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 .     

Microcalorimetric qualitative analysis of biofilm development in porous media used in wastewater treatment by constructed wetland

In wastewater treatment by constructed wetland, the biodegradation capability of the biomass developed in the soil is one of the most important factors. For this kind of treatment unit, soil properties are studied to improve its filtration capacity and hydraulic residence time of the wastewater. The impact of soil properties like porosity and soil components on biomass development and biodegradation capacity seem to be less studied certainly due to the complexity of microbial identification techniques currently used. The study presented here is a preliminary work to validate that calorimetric technique could be a tool in the understanding of biodegradation capacity of wastewater treatment processes. Biofilm is preliminary developed in columns filled with different porous materials of well known porosity and constitutive components. These columns are fed with the same continuous flow of synthetic solution (C, N, and P) as a substrate amending during 3 weeks. Then each week, 2 mL samples of porous media from these columns are analyzed in isothermal calorimeter for 48 h. Net heat flow is recorded before and after substrate injection. This work results in the definition of the procedure for batch experiments in calorimeter for wastewater process efficiency. The results of these experiments show that the microbial reaction due to substrate amendment is highly depending on the porous material used for biofilm growth. Indeed calorimetric signals recorded lead to conclude that biofilm grown on plastic beads has a faster and more intensive reaction to glucose amendment than biofilm grown on glass beads. At least, two glass beads samples analyzed in the calorimeter after the same duration of feeding with synthetic solution have very different response to glucose or synthetic solution.     

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.      

In situ generated cellulose nanoparticles to enhance the hydrophobicity of paper

Handsheets with in situ generated cellulose nanoparticles were made from oxidized pulp fibers prepared by 2,2,6,6-tetramethylpiperidinyl-1-oxyl-mediated oxidation of kraft fiber with sodium hypochlorite and sodium bromide. The oxidized pulp fibers were blended prior to handsheet formation for short times (1–3 min). From gravimetric analysis of the supernatant, yield of cellulose nanoparticles generated from this blending process were up to 9.5 dry wt%. Scanning electron microscopy showed that the handsheets fabricated in a wetlay process had increased smoothness with increased blending time. A significant decrease in water vapor transmission rate for the sheets supported the hypothesis that cellulose nanoparticles fill the empty spaces between pulp fibers throughout the handsheet affording a more dense structure. Oxidation significantly enhanced the tensile index of the handsheets and this value was further improved by blending for 2 min. The handsheets were treated with a solution of octadecylamine (ODA) modifying the surface chemistry of the paper. Irreversibly adsorbed ODA on the oxidized cellulose surfaces after extensive extraction was confirmed by Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy. Sessile drop contact angle tests for modified handsheets illustrated its enhanced hydrophobicity with contact angles over 90°. Overall the study developed a novel route to make paper with enhanced functionality without the need to separately deposit nanocellulose onto the paper surface.     

An electrochemical immunosensor based on covalent immobilization of okadaic acid onto screen printed carbon electrode via diazotization-coupling reaction

In this work, an electrochemical method based on the diazonium-coupling reaction mechanism for the immobilization of okadaic acid (OA) on screen printed carbon electrode was developed. At first, 4-carboxyphenyl film was grafted by electrochemical reduction of 4-carboxyphenyl diazonium salt, followed by terminal carboxylic group activation by N-hydroxysuccinimide (NHS), N-(3-dimethylaminopropyle)-N′-ethyle-carbodiimide hydrochloride (EDC). Hexamethyldiamine was then covalently bound by one of its terminal amine group to the activated carboxylic group. The carboxyl group of okadaic acid was activated by EDC/NHS and then conjugated to the second terminal amine group on other side of the hexamethyldiamine through amide bond formation. After immobilization of OA, an indirect competitive immunoassay format was employed to detect OA. The immunosensor obtained using this novel approach allowed detection limit of 1.44 ng/L of OA, and was also validated with certified reference mussel samples.     

Thielavin B methyl ester: a cytotoxic benzoate trimer from an unidentified fungus (MSX 55526) from the Order Sordariales

As part of our ongoing investigation of filamentous fungi for anticancer leads, an active fungal extract was identified from the Mycosynthetix library (MSX 55526; from the Order Sordariales). Bioactivity-directed fractionation yielded the known ergosterol peroxide (2) and 5α,8α-epidioxyergosta-6,9(11),22-trien-3β-ol (3), and a new benzoate trimer, termed thielavin B methyl ester (1). The structure elucidation of 1 was facilitated by the use of HRMS coupled to an APPI (atmospheric pressure photoionization) source. Compound 1 proved to be moderately active against a panel of three cancer cell lines.