Sur Les Groupes D’Homotopie Des Espaces Dont La Cohomologie Modulo 2 Est Nilpotente

The main object of this note is to prove the following generalisation of a theorem of Serre. A simply connected space of finite type whose mod. 2 cohomology is nilpotent (and non-trivial) has infinitely many homotopy groups which are not of odd torsion. Incidentally we show that for every fibrationF( _→ ^ί )E ( _→ ^p )B, satisfying certain mild conditions, the following holds. If a classx in the mod. 2 cohomology ofE belongs to the kernel ofi*, then some power ofx belongs to the ideal generated by the image underp* of the mod. 2 reduced cohomology ofB.      

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Miscellany on traces in ℓ-adic cohomology: a survey

We discuss classical questions concerning traces of elements of Galois groups or correspondences in ℓ-adic cohomology, mostly over finite or local fields, such as rationality and independence of ℓ, integrality, congruences modulo powers of ℓ or p. We report on the progress that has been made on this topic during the past ten years.     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005