MORPHIC MODULES

A module M is called morphic if M/M α ? ker(α) for all endomorphisms α in end(M), and a ring R is called a left morphic ring if _RR is a morphic module. We consider the open question when the matrix ring M_n(R) is left morphic by relating it to when Rⁿ is morphic as a left R-module. More generally, we investigate when M being morphic implies that end(M) is left morphic, and conversely. Finally, we relate the morphic condition to internal cancellation in the module.     

Isometric Deformations of Compact Hypersurfaces

In 1955 N. Kuiper and J. Nash proved that given a C embeddingF of a C Riemannian n -manifold (M,g) in E ⁿ⁺¹ which is short in the sense that the metric induced by F is less thang, there is a C ¹ isometric embedding which is arbitrarily C ⁰-close to F. We extend the Nash--Kuiper result for compact M to the case of deformations. In other words, we prove that given a continuous family of short C embeddings ( ) of a compact Riemannian n-manifold M , there is an isometric deformation through C ¹ embeddings which is C ⁰ -close to F. With more assumptions which are typically met in practice, this result is shown to hold in the more difficult case where F(s) is short for s>0 andF(0) is isometric. We use this to prove that if a C convex hypersurface is sufficiently close to being planar in an average sense (e.g. an oblate spheroid in E ³ with axis ratio more than , then it admits an isometric deformation which increases the enclosed volume.     

Antisymmetry and stability of aqueous systems. III. Conformations of the hexagonal rings

The antisymmetry of proton configurations was studied for the hexagonal water rings with different conformations. The change in the direction of all hydrogen bonds was used as an additional symmetry operation. The ring configuration energies were calculated using the intermolecular interaction potentials. For different ring conformations, the relationships between antisymmetry and energy were analyzed and compared.     

超格的商结构

通过引入超格的强闭集、上半补超格、数量上界单位元等概念,引出超格上的等价关系.构造数量上界单位集,在此基础上进一步研究超格的一些性质.商代数结构定理的建立对于完善超格的商结构具有实际意义.     

一类Block型李代数的分类和中心扩张

本文我们决定了一类Block型李代数$\BB$在同构意义下的分类和中心扩张, 其中$q$是一个非零复数. 我们的结果推广了以前的一些结果.     

Infrared spectroscopy of racemic and enantiomeric forms of atenolol

The molecular structure of conformational isomorphs given by X-ray diffraction for racemic and enantiomeric atenolol were optimized at the HF/6-31G* level of theory and the infrared spectra of the structure were calculated. These spectra are used to characterize the differences between the various atenolol conformers. The spectra of the (R,S)- and S-atenolol solid forms were recorded and the bands corresponding to the functional groups identified with the aid of the calculated spectra, fitting analysis, temperature effect and H/D isotopic exchange. Particular attention was paid to the stretch vibration modes of the functional groups present in the atenolol.     

The complete isomorphism class of an operator space

Suppose is an infinite-dimensional operator space and is a positive integer. We prove that for every there exists an operator space such that the formal identity map is a complete isomorphism, is an isometry, and . This provides a non-commutative counterpart to a recent result of W. Johnson and E. Odell.

     

Uniform algebra isomorphisms and peripheral multiplicativity

Let be a surjective operator between two uniform algebras with . We show that if satisfies the peripheral multiplicativity condition for all , where is the peripheral spectrum of , then is an isometric algebra isomorphism from onto . One of the consequences of this result is that any surjective, unital, and multiplicative operator that preserves the peripheral ranges of algebra elements is an isometric algebra isomorphism. We describe also the structure of general, not necessarily unital, surjective and peripherally multiplicative operators between uniform algebras.

     

Transformational antiatomic characteristic of ordered sets

To any ordered set with a universally maximal element, a semigroup of its transformations with some natural properties that defines the ordered set up to an isomorphism is assigned. The system of such transformation semigroups is proved to be the minimal element in the set of all defining systems of transformation semigroups with respect to the following ordering: one system precedes another if for each ordered set from the class in question, the semigroup of its transformation belonging to the first system is contained in the semigroup of its transformation from the second system. Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 112–119, July, 1999.