The t-analog of the level one string function for twisted affine Kac–Moody algebras

We study Lusztig?s t-analog of weight multiplicities, or affine Kostka–Foulkes polynomials, associated to level one representations of twisted affine Kac–Moody algebras. We obtain an explicit closed form expression for the unique t-string function, using constant term identities of Macdonald and Cherednik. This extends previous work on t-string functions for the untwisted simply-laced affine Kac–Moody algebras.     

On degrees of maps between Grassmannians

Let G_n,k denote the oriented grassmann manifold of orientedk-planes in ℝⁿ. It is shown that for any continuous mapf: G_n,k → G_n,k, dim G_n,k = dim G_m,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂG_m,l → ℂG_n,k,h: ℍG_m,l → ℍG_n,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained.     

Effect of the physico-chemical properties of vanadia/praseodymia on cyclohexanol decomposition

Vanadia supported on praseodymia (2, 6 and 10 wt.% V₂O₅) were prepared by wet impregnation and characterized by energy dispersive X-ray analysis (EDAX), X-ray diffraction (XRD), TGA/DTA and BET surface area measurements. Decomposition of cyclohexanol was conducted over these catalysts in the vapor phase. Acidity of the catalysts was measured by temperature programmed desorption using ammonia as a probe molecule. The structural and acidic properties were correlated to the total conversion and cyclohexene selectivity.     

Acid-base properties and catalytic activity of ABO3 (perovskite-type) oxides consisting of rare earth and 3d transition metals

The surface acidity/basicity of perovskite-type mixed oxides (LaCrO₃, PrCrO₃, SmCrO₃, LaMnO₃, PrMnO₃, SmMnO₃, LaFeO₃, PrFeO₃, SmFeO₃, LaCoO₃, PrCoO₃, SmCoO₃, LaNiO₃, PrNiO₃ and SmNiO₃) are reported. These properties have been correlated with the catalytic activity of these oxides towards esterification of acetic acid usingn-butanol.     

Synthesis,spectra and redox behavior of copper(II) complexes of curcumin diketimines as models for blue copper proteins

Several new Cu^II complexes, having positive reduction potentials in an in situmanner, were synthesized by reaction of the Knoevenagel condensate, 4-salicylidene-1,7-bis(4-hydroxy-3-methoxyphenyl)-1,6-heptadiene-3,5-dione (from curcumin) with 4-X-anilines and CuCl₂. The solution electronic spectra of these complexes show intense absorption around 530 nm with unusual high extinction values (, 1600--3600 m^-1 cm^-1) due to the low symmetry L--d (Cu) LMCT transition. The e.s.r. spectral features with g _|| > g _|| > 2.0 having four g _|| values and a broadening of the g _||component with moderately low A _|| (110 × 10^-4 cm^-1) also suggest a lower symmetry around Cu^II. The cyclic voltammetric studies of the Cu^II complexes in MeCN show a positive reduction potential (E _pc=502--138 mV) with high peak-to-peak separation (E _p=87--335 mV). The higher and low A _||values together with positive reduction potentials for these Cu^II complexes suggest that they can mimic the functional properties of blue copper proteins, but have poor redox stability.     

New processable polyaromatic amides curable by intramolecular cyclization. XVI

New Processable Polyaromatic amides were prepared from 2,2′-diiododiphenyl-4,4′-dicarbonyl dichloride (I) and several aromatic diamines. Phenylethynyl groups were introduced in these polymides by replacing the iodine groups with copper phenyl acetylide. On thermal curing, 2,2′-di(phenylethynyl)biphenyl group undergoes intramolecular cyclization to form 9-phenyl dibenzanthracene derivative. The cured polymers showed increased heat and chemical stabilities. No melting points were observed for all the polymers below 500°C. The viscosity of the polymers was decreased on substitution of the iodine by phenylethynyl groups.     

Selective formation of cumene on pillared clays by isopropylation of benzene

Summary Cumene is prepared selectively through an eco-friendly route using naturally available montmorillonite clay as the green catalyst. Pillaring of montmorillonite is done to improve the structural stability for long-term use. Alumina pillaring and the influence of mixed pillaring with zirconia and chromia on the structural as well as textural properties are characterized. Montmorillonite shows very high conversion, selectivity and regenerability upon pillaring towards isopropylation of benzene.     

Nanoparticle mixing through rapid expansion of high pressure and supercritical suspensions

Mixing of binary mixtures of nanopowders afforded by rapid expansion of high pressure and supercritical suspensions (REHPS) is investigated to examine the roles of two previously reported deagglomeration mechanisms. The quality of mixing was characterized through intensity and scale of segregation using concentration data obtained through energy dispersive X-ray spectroscopy; the corresponding deagglomeration was quantified using differential mobility and image analyses in conjunction with electron microscopy. Increasing the pressure from which expansion was carried out, and decreasing the nozzle diameter led to improved deagglomeration. However, increased pressure alone did not influence the mixture quality, which was found to also depend on the scale of mixedness of the constituents before transport through the nozzle, establishing that the REHPS mixing is significantly improved by improving the quality of the premix. The scale of segregation correlated with the size of the most energetic eddies present during flow through the nozzle, both of which increased with nozzle diameter, corroborating the importance of previously reported shear-induced deagglomeration mechanism. Finally, REHPS was also shown to be capable of deagglomerating carbon nanotube bundles and mix them well with alumina, silica, and titania at submicron scale.     

Use of vitamin B2 for fluorescence detection of thymidine-related single-nucleotide polymorphisms

In combination with abasic site (AP site)-containing DNAs, potential use of a biotic fluorescence compound, Vitamin B₂ (riboflavin), is demonstrated for the fluorescence detection of the thymine (T)-related single-nucleotide polymorphisms. Our method is based on construction of the AP site in DNA duplexes, which allows small ligands to bind to target nucleotides accompanied by fluorescence signaling: an AP site-containing probe DNA is hybridized with a target DNA so as to place the AP site toward a target nucleobase, by which hydrophobic microenvironments are provided for ligands to recognize target nucleotides through stacking and hydrogen-bonding interactions. In 10 mM sodium cacodylate buffer solutions (pH 7.0) containing 100 mM NaCl and 1.0 mM EDTA, Vitamin B₂ is found to selectively bind to T (K₁₁ = 1.8 × 10⁶ M⁻¹ at 5 °C) over other nucleobases, and this is accompanied by significant quenching of its fluorescence. While the sensing functions depend on the flanking sequences to the AP site, Vitamin B₂ is applicable to the detection of T/C (cytosine), T/G (guanine) and T/A (adenine) mutation sequences of the CYP2A6 gene, where the flanking nucleobases are guanines in both positions (-GXG-, X = AP site).     

On homeomorphisms and quasi-isometries of the real line

We show that the group of piecewise-linear homeomorphisms of having bounded slopes surjects onto the group of all quasi-isometries of . We prove that the following groups can be imbedded in : the group of compactly supported piecewise-linear homeomorphisms of , the Richard Thompson group , and the free group of continuous rank.