HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…     

线性规划的符号跟踪算法

分析了只含一个约束条件的线性规划最优基变量的特征，将其运用到搜寻含m个约束条件的线性规划的最优基变量，从而提出了线性规划的符号跟踪算法，为线性规划求解提供了新途径。     

低速二维流动的粒子仿真研究

本文运用信息保存法对低速二维的流动现象进行模拟，考察了低速条件下的有限平板绕流以及微槽道气体流动问题。研究表明：在对低速流动的模拟过程中，运用IP法在能够获得较好的结果的同时，具有比DSMC方法更高的计算效率。     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。     

求解非对称线性方程组的QMRGCGS方法

1 引言 求解非对称线性方程组Ax=b的双共轭梯度方法(BCG)[3]和它的变形共轭梯度平方方法(CGS)[6]都有典型的不规则收敛行为,后来Freund和Nachtigal提出一种BCG类方法,即拟极小剩余方法(QMR)[7],用来补救BCG方法的收敛性并且产生了光滑的收敛曲线。然而,象BCG方法一样,QMR方法要用到系数矩阵A及其转置A~T与向量的乘积,为了解决这一问题,Freund提出TFQMR方法,此方法具有拟极小剩余性,同时不需用到A~T与向量的乘积。     

The Linear Rational Pseudospectral Method with Preassigned Poles

We present a linear rational pseudospectral (collocation) method with preassigned poles for solving boundary value problems. It consists in attaching poles to the trial polynomial so as to make it a rational interpolant. Its convergence is proved by transforming the problem into an associated boundary value problem. Numerical examples demonstrate that the rational pseudospectral method is often more efficient than the polynomial method.     

Performance of noise barriers with various edge shapes and acoustical conditions

The performances of barriers having different shapes and surface conditions were tested using the boundary element method in a well-controlled environment. The heights and widths of the barriers were standardized and the insertion losses for six receiver positions were averaged and compared. Figures displaying the results allow for straightforward barrier performance estimation. It was shown that absorbing and soft edges significantly improve the efficiency of the barrier, but configuration modifications provide only a slight improvement. The soft T-shaped barrier produces the highest performance. A 3 m high T-shaped barrier provides the same performance as a 10 m high plain barrier. The spectral efficiency was also investigated. The insertion loss spectra for the absorbing and the soft barriers exhibit a similar shape, but the rigid barrier differs from these two.     

Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.