A generating function for all semi-magic squares and the volume of the Birkhoff polytope

We present a multivariate generating function for all n×n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B _n of n×n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B _n and any of its faces.     

一种基于三维激光点云数据的单木树冠投影面积和树冠体积自动提取算法

树冠投影面积和树冠体积是研究单木生物量估测、三维绿量测算等的重要测量因子。针对树冠结构复杂、形态各异,树冠因子难以精确测量等问题,为实现单木树冠投影面积和树冠体积的自动提取和精准测量,以三维激光扫描获取的树木点云数据为数据源,运用平面散乱点集凸包算法——Graham扫描算法和不规则体切片分割累加算法,以VC++6.0和Matlab 7.0混合编程,实现树冠投影面积和树冠体积的自动提取。以实验区选取具有代表性的22株不同树种的样木为研究对象,并与传统人工测量方法进行了对比分析。试验结果表明,树冠投影面积人工测量(A₄)结果与点云数据的自动计算(A_V)结果相关性较好,r=0.964(p<0.01),A₄高于A_V的平均值为25.5%。近似规则几何体方法树冠体积测量(V_C)结果与基于点云数据的自动计算(V_VC)结果之间呈现较强的相关性,r=0.960(p<0.001),V_C低于V_VC的平均值为8.03%。该方法基于高精度单木点云数据,实现了树冠结构的高精度快速重构、单木树冠投影面积和树冠体积的无损自动提取,可以为单木树冠结构的研究提供参考,在精准林业领域具有推广应用价值。     

棱镜-光栅-棱镜分光模块整体化设计及衍射特性分析

PGP模块是超光谱成像仪中重要分光器件。为了能够在制作前有效预测PGP整个系统的衍射效率分布及其衍射特性,提出了PGP整体化设计方法。从体位相全息光栅设计角度出发,结合棱镜与光栅各项参数的制约关系,编制了计算PGP整体衍射效率的分析软件,综合考察了棱镜与光栅各项参数对PGP模块衍射特性的影响,讨论了光栅布拉格波长的漂移特性,据此设计了一种用于成像光谱仪的宽波段高衍射效率PGP分光模块。模拟结果表明：棱镜1材料的色散系数越小,PGP的光谱带宽越窄;光栅布拉格波长的漂移增大了PGP模块和光栅的光谱带宽,带宽增大使光栅的角度选择性随之增大,拓宽了棱镜1材料的选择要求;棱镜1顶角、光栅的胶层厚度和相对介电常数调制度等参数是影响PGP衍射效率分布的重要因素,制作时需要精确控制。利用此方法设计的PGP分光模块在400～1 000 nm波段范围内衍射效率不低于50%,并给出具体设计参数,这对PGP制作具有一定的参考价值。     

石油中间馏分中异构烷烃的分子识别

以石油加氢异构中间馏分及直馏柴油为研究对象,采用气相色谱/质谱联用技术对异构烷烃的分子形态进行了研究。实验表明各碳数异构烷烃组分在毛细管气相色谱柱上表现出明显的按取代基个数簇分离的现象。对异构烷烃的异构程度进行了表征,得到不同取代基个数的异构烷烃的保留指数(RI)定性表;同时根据化合物的质谱断裂规律,参考文献数据并结合碳数及沸点规律,对73种甲基取代的异构烷烃及10种生物标记的化合物单体进行了结构定性,并计算了保留指数。为在分子水平上认识航空煤油及柴油等石油中间馏分中的异构烷烃提供了基础。定性结果表明:在研究的加氢异构中间馏分中,异构烷烃主要由单取代基和二取代基的异构烷烃组成;而在直馏柴油中,单取代基异构烷烃和类异戊二烯类生物标记化合物丰度较高。     

Upscaling pollutant dispersion in the Mexico City Metropolitan Area

Pollutant emission is an important problem in megacities such as Mexico City, imposing serious threats to human health and economic activity. Public policies oriented to deal with pollutant management ought to be based upon a close understanding of the transport mechanisms involved in the commonly complex network of streets and buildings. Modeling and simulation tools have proved to be useful for understanding field measurements and developing efficient monitoring strategies. The aim of this work is to provide estimations of the (longitudinal and transverse) dispersion coefficients in upscaled models for pollutant transport in the Mexico City Metropolitan Area (MCMA). To this end, we use the method of volume averaging, which allows calculation of the dispersion coefficients by solving the associated closure problems in some representative regions of the MCMA. The results show that local geometry has an important effect upon contaminant dispersion, especially in the direction that is transverse to the pressure gradient. This suggests that, although winds can remove an important amount of atmospheric contaminants, high transversal dispersion can help in a fast spreading of contaminants within the street network.     

New closed-form Green function and integral formula for a thermoelastic quadrant

In this study a new Green’s function and a new Green-type integral formula for a boundary value problem (BVP) in thermoelastostatics for a quadrant are derived in closed form. On the boundary semi-straight-lines twice mixed homogeneous mechanical boundary conditions (one boundary semi-straight-line is free of loadings and normal displacements and tangential stresses are prescribed on the other one) are prescribed. The thermoelastic displacements are subject by a heat source applied in the inner points of the quadrant and by mixed non-homogeneous boundary heat conditions (on one boundary semi-straight-line the temperature is prescribed and the heat flux is given on the other one). When thermoelastic Green’s function is derived the thermoelastic displacements are generated by an inner unit point heat source, described by δ Dirac’s function. All results are obtained in elementary functions that are formulated in a special theorem. A closed-form solution for a particular BVP of thermoelastostatics for a quadrant also is included. Using the proposed approach it is possible to extend the obtained for quadrant results to any other canonical Cartesian domain.     

Jump Condition for Diffusive and Convective Mass Transfer Between a Porous Medium and a Fluid Involving Adsorption and Chemical Reaction

In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.     

Complementarity of CFD, experimentation and reactor models for solving challenging fluidization problems

Experimentalists, numerical modellers and reactor modellers need to work together, not only just for validation of numerical codes, but also to shed fundamental light on each other＇s problems and underlying assumptions. Several examples are given, Experimental gas axial dispersion data provide a means of choosing the most appropriate boundary condition （no slip, partial slip or full slip） for particles at the wall of fluidized beds. CFD simulations help to identify how close ＂two-dimensional＂ experimental columns are to being truly two-dimensional and to representing three-dimensional columns. CFD also can be used to provide a more rational means of establishing assumptions needed in the modelling of two-phase fluidized bed reactors, for example how to deal with cases where there is a change in molar flow （and hence volumetric flow） as a result of chemical reactions.     

到欧氏空间的等距极小浸入

本文研究了欧氏空间极小子流形的测地球的体积增长,给出了一个黎曼流形可等距极小浸入到欧氏空间的一个必要条件,并给出了具非正截曲率的欧氏空间极小超曲面的一个分类．