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.     

Precise lattice parameter measurements in CsCl-Br solid solutions between room temperature and 90°K by powder x-ray diffraction

Solid solutions of CsCl-Br in five different concentrations were prepared in sealed quartz tubes by heating the mixture to 1123°K for 6–8 hr and quenching to room temperature. X-ray diffractograms were taken at eight different temperatures between room temperature and 90°K for these solid solutions using the YPC50NM powder diffractometer and a continuous flow cryostat. The observed lattice parameters for each sample at each temperature obtained from the powder diffractograms were then extrapolated to give the true lattice parameters using the least square method with Nelson-Riley extrapolation scheme. The values of the true lattice parameters at each concentration and at each temperature were tabulated and the results discussed. It is shown that the lattice parameters vs temperature for some concentrations exhibit an anomalous behaviour. Contribution No. 691     

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.     

Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

On accurate boundary conditions for a shape sensitivity equation method

This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd.     

绝对连续测度的Loeb代数

It is proved that if μ and v be finite measures on a measurable space (X,S) and v is absolutely continuous with respect to v, then it is holds that L(^*S,^*v) C L(^*S,^*v), while L(^*S,^*v) and L(^*S,^*v) are the Loeb algebras with respect to measure spaces (X,S,μ) and(X,S,μ).