RLW—Burgers方程的精确解

借助未知函数的变换，ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程化为易于求解的齐次形式的方程，从而得到ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程的精确解。     

Sur les sous-groupes nilpotents du groupe de Cremona

Résumé. Nous décrivons les sous-groupes nilpotents non virtuellement abéliens du groupe des transformations birationnelles du plan projectif complexe: un tel groupe est d'ordre fini ou virtuellement métabélien.      

Crystallographic Analysis of FCC ? BCT Martensitic Transformation in the Alloy Fe-22% Ni-0.8% C

The infinitesimal deformation (ID) approach is applied to analyse the crystallography involved in the fcc to bct martensitic transformation for the case of (101)_γ[<formula><overline>1</overline>01</formula>]_γ twinning shear as LIS (lattice invariant shear) system in the alloy Fe-22% Ni-0.8% C. Analytical solutions are derived for habit plane orientation, orientation relationships between austenite and martensite phases, and the magnitude of the total shape deformation, etc. In order to compare numerical solutions with the ID approach and phenomenological crystallographic theory, the corresponding crystallographic parameters are calculated by using the Ledbetter and Dunn (L-D) theory. The numeric values obtained are compared with the predictions of the phenomenological crystallographic theories, and with experimental results.     

Specific features of the reactions of quinazoline and its 4-hydroxy and 4-chloro substituted derivatives with C-nucleophiles

Reactions of quinazoline 1 with indole, pyrogallol and 1-phenyl-3-methylpyrazol-5-one in the presence of acid led to C-4 adducts 2, 3 and 5. Adduct 4 is formed by heating 1 with 1,3-dimethylbarbituric acid without acid catalysis. 1-Phenyl-3-methylpyrazol-5-one reacts with 1 without acid catalysis to form dipyrazolylmethane 6. 4-Chloroquinazoline 8 reacts with 1-phenyl-3-methylpyrazol-5-one to form 4-(1-phenyl-3-methyl-5-oxopyrazol-4-yl) quinazoline 9 and dipyrazolylmethane 6. Heating 8 with 2-methylindole leads to the formation of 4-(2-methylindol-3-yl) quinazoline 10 and tris(2-methylindol-3-yl)methane 11.     

Topological approach to solve frame structures using topological collections and transformations

The present work tackled the modeling of frame structures using a topological approach based on the concepts of topological collections and transformations. The topological collections are used to specify the interconnection law between the frame structures and the transformations that are used to describe their behavior. As a language allowing the application of this approach, we applied the MGS (Modeling of General System) language. To validate this approach, we studied the case of two- and three-dimensional frame structures. Then, the results obtained using the MGS language are presented and compared to those obtained by the structural calculation software by the finite-element method RDM6. For both studied cases, we find that the results obtained by MGS language based on the notions of topological collections and transformations and those obtained by the RDM6 software based on the finite element method are very close, which validates our approach. Using this topological approach, any structure can be characterized by local relations between its elements, thus making it possible to dissociate its topology and its physics. Indeed, in our topological approach, we separately define the topology of the studied frame structure and the local behavior law as well as the equilibrium equations of its various components. Therefore, this topological approach might be generalized to model complex systems which can be considered as a set of local elements linked by a neighborhood relationship.     

Transformation of grouped data to near normality

Box and Cox (1964) proposed a power transformation which has proven utility for transforming ungrouped data to near normality. In this paper, we extend its applicability to grouped data. Illustrative examples are presented and the asymptotic properties of the estimators derived.