Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

On co-semihereditary rings

A ringR is left co-semihereditary (strongly left co-semihereditary) if every finitely cogenerated factor of a finitely cogenerated (arbitrary) injective leftR-module is injective. A left co-semihereditary ring, which is not strongly left co-semihereditary, is given to answer a question of Miller and Tumidge in the negative. If _R U _S defines a Morita duality,R is proved to be left co-semihereditary (left semihereditmy) if and only ifS is right semihereditary (right co-semihereditary). Assuming thatS⩾R is an almost excellent extension,S is shown to be (strongly) right co-semihereditary if and only ifR is (strongly) right co-semihereditary. Project supported by the National Natural Science Foundation of China.     

一类最高权向量环的Krull维数

本文给出Om×GLn作用于Cm,n上的复多项式环上的最高权向量环的Krull维数公式,从而改正了Aslaksen,Tan及Zhu的一个错误.     

有限局部环Z/2\+kZ上斜对称矩阵标准形和伪辛群的阶

设R=Z/2\+kZ(k>1)是\{2\}[TX-]为非单位的有限局部环. 该文首先确定了R上斜对称矩阵标准形. 设G\+m\-p(R,H)={P∈GL\-m(R)|PHP′=H}是由矩阵H确定的伪辛群,其中H=[JB((][HL(2]0[]I\+\{(v)\}\=-I\+\{(v)\}[]0[HL)][JB))]Δ，Δ=[JB((][HL(2]\{2\}[TX-]\+\{k-1\}[]\{1\}[TX-]\=-\{1\}[TX-][]0[HL)][JB))]. 其次,计算了伪辛群G\+m\-P(R,H)的阶|G\+m\-P(R,H)|.     

Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

Synthesis and characterization of new thermally stable copoly(ester–amide)s from diester–dicarboxylic acids

Three new aromatic diester–dicarboxylic acids containing furan rings, namely, benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-phenyl ester-4,4^′-dicarboxylic acid, benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-phenyl ester-3,3^′-dicarboxylic acid and benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-naphthyl ester-2,2^′-dicarboxylic acid were synthesized by the reaction of benzofuro[2,3-b]benzofuran-2,9-dicarbonyl chloride with 4-hydroxybenzoic acid, 3-hydroxybenzoic acid and 3-hydroxy-naphthalene-2-carboxylic acid, respectively. Diester–dicarboxylic acids were characterized by FT-IR and NMR spectroscopy and elemental analyses. Then, these monomers were converted to aromatic copoly(ester–amide)s by their reaction with various aromatic diamines via the direct polycondensation. These polymers were characterized by viscosity measurements, solubility tests, FT-IR, Ultraviolet and ¹H-NMR spectroscopy and thermogravimetry. The polymers with inherent viscosities in the range of 0.16–0.37 dl/g in dimethyl sulfoxide at 30 °C were obtained in high yield. Most of them dissolved readily at room temperature in polar solvents. The synthesized copoly(ester–amide)s possessed glass-transition temperatures from 210–255 °C. The copoly(ester–amide)s exhibited excellent thermal stabilities and had 10% weight loss at temperature above 295 °C under nitrogen atmosphere.