Vibrational spectra of (NH4)3ZnCl5

IR and Raman spectra of (NH₄)₃ZnCl₅ have been recorded. The observed spectra have been analysed on the basis of the vibrations of ZnCl ₄ ²⁻ and NH ₄ ⁺ ions. The appearance of multiple Raman bands indicates the presence of two different types of ammonium ions. The effect of anisotropic crystalline field over the ZnCl₄ and NH₄ tetrahedra is also discussed. The assignment of internal modes has been verified by the potential energy distribution calculations.     

Generalized indices of operators inB(H)

A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form, practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H). Project supported by the National Natural Science Foundation of China     

Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems

In this paper, we compare two strategies for constructing linear programmingrelaxations for polynomial programming problems using aReformulation-Linearization Technique (RLT). RLT involves an automaticreformulation of the problem via the addition of certain nonlinear impliedconstraints that are generated by using the products of the simple boundingrestrictions (among other products), and a subsequent linearization based onvariable redefinitions. We prove that applying RLT directly to the originalpolynomial program produces a bound that dominates in the sense of being atleast as tight as the value obtained when RLT is applied to the jointcollection of all equivalent quadratic problems that could be constructed byrecursively defining additional variables as suggested by Shor.     

A generalized Adadorov theory for anisotropic thin-walled beams

This paper presents a generalized Adadorov theory for anisotropic thin—walled beams. The theory takes account of the shear strain of the middle surface, which exerts a significant influence on the anisotropic thin-walled beams. A new approach is established to solve the governing equations, which have the same form for both open and closed section beams. The numerical examples show that the effects of the shear strain cannot be neglected for this class of beams.This work was part of research project supported by the National Natural Science Foundation of China     

A discontinuous Galerkin method/HLLC solver for the Euler equations

This paper proposes a fully three‐dimensional non‐linear Euler methodology for solving aerodynamic and acoustic problems in the presence of strong shocks and rarefactions. It uses a discontinuous Galerkin method (DGM) within the element, and a Riemann solver (HLLC) at the boundaries to propagate rarefactions while preserving the entropy condition and capturing shocks with no spurious oscillations. This approach is thought to marry the best aspects of finite element and finite volume methods, achieving conservation while not requiring the solution of a large matrix. Examples in which shock and rarefaction waves are well captured are presented and the propagation of acoustic pulses is well demonstrated. Copyright © 2003 John Wiley & Sons, Ltd.     

The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.     

A co‐ordinate system independent streamwise upwind method for fluid flow computation

A new co‐ordinate invariant streamwise upwind formulation for convection dominated flows is developed. The eddy diffusivity/viscosity is added directly to the equations in order to remove the oscillations in the solution. The equations then can be solved by any high‐order scheme and the solution retains the accuracy of the high‐order scheme. The accuracy and reduced lateral thickness growth rate are demonstrated with several numerical examples, including pure convective flows and lid‐driven cavity flow. The lateral spreading due to the numerical diffusion is controlled by the anisotropic tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

一类非线性弹簧振子的周期性振动

本文用数值计算的方法讨论了一类非线性弹簧振子的周期性振动及其特点．