Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points

A family of probability measures on the unit ball in generates a family of generalized Steiner (GS-)points for every convex compact set in . Such a “rich” family of probability measures determines a representation of a convex compact set by GS-points. In this way, a representation of a set-valued map with convex compact images is constructed by GS-selections (which are defined by the GS-points of its images). The properties of the GS-points allow to represent Minkowski sum, Demyanov difference and Demyanov distance between sets in terms of their GS-points, as well as the Aumann integral of a set-valued map is represented by the integrals of its GS-selections. Regularity properties of set-valued maps (measurability, Lipschitz continuity, bounded variation) are reduced to the corresponding uniform properties of its GS-selections. This theory is applied to formulate regularity conditions for the first-order of convergence of iterated set-valued quadrature formulae approximating the Aumann integral.      

A New Proof of Hamilton's Theorem on Harmonic Maps from Manifolds with Boundary

We give a simple proof of the well-known Hamilton's result [1] on the heat flows and harmonic maps from manifolds with boundary using the approach of Ding-Lin [2].     

On the Equivalence of Extended Generalized Complementarity and Generalized Least-Element Problems

In this paper, we derive some equivalences of generalized nonlinear programs, generalized least-element problems, and extended generalized complementarity problems under certain regularity and growth conditions. We also generalize the notion of a Z-map for point-to-set maps. Our results extend recent results by Schaible and Yao (Ref. 1).     

A NOTE ON CONSTRUCTION OF HIGHER-ORDER SYMPLECTIC SCHEMES FROM LOWER-ORDER ONE VIAFORMAL ENERGIES

1.IntroductionFirstofall,let'srecallthedefinitionsofsymplecticschemes,revertibleschemes,andFeng'swayofconstructionofsymplecticmethodsviageneratingfunctions.Aswell-known,thephaseflow{g',tER}ofanyHamiltoniansystem(whereJ~I--i:n1,H:RZn-- RIisasmoothfunc...     

辛群的ω子集的拓扑结构

所有以单位圆周上的ω为一固定特征的辛矩阵构成实辛群SP（2n）中之一超曲面．本文研究此超曲面与它在Sp（2n）中之补集的拓扑结构．     

Hamilton体系下环扇形域的Stokes流动问题

基于极坐标下Stokes流的基本方程,将径向坐标模拟为时间坐标,推导了Hamilton体系下Stokes流动问题的对偶方程,采用本征向量展开法对环扇形域Stokes流动问题进行了分析,并给出了相应的实际算例,其结果说明了本文方法的有效性。     

Hydroxyl and acid number prediction in polyester resins by near infrared spectroscopy and artificial neural networks

Back-propagation artificial neural networks (BP-ANN) are applied for modeling hydroxyl number and acid value of a set of 62 samples of polyester resins from their near infrared (NIR) spectra. The results are compared to the classical calibration approaches, i.e. principal component regression (PCR) and partial least squares (PLS). The set of available samples is split into: (i) a training set, for models calculation; (ii) a test set, for setting the correct number of latent variables in PCR and PLS and for selecting the end point of the training phase of BP-ANN; (iii) a “production set” of samples, which are predicted to evaluate the models predictive ability. This approach guarantees that the predictive ability of the models is evaluated by genuine predictions. BP-ANN resulted always better than the classical PCR and PLS, from the point of view of the predictive ability. The study of the breakdown number of experiments to include in the training set showed instead that this factor does influence PCR and PLS at a lesser degree than what happens for BP-ANN. The latter approach requires a larger number of experiments for obtaining good results. The choice of optimal training sets is efficiently performed by Kohonen self-organizing maps (SOMs). It can be concluded that FT-NIR spectroscopy and BP-ANN models can be properly employed for monitoring the polyesterification of dicarboxylic acids with diols by predicting the acid and hydroxyl numbers directly along the process line.     

Another Construction of Cartesian Authentication Codes from Geometry of Classical Groups

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