THE MAXIMAL LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS

ABSTRACT

We study the notion of a (general) left quotient ring of an alternative ring and show the existence of a maximal left quotient ring for every alternative ring that is a left quotient ring of itself.     

Fragments with finiteness conditions in particular over group rings

Abstract length functions on groups were introduced by Lyndon [5]. In [2] Chiswell showed that for a group action on an IR-tree there is a length function associated with each point of the tree, and moreover any length function can occur in this way. This paper establishes necessary and sufficient conditions for two length functions to arise from the same action of a group on a tree.     

The structure of simple silicate glasses in the light of Middle Infrared spectroscopy studies

The aim of the work is to determine the internal structure of simple silicate glasses based on structural studies. Due to the absence of the long-range order, the X-ray methods usually applied in the studies of crystalline materials are of low applicability in the investigations of glasses. Therefore, spectroscopic methods, such as Middle Infrared (MIR), which make it possible to ‘see’ the short- and the middle-range orders are extremely suitable in their studies. MIR investigations have shown that the glasses studied exhibit domain composition, which corresponds to the order of certain crystalline phases. Analysis of the MIR spectra of simple silicate glasses and their mathematical decomposition allowed us to identify the bands characteristic for ring systems as well as those originating from Si-O⁻, Si = O defects. Appearance of the bands characteristic for pseudolattice ring vibrations (740-600 cm^− 1) in the MIR spectra of glasses is an evidence of the existence of over-tetrahedral order.     

Synthesis of C-1 indol-3-yl substituted tetrahydroisoquinoline derivatives via a Pictet-Spengler approach

A protocol for the diastereoselective synthesis of C-1 indol-3-yl substituted tetrahydroisoquinoline derivatives via Pictet-Spengler condensation with L-DOPA or l-DOPA derivatives and 1H-indole-3-carbaldehydes is presented. The protocol is used for the successful synthesis of several tetrahydroisoquinolines as well as diketopiperazine fused analogues.     

Synthesis and Characterization of Planar Five‐Ring‐Fused Dithiophene‐dione

A series of new organic semiconductors based on s‐indaceno[1,2‐b:5,6‐b′]dithiophene‐4,9‐dione was successfully synthesized and characterized. The electron withdrawing carbonyl group lowers the LUMO energy levels, leading to increased electronegativities, which is beneficial for high photo‐stability in air. The n‐alkyl substituted compounds, 1c and 1d , crystallize with the rigid coplanar systems packed into slipped face‐to‐face π‐stacks. Interestingly, 1c and 1d also show liquid crystalline behaviors, which give highly ordered molecular packing over large area.     

New approaches to synthesis of tris[1,2,4]triazolo[1,3,5]triazines

Thermal cyclization of 3-R-5-chloro-1,2,4-triazoles (R = Cl, Ph) afforded 2,6,10-tri-R- tris[1,2,4]triazolo[1,5-a:1′,5′c:1″,5″-e][1,3,5]triazines 5 (R = Ph) and 7 (R = Cl). These compounds are first representatives of this class of heterocycles, whose structures were unambiguously established. Treatment of these compounds with nucleophiles (H₂O/NaOH, NH₃) results in the triazine ring opening to give compounds consisting of three 1,2,4-triazole rings linked in a chain. For example, treatment of cyclic compound 5 with aqueous alkali affords 3-phenyl-1-3-phenyl-1-(3-phenyl-1H-1,2,4-triazol-5-yl)-1,2,4-triazol-5-yl-1H-1,2,4-triazol-5-one. Treatment of 3,7,11-triphenyltris[1,2,4]triazolo[4,3-a:4′,3′c:4″,3″-e][1,3,5]triazine (2) with HCl/SbCl₅ leads to the triazine ring opening giving rise to 5-(3-chloro-5-phenyl-1,2,4-triazol-4-yl)-3-phenyl-4-(5-phenyl-1H-1,2,4-triazol-3-yl)-1,2,4-triazole. Thermal cyclization of the latter produces 3,7,10-triphenyltris[1,2,4]triazolo[1,5-a:4′,3′c:4″,3″-e][1,3,5]triazine (13). Thermolysis of both cyclic compound 2 and cyclic compound 13 is accompanied by the Dimroth rearrangement to yield 3,6,10-triphenyl-tris[1,2,4]triazolo[1,5-a:1′, 5′-c:4″,3″-e][1,3,5]triazine (14). Compounds 13 and 14 are the first representatives of cyclic compounds with this skeleton. ¹³C NMR spectroscopy allows the determination of the isomer type in a series of tris[1,2,4]triazolo[1,3,5]triazines.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 706–712, March, 2005.     

Linking systems in nonelementary abelian groups

Linked systems of symmetric designs are equivalent to 3-class Q-antipodal association schemes. Only one infinite family of examples is known, and this family has interesting origins and is connected to important applications. In this paper, we define linking systems, collections of difference sets that correspond to systems of linked designs, and we construct linking systems in a variety of nonelementary abelian groups using Galois rings, partial difference sets, and a product construction. We include some partial results in the final section.     

Optical‐fiber microcoil waveguides and resonators and their applications for interferometry and sensing

In this work, recent progress in the theoretical and experimental studies of optical‐fiber microcoil waveguides and resonators, as well as their various applications are reviewed. In particular, the focus is set on sensing and interferometry applications. It is shown that due to its inherently low propagation and fiber‐coupling losses, fiber‐microcoil based sensors and interferometers offer substantial enhancement of sensitivity and compactness compared to other types of devices. Recent progress in the realization and experimental characterization of such structures is presented and the theoretical tools to analyze the impact of real‐world nonuniformities on the characteristics of fiber‐microcoil structures are provided.     

Intramolecular-Prins-cyclization: a novel synthesis of hexahydro-2H-furo[3,2-c]pyran derivatives

p-Toluenesulfonic acid is found to catalyze the coupling of (Z)-hex-3-ene-1,6-diol with a series of aldehydes by means of intramolecular-Prins-cyclization to provide the corresponding hexahydro-2H-furo[3,2-c]pyran derivatives in good yields with complete cis-selectivity, whereas the coupling of (E)-hex-3-ene-1,6-diol with aliphatic aldehydes gave trans-fused bicyclic furopyrans.