Counting alternating knots by genus

It is shown that the number of alternating knots of given genus g>1 grows as a polynomial of degree 6g−4 in the crossing number. The leading coefficient of the polynomial, which depends on the parity of the crossing number, is related to planar trivalent graphs with a Bieulerian path. The rate of growth of the number of such graphs is estimated.     

Triangular hyperbolic buildings

We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of such a polyhedron is a hyperbolic building, whose apartments are hyperbolic planes tessellated by regular triangles with angles $\pi /4$. The fundamental groups of the polyhedra are hyperbolic, torsion free, with property (T). To cite this article: R. Kangaslampi, A. Vdovina, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Rational ligand design for metal ion recognition. Synthesis of a N-benzylated N2S3-donor macrocycle for enhanced silver(I) discrimination

Four previously documented ligand design strategies for achieving Ag(I) discrimination have been applied to the design of a new N-benzylated N2S3-donor macrocycle; the latter shows high selectivity for Ag(I) over Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Pb(II) in log K and bulk membrane transport studies.     

Copper-coated microsprayer interface for on-line sheathless capillary electrophoresis electrospray mass spectrometry of carbohydrates

A sturdy home-built sheathless CE/ESI-QTOF-MS system was developed and optimized for carbohydrate analysis. The interface and employed methodology provided a simple analytical solution to laborious CE/MS interfacing methods and to problems in characterization of complex carbohydrate mixtures that require high-resolution separation of the components. The CE/ESI interface, feasible in any MS laboratory, consists of a one-piece CE column having the CE terminus in-laboratory shaped as a microsprayer and coated with copper. The CE microsprayer was inserted into an in-house made stainless steel clenching device and the whole assembly was mounted onto a quadrupole TOF mass spectrometer. The analytical potential of the interface in terms of suitability, microsprayer performance, copper coat durability, ionization efficiency, spray stability, and sensitivity was tested first on a simple mixture of standard saccharides, which were separated, resolved, and detected with high separation efficiency. The approach was next assessed for the screening of a biological sample, a complex mixture of O-glycosylated sialylated amino acids from urine of a patient suffering from Schindler disease. Preliminary data allow this method to be considered as one of general applicability in structural glycobiology and glycomics and easy to be implemented for proteomic surveys as well.     

Heat conduction in transversally graded laminates with non-uniform microstructure

Two-component laminates made of conductors distributed non-periodically as laminas along one direction are considered in this note. The macroscopic properties of these laminates are described by continuous slowly-varying functions across laminas. In order to analyse heat conduction, the approach, called the tolerance modelling, is used. The aim of this note is to use averaged equations of the tolerance model for transversally graded laminates to analyse stationary heat conduction across laminas. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Normal extensions of subnormal linear relations via quaternionic Cayley transforms

A quaternionic Cayley transform for linear relations is introduced and some of its properties are exhibited. We emphasize the role played by the linear relations whose quaternionic Cayley transforms are unitary operators, which happen to be normal relations, and investigate the class of those linear relations which extend to such normal relations.     

DG-Injective Covers, #-Injective Covers

Let R be a left noetherian ring. We show that every complex of left R-modules has a #-injective cover. We use this result to prove that the class of DG-injective complexes is covering if and only if the ring R is regular.     

Stereoselective C-X and regioselective C-H activation to,and selective C(sp2)-C(sp3) reductive elimination from,platinum compounds with thiophene-derived ligands

Several thiophene-based N^C ligands were synthesized. Strategically, a bromide was incorporated on the 2-position of the thiophene ring. When allowed to react with the platinum tetramethyl dimer, [Pt₂Me₄(µ-SMe₂)₂], platinum(IV) platinacycles were formed by oxidative addition of the C(sp²)-X bond. These platinum(IV) compounds were characterized by NMR and HRMS. The platinum (IV) compounds were subsequently subjected to thermolysis. A series of reactions occurred, including selective C-C reduction elimination and selective C-H oxidative addition, giving mixtures of platinum(II) products with varying degrees of regioselectivity.     

Separations of antifungal compounds in capillary electrophoresis with two anionic cyclodextrins

CD‐CZE methods were developed for complete stereoisomeric separations of a series of six γ‐lactam analogues, of which some were neutral, or cationic depending on the background electrolyte nature. The tested cyclodextrin was the versatile sulfobutylether‐ β‐CD, used either in a phosphate buffer using capillaries dynamically coated with polyethylene oxide or in a borate buffer using uncoated capillaries. Long‐end and short‐end modes and concentration variations of chiral selectors allowed finding conditions of complete separation of four out of the six derivatives (i.e., 1 , 2 , 3, and 4 ) in short run times, confirming their broad range of applications. To separate the two last compounds, the highly sulfated‐ γ‐CD was examined as chiral selector in acidic phosphate conditions. The enantiomers of the γ‐lactam analogues 5 and 6 were baseline resolved with 5.5 and 4%, respectively as concentration in the buffer.