Multivariate Reversed Hazard Rates and Inactivity Times of Systems

Methodology and Computing in Applied Probability - The family of the multivariate conditional hazard rate functions often reveals to be a convenient tool to describe the joint probability...     

Composition factors of indecomposable modules

Let be a connected, basic finite dimensional algebra over an algebraically closed field. Our main aim is to prove that if is biserial, its ordinary quiver has no loop and every indecomposable -module is uniquely determined by its composition factors, then each indecomposable -module is multiplicity-free.

     

Classification of Nonorientable 3-Manifolds Admitting Decompositions into ≤ 26 Coloured Tetrahedra

The present paper adopts a computational approach to the study of nonorientable 3-manifolds: in fact, we describe how to create an automaticcatalogue of all nonorientable 3-manifolds admitting coloured triangulationswith a fixed number of tetrahedra. In particular, the catalogue has been effectively produced and analysed for up to 26 tetrahedra, to reach the complete classification of all involved 3-manifolds. As a consequence, the following summarising result can be stated:THEOREM I. Exactly seven closed connected prime nonorientable3-manifolds exist, which admit a coloured triangulation consisting of atmost 26 tetrahedra.More precisely, they are the four Euclidean nonorientable 3-manifolds, the nontrivial S2 bundle overS1, the topological product between thereal projective plane RP2 andS1, and the torus bundle overS1, with monodromy induced by matrix(10 -11).     

Rank Properties in Finite Semigroups II: The Small Rank and the Large Rank

This paper is concerned with the application of two possible definitions of rank to certain well-known semigroups.AMS Subject Classification (2000), 20M10     

Synthèse d'hétérocycles en catalyse par transfert de phase

A general study of the chemical behavior of heterocyclic anions, dianions and dianionic reagents under phase transfer catalysis conditions allowed us to synthesize various heterocyclic compounds such as imidazo[2,1-b]thiazole and derivatives; imidazo[2,1-b]thiazine and imidazo[2,1-b]benzothiazepine. Reaction conditions e.g., catalyst, solvent, temperature, etc., are indicated.     

Synthesis of 2-amino-3-hydroxy- and of 2,3-diamino-3H-1,4-benzodiazepines

A new synthesis of 7-chloro-2,3-diamino-5-phenyl-3H-1,4-benzodiazepines is described, which allows for the preparation of compounds bearing the same or different substituents at the 2 and 3 positions, starting from 2-amino-7-chloro-3-hydroxy-5-phenyl-3H-1,4-benzodiazepines.     

Synthesis of some 3,7-disubstituted quino[3,2-c][1,8]naphthyridines

The preparation of some 3,7-disubstituted-5,6-dihydroquino[3,2-c][1,8]naphthyridines ( 6 ) by the condensation of 7-substituted-2,3-dihydro-1,8-naphthyridin-4-(1H)ones ( 5 ) with o-aminoacetophenone or o-aminobenzophenone is described. All the 5,6-dihydroderivatives 6 were transformed into the fully aromatic compounds 7 by heating with nitrobenzene. Only a few quino[3,2-c][1,8]naphthyridines were previously described.     

Der Einfluß großer Salzkonzentrationen auf die Oxydationsreaktion von Fe(phen) 3 2+ mit Ce(IV) in Schwefelsäure

The influence of NaClO₄, NaCl and Na₂SO₄ on the oxidation of Fe(phen) ₃ ²⁺ by Ce(IV) was investigated by means of the stopped-flow method. At the concentrations range of NaClO₄ and NaCl 0.1–1.0M the rate constant values decrease from 1.03·10⁵ to 0.56·10⁵M^–1s^–1 and from 1.08·10⁵ to 0.81·10⁵M^–1s^–1 respectively.In varying concentrations of Na₂SO₄ solutions (0.05–0.35M) the rate constant values decrease from 1.05·10⁵M^–1s^–1 to 0.45·10⁵M^–1s^–1.Taking into account the negative salt effect the mechanism of the reaction progress is proposed.

     

Determination of thallium and lead in cadmium salts by anodic stripping voltammetry with addition of surfactants to suppress the cadmium peaks

Conditions have been found which make possible the determination of thallium and/or lead in cadmium and its salts without preliminary separation. The electrochemical activity of the cadmium, which usually interferes in the determination of thallium, is inhibited by the addition of 0.01% of polyethylene glycol of M.W. 4000. Thallium is determined by electrolysis at ?0.74 V vs. SCE, in 0.1M EDTA solution: 10^?1M thallium can be determined in the presence of 0.1M cadmium, while copper and lead at 10^?2M and 10^?5M respectively do not interfere. Lead is determined in 0.1M acetic acid containing 0.1% cetyltrimethylammonium bromide (CTAB). The addition of CTAB shifts the cadmium peak, as well as the optimum deposition potential for cadmium, to more negative values, making it possible to determine lead in the presence of cadmium as long as the deposition potential lies in the range between ?0.50 and ?0.56 V vs. SCE. Lead can be determined in the presence of ten times as much thallium.     

Derivatives of M(η5-C5H5)2 (M = Mo,W) with alkenylpyridines and related ligands

Reactions of ligands 2-vinylpyridine 1, 4-vinylpyridine 2, 2-allylpyridine 3, 1-allylpyrazole 4, acrylonitrile 5 and allylcyanide 6 with the metallocene derivatives [Mo(η⁵-C₅H₅)₂H₃][PF₆] 7, [Mo(η⁵-C₅H₅)₂HI] 8, [W(η⁵-C₅H₅)₂H₃] [PF₆] 9, [Mo(η⁵-C₅H₅)₂H₂] 10, [M(η⁵-C₅H₅)₂Br₂], M = Mo 11, M = W 12 are described. Reaction of 7 with 1, 8 with 1, 3 with 8 and 4 with 8 gave mixtures of metallocyle isomers resulting from coordination of the nitrogen atom to molybdenum followed by internal hydrometallation; reaction of 11 with 1 gave an olefinic π complex; reaction of either 9 or 11 with 1 gave intractable oils; reactions of 8 with 2, 11 with 5, 12 with 5, 11 with 6 and 12 with 6 yielded monosubstituted products in which the ligand is N-coordinated.