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.     

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.     

Partial molal heat capacities of aqueous tetraalkylammonium bromides as functions of temperature

Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate for aqueous Bu₄NBr over a similar temperature range. These data, along with similar data for Me₄NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions.     

Chemical analysis of acidic silicon etch solutions: I. Titrimetric determination of HNO3, HF, and H2SiF6

The chemical etching of silicon using HF-HNO₃ mixtures is a widely used process in the processing of silicon wafers for microelectronic or photovoltaic applications. The control of the etch bath composition is the necessary condition for an effective bath utilization, for the replenishment of the consumed acids, and to maintain a certain etch rate. The present paper describes two methods for the total analysis of the individual etch bath constituents HF, HNO₃, and H₂SiF₆. Both methods start with an aqueous acid-base titration determining the total acid concentration and the concentration of H₂SiF₆. The first method is an acid-base titration using a 0.1 mol L⁻¹ methanolic solution of cyclohexylamine (CHA) as non-aqueous titrant to determine the content of nitric acid. Then, the amount of hydrofluoric acid is calculated from the difference between the total acid and nitric acid content. The second method is based on the determination of the total fluoride concentration using a fluoride ion-selective electrode (F-ISE). The content of hydrofluoric acid is obtained from the difference between the total fluoride content and the amount of fluoride bound as H₂SiF₆. The amount of nitric acid results finally calculated as difference to the total acid content.