Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

Efficient Synthesis of Nitroflavones by Cyclodehydrogenation of 2′-Hydroxychalcones and by the Baker-Venkataraman Method

Summary. Several nitroflavone derivatives were synthesized by cyclodehydrogenation of 2′-hydroxychalcones and by the Baker-Venkataraman approach, starting from 2′-hydroxyacetophenones and benzoic acid derivatives. Nitroflavones synthesised by the first synthetic approach were obtained in better global yields than those obtained by the later method. The structures of all new compounds were elucidated by microanalyses, 1D and 2D NMR, IR, and mass spectroscopic measurements.     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

Excess isentropic compressibility and speed of sound of the ternary mixture 2-propanol + diethyl ether + n-hexane and the constituent binary mixtures at 298.15 K

Speed of sound and densities of the ternary mixture 2-propanol + diethyl ether + n-hexane and also the binary mixtures 2-propanol + diethyl ether and 2-propanol + n-hexane have been measured at the entire composition range at 298.15 K. The excess isentropic compressibilities and the excess speed of the sound have been calculated from experimental densities and speed of sound. These excess properties of the binary mixtures were fitted to Redlich-Kister equation, while the Cibulka’s equation was used to fit the values related to the values to the ternary system. These excess properties have been used to discuss the presence of significant interactions between the component molecules in the binary mixtures and also the ternary mixtures. Speed of sound of the binary mixtures and the ternary mixture have been compared with calculated values from free length theory (FLT), collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR) and Junjie’s relation (JR). The results are used to compare the relative merits of these theories and relations in terms of the root mean square deviation relative (RMSD_r).     

Locally symmetric positively curved Finsler spaces

We showed that any compact locally symmetric Finsler metric with positive flag curvature must be Riemannian. Dedicated to Professor Karsten Grove on the occassion of his sixtieth birthday Received: 8 May 2006     

Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finiteelement domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques suchas calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy methodand the theory of prior estimates are adopted.Optimal order estimates in L~2 norm are derived for the error inthe approximate solution.     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量

利用碱性条件下黄酮与Al3 生成粉红色络合物在可见光区510 nm处有最大吸收的特性,以芦丁为标样,采用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量,并与HPLC标准方法测定结果进行比较,发现各平行样的测定结果基本一致,最大偏差为268.38 mg/100 g,最小偏差为52.77 mg/100 g.该法简便快捷,结果相对准确,可作为蜂胶超临界CO2萃取物中总黄酮含量快速评估的一种方法.