The Automaton Realization of Iterated Wreath Products of Cyclic Groups

We study profinite groups which are infinitely iterated wreath products W _∞ = …?C _{n 2} ?C _{n 1} of finite cyclic groups via combinatorial language of transducers. Namely, we provide a naturally defined automaton realization of the group W _∞ by an automaton over a changing alphabet. Our construction gives a characterization of these profinite groups as automaton groups, i.e. as groups generated by a single automaton.     

Smarandache Vertices of the Graphs Associated to the Commutative Rings

Let R be a commutative ring with identity 1 ≠ 0. A nonzero element a in R is said to be a Smarandache zero-divisor if there exist three different nonzero elements x, y, and b (≠ a) in R such that ax = ab = by = 0, but xy ≠ 0. We will generalize this notion to the Smarandache vertex of an arbitrary simple graph and characterize the Smarandache zero-divisors of commutative rings (resp. with respect to an ideal) via their associated zero-divisor graphs. We illustrate them with examples and prove some interesting results about them.     

A Survey for the Spectrum of Triangles over Sequence Spaces

Abstract

In the present paper, we summarize the recent literature concerning the spectrum and fine spectrum with respect to Goldberg’s classification of some operators represented by an infinite matrix over certain sequence spaces.     

On Singular Varieties Having an Extremal Secant Line

ABSTRACT

Let X be a nondegenerate subvariety of degree d and codimension e in the projective space ? ⁿ . If X is smooth, any multisecant line to X cuts X along a 0-dimensional scheme of length at most d ? e + 1. Moreover, smooth varieties X having a (d ? e + 1)-secant line (an extremal secant line) have been completely classified, extending del Pezzo and Bertini classification of varieties of minimal degree. In this article, we almost completely classify possibly singular varieties having an extremal secant line, without any assumptions on the singularities of X. First, we show that, if e ≠ 2, a multisecant line to X meets X along a 0-dimensional scheme of length at most d ? e + 1. Then, we completely classify singular varieties having a (d ? e + 1)-secant line for e ≠ 3. A partial result is provided in case e = 3.     

Covering morphisms

Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case.     

Study of the crystal shape and its influence on the anti‐tumor activity of tumor necrosis factor‐related apoptosis‐inducing ligand (Apo2L/TRAIL)

This paper describes a method about the crystal shape control improving the anti‐tumor activity of tumor necrosis factor‐related apoptosis‐inducing ligand (Apo2L/TRAIL) in a batch cooling suspension crystallization by selecting pH values as a controllable variable. Three shaped TRAIL crystals could be obtained under different pH conditions, among which the hexagonal plate crystals had the highest specific activities against tumor cell line. The relationship among pH values, trimer contents and the specific activities of crystals and the purified TRAIL solutions were investigated. The results showed that different trimer contents resulted from pH altering in crystals and protein solutions is a main reason for their different specific activities. The studies may supply a new method to improve the bioactivity of TRAIL agent during its production and storage. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electric‐field‐induced internal deformation in piezoelectric BiB3O6 crystals

For the first time electric‐field‐induced atomic displacements (internal strains) in non‐ferroelectric polar BiB₃O₆ single crystal plates (point symmetry 2) were investigated using X‐ray diffraction technique. The intensity variations of selected Bragg reflections were collected for three different orientations of the applied external electric field vector with respect to the crystal lattice and used for calculating the microscopic structural response of BiB₃O₆. Due to the limited number of the reflections providing measurable changes in Bragg intensities we restricted ourselves in analyzing the shift of the B₃O₆ sublattice relative to the Bi one. In addition, we considered the deformation of the Bi‐O, B(1)‐O and B(2)‐O bond lengths and identified the [B(2)O₃] group as the most sensitive structural unit to an external electric perturbation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Highly stereoselective synthesis of (Z)-3-methoxy-1-methyleneisoindoles via DMAP catalyzed cyclization of methyl 2-alkynylbenzimidates

A DMAP (4-dimethylaminopyridine) catalyzed cyclization of methyl 2-alkynylbenzimidates has been developed, which affords 3-methoxy-1-methyleneisoindoles with excellent Z-stereoselectivity under mild and transition-metal-free conditions. The (Z)-3-methoxy-1-methyleneisoindole products can be converted to corresponding 3-amino-1-methyleneisoindoles, 3-methoxy-isoindoles, 3-methyleneisoindolinones and isoindolinones with high efficiency.