非均匀散射层矢量辐射传输(VRT)方程高阶散射解的迭代法

将散射介质层在z轴方向划分成薄层，用薄层的一阶散射强度、Fourier变换和迭代方法求解散射介质整层的矢量辐射传输(VRT)方程的高阶散射解.该方法将一阶散射与高阶散射迭代结合起来，计算公式简明，可计算高阶迭代解，计算时间少.计算结果与一层均匀散射介质的VRT方程一阶Mueller矩阵解、半空间均匀散射介质二阶Mueller矩阵解、以及离散坐标-特征值特征矢量法的VRT热辐射的数值解作了全面的比较.提出并讨论了非均匀散射层主动与被动VRT方程的高阶解.本计算程序可以通用于非球形粒子多层结构及非均匀介质的散射和热辐射计算. 关键词： VRT方程 分层 迭代解     

空气比热容比实验的非绝热问题

通过一系列的实验数据分析，发现空气比热容比实验中非绝热现象不可以忽略．     

Hydrodynamical limit for a drift-diffusion system modeling large-population dynamics

In this paper we study the stability of the following nonlinear drift-diffusion system modeling large population dynamics ∂_tρ+div(ρU−ε∇ρ)=0, divU=±ρ, with respect to the viscosity parameter ε. The sign in the second equation depends on the attractive or repulsive character of the field U. A proof of the compactness and convergence properties in the vanishing viscosity regime is given. The lack of compactness in the attractive case is caused by the blow-up of the solution which depends on the mass and on the space dimension. Our stability result is connected, depending of the character of the potentials, with models in semiconductor theory or in biological population.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Diphenylmethane transformations over boron trifluoride modified alumina and silica-alumina

Transformations of diphenylmethane were investigated in a flow system in the presence of alumina and silica-alumina modified with boron trifluoride at atmospheric pressure and elevated temperatures. Hydrogen transfer reaction was observed on addition of tetralin to the substrate stream. This revised version was published online in August 2006 with corrections to the Cover Date.     

Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Si微电阻桥温度分布与热传导特性的显微Raman光谱研究

采用显微Raman光谱方法对红外目标模拟器中重掺杂Si微电阻桥单元的热传导特性进行研究，根据Si桥的实际特性建立相应的Raman散射模型，通过测量Raman峰位的移动得到高功率激光辐照下测量点的温度.对Si桥桥面分别进行了沿某些特殊线段的逐点线扫描和覆盖全部桥面的面扫描，得到各点的温升及其分布.用基于有限元分析的软件结合Si桥结构参数对各测量点的温升进行了模拟计算，其结果在热导分布的基本趋势上与实验相一致.实验细致地揭示了热导分布的局域起伏，反映出实际器件的不均匀性，为改进器件设计、优化器件性能提供了实验依据. 关键词： Raman光谱 Si桥 温度分布 热导