Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

A transport model for the evolution of urban systems

When comparing an urban system to an elasto-plastic lattice, an analogy to the solid state of matter can be exploited using the concepts of the band theory similarly. Thereafter, the population dynamics – in a region of certain stability in the state space and within appropriate energy bands – can be described in terms of Cellular Automata, with two mobile agents or pseudo particles: the inhabitant (representative of an average individual) and the recurson (representative of its multidimensional resources). As in the solid state, transition rules take the form of two coupled transport equations, comprising the terms equivalent to the generation-recombination and circulation processes. The first process can be compared to a predator–prey growth model, typical of Ecology; whereas the circulation process – composed of a drift component and a diffusion component – should be compared to the concentration-sprawl demographic balance seen in urban occupation and dynamics. Thus, it needs to be defined and determined an urban potential function, an equivalent population charge, mobility and diffusion parameters, as well as net growth factors. This analogy, discussed within the context of a case study for Great Mendoza, plausibly explains the varied growth rates of the political departments, as well as the principal urban trends for spatial occupation.     

基于主被动合作博弈的医患关系研究

针对我国医患关系日趋紧张,医患矛盾逐渐凸显这一问题,在对中国近五年医患事件进行分析的基础上,分别从信任程度、信息不对称程度、诊疗代价等多个视角出发,利用演化博弈理论和复制动态方程,构建了医患双方合作策略选择演化博弈模型,探究了影响医患关系演化的相关因素。研究表明:从长期来看,医患关系博弈系统存在两种演化路径:主动合作和被动合作;增大医患双方的信任程度,减小医患双方的信息不对称程度,降低医患双方合作成本,增大以政府为主导的仲裁机构对医患双方的奖励和惩罚都将会促使医患双方由被动合作转向主动合作。     

Some selected problems of nonaqueous microemulsions — phase diagrams and variation of the composition in the quaternary and ternary systems

A variety of quaternary and ternary systems of the type of dodecane/aliphatic alcohols/Na-dodecyl sulphate/water or a water-replacing component (formamide, ethylene glycol, propylene glycol, propylene carbonate, dimethylsulfoxide, acetonitrile) were subjected to a comparative analysis of microemulsification. The compositions of the systems of the type of oil/surfactant/cosurfactant/water or nonaqueous liquid were changed with respect to surfactant (Na-dodecyl sulfate and triton X 114) concentration, cosurfactant (homologous aliphatic alcohols) concentration and mixing ratio of water and water-replacing component. The appertaining phase diagrams were plotted and compared with those of aqueous systems.The experimental results suggest that the phase regions, which are designated as nonaqueous microemulsions, probably represent, not only microemulsions in the usual sense, but a separate kind of mixed phase whose microstructure is examined by special studies. Analogously to aqueous microemulsion systems, transparency and spontaneous formation of homogeneous multicomponent systems cannot serve as the sole criteria for waterless microemulsion formation. But they are important guiding properties of microemulsion formation in multicomponent systems.The variety of components involved in the chemical composition and the current insufficient knowledge do not permit to generally decide whether nonaqueous systems can be assigned to microemulsions or to molecular solutions. For clarifying this problem a detailed examination of the miscibility behavior, especially that of binary systems as a function of temperature, and the role that surfactant and cosurfactant play in the formation of homogeneous systems will be necessary.     

An active-set projected trust-region algorithm with limited memory BFGS technique for box-constrained nonsmooth equations

In this article, by means of an active set and limited memory strategy, we propose a trust-region method for box-constrained nonsmooth equations. The global convergence and the superlinear convergence are established under suitable conditions.     

Isotopic Characterization of 100% Agave Tequila (Silver,Aged and Extra-Aged Class) for Its Use as an Additional Parameter in the Determination of the Authenticity of the Beverage Maturation Time

Isotopic ratios of δ¹³C_VPDB and δ¹⁸O_VSMOW have been used as an additional parameter to ensure the authenticity of the aging time of 100% agave tequila. For this purpose, 120 samples were isotopically analyzed (40 silver class, 40 aged class, and 40 extra-aged classes). The samples were obtained through a stratified sampling by proportional allocation, considering tequila producers from the main different regions of Jalisco, Mexico (Valles 41%, Altos Sur 31%, Cienega 16%, and Centro 12%). The results showed that the δ¹³C_VPDB was found in an average of −12.85 ‰ for all the analyzed beverages, with no significant difference between them. Since for all the tested samples the Agave tequilana Weber blue variety was used as source of sugar to obtain alcohol, those results were foreseeable, and confirm the origin of the sugar source. Instead, the results for δ¹⁸O_VSMOW showed a positive slope linear trend for the aging time (silver class 19.52‰, aged class 20.54‰, extra-aged class 21.45‰), which is associated with the maturation process, there are oxidation reactions that add congeneric compounds to the beverage, these can be used as tracers for the authenticity of the aging time. Additionally, the experimental data showed homogeneity in the beverages regardless of the production region, evidencing the tequila industry’s high-quality standards. However, a particular case occurs with the δ¹⁸O_VSMOW data for the silver class samples, in which a clear trend is noted with the altitude of the region of origin; therefore, this information suggests that this analytical parameter could be useful to authenticate the regional origin of beverage.     

三维荧光光谱的特征区域选择方法

将数学中的二元凸函数判定和数据挖掘中的聚类分析方法结合,提出了针对三维荧光的光谱区域选择方法,并利用此种方法从光谱图中提取出含有丰富光谱信息的凸集区域。对水体中总有机碳的检测和白酒中黄曲霉素的检测进行了实验研究,实验结果表明,采用本文提出的三维荧光光谱区域选择方法提高了模型的精度,与利用全光谱所建立的回归模型相比,模型精度分别提高了6.17%和4.97%。     

中西部地区人口就近城镇化意愿的受教育程度差异研究

基于对中西部地区15个省市农业转移人口就近城镇化意愿的问卷调查数据,以社会认同度为研究视角,构建多群组结构方程模型分析中西部地区人口就近城镇化的受教育程度差异及其影响因素。研究结果表明:个人特征差异性对中西部地区不同受教育程度的农业转移人口的就近城镇化意愿影响显著;中西部地区不同受教育程度的农业转移人口的社会认同度与其就近城镇化意愿显著正相关,且社会认同度对中西部地区小学及以下学历的农业转移人口就近城镇化意愿的影响最显著,大专及以上学历的农业转移人口的就近城镇化意愿受社会认同度的影响最小。     

Well‐posedness and approximation of solutions of linear divergence‐form elliptic problems on exterior regions

This paper describes well‐posedness, spectral representations, and approximations of solutions of uniformly elliptic, second‐order, divergence form elliptic boundary value problems on exterior regions U in when N ≥ 3. Inhomogeneous Dirichlet, Neumann, and Robin boundary conditions are treated. These problems are first shown to be well‐posed in the space E¹(U) of finite‐energy functions on U using variational methods. Spectral representations of these solutions involving Steklov eigenfunctions and solutions subject to zero Dirichlet boundary conditions are described. Some approximation results for the A‐harmonic components are obtained. Positivity and comparison results for these solutions are given. Copyright © 2014 John Wiley & Sons, Ltd.