Large Discrepancy In Homogenous Quasi-Arithmetic Progressions

We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy.     

Nonaqueous diazotization of 4-amino-3-arylisothiazole-5-carboxylate esters

4-Amino-3-arylisothiazole-5-carboxylate esters are converted to the corresponding desamino, chloro, bromo, and iodo esters by processes involving nonaqueous diazotization. These related procedures open up the possibility for the conversion of readily available heterocyclic ortho-amino esters and nitriles to related heterocyclic derivatives, which are not easily obtained by alternate routes.     

A short and efficient synthesis of grisan

A three-step synthesis of grisan (spiro[benzofuran-2(3H)-1′-cyclohexane]), using methoxymethoxybenzene and 1-chloromethylcyclohexene as starting materials, is described.     

Acetylene weak bands at 2.5 μm from intracavity Cr:ZnSe laser absorption observed with time-resolved Fourier transform spectroscopy

The spectral dynamics of a mid-infrared multimode Cr(2+):ZnSe laser located in a vacuum sealed chamber containing acetylene at low pressure is analyzed by a stepping-mode high-resolution time-resolved Fourier transform interferometer. Doppler-limited absorption spectra of C(2)H(2) in natural isotopic abundance are recorded around 4000 cm(-1) with kilometric absorption path lengths and sensitivities better than 3 10(-8) cm(-1). Two cold bands are newly identified and assigned to the ν(1)+ν(4) (1) and ν(3)+ν(5) (1) transitions of (12)C(13)CH(2). The ν(1)+ν(5) (1) band of (12)C(2)HD and fourteen (12)C(2)H(2) bands are observed, among which for the first time ν(2)+2ν(4) (2)+ν(5) (-1).     

Latex particles bearing hydrophilic grafted hairs with controlled chain length and functionality synthesized by reversible addition–fragmentation chain transfer

A method is described for synthesizing latex particles with anchored hairs by the grafting of hydrophilic chains, synthesized by reversible addition–fragmentation chain transfer, onto functionalized latex particles. These have the potential to bind biologically active species. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1188–1195, 2003     

Killing tensors as irreducible representations of the general linear group

We show that the vector space of fixed valence Killing tensors on a space of constant curvature is naturally isomorphic to a certain highest weight, irreducible representation of the general linear group. The isomorphism is equivariant in the sense that the natural action of the isometry group corresponds to the restriction of the linear action to the appropriate subgroup. As an application, we deduce the Delong–Takeuchi–Thompson formula on the dimension of the vector space of Killing tensors from the classical Weyl dimension formula. To cite this article: R.G. McLenaghan et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Focused ion beam Moiré method

A focused ion beam (FIB) Moiré method is proposed to measure the in-plane deformation of object in a micrometer scale. The FIB Moiré is generated by the interference between a prepared specimen grating and FIB raster scan lines. The principle of the FIB Moiré is described. The sensitivity and accuracy of deformation measurement are discussed in detail. Several specimen gratings with 0.14 and 0.20 μm spacing are used to generate FIB Moiré patterns. The FIB Moiré method is successfully used to measure the residual deformation in a micro-electro-mechanical system structure after removing the SiO₂ sacrificial layer with a 5000 lines/mm grating. The results demonstrate the feasibility of this method.     

Potent New Heterogeneous Asymmetric Catalysts

A set of new, air‐stable, Rh^I‐based heterogeneous asymmetric hydrogenation catalysts have been synthesised, characterised, and tested. Individual members of this new family all exhibit good enantioselectivity.     

Organometallic alkane CH activation

The title topic is reviewed with emphasis on catalysis and on recent advances. Alkane σ complexes, Shilov chemistry and oxidative addition routes are covered. Attention is also given to σ bond metathesis, surface-bound organometallics and CH activation involving carbene complexes. Closely related reactions of non-alkane substrates such as the Murai reaction are also discussed.