计算行列式的参数法

针对主对角线(或次对角线)两侧元素分别相同的行列式,给出计算该类型行列式的一种参数方法.     

基于混沌理论和改进径向基函数神经网络的网络舆情预测方法

网络舆情发展趋势具有混沌系统的特征, 提出一种基于EMPSO-RBF神经网络的方法对网络舆情的发展趋势进行预测. 首先根据Lyapunov指数证明网络舆情具备混沌的特征, 然后对网络舆情时间序列数据进行相空间重构, 最后采用EMPSO-RBF方法进行预测, 并和其他模型进行对比试验, 实验结果表明EMPSO-RBF方法具有较高精确度.     

具有时滞和扩散的随机捕食-食饵系统

该文建立一个具有时滞和食饵扩散的随机捕食-食饵模型.首先,确定系统对任何正初始值存在唯一全局正解;其次,给出了种群灭绝与平均持续生存的条件;最后,给出数值例子支撑该文的结论.     

Synthesis and Structure of a New Coordination Polymer Based on Indium and 1,4-Benzenedicarboxylate

A new coordination polymer {[In(bdc)(OH)]·4H2O}n(H2bdc=1,4-benzenedi-carboxylic acid) has been synthesized through hydrothermal conditions,and was characterized by X-ray single-crystal diffraction and other measurements.The complex crystallizes in the orthorhombic system,space group Imma with a=18.3621(13),b=7.1932(5),c=11.8278(8),V=1562.24(19)3,Z=4.Dc=1.565g/cm3,Mr=368.00,F(000)=728,μ(MoKα)=1.542 mm-1,S=1.019,R=0.0468 and wR=0.1326 for 884 observed reflections(2σ(Ⅰ)).The title compound represents a 3-D framework containing four kinds of tunnels in different shapes and sizes.     

On the matching polynomial of subdivision graphs

Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of the matching polynomial and Hosoya index of S(G) are obtained. As an application, we prove a combinatorial identity.     

弱向量变分不等式的解集及其连通性

建立Hausdorff拓扑向量空间的非空凸子集到其值域为连续线性映射空间L(X, Y) 内的C -单调映射的弱向量变分不等式和它的纯量型变分不等式问题解的存在性, 讨论该弱向量变分不等式与之相联系的纯量型变分不等式解集的关系, 利用映射的C -弱次连续和C -单调性及其集值映射的不动点定理,通过纯量型变分不等式解集所诱导的集值映射所具有的特性给出弱向量变分不等式解集的连通性.     

The Structure of Vector Bundles on Non-primary Hopf Manifolds∗

Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to Cⁿ ? {0}. The authors show that there exists a line bundle L over X such that E ? L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π^?(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.     

等价标准形的考研试题研究

等价标准形的应用是高等代数的考研热点之一.以等价标准形定理为依据,归纳和总结矩阵等价标准形的典型问题与方法,剖析典型考研试题,把握考研热点,引导方法技巧,拓宽解题思维.     

具有扭转耦合效应的复合薄壁梁黎斯基的性质和指数稳定性(英文)

研究了具有扭转耦合效应的复合薄壁梁黎斯基的性质以及指数稳定性.首先证明该系统决定算子的预解式是紧的,且可生成群.其次,通过对该系统算子谱的渐近分析,证明了除至多有限个本征值外,其算子的谱是单重可分离的.特殊地,我们获得了自由系统的频率渐近表达式,因而利用克尔德什定理,证明了在希尔伯特状态空间中算子广义本征函数列的完备性.最后,结合黎斯基的性质及算子谱的分布证明了该系统的指数稳定性.     

Congruences for cubic partition pairs modulo powers of 3

Let b(n) be the number of cubic partition pairs of n. We establish three congruences for b(n) modulo arbitrary powers of 3. Meanwhile, we prove some conjectures proposed by the first author.