水闸闸室结构三维样条边界元分析

用三维样边界元法分析水闸闸室结构。底板，闸墩和载水墙等为其子结构，交通桥，工作桥和胸墙等处理为内部支撑。地基和边载可以是任意的，只要能给定地表位移面力关系。在各种工况下，不论是设置平板门还是弧形门，是平底板是反拱底板，即使在稀疏剖分下也能给出高精度的位移场，应力场和地基反力场。     

Distributive lattices of numberings

We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the second — to the cardinality of a set of special elements, of the initial numbering. Supported by INTAS grant No. 00-429. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 83–102, January–February, 2007.     

GF(2)上本原多项式的三项倍式的次数研究

研究了二元域上本原多项式的三项倍式的计数问题,通过对三项倍式进行分类,导出了本原多项式三项倍式最低次数的一个上界.利用这一结果,使构造本原多项式的次数最低的三项倍式的计算复杂性降到原来的九分之一.     

Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

A BOUNDARY ELEMENT METHOD FOR A NONLINEAR BOUNDARY VALUE PROBLEM IN STEADY-STATE HEAT TRANSFER IN DIMENSION THREE

In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given.     

有限体积KFVS方法在二维溃坝中的应用

本文采用了基于KFVS格式的有限体积方法 (FVM)求解了控制水流运动的二维浅水方程 ,建立了二维水坝瞬间溃坝的洪水演进模型 .并应用此模型模拟了二维非对称溃坝和对称溃坝情形下坝左下角有障碍物时的洪水波演进过程 .模拟结果表明该数学模型对二维浅水运动的模拟很有效 .     

有限局部环Z/2\+kZ上斜对称矩阵标准形和伪辛群的阶

设R=Z/2\+kZ(k>1)是\{2\}[TX-]为非单位的有限局部环. 该文首先确定了R上斜对称矩阵标准形. 设G\+m\-p(R,H)={P∈GL\-m(R)|PHP′=H}是由矩阵H确定的伪辛群,其中H=[JB((][HL(2]0[]I\+\{(v)\}\=-I\+\{(v)\}[]0[HL)][JB))]Δ，Δ=[JB((][HL(2]\{2\}[TX-]\+\{k-1\}[]\{1\}[TX-]\=-\{1\}[TX-][]0[HL)][JB))]. 其次,计算了伪辛群G\+m\-P(R,H)的阶|G\+m\-P(R,H)|.