Uniform a priori estimates for positive solutions of the Lane–Emden equation in the plane

We prove that positive solutions of the Lane–Emden equation in a two-dimensional smooth bounded domain are uniformly bounded for all large exponents.     

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.     

Orthogonalization of block variables by subspace-projection for quantitative structure property relationship (QSPR) research

A subspace-projection method is developed to construct orthogonal block variable, which is originally from some kinds of series of topological indices or quantum chemical parameters. With the help of canonical correlation analysis, the orthogonal block variables were used to establish the structure-retention index correlation model. The regression of only few new orthogonal variables obtained by canonical correlation analysis against retention index shows significant improvement both in fitting and prediction ability of the correlation model. Moreover, the quantitative intercorrelation between the different block variables of topological indices can also be evaluated with the help of the subspace-projection technique proposed in this work.     

Transformation of 5‐Hydroxy‐ to (5‐Chloropentanoyl)amino Derivatives under ‘Direct Amide Cyclization’ Conditions

The application of the ‘direct amide cyclization’ conditions to the linear δ‐hydroxy diamide 11 is described (Scheme 3). Instead of the cyclization to the expected nine‐membered cyclodepsipeptide, only the chloro acid 12 was obtained. Its formation could be explained by consecutive formation of the 1,3‐oxazol‐5(4H)‐one 16 and the six‐membered imino lactone 17 as intermediates (Scheme 4). The spontaneous isomerization of the latter gave 12 in a good yield.     

关于矩阵迹的Bellman不等式

本文证明了矩阵迹的Bellman不等式: tr(AB)~n≤tr(A~nB~n) 其中A,B为半正定Hermite矩阵,n为自然数。     

Affinit?tschromatographie der Insulinantik?rper

Ohne Zusammenfassung     

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.