DOMAIN DECOMPOSITION PRECONDITIONERS FOR SECOND-ORDER HYPERBOLIC EQUATIONS ON L-SHAPED REGIONS

Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.     

一族超线性收敛的投影拟牛顿算法

本文将梯度投影与拟牛顿法相结合，给出了求解一般线性约束非线性规划问题含两组参数的算法族．在一定的条件下证明了算法族的全局收敛性与它的子族的超线性收敛速度，并给出了投影Ｄ．Ｆ．Ｐ方法、投影ＢＦＧＳ方法等一些特例．     

Derivatives of probability functions and some applications

Probability functions depending upon parameters are represented as integrals over sets given by inequalities. New derivative formulas for the intergrals over a volume are considered. Derivatives are presented as sums of integrals over a volume and over a surface. Two examples are discussed: probability functions with linear constraints (random right-hand sides), and a dynamical shut-down problem with sensors.     

梯度投影算子的广义陡度引理及其应用

在一般闭凸集上建立了梯度投影算子的广义陡度引理,利用它证明了几种松 弛搜索下梯度投影算法的全局收敛性、强收敛性以及若干良好的收敛性质.     

三项混合共轭梯度算法及其收敛性

本文对求解无约束优化问题提出一类三项混合共轭梯度算法,新算法将Hestenes- stiefel算法与Dai-Yuan方法相结合,并在不需给定下降条件的情况下,证明了算法在Wolfe线搜索原则下的收敛性,数值试验亦显示出这种混合共轭梯度算法较之HS和PRP的优势．     

X-ray diffraction line profile from the aggregate of distorted crystallites. II

An expression for the fourth moment of the line profile in terms of several strain derivatives and the possibility of measuring the ‘wavelength’ of crystal distortions (λ) for any sinusoidally varying component of the strain are available. The experimental means for evaluating such strain derivatives in the expression for the fourth moment was earlier described. A numerical method for evaluating this wavelength and its subsequent use to determineλ in several samples ofα-brass is presented here. The data used are taken from the earlier paper of the authors. An attempt has been made to interpret the values ofλ and their changes with cold working and annealing in terms of lattice strain.     

Electric quadrupole interaction at 111Cd and 119Sn in isostructural NiIn and CoSn compounds

The perturbed angular correlation technique and Mössbauer spectroscopy were applied to study the electric field gradient on ¹¹¹Cd and ¹¹⁹Sn probe atoms in isostructural NiIn and CoSn compounds. The ¹¹¹Cd PAC measurements performed in the temperature range 80--1100 K demonstrated the existence of two axially symmetric EFG's in each of the investigated compounds, related to the 2(d) and 1(a) probe sites in the B35 structure. A 1(a)-site preference for Cd probes in CoSn compound was observed. The temperature dependence of the quadrupole frequencies for ¹¹¹Cd in both compounds, interpreted in terms of the empirical model proposed by Christiansen et al.[1], follows a T^3/2 relation with different slope parameters for each of the observed frequencies. These results are combined with the data from the Mössbauer experiment. The ¹¹⁹Sn Mössbauer spectra taken at liquid nitrogen and at room temperatures showed two quadrupole split doublets with the intensity ratio 2:1 for CoSn and 8:1 for NiIn_0.99Sn_0.01sample, giving an evidence of 2(d)-site preference for tin atoms in NiIn. The EFG values measured on ¹¹⁹Sn are 2.5 to 4 times larger than those on ¹¹¹Cd nuclei, while the ratio of the respective Sternheimer antishielding factors is equal to 0.77. Within the limits of errors no differences were observed in the magnitude and temperature dependence of Debye--Waller factors for 2(d) and 1(a) ¹¹⁹Sn positions in CoSn and NiIn lattices.     

Analysis and Optimization of Stability Robustness Bounds for Discretized Systems

In this paper, robustness bounds for the perturbations of continuous-time systems to ensure the stability of their discretized counterparts are developed. Both zero-order hold and P-step matrix integrators are considered. The effect of the sampling time on the robustness bounds is studied via examples. To determine how well a simulated system will retain the robustness properties of the continuous-time system being simulated, a new criterion for the selection of the simulation method and time step is introduced. Both implicit and explicit robustness measures for sampled-data systems are obtained.     

Review of brookhaven nuclear transparency measurements (p,2p) reactions at largeQ 2

In this contribution we summarize the results of two experiments to measure the transparency of nuclei in the (p,2p) quasi-elastic scattering process near 90‡ in thepp center-of-mass. The incident momenta went from 6 to 14.4 GeV/c, corresponding to 4.8 <Q ² < 127 (GeV/c)². First, we describe the measurements with the newer experiment, E850, which has more complete kinematic definition of quasi-elastic events. E850 covers a larger range of incident momenta, and thus provides more information regarding the nature of the unexpected fall in the transparency above 9 GeV/c. Second, we review the techniques used in an earlier experiment, E834, and show that the two experiments are consistent for the carbon data. We use the transparencies measured in the five nuclei from Li to Pb to set limits on the rate of expansion for protons involved in quasi-elastic scattering at large momentum transfer.     

Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems

We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. The state equation is discretized by the explicit fourth order Runge-Kutta scheme and the controls are approximated by discontinuous piecewise affine ones. We then propose an approximate gradient projection method that generates sequences of discrete controls and progressively refines the discretization during the iterations. Instead of using the exact discrete directional derivative, which is difficult to calculate, we use an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation by the same Runge-Kutta scheme and the integral involved by Simpson's integration rule, both involving intermediate approximations. The main result is that accumulation points, if they exist, of sequences constructed by this method satisfy the weak necessary conditions for optimality for the continuous problem. Finally, numerical examples are given.