激光传输大气参量测量精度要求的数值分析

 就激光大气传输湍流热晕相互作用下大气参量测量误差对激光传输效果（平均功率密度）的影响进行了数值分析，并以典型的激光传输条件为例，分析了对激光大气传输影响最为敏感的3个大气参量——风速、吸收系数以及湍流结构常数的测量精度要求。综合不同传输距离下大气参量测量误差对传输效果的影响，大气风速的测量精度要求为±10%，吸收系数及湍流结构常数的测量精度要求分别为±5%和±15%。     

Indirect carbon–carbon spin–spin couplings across one,two and three bonds in pyridine and diazine systems: experiment and theory

An excellent linear correlation is found between a large body of experimental spin–spin carbon–carbon couplings, J(CC), across one, two and three bonds in pyridine and diazine ring systems and the corresponding B3PW91/6‐311++G(d,p)//B3PW91/6‐311++G(d,p) computations. The correlation does not differ significantly from the simplest relationship possible, J(CC)_exp. = J(CC)_calcd., within a small and random spread of about 1 Hz. There are 276 experimental values considered, and 124 out of these are new and come from the present work. The aromatic carbon–carbon couplings vary from ?7.6 through +78.5 Hz. It is shown that the correlation provides a reliable tool for predictions of the signs of aromatic J(CC)'s even if the magnitudes of the latter are of the order of 1 Hz. It is demonstrated, for the first time, that the relatively weak ² J(CC) couplings, in the heteroaromatic systems studied, can bear either sign and span a considerable range of about 11 Hz. The character of the correlation indicates that rovibronic effects on aromatic J(CC)'s and those of nuclear motions on aromatic J(CC)'s are practically negligible. All of this is in a perfect agreement with our recent extensive studies on aromatic J(CC)'s in analogous benzene ring system. Substituent effects on the aromatic J(CC)'s turn out to be significant not only for ¹J(CC)'s but also for most of ³J(CC)'s and ² J(CC)'s, and the computation neatly reciprocates these trends. Copyright © 2008 John Wiley & Sons, Ltd.     

Diastereofacial selectivity in some 4‐substituted (X) 2‐adamantyl derivatives: electronic versus steric effects

π‐Facial selectivity data for the reduction and methylation of some 4^ax‐substituted (X) 2‐adamantanones ( 3 , Y = O) as well as the nucleophilic trapping of secondary and tertiary 4^ax‐substituted (X)‐2‐adamantyl cations ( 4 ; R = H and CH₃, respectively) and the 4‐methylene‐2‐adamantyl radical ( 8 ) are presented. The pronounced anti‐face selectivities observed for ( 3 , Y = O and 4 , R = CH₃) emphasize the importance of the steric factor as expected for systems with a strong steric bias. However, the dominant syn‐face capture of 4 (R = H) was completely unexpected and highlights a subtle interplay between steric and electronic effects. Finally, the very high anti‐face stereoselectivity for the trapping of ( 8 ) with the trimethylstannyl anion (Me₃Sn^?) is rationalized in terms of an electrostatic effect overwhelming the steric factor. Copyright © 2007 John Wiley & Sons, Ltd.     

Algebraic Rate of Decay for the Excess Free Energy and Stability of Fronts for a Nonlocal Phase Kinetics Equation with a Conservation Law. I

This is the first of two papers devoted to the study of a nonlocal evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider subcritical temperatures, for which there are two local equilibria, and begin the proof of a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibria; i.e., the fronts. We shall show in the second paper that an initial perturbation v ₀ of a front that is sufficiently small in L ² norm, and sufficiently localized that x ² v ₀(x)² dx<, yields a solution that relaxes to another front, selected by a conservation law, in the L ¹ norm at an algebraic rate that we explicitly estimate. There we also obtain rates for the relaxation in the L ² norm and the rate of decrease of the excess free energy. Here we prove a number of estimates essential for this result. Moreover, the estimates proved here suffice to establish the main result in an important special case.on leave from     

Inverse Problem for a Class of Two-Dimensional Diffusion Equations with Piecewise Constant Coefficients

In this paper, we consider an inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and an asymptotic expansion of the solution of the diffusion equations. A numerical method that reduces the inverse problem to a sequence of nonlinear least-square problems is proposed and tested on synthetic data.     

一类非线性代数方程组的并行迭代算法

１．引言考虑非线性代数方程组这里,　　　　　　　　　　　　　　　　　　　　　　　　　　　　为连续的对角映射,二者的导函数均存在,但并不一定连续．这类非线性代数方程组具有丰富的实际背景．譬如,Ｓｔｅｆａｎ问题和许多弱非线性椭圆型偏微分方程,就可归结为（１．１）的数值求解问题．根据方程组（１．１）的特殊结构,并利用矩阵多重分裂思想,文ｔＺ］讨论了一类并行非线性Ｇａｕｓｓ－Ｓｅｉｄｅｌ型迭代算法．这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文［８］进一步研究了一类并行多分…     

Robust tracking for MIMO nonlinear time-dependent mismatched uncertain systems: non-adaptive versus adaptive control

This paper considers the problem of robust output-tracking controlfor multi-input multi-output (MIMO) nonlinear systems in thepresence of mismatched time-dependent uncertainties. It firstgeneralizes the stable combined-variable perturbation method(SCVPM) which was proposed by Li et al. (1996) to derive a newrobust controller and its adaptive version for MIMO systemsto track a desired trajectory. It is shown that both controllersnot only stabilize the closed-loop systems but also guaranteethat the tracking errors remain in an O() neighbourhood of theorgin, where is a small design parameter of the controller.Moreover, the adaptive robust controller is only based on thenominal system, and no a priori data on the uncertainties areneeded. Therefore, it is more feasibly implemented than thenon-adaptive controller.     

Positivity of polarizations of -positive maps

It is shown that polarization formulas have explicit matrix representations. This enables us to prove that polarization formulas of -positive maps between -algebras are coordinatewise positive.

     

Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies

A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on -D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification supplies limited qualitative information concerning the imperfect bifurcation diagrams of the detected bifurcation points.

     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.