature. Received 17 July 2001     

三级近似束流光学计算程序

为了精确计算束流在离子光学系统中的传输,用Visual FORTRAN 6.5语言编写了一个计算程序,长约13000行. 此程序可以计算由三圆筒单透镜、三膜片单透镜、双元筒透镜、均匀场静电加速管、磁四极透镜、六极磁铁、静电四极透镜、偏转磁铁、螺线管透镜、ExB~正交电磁场分析器、静电偏转器、漂浮管、QWR(Quarter Wave Resonators)和SLR(Split Loop Resonators)射频加速元件等元件任意组成的离子光学系统. 粒子轨迹的计算可精确到三级近似. 粒子的分布类型也可以有多种选择. 程序具有最优化计算功能,即可以自动调整元件的参数,以实现所需要的光学条件. 各元件之后的横向和纵向相图以及系统的束流包络线以图形方式显示在屏幕上.     

Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.