Vector maximisation and lagrange multipliers

The Lagrangean function for scalar constrained optimisation problems is extended in a directly analogous manner to constrained vector optimisation problems. Some simple saddle point results are presented for vector maxima sets. Conditions are given for the characterisation of the vector maximum set of the original vector problem in terms of the vector maximum sets with respect to the vector Lagrangeans. Finally some attention is given to Lagrangean relaxation for vector optimisation problems as an extension of a result of Everett.     

On vector variational inequalities

In this paper, we study vector variational inequalities. The concept of weaklyC-pseudomonotone operator is introduced. By employing the Fan lemma, we establish several existence results. The new results extend and unify existence results of vector variational inequalities for monotone operators under a Banach space setting. In particular, existence results for the generalized vector complementarity problem with weaklyC-pseudomonotone operators in Banach space are obtained.This research was partially supported by the National Science Council of the Republic of China under Contract NSC 84-2121-M-110-008.     

Vectorized poisson solvers for the Navier–Stokes equations

The advent of vector and massively parallel computers offers researchers the possibility of enormous gains in execution time for scientific and engineering programs. From the numerical point of view, such programs are frequently based on the inversion of sparse, diagonally banded matrices. Conventional scalar solvers often perform poorly on vector machines due to short effective vector lengths, and thus appropriate methods must be chosen for use with vector machines. In this paper a number of commonly used solvers are tested for the Navier–Stokes equations, in both scalar and vector form, on two vector architecture machines. A new method is presented which performs well in both vector and scalar form on a range of vector architectures.     

On a domination property for vector maximization with respect to cones

We give a corrected version of Theorem 2.1 of Ref. 1.The author is indebted to D. T. Luc, Hungarian Academy of Sciences, Budapest, Hungary, for pointing out his error in the proof of the original version of Theorem 2.1 in Ref. 1.     

Vector Variational Inequalities for Nondifferentiable Convex Vector Optimization Problems

In this paper, we consider a nondifferentiable convex vector optimization problem (VP), and formulate several kinds of vector variational inequalities with subdifferentials. Here we examine relations among solution sets of such vector variational inequalities and (VP). Mathematics Subject classification (2000). 90C25, 90C29, 65K10 This work was supported by the Brain Korea 21Project in 2003. The authors wish to express their appreciation to the anonymous referee for giving valuable comments.     

反应N(2D)+H2→NH+H和N(2D)+D2→ND+D的立体动力学理论研究.

基于Ho等人的精确势能面(J. Chem. Phys. 119, 3063(2003))研究,运用准经典轨线方法计算了21.3 kJ/mol碰撞能下反应N(²D)+H₂→NH+H和N(²D)+D₂→ND+D的产物与反应物之间的矢量相关．发现两个反应的产物角分布都是前向和后向呈现峰值分布,产物的转动角动量矢量j′不仅是取向的,而且是在y轴负方向上定向的．两个反应显示出的同位素效应主要归因于同位素质量的差别．     

反应物振动激发对O(3P)+D2→OD+D立体动力学的影响

运用准经典轨线方法,基于Roger的³A"势能面,在碰撞能为104.5 kJ/mol时对O(³P)+D₂反应的立体动力学性质进行了理论研究. 详细讨论与产物矢量相关的的极化分布函数以及四个极化微分反应截面进行了. 结果表明,产物OD的立体动力学性质对反应物分子H_{2相似文献}   

基于支持向量机测定水质中硝酸盐含量

针对水质中被测物硝酸盐与干扰物铁离子、铬离子紫外吸收谱线严重重叠的问题,将支持向量机应用于混合重叠光谱分析中,利用核函数将重叠的光谱数据进行高维空间变换后求得SVM回归模型,实现硝酸盐含量的光谱检测。实验结果表明:硝酸盐浓度在0.5—10mg/L范围内,所测得含量的最大相对误差为3.2%;平均回收率为100.9%,本法与传统的方法相比,要求条件较低,不需要物理或化学的分离,分析速度快,有望应用于在线监测污水中硝酸盐的含量。     

On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥x∥₀. Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution.Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors {b_i}, known to emerge from such sparse constructions, Ax_i = b_i, with sufficiently sparse representations x_i, we seek the matrix A. In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A, depending on the quantity and nature of the set {b_i}, and the sparsity of {x_i}. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A, in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing.     

VPγ radiative decay of resonances dynamically generated from the vector meson–vector meson interaction

We evaluate the radiative decay into a vector, a pseudoscalar and a photon of several resonances dynamically generated from the vector–vector interaction. The process proceeds via the decay of one of the vector components into a pseudoscalar and a photon, which have an invariant mass distribution very different from phase space as a consequence of the two vector structure of the resonances. Experimental work along these lines should provide useful information on the nature of these resonances.