Noneuclidean harmonic analysis,the central limit theorem,and long transmission lines with random inhomogeneities

This is an expository paper. The derivation of the ordinary central limit theorem using the Fourier transform on the real line is reviewed. Harmonic analysis on the Poincaré-Lobatchevsky upper half plane H is sketched. The Fourier inversion formula on H reduces to that for the classical integral transform of F. G. Mehler (1881, Math. Ann.18, 161–194) and V. A. Fock (1943, Compt. Rend. Acad. Sci. URSS Dokl N. S.39, 253–256), for example. This result is then used to solve the heat equation on H, producing a non-Euclidean analogue of the density function for the Gaussian or normal distribution on H. The non-Euclidean central limit theorem for rotation invariant distributions on H with an application to the statistics of long transmission lines is also discussed.     

Synthesis and thermoelectric properties of YbSb2Te4

The study of the ternary phase diagram Yb–Sb–Te has led to the synthesis of YbSb₂Te₄ as a pure phase by way of high energy ball milling followed by annealing, whereas typical high temperature powder metallurgy leads to multiphase sample with impurities of the very stable YbTe. The Hall mobility, Seebeck coefficient, electrical resistivity and thermal conductivity of the layered compound YbSb₂Te₄ were measured in the range of 20–550 °C. The thermoelectric figure of merit peaks at 525 K and reaches 0.5. Of particular interest is the very low lattice thermal conductivity (as low as a glass) which makes YbSb₂Te₄ and related compounds promising thermoelectric materials. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Tighter Erdős‐Pósa Function for Long Cycles

We prove that there exists a bivariate function f with such that for every natural k and ?, every graph G has at least k vertex‐disjoint cycles of length at least ? or a set of at most vertices that meets all cycles of length at least ?. This improves a result by Birmelé et al. (Combinatorica, 27 (2007), 135–145), who proved the same result with .     

Applications of vectorized gold nanoparticles to the diagnosis and therapy of cancer

This critical review focuses on the anti-cancer fight using gold nanoparticles (AuNPs) functionalized with chemotherapeutic drugs in so-called "complexes" (supramolecular assemblies) and "conjugates" (covalent assemblies) as vectors. There is a considerable body of recent literature on various tumor-imaging techniques using the surface plasmon band (SPB) and the "passive" and "active" vectorization of anti-cancer drugs. This article reviews the main concepts and the most recent literature data with emphasis on AuNP preparation, cytotoxicities and use in selective targeting of cancer cells with over-expressed receptors for diagnosis and therapy (108 references).     

Polyboramines for Hydrogen Release: Polymers Containing Lewis Pairs in their Backbone

The one‐step polycondensation of diamines and diboranes triggered by the in situ deprotonation of the diammonium salts and concomitant reduction of bisboronic acids leads to the assembly of polymer chains through multiple Lewis pairing in their backbone. These new polyboramines are dihydrogen reservoirs that can be used for the hydrogenation of imines and carbonyl compounds. They also display a unique dihydrogen thermal release profile that is a direct consequence of the insertion of the amine–borane linkages in the polymeric backbone.     

Morphology and properties of waterborne adhesives made from hybrid polyacrylic/montmorillonite clay colloidal dispersions showing improved tack and shear resistance

The morphology and adhesive properties of waterborne films from n-butyl acrylate/methyl methacrylate/montmorillonite clay hybrid polymer latexes which were synthesized by miniemulsion polymerization in the presence of a reactive organoclay ((2-methacryloylethyl) hexadecyldimethylammonium modified montmorillonite, CMA16) were investigated. It was found by cryo-TEM analysis that the hybrid dispersions were a mixture of colloidal particles composed of a small fraction of free montmorillonite clay platelets, polymer latex particles, polymer particles to which one or more clay platelets where adhered onto its surface and a fraction of colloidal material consisted of a clay platelet with a polymer lob adhered to either side, in other words hybrid particles with a dumbbell-like morphology. The films made from these waterborne hybrid dispersions presented a homogeneous dispersion of the clay platelets and exfoliated morphology. The shear adhesion failure temperature (SAFT) and shear resistance of the hybrid latex films synthesized with CMA16 were better than those prepared with a commercial clay (Cloisite 30B), but presented a liquid-like probe-tack performance. When allyl methacrylate (AMA) was added in the formulation, SAFT and shear resistance improved, but the film had a very low energy of adhesion due to the excessively crosslinked matrix. In order to reduce crosslink density and thus improve the adhesion energy, small amounts of chain transfer agent, in this case n-dodecyl mercaptan (n-DDM), were used in the miniemulsion polymerization process. Adhesive films made from these waterborne hybrid dispersions showed excellent SAFT and shear resistance, and good energy of adhesion.      

Tandem oxidation of allylic and benzylic alcohols to esters catalyzed by N-heterocyclic carbenes

N-heterocyclic carbenes catalyze the oxidation of allylic, propargylic, and benzylic alcohols to esters with manganese(IV) oxide in excellent yields. A variety of ester derivatives can be synthesized, including protected carboxylates. This one-pot tandem oxidation represents the first organocatalytic oxidation of alcohols to esters. Saturated esters can also be accessed from aldehydes using this method. Through the utilization of a chiral catalyst, the acyl-heteroazolium intermediate becomes a chiral acylating agent, which can desymmetrize meso-1,2-diols. [reaction: see text].     

Hydroacylation of activated ketones catalyzed by N-heterocyclic carbenes

N-heterocyclic carbenes derived from triazolium salts are effective catalysts between 10 and 15 mol % for the hydroacylation of activated ketones. The reducing equivalent is generated via the interaction of a nucleophilic carbene species and an aromatic aldehyde. The subsequent alcohol product can undergo an acylation event with the resulting acyl heteroazolium intermediate formed in situ between the NHC and the aldehyde. This unprecedented multiple bond-forming reaction can accommodate aromatic aldehydes as the hydride source and various electron-deficient ketones. Preliminary mechanistic evidence indicates that the reduction and acylation steps are sequential operations. The intramolecular variant of this organocatalytic reaction affords benzofuranones in good yield.