强酸性树脂催化合成甲基丙烯酸十六酯

针对强酸性树脂作为催化剂较均相强酸催化剂具有产率高、产品纯化简单、产生的废液少、设备无腐蚀性、可再生等优点，研究了在强酸树脂催化下甲基丙烯酸与十六醇反应合成甲基丙烯酸十六酯的工艺条件．以产率为指标，对原料比、催化剂用量、反应温度、反应时间、阻聚剂用量等因素进行优化．结果表明，原料质量比1．3：1，催化剂质量分数10％，反应温度145℃，反应时间5h，阻聚剂质量分数0．8％为最佳优化条件，反应产率可达95％以上。     

Fine three-dimensional P-wave velocity structure beneath the capital region and deep environment for the nucleation of strong earthquakes

A detailed 3-D P-wave velocity model of the crust and uppermost mantle under the capitol region is determined with a spatial resolution of 25 km in the horizontal direction and 4-17 km in depth. We used 48750 precise P-wave arrival time data from 2973 events of local crustal earthquakes, controlled seismic explosions and quarry blasts. These events were recorded by 123 seismic stations. The data are analyzed by using a 3-D seismic tomography method. Our tomographic model provides new information on the geological structure and complex seismotectonics of this region. Different patterns of velocity structures show up in the North China Basin, the Taihangshan and the Yanshan Mountainous areas. The velocity images of the upper crust reflect well the surface geological, topographic and lithological features. In the North China Basin, the depression and uplift areas are imaged as slow and fast velocity belts, respectively, which are oriented in NE-SW direction. The trend of velocity anomalies is the same as that of major structure and tectonics. Paleozoic strata and Pre-Cambrian basement rocks outcrop widely in the Taihangshan and Yanshan uplift areas, which exhibit strong and broad high-velocity anomalies in our tomographic images, while the Quaternary intermountain basins show up as small low-velocity anomalies. Most of large earthquakes, such as the 1976 Tangshan earthquake (M 7.8) and the 1679 Sanhe earthquake (M 8.0), generally occurred in high-velocity areas in the upper to middle crust. However, in the lower crust to the uppermost mantle under the source zones of the large earthquakes, low-velocity and high-conductivity anomalies exist, which are considered to be associated with fluids, just like the 1995 Kobe earthquake (M 7.2) and the 2001 Indian Bhuj earthquake (M 7.8). The fluids in the lower crust may cause the weakening of the seismogenic layer in the upper and middle crust and thus contribute to the initiation of the large crustal earthquakes.     

求强非线性动力系统周期解的MH法和EMH法

提出了改进的谐波平衡法即MH法和EMH法,用于求强非线性系统周期解.MH法直接应用于求解大参数参变系统:x a(t)x b(t)x=c(t).应用谐波平衡法求解强非线性系统,当谐波项取得较少时,求解结果精度低,为此引入最小二乘原理对谐波平衡法加以改进,计算结果精度高.EMH法用于求强非线性自治与非自治系统:x F(x,x)=0和x F(x,x,Ωt)=0的周期解,由于F呈非线性,不能直接应用MH法,为此,先由能量原理得出一次近似解,再引入牛顿迭代原理,得到关于修正量的周期系数方程;用MH法求此修正量,得到的结果精度较高.     

条件故障下3-元n-立方体的容错分析

研究了条件边故障下3-元n-立方体中较大连通分支点的数目,进而证明了3-元n-立方体是(4n－6)-条件边故障强Menger边连通的。最后通过一个反例说明该结果是最优的。     

ND样本加权回归函数估计的强相合速度

设{ε_i,1≤i≤n}为ND随机误差序列, 利用ND序列的Bernstein不等式, 在非参数回归模型Y_i=g(x_i)+ε_i(1≤i≤n)下, 研究未知函数g(x)加权核估计g_n(x)的强相合速度,
从而将加权回归函数估计的相合性推广到ND样本.     

NSD样本最近邻密度估计的相合性

利用负超可加相依(NSD)序列的Bernstein不等式和Borel-Cantelli引理, 给出NSD样本最近邻密度估计和失效率函数估计的(弱)强相合性、 一致强相合性和(一致)强相合速度.     

基于强互惠理论的漳河流域跨界水资源冲突水量协调方案设计

水量的分配方案在一定程度上影响因水量短缺引发的跨界水资源冲突的发展进程.从政府强互惠的角度入手，设计水量协调方案，寻求漳河流域跨界水资源冲突的协调途径是一个新的视角.基于这一思想，从政府的强互惠政策角度对漳河流域跨界水资源冲突系 统建模，从经济效益和社会效益两方面建立政府Agent和用水Agent 的目标函数，以强互惠表现的节水激励和水权交易为例，分别建立强互惠下的节水激励模型和水权交易模型，通过粒子 群优化算法求解，得出两种政策下漳河流域跨界水资源冲突的水量协调方案.水量的协调方案表明：政府强互惠的表现——节水激励和水权交易可以重新调整漳河流域的水量分配方案，以此来减少缺水量，协调漳河流域的跨界水资源冲突.     

强边着色猜想问题的最优图

著名图论专家Erds和Nesetǐil对图的强边色数上界提出了一个猜想:当最大度Δ为偶数时,χ's(G)≤5/4Δ~2;当最大度Δ为奇数时,χ's(G)≤1/4(5Δ~2-2Δ+1);并且给出了当Δ=4时的最优图.此处构造了一族图,并证明了当最大度为奇数时,如果Erd9s和Ne2etǐil提出的强边着色猜想成立,则猜想中的上界是最优的.     

Leibniz代数的导子扩张

通过给出强双导子的概念,证明强双导子可以给出Leibniz代数的导子扩张,并给出构造Leibniz代数的一种新方法.     

φ混合序列乘积和的强大数定律

建立了φ混合序列的矩不等式,利用这个不等式得到了φ混合序列的三级数定理及乘积和的强大数定律。