关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

多个相异性矩阵的数据分析

本文给出了分析多个相异性矩阵的三种方法.首先找到了一种图表示,使我们对所有相异性矩阵有一个总体的了解;其次定义了一个新的相异性矩阵,它可以看作是对所有原始相异性矩阵的一个折衷处理;最后提出了一种MIMU方法.在文中我们还对由上述方法得到的坐标图进行了比较.     

On a point of order

A method of using algebraic curves to obtain estimates of critical points accurate enough to identify them as simple algebraic numbers (if that is what they are) is discussed and illustrated with an application to the (q-state Potts model on the triangular lattice for cases of pure two-site interactions and pure three-site interactions. In the latter case the critical point is conjectured to be . In a similar conjecture for the critical percolation probability on thedirected square lattice,q _c ^1/2 (q _c +3)=2(q _c +p _c =1).     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Comparison of procedures for correction of matrix interferences in the multi-element analysis of soils by ICP-AES with a CCD detection system

Three procedures, matrix matching, plasma optimisation and single-point standard-addition, have been evaluated to ascertain the best procedure for simultaneous multi-element analysis of industrial soils by ICP-AES with CCD detection. A standard reference material, CRM143 from the Bureau Communautaire de Réference (BCR), has been analysed for Cd, Cr, Cu, Mn, Ni and Pb using the three different matrix interference correction procedures. All three procedures give comparable results which are in good agreement with the BCR values, except for Cr. The single-point standard addition procedure was chosen, on the basis of economy and ease of implementation, to correct for matrix interferences in the determination of Cd, Co, Cr, Cu, Mn, Mo, Ni, Pb, Sn and V in soil samples collected from an industrial site in England. Concentrations of some of the elements were found to vary greatly with sampling depth. For example, the concentration of Mn, determined using the atomic line at 279.920 nm, increased from 426 ± 3 g/g at a depth of 18–28 cm to 5996 ± 144 g/g at 60–85 cm.     

Mass spectrometric analysis of low molecular mass polyesters by laser desorption/ionization on porous silicon

A low molecular mass polyester was analyzed by desorption/ionization on porous silicon (DIOS) mass spectrometry. The results were compared with those of matrix-assisted laser desorption ionization (MALDI) mass spectrometry using matrixes of alpha-cyano-4-hydroxycinnamic acid (CHCA) and 10,15,20-tetrakis(pentafluorophenyl)porphyrin (F20TPP). The CHCA matrix was not suitable for characterization of low molecular mass components of the polyester because the matrix-related ions interfered with the component ions. On the other hand, the F20TPP matrix showed no interference because no matrix-related ions appeared below m/z 822. However, the solvent selection for determining optimal conditions of sample preparation was limited, because F20TPP does not dissolve readily in any of the available organic solvents. In the DIOS spectra, the polymer ions were observed at high sensitivity without a contaminating ion. No matrix is needed for DIOS spectra of low molecular mass polyesters, facilitating sample preparation and selectivity of a precursor ion in post-source decay measurements.