Preconcentration and separation of trace Pd(II) and Pt(IV) with silica gel bonded by aminopropyl-benzoylazo-4-(2-pyridyl-azo)-resorcinol

This paper reports a simple and highly selective method for preconcentrating and separating of trace Pd(II) and Pt(IV) with silica gel bonded by aminopropyl-benzoylazo-4-(2-pyridy-lazo)-resorcinol (ABPR-SG). ABPR-SG is stable in solution from 6 mol/L HCl to pH 7.0 and in common organic solvents. The maximum adsorptive capacity of Pd(n) on ABPR-SG is 362 μmol/g. After preconcentration and separation by using ABPR-SG column, Pd(II) and Pt(IV) of μg/L level in artificial water samples can be measured reliably by common spedrophotometry. The maximum concentration factors of Pd(II) and Pt(IV) on ABPR-SG column are 143 and 125 respectively. The chromatographic column packed with ABPR-SG can be reused. The method is simple and efficient.     

Size of support of initial heat distribution in the 1D heat equation

The size of support of initial heat distribution is determined by the heat flow observed either at any fixed time or at any fixed position     

Advanced form-finding for cable-strut structures

A numerical method is presented for form-finding of cable-strut structures. The topology and the types of members are the only information that is required in this form-finding process. Dummy members are used to transform the cable-strut structure with supports into self-stressed system without supports. The requirement on rank deficiencies of the force density and equilibrium matrices for the purpose of obtaining a non-degenerate d-dimensional self-stressed structure has been explicitly discussed. The spectral decomposition of the force density matrix and the singular value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required rank deficiencies of the force density and equilibrium matrices, respectively. Based on numerical examples it is found that the proposed method is very efficient, robust and versatile in searching self-equilibrium configurations of cable-strut structures.     

Two regularization methods for backward heat problems with new error estimates

We introduce two new methods for solving a backward heat conduction problem. For these two methods, we give a stability analysis with new error estimates. Meanwhile, we investigate the roles of the regularization parameters in these two methods. Numerical results show that our algorithm is effective.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Spectrally Adjustable Picosecond Dye Laser Pulses Generated with Nanosecond Nitrogen Lasers

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具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．     

On duality bound methods for nonconvex global optimization

A counter-example is given to several recently published results on duality bound methods for nonconvex global optimization.