One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

MULTIDIMENSIONAL GOURSAT PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATIONS

In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.     

Combinational simulations of free energy of polymer solution

It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be simulated with the random self-avoiding walk model on the simple cubic lattice for multichain systems. The obtained results indicated that both the conformational entropy and the mixing heat are consistent with the scaling laws wry well.     

A testbench for the nested dipole hypothesis of Kosterlitz and Thouless

We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.     

Preparation and evaluation of nickelmesogen for micropacked gas chromatography

The preparation and mesomorphic properties of a substituted bis(dithiolene)nickel complex derived from 4, 4'-dimethoxybenzil are reported. The phase transition temperatures were based on data obtained by polarized light microscopy and differential scanning calorimetry. The mesogenic phase existed over the temperature range from 77 to 175 degrees C. A novel micropacked column (1.5 or 3 m x 1 mm i.d.) prepared from the slurry of bis[1,2-bis(4-n-undecyloxyphenyl)ethane-1,2-dithiolene] nickel(II) (5%, w/w), coated on Chromosorb W was applied for the separation of dialkyl sulfides. The non-linearity (discontinuity) of Van't Hoff plots suggests that the liquid crystal property existed even in the coated phase. Factors affecting the retention and the sample selectivity on the prepared column were examined by using a flame photometric detector (FPD). The separation might be based on the mechanism of ligand exchange, shape selectivity and polarity interaction besides the vapor pressure. LOD for the determination of dialkyl sulfides was below 1 ng for most of the analytes.     

Ar—Kr溶液扩散系数的分子动力学模拟及其与温度的关系

用分子动力学模拟方法研究确定Ａｒ－Ｋｒ溶液的自扩散系数Ｄ１、Ｄ２和互扩散系数Ｄ１２以及它们随温度变化的规律。结果表明，分别用Ｇｒｅｅｎ－Ｋｕｂｏ法和Ｅｉｎｓｔｅｉｎ法得到的扩散系数在数值上一致；该溶液的３种扩散系数均满足Ｄ＝Ｄ０ｅ＾Ｅ／ＲＴ关系。     

MgO•3B2O3-18%MgSO4-H2O过饱和溶液析出固相组成和机理研究

针对青藏高原盐湖卤水析盐过程的特点, 模拟合成MgO•3B₂O_3-18%MgSO_4-H₂O过饱和溶液, 在150 ℃水热条件下对析出固相进行研究. 用化学分析方法、X射线衍射、红外光谱进行物相鉴定. 提出了可能的结晶反应机理, 分析了水热温度对析出物相的影响及MgSO₄对硼酸镁盐的盐溶效应随水热温度的变化.