关于Z-空间的对偶空间的讨论

本文以自然的方式定义了从Z-空间X到Z-空间Y的有界线性算子的和以及它们的数乘.从而得到了与赋范空间的对偶空间理论类似的一系列结论.     

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     

Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

The differential equation satisfied by a plane curve of degree n

Eliminating the arbitrary coefficients in the equation of a generic plane curve of order n by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions.     

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 note on the growth of topological Sidon sets

We give an estimate for the number of elements in the intersection of topological Sidon sets inR ⁿ with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofR ⁿ to be a topological Sidon set.     

基于遗传算法的二层线性规划问题的求解算法

本研究了下层以最优解返回上层的二层线性规划问题的遗传算法。在提出可行度概念的基础上，构造了二层线性规划上层规划问题的适应度函数，由此设计了求解二层线性规划问题遗传算法。为了提高遗传算法处理约束的能力，在产生初始种群时将随机产生的初始种群变为满足约束的初始种群，从而避免了使用罚函数处理约束带来的困难，最后用实例验证了本提出的二层线性规划的遗传算法的有效性。     

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.