Singular Solutions of Fully Nonlinear Elliptic Equations and Applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of , and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén–Lindel?f result as well as a principle of positive singularities in certain Lipschitz domains.     

Solvability of Uniformly Elliptic Fully Nonlinear PDE

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the Hamilton–Jacobi–Bellman–Isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.     

旋转流体斜压波三维温度结构实验研究

实验研究了负径向温度梯度下转坏系统中斜压流体的对流运动，获得了该系统中旋转流体斜压波的一般特征，通过对斜压波温度场多层次细网格测量，得到了斜压波三维温度结构和表面波状急流的温度分布，并就波－波转换的不稳定性问题作了初步分析．     

Finite p-Groups with Few Non-major k-Maximal Subgroups

A subgroup of index p~k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p~2 and δ_(d(G)-1)(G) = 0,respectively.     

Systemic analysis of structures and contents of nitrogen-containing compounds and other non-hydrocarbons in crude oils in conjunction with chemometric resolution technique.

A method is described for the systemic identification and quantitative analysis of nitrogen-containing compounds and other non-hydrocarbons in crude oils. The pre-fractionation of a crude oil sample into 7 fractions was performed by di-adsorption column chromatography using neutral aluminum oxide and silica gel. A subsequent high-resolution separation of individual components was achieved by using capillary column gas chromatography, and compound types were detected by a mass spectrometer. In conjunction with a chemometric method, the compounds in the fractions were further resolved or separated, which made it possible to identify some nitrogen-containing compounds and other non-hydrocarbons in crude oils. To a certain extent, this method could relieve the difficulty of classical analysis in identifying those species with very low contents or incompletely separation, particularly in the cases where authentic standards were not available for addition into the unknown samples in order to reveal what indeed existed in them. The structures and contents of 168 nitrogen-containing compounds in one crude sample and 60 non-nitrogen-containing compounds in one of non-hydrocarbon fractions of this oil sample were determined, and the addition-recovery examination of some standard compounds showed that the analytical veracity was satisfactory.     

Dual facet of gold(III) in the reactions of gold(III) and porphyrins

We have firstly demonstrated the dual facet of gold(III) in the reaction between gold(III) and porphyrins, which could be tuned through changing the counter ions, ligands and the electronic effect of the substituents of the porphyrins.     

Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle

We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of ? ⁿ . The simplicity and robustness of our maximum principle-based argument provides for its applicability to many elliptic inequalities and systems, including quasilinear operators such as the p-Laplacian, and nondivergence form fully nonlinear operators such as Bellman-Isaacs operators. Our method gives new and optimal results in terms of the nonlinear functions appearing in the inequalities, and applies to inequalities holding in the whole space as well as exterior domains and cone-like domains.