Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.     

Pure Skew Lattices in Rings

Given a ring $R$, let $S\subseteq R$ be a pure multiplicative band that is closed under the cubic join operation $x\nabla y = x+y+yx-xyx-yxy.$ We show that $\left( S,\cdot,\nabla\right) $ forms a pure skew lattice if and only if $S$ satisfies the polynomial identity $\left(xy-yx\right)^{2}z = z\left(xy-yx\right)^{2}$. We also examine properties of pure skew lattices in rings.     

CsMoO2(HO3P–CH2–PO3): a new metallodiphosphonate with a hybrid framework

Crystals of caesium molybdeno­methyl­enedi­phospho­nate, [CsMoO₂(CH₃O₆P₂)], were hydro­thermally synthesized at 473 K. The monoclinic structure, as determined from single‐crystal X‐ray diffraction, is two‐dimensional and consists of stacked mixed layers of corner‐sharing tetrahedral di­phosphon­ate groups and MoO₆ octahedra, between which Cs⁺ cations are intercalated.     

Studies on the Chemistry of Thienoannelated O , N - and S , N -Containing Heterocycles, 28 [1]. Synthesis of Imidazo[1,5- d ]thieno[2,3- b ][1,4]thiazine Derivatives as GABA -Receptor Ligands

Summary.  GABA-receptor-ligands are still very interesting in drug-development. Usually benzodiazepines are used in the treatment but they have serious side-effects. Thus, a recently synthesized quioxaline derivative which showed reduced side-effects in an animal model was used as a model-substance. The cyclus was modified to optimize the pharmacological profile. Accordingly, a series of imidazo-thieno-thiazines was synthesized starting from 5-acetyl-2-chloro-3-nitrothiophene to yield 6-ethyl-2,3-dihydro-1H-thieno[2,3-b][1,4]thiazine-2-one. Reaction with potassium tert-butoxide and diethylchlorophosphate gave an intermediate, which resulted in the desired ring system after adding the corresponding isocyanides and potassium tert-butoxide. Corresponding author. E-mail: thomas.erker@univie.ac.at Received August 6, 2002; accepted August 13, 2002     

A Heuristic Decomposition Algorithm for Scheduling Problems on Mixed Graphs

We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a _ij >0 and a _ji >0 may be given where a _ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//C_max belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given.     

7-Deazaadenosine: Oligoribonucleotide building block synthesis and autocatalytic hydrolysis of base-modified hammerhead ribozymes

A 7-deazaadenosine ( = tubercidin; c⁷A; 1 ) building block for solid-phase oligoribonucleotide synthesis was prepared. The amino group of 1 was protected with the (dimethylamino)methylidene residue (→ 3 ), and the monomethoxytrityl group was introduced at OH? C(5′) (→ 4 ). Protection of OH? C(2′) was carried out by silylation, showing that use of the (i-Pr)₃Si group resulted in high 2′-O-selectivity (→ 5b , 80%). Reaction of 5b with PCl₃ afforded the phosphonate 7 which was used in solid-phase oligoribonucleotide synthesis. The autocatalytic hydrolysis of hammerhead ribozymes using pG-G-G-A-G-U-C-A-G-U-C-C-C-U-U-C-G-G-G-G-A-C-U-C-U-G-A-A-G-A-G-G-C-G-C as substrate strand (S) and modified G-C-G-C-C-G-A-A-A-C-U-C-C-C as enzyme strand (E) was studied. When c⁷A replaced A¹³ or A¹⁴, a small decrease of catalytic activity was observed, while modification in position A¹⁵ enhanced the autocatalytic hydrolysis. The results demonstrate, that the atom N(7) of adenosine in any of these positions is not crucial for ribozyme action.     

ESCA-Analysis of tin compounds on the surface of hydroxyapatite

The formation of tin compounds on the surface of hydroxyapatite, the main crystalline component of teeth, is discussed controversially. SnF₂ is used as an anticaries agent in toothpaste preparations. Pure hydroxyapatite (HAP) is treated with extracts of commercially available toothpastes containing tin fluoride and analyzed by electron spectroscopy (ESCA). Survey spectra and depth profiles are recorded. The chemical shifts measured for the HAP samples are compared with those of standard tin compounds. It is concluded that on the surface of hydroxyapatite a mixture of two-valent fluoro-phosphato compounds is formed. SnO is not found in the mixture.     

Was ist „Molybdänsäure”︁ oder „Polymolybdänsäure”︁?

What is “Molybdic Acid” or “Polymolybdic Acid”? According to a comparative study of the literature, supplemented by well-aimed experimental investigations and equilibrium calculations, the terms “molybdic acid” or “polymolybdic acid”, used for many substances, species, or solutions in the literature, are applicable to a species, a solution, and two solids:

• a) The monomeric molybdic acid, most probably having the formula MoO₂(OH)₂(H₂O)₂(? H₂MoO₄, aq), exists in (aqueous) solution only and never exceeds a concentration of ≈ 10^?3 M since at higher concentrations it reacts with other monomemeric molybdenum (VI) species to give anionic or cationic polymers.
• b) A concentrated (>0.1 M Mo^VI) aqueous molybdate solution of degree of acidification P = 2 (realized, e. g., by a solution of one of the Mo^VI oxides; by any molybdate solutions whose cations have been exchanged by H₃O⁺ on a cation exchanger; by suitable acidification of a molybdate solution) contains 8 H₃O⁺ and the well-known polyanion Mo₃₆O₁₁₂(H₂O)₁₆^8? exactly in the stoichiometric proportions.
• c) A glassy substance, obtained from an alkali metal salt-free solution prepared according to (b), refers to the compound (H₃O)₈[Mo₃₆O₁₁₂(H₂O)₁₆]·xH₂O, x = 25—29.
• d) A solid having the ideal composition [(H₃O)Mo₅O₁₅(OH)H₂O·H₂O]∞ consists of a polymolybdate skeleton (the well-known ?decamolybdate”? structure), in the tunnels of which H₃O⁺ and H₂O are intercalate. The structure is very unstable if only H₃O⁺ cations are present, but it is enormously stabilized by a partial exchange of H₃O⁺ by certain alkali or alkaline earth metal cations.

For the compounds MoO₃, MoO₃·H₂O, and MoO₃·2H₂O the term ?molybdic acid”? is unjustified. The commercial product ?molybdic acid, ≈85% MoO₃”? is the well-known polymolybdate (NH₄)₂O·4 MoO₃ with a layer structure of the polyanion.