Photo-Controlled Macroscopic Self-Assembly Based on Photo-Switchable Hetero-Complementary Quadruple Hydrogen Bonds

A photo-switchable hetero-complementary quadruple H-bonding array, which consists of an azobenzene-derived ureidopyrimidinone (UPy) module ( Azo-UPy ) and a nonphotoactive diamidonaphthyridine (DAN) derivative ( Napy-1 ), is constructed based on a reversible photo-locking approach. Upon UV (390 nm)/Vis (460 nm) light irradiations, photo-switchable quadruple H-bonded dimerization between Azo-UPy and Napy-1 can be achieved with exhibiting 4.8×10⁴-fold differences in binding strength (ON/OFF ratios). Furthermore, smart polymeric gels with unique photo-controlled macroscopic self-assembly behavior can be fabricated by introducing such quadruple H-bonding array as photo-regulable noncovalent interfacial connections.     

两个DEA的逆问题的解法的探讨

文[1]提出了两个DEA的逆问题，并用搜索法来解．而本文根据所证的定理，对每个问题一般只要解二、三个线性规划问题就能得到答案．     

The number of powers of 2 in a representation of large even integers II

It is proved that for any integerk≥ 54 000, there isN _k >0 depending onk only such that every even integer ≥N _k is a sum of two odd prime numbers andk powers of 2. Project partially supported by RGC Research Grant (No.HKU 7122/97P) and Post-Doctoral Fellowship of the University of Hong Kong.     

关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

Equivalence of variational inequality problems to unconstrained minimization

In this paper we propose a class of merit functions for variational inequality problems (VI). Through these merit functions, the variational inequality problem is cast as unconstrained minimization problem. We estimate the growth rate of these merit functions and give conditions under which the stationary points of these functions are the solutions of VI. This work was supported by the state key project “Scientific and Engineering Computing”.     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

VRPTW的扰动恢复及其TABU SEARCH算法

本文对带时间窗的车辆路线安排扰动恢复问题进行了讨论,分析了各种可能的扰动:增加减少客户,时间窗、客户需求及路线可行性的扰动,构造了扰动模型.利用禁忌搜索算法对问题进行求解,同时通过对模型参数重新设置,得到了多个满足要求的不同的解,这样使解更具有实际可行性和有效性.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.