Striking alkenol versus allenol reactivity: metal-catalyzed chemodifferentiating oxycyclization of enallenols

An efficient chemodivergent metal-controlled methodology for the generation of different highly functionalized oxygen heterocycles from common enallenol substrates has been developed. Chemoselectivity control in the O-C functionalization of an enallenol can be achieved through the choice of catalyst: AuCl(3), PdCl(2), and [PtCl(2)(CH(2)=CH(2))](2) exclusively afford dihydrofurans through selective activation of the allenol moiety, whereas FeCl(3) solely gives tetrahydrofurans or tetrahydropyrans through selective activation of the alkenol moiety. We have also shown that a combination of metal-mediated hydroalkoxylation and allenic aminocyclization reactions can lead to a useful preparation of the tetrahydrofuro[3,2-b]piperidine core of the antimalarial alkaloid isofebrifugine. These divergent heterocyclization reactions have been developed experimentally and additionally, their mechanisms have been investigated by a theoretical study.     

Matrix-assisted laser desorption/ionization-mass spectrometry of cuticular lipid profiles can differentiate sex, age, and mating status of Anopheles gambiae mosquitoes

Malaria is a devastating mosquito-borne disease, which affects hundreds of millions of people each year. It is transmitted predominantly by Anopheles gambiae, whose females must be >10 days old to become infective. In this study, cuticular lipids from a laboratory strain of this mosquito species were analyzed using a mass spectrometry method to evaluate their utility for age, sex and mating status differentiation. Matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS), in conjunction with an acenaphthene/silver nitrate matrix preparation, was shown to be 100% effective in classifying A. gambiae females into 1, 7–10, and 14 days of age. MALDI-MS analysis, supported by multivariate statistical methods, was also effective in detecting cuticular lipid differences between the sexes and between virgin and mated females. The technique requires further testing, but the obtained results suggest that MALDI-MS cuticular lipid spectra could be used for age grading of A. gambiae females with precision greater than with other available methods.     

On the sum of the Laplacian eigenvalues of a tree

Given an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L=D-A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k∈{1,…,n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenkovi? and Gutman [10].     

A note on the Hilbert scheme of twisted cubics

We show the component of the Hilbert scheme of twisted cubic curves is the blowup of the variety of determinantal nets along the subvariety of nets with a fixed plane.     

Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).     

Hilbert-Carleman and regularized determinants for linear operators

A general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the main properties of the extended determinants, obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended tracestr(A ^k ) of iterations and regularized determinants.This paper is a continuation of the paper [GGKr].     

N.m.r. spectra of cyclic amines. II—Factors influencing the chemical shifts of α-protons in aziridines

Proton magnetic resonance spectra of trans and cis-2,3-diphenylaziridine (1 and 2) and their N-ethyl derivatives 3 and 4 were measured in carbon tetrachloride, chloroform, and benzene-d₆ at low temperatures (1 and 3) and in dry conditions (1 and 2). On the basis of these results it was concluded that an N-ethyl group exerts a shielding influence on a cis ring proton and a deshielding influence on a trans ring proton. From results obtained by measuring the ¹H n.m.r. spectra of 1–4 in deuterochlorofom-trifluoroacetic acid it was derived that the lone pair of the aziridine nitrogen exerts a shielding influence on cis related ring hydrogens. In most N-alkylaziridines the effect of the N-alkyl group predominates.     

A Convenient Alkyl,Cycloalkyl and Aralkyl Disulfides Synthesis from Aliphatic and Aromatic Aldehydes,Aliphatic Ketones and Cycloketones

The reaction of aliphatic and aromatic aldehydes, aliphatic ketones, and cycloketones with hydrogen sulfide in anhydrous pyridine tiethylamine medium, provides a satisfactory method for preparation of alkyl, cycloalkyl, and aralkyl disulfides.