4-乙烯基吡啶与丙烯酰胺共聚合的研究

以过硫酸钾为引发剂 ,采用溶液自由基共聚合方法 ,实现了丙烯酰胺 (AM)与 4 乙烯基吡啶 (4 VP)的共聚合 .通过详细研究共溶剂体系、单体总浓度、反应温度、反应时间及引发剂量对共聚合过程中转化率和分子量的影响 ,从而确定了适宜的共溶剂体系和最佳的工艺条件 .用紫外分光光度法测得了共聚物的组成 .用Kelen Tudos方法 ,求得 4 乙烯基吡啶 (4 VP)和丙烯酰胺 (AM)单体的竞聚率 ,r4 VP =0 6 4 4 ,rAM =0 371.最后通过FTIR和1 3C NMR表征共聚物的结构并验证了共聚物的组成 .     

Boussinesq方程解的部分正则性

本文考虑Boussinesq方程一类合适弱解的部分正则性.我们先运用广义能量不等式和奇异积分理论得到一些无维量的估计;再通过合适弱解满足的等式,运用迭代技巧,推导出温度场的小性估计;最后由尺度分析(scaling arguments)得到了一类合适弱解的部分正则性.     

On a nonhomogeneous Burgers’ equation

In this paper the Cauchy problem for the following nonhomogeneous Burgers’ equation is considered : (1)u _t +uu _x =μu _xx −kx,x ∈R,t > 0, where μ and k are positive constants. Since the nonhomogeneous term kx does not belong to any L^p(R) space, this type of equation is beyond usual Sobolev framework in some sense. By Hopf-Cole transformation, (1) takes the form (2)ϕ _t −ϕ _xx = −x ² ϕ. With the help of the Hermite polynomials and their properties, (1) and (2) are solved exactly. Moreover, the large time behavior of the solutions is also considered, similar to the discussion in Hopf’s paper. Especially, we observe that the nonhomogeneous Burgers’ equation (1) is nonlinearly unstable.     

用高分子保护的纳米MgO的合成

本文利用高分子表面保护的化学沉淀方法成功地制备了粒径分布均匀的类球型纳米MgO。并对所制得的纳米粒子采用红外光谱（IR）、透射电镜（TEM）、差热及热重分析（TG－DTA）和X射线衍射（XRD）等现代分析测试手段进行了表面形貌、结构、晶形和组成等的表征。结果表明利用高分子的表面保护作用能够控制纳米微粒的形状和大小;由于聚乙烯醇分子中多羟基与金属离子间强的相互作用,因此获得的纳米微粒径更小,分散性更好。     

MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETO- HYDRODYNAMIC EQUATIONS

The two-dimensional magneto-hydrodynamic (MHD) equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence,are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.     

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβwith β≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.     

工件可自由下线最小化总完工时间的平行分批排序问题

考虑工件可自由下线最小化总完工时间的有界平行分批排序问题. 在该问题中, 一台平行批机器可以同时处理 b 个工件作为一个平行批, 这里b 是批容量, 一个批的加工时间等于分配给这个批的工件的最大加工时间. 关于可自由下线工件, 每一个工件的完工时间等于包含这个工件的批的开工时间与工件的加工时间的和. 也就是, 如果一个批B 有一个开工时间S, 那么包含在批B 中的每一个工件J_j 的开工时间定义为S, 而它的完工时间定义为S+p_j, 这里p_j 是工件J_j 的加工时间. 对此问题, 首先研究最优排序的一些性质. 然后, 基于这些性质, 给出一个运行时间为O(n^{b (b-1)})的动态规划算法.     

有关二维Euler方程的一些估计

首先得到Ｌｏｒｅｎｔｚ空间中的一些结果,然后在此基础上得到了有关二维Ｅｕｌｅｒ方程解的一些估计。这些估计与该方程当初始旋度ω０∈Ｌ＾－１∩Ｌ＾ｐ（ｐ〉１）时解的唯一性有关。     

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM) system for quantum fluids with a linear density dependent viscosity in a 3D torus.By introducing the cold pressure P_c,we prove the global existence of weak solutions with the pressure P+P_c,where P=Aρ^γ with γ≥1.Our main result extends the one in [13] on the quantum Navier-Stokes equations to the CNSLLM system.