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     

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.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

C^＊—模理论的若干结果

本文把代数结构与分析体系结合起来，运用同调的方法，较系统地确定了A上C^*－模的部分理论，这里A为复数域C上的交换C^*－代数。即不仅定义了与C^*－模有关的某些新概念，而且还得到了有关C^*－模的若干结果。     

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.     

Synthesis and structural characterization of [PhE(BNMe2)2]2 (E = P or As): Six-Membered P2B4 and As2B4 Rings with Unusual Structures

The reaction of either Li₂PPh or Li₂AsPh with the diborane(4) derivative B₂(NMe₂)₂Br₂ affords the compounds [PhP(BNMe₂)₂]₂ ( 1 ) or [PhAs(BNMe₂)₂]₂ ( 2 ) in good yield. Both 1 and 2 have cyclic structures featuring non-planar P₂B₄ or As₂B₄ six-membered rings which have chair configurations. Although all four borons in each ring have planar coordination, the two phosphorus or arsenic centers have different degrees of pyramidalization. Bond distances within the rings indicate that the B? B, B? P or B? As bonds are single, whereas the exo-B? N bond lengths are consistent with significant π-bonding. The ring structures of 1 and 2 are in sharp contrast to the related boron-nitrogen species (t-BuN)₂N₄Me₄ which has a nido-N₂B₄ framework. The attempted synthesis of the nitrogen analogue of 1 or 2 by using a similar approach did not result in the isolation of [PhN(BNMe₂)₂]₂, instead the tetramino diborane(4) species [B(NMe₂)NHPh]₂ ( 3 ), which has a structure similar to other tetramine diborane(4) compounds, was isolated.