曲线的一类非线性多分辨率算法及其收敛性

在曲线的多分辨率分析基础上,构造了一种新的非线性三分多分辨率算法.并研究这个正则三分多分辨率算法的收敛性和稳定性,进一步,证明了小波参数的收敛性精密地依靠这个基本的多分辨率细分算法的收敛性.     

生产计划中阶梯型价格原料最优配置

按照规模经济效应,商品价格会随着订购量的增大而减小(即打折).根据生产实际,本文提出了商品的阶梯型价格,建立了最优生产计划模型.该计划模型有选择性地生产能够获最大利润的产品,并且可以对生产所需的原料进行最优配置;基于最优化理论与方法,给出了求解所建模型的有效算法,通过实例验证了算法的可行性和有效性.     

广义单纯形—中心设计I_(λ-)最优观测频数的一般解析表达式

本文引进发生函数矩阵与同构向量两个概念,利用它们讨论了与Scheffè单纯形—中心设计有关的0-1矩阵的一些性质。在I_(λ-)最优观测配置的分块算法的基础上,本文给出了q分量n阶广义单纯形—中心设计I_(λ-)最优观测频数的一般解析表达式。     

金属薄膜短脉冲激光冲击热机耦合问题

从电子-声子相互作用的双曲型两步热传导模型出发,考虑到金属体内晶格对热传导的影响,采用有限元法,直接在时间域中求解了金属薄膜内受短脉冲激光加热的二维热机耦合问题,避免了以往因电子-声子能量方程之间的耦合关系给二维热响应问题解析求解带来的困难,提高了用数值反变换工作时计算的精度,减少了工作量,得到了金属薄膜内二维热机耦合问题的温度、位移和应力的变化规律.     

Cage strain in nitro-substituted 1,3,5,7-tetraazacubanes

Homodesmotic reactions were designed for the computation of strain energies (SE) for four nitro-substituted 1,3,5,7-tetraazacubane derivatives. Total energies of the optimized geometric structures at the DFT-B3LYP/6-31G* and DFT-B3LYP/6-311G** levels were used to derive the SE. The variation of SE with respect to the number of substituents is similar with both basis sets. The SE value is 237.32 kcal/mol at the B3LYP/6-311G** level for 2,4,6,8-tetranitro-1,3,5,7-tetraazacubane, which is unexpectedly much larger than that of its cubane analogue. The SE increases remarkably with more nitro groups being attached to the cage skeleton of tetraazacubane. The ‘bending’ of the bonds within the cubic skeleton attributes to the increase of strains as the attached number of nitro groups increases.     

金属蒸汽中的激光维持爆震波

 应用我们发展的一个激光与金属蒸汽相互作用的简化物理模型对激光维持爆震波的点火激励、传播规律作了数值研究并取得了较好的结果。计算得到的LSD波阈值与激光脉宽的关系表现出典型的幂规律I_th∝τ^-1/2。此外，还得到了一些关于LSD波屏蔽效应的有益结果。在LSD波充分发展的阶段，LSD波阵面的光学厚度可达5~10的量级，这表明LSD波具有很强的屏蔽作用。     

VPE生长CdS外延膜的光学性质与光学双稳态

本文报导了在透明的CaF2衬底上采用气相外延(VPE)方法生长的高质量CdS薄膜。通过对其发射和吸收光谱以及光双稳特性的研究,表明这种外延膜的性质与体单晶相似。     

积域上粗糙核Marcinkiewicz积分的Lp有界性

本文证明了积域上的Marcinkiewicz积分算子μΩ是Lp( Rn× Rm) (11),而不需添加任何光滑性条件. 本文结果可视为Stein结果的一个改进.     

Unoriented Laplacian maximizing graphs are degree maximal

A connected graph is said to be unoriented Laplacian maximizing if the spectral radius of its unoriented Laplacian matrix attains the maximum among all connected graphs with the same number of vertices and the same number of edges. A graph is said to be threshold (maximal) if its degree sequence is not majorized by the degree sequence of any other graph (and, in addition, the graph is connected). It is proved that an unoriented Laplacian maximizing graph is maximal and also that there are precisely two unoriented Laplacian maximizing graphs of a given order and with nullity 3. Our treatment depends on the following known characterization: a graph G is threshold (maximal) if and only if for every pair of vertices u,v of G, the sets N(u)?{v},N(v)?{u}, where N(u) denotes the neighbor set of u in G, are comparable with respect to the inclusion relation (and, in addition, the graph is connected). A conjecture about graphs that maximize the unoriented Laplacian matrix among all graphs with the same number of vertices and the same number of edges is also posed.