A note on equivariant Euler characteristic

We give a new equivariant cohomological characterization of the equivariant Euler characteristic of aG-simplicial set as defined by Brown. This implies in particular that the equivariant Euler characteristic is aG-homotopy invariant.     

Spectral behaviour of eosin Y in different solvents and aqueous surfactant media

Photophysical behaviour of the anionic xanthene dye, eosin Y (EY) was investigated in solvents of different polarities as well as in the presence of aqueous cationic surfactants. From the correlation between E(T)(30) and Kosower Z values of EY in different solvents, subsequent parameters for EY were determined in the presence of surfactants. A red shift, both in the absorption and emission spectra of EY, was observed with decreasing solvent polarity. Dimerisation of EY was found to be dependent on solvent polarity. Cationic surfactants retarded the process of dimerisation, which were evident from the lower dimerisation constant (K(D)) values, compared to that of in pure water. Dye-surfactant interaction constants were determined at different temperatures (298-318 K) and subsequently the thermodynamic parameters, viz., ΔG°, ΔH° and ΔS° were evaluated using the interaction constant values. The fluorescence spectra of EY followed the same trend as in the absorption spectra, although with lesser extents. Stokes shifts were calculated and correlated with the polarity of the medium. Fluorescence of EY was initially quenched by the cationic surfactants in their pre-micellar region, which then followed a red shift with intensity enhancement. Fluorescence quenching was found to be of Stern-Volmer type where the excited state lifetime of EY remained unchanged in different surfactant media. However, the anisotropy value of EY was changed in the post micellar region of surfactants.     

A nonpeptidic reverse-turn scaffold stabilized by urea-based dual intramolecular hydrogen bonding

A novel nonpeptidic reverse-turn scaffold containing urea fragments that are connected by a conformationally constrained D-prolyl-cis-1,2-diaminocyclohexane (D-Pro-DACH) linker is reported. The scaffold adopts a well-defined reverse-turn conformation that is stabilized by dual intramolecular hydrogen bonding in both solution and solid states.     

An Alternate Approach to Optimal L 2-Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for deriving optimal error estimates for finite element approximations to parabolic problems with smooth initial data and hence, it unifies both theories, that is, one for smooth initial data and other for nonsmooth data. Moreover, the proposed technique is also extended to a semidiscrete mixed method for linear parabolic problems. In both cases, optimal L ²-error estimates are derived, when the initial data is in L ². A superconvergence phenomenon is also observed, which is then used to prove L ^∞-estimates for linear parabolic problems defined on two-dimensional spatial domain again with rough initial data.     

Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow

Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L^∞( L ²) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L^∞( L ²) as well as in L^∞( H )‐norms and the pressure in L^∞(L²)‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Dynamics of solid-melt front migration from a reaction–diffusion model

Using physical experiments we investigated the evolution of thermally driven melt patterns in a semi-infinite solid crystalline phase subjected to uniform heating from one side, maintaining melting temperature. We treat the melt initiation phenomenon theoretically in the perspective of two-phase interactions on the microscopic level, and propose a new reaction–diffusion model based on the prey–predator dynamics. This model predicts the fractal behavior of melt fronts observed in the experiments.     

Conformational aspects of caryophyllene. Population of stable conformers and ring inversion barrier of trans cyclononene ring portion

Cmr measurements of caryophyllene revealed two major conformers equilibrating in a ratio 76:24 at room temperature. The energy ordering of four possible conformers of caryophyllene predicted by molecular mechanics calculations agrees well with the experimental observation. The barrier of interconversion between the two conformers was determined as 16.25 kcal/mol.     

Interaction of ZnS nanoparticles with flavins and glucose oxidase: A fluorimetric investigation

Interactions of luminescence, water soluble ZnS nanoparticles (NPs) with flavins and glucose oxidase have been thoroughly investigated through optical spectroscopy. The photoluminescence of ZnS nanoparticles was quenched severely (～60%) by riboflavin while other flavins such as flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD) show quenching to different extents under analogous conditions. However, interestingly no effect in luminescence intensity of ZnS NPs was observed with protein bound flavins such as in glucose oxidase. Fluorescence lifetime measurement confirmed the quenching to be static in nature. Scavenging of photo-generated electron of ZnS nanoparticles by the flavin molecules may be attributed to the decrease in luminescence intensity. Quenching of ZnS nanoparticles with flavins follows the linear Stern–Volmer plot. The Stern–Volmer constants decreased in the following order: K_S?V (Riboflavin)> K_S?V (FAD)> K_S?V (FMN). This interaction study could generate useful protocol for the fluorimetric determination of riboflavin (vitamin B₂) content and also riboflavin status in biological systems.