一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

电沉积n—CdSe在多硫溶液界面上的电荷转移机理

通过测定平带电位,澄清了OH~-离子在CdSe电极上的吸附情况,发现在S、S~(2-)、OH~-溶液中S~(2-)离子优先吸附,结合旋转环盘电极测量,证明n-CdSe电极在多硫溶液界面上的电荷转移过程。     

QUENCHING PROBLEMS OF DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION

This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.     

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

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     

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.     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

An algebraic multigrid solver for Navier-Stokes problems

An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh-independent. The scaling of computing time with mesh size is therefore close to the optimum.     

VISCOSITY SOLUTION THEORY OF A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS Ⅰ. UNIQUENESS AND EXISTENCE OF VISCOSITY SOLUTIONS

ThisresearchissupportedbytheNationalNaturalSciencesFoundationofChina.1.IntroductionInthispaper,weseektoestablishthecomparisonprinciple,regularity,ekistenceandsomegeometricpropertiesoftheinterfaceoftheviscositysolutionsforthefollowingfullynonlineardegenerateequations(Problem(C)):withFsatisfyingthefollowingassumptions:Fisdegenerateparabolic,i.e.F(q,X Y)5F(q,X),VY20,whereSadenotesthespaceofnxnsymmetricmatriceswiththeusualordering.wherellXlll~ItrX l ltrX--l,X~X X--,X 20,X--50,A,B20,p>2…     

谱约束下对称正交对称矩阵束的最佳逼近

讨论了对称正交对称矩阵的广义逆特征值问题，得到了通解表达式和最佳解的表达式。