Existence and Weyl’s law for spherical cusp forms

Let G be a split adjoint semisimple group over and a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of . This proves a conjecture of Sarnak for -split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula. Received: April 2005 Revision: June 2006 Accepted: October 2006     

Spectrofluorometric studies on the binding interaction of bioactive imidazole with bovine serum albumin: a DFT based ESIPT process

Bioactive imidazole derivatives were synthesized and characterized by NMR spectra, mass and CHN analysis. An excited state intramolecular proton transfer (ESIPT) process in hydroxy imidazole has been studied using emission spectroscopy. In hydrocarbon solvent, the tautomer emission predominates over the normal emission and in alcoholic solvent like ethanol; a dramatic enhancement of normal emission is observed which was due to increased solvation. DFT calculation on energy, charge distribution of the rotamers in the ground and excited states of the imidazole derivative were performed and discussed. PES calculation indicates that the energy barrier for the interconversion of two rotamers is too high in the excited state than in the ground state. The interaction between bioactive imidazole derivative and bovine serum albumin (BSA) was investigated.     

Solvatochromic analysis of some N-nitroso oxime derivatives--Taft and Catalan approach

Some novel N-nitroso oxime derivatives were synthesized and characterized by (1)H, (13)C, (1)H-(1)H and (1)H-(13)C COSY NMR spectra. The spectra of all these N-nitroso oximes reveal the presence of two isomers labelled as E (-NOH group is anti to N-N=O moiety) and Z (-NOH group is syn to N-N=O moiety) in solution and the coupling constants ruled out the possibility of normal chair conformation. From the theoretical studies and coupling constant values it was found that both E (major) and Z (minor) isomers of N-nitroso oximes exist as an equilibrium mixture of CA and boat conformation (B(1)) and this was also supported by DFT calculation. The photophysical properties of these oxime derivatives were studied and the observed lower fluorescence quantum yield may be due to an increase in the non-radiative deactivation rate constant. This is attributed due to the presence of non-chair conformation of N-nitroso oxime derivatives.     

Luminescent study on the binding interaction of bioactive imidazole with bovine serum albumin-A static quenching mechanism

Novel bioactive imidazole derivatives were synthesized and characterized by NMR spectra, mass and CHN analysis. The interaction between the imidazole derivative and bovine serum albumin (BSA) was investigated by fluorescence and UV-vis absorption spectroscopy. The fluorescence quenching of BSA by the imidazole derivatives may be due to the formation of imidazole-BSA complex. The fluorescence quenching mechanism of BSA by imidazole was analyzed and the binding constant has been calculated. The binding distance between imidazole and BSA was obtained based on Forester's non-radiation energy transfer (FRET). The effect of some common ions on the binding constant between imidazole and BSA was also examined.     

Scattering studies of hydrophobic monomers in liposomal bilayers: an expanding shell model of monomer distribution

Hydrophobic monomers partially phase separate from saturated lipids when loaded into lipid bilayers in amounts exceeding a 1:1 monomer/lipid molar ratio. This conclusion is based on the agreement between two independent methods of examining the structure of monomer-loaded bilayers. Complete phase separation of monomers from lipids would result in an increase in bilayer thickness and a slight increase in the diameter of liposomes. A homogeneous distribution of monomers within the bilayer would not change the bilayer thickness and would lead to an increase in the liposome diameter. The increase in bilayer thickness, measured by the combination of small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS), was approximately half of what was predicted for complete phase separation. The increase in liposome diameter, measured by dynamic light scattering (DLS), was intermediate between values predicted for a homogeneous distribution and complete phase separation. Combined SANS, SAXS, and DLS data suggest that at a 1.2 monomer/lipid ratio approximately half of the monomers are located in an interstitial layer sandwiched between lipid sheets. These results expand our understanding of using self-assembled bilayers as scaffolds for the directed covalent assembly of organic nanomaterials. In particular, the partial phase separation of monomers from lipids corroborates the successful creation of nanothin polymer materials with uniform imprinted nanopores. Pore-forming templates do not need to span the lipid bilayer to create a pore in the bilayer-templated films.     

Breather-like director reorientations in a nematic liquid crystal with nonlocal nonlinearity

The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformations and adopt space curve mapping procedure to analyze the dynamics. The NLC is governed by an integro-differential perturbed nonlocal nonlinear Schrödinger equation and we solve the same using Jacobi elliptic function method aided with symbolic computation and construct an exact solitary wave solution. In order to better understand the effect of nonlocality on the director reorientations of nematic liquid crystal, we have constructed the component forms of director axis using Darboux vector transformation. This intriguing property as a result of the relation between the coherence of the breather-like solitary deformation and the nonlocality reveals a strong need for a deeper understanding in the theory of self-localization in NLC systems.     

Photophysical Properties of Novel Picrate Derivatives – Solvent Effect

H and ¹³C NMR spectra were recorded for some novel picrate derivatives derived from 3,3-dimethyl-2,6-diarylpiperidin-4-ones and 3-benzyl-2,6-diarylpiperidin-4-one. The photophysical properties of the picrate derivatives were studied in several solvents, which include a wide range of apolar, polar and protic media. The observed lower fluorescence quantum yield may be due to an increase in the non-radiative deactivation rate constant. This is attributed due to the presence of increased electrostatic interaction between N-protonated piperidone ring and picryl anion ring so that the picryl anion ring lies perpendicular to the plane of the N-protonated piperidone ring i.e., non co-planarity. Such a geometrical change in the excited state leads to an important Stokes shift, reducing the reabsorption and reemission effects in the detected emission in highly concentrated solutions. The higher fluorescence quantum yield of the picrate derivatives are observed in polar media.     

Large-eddy Simulation of Motored Flow in a Two-valve Piston Engine: POD Analysis and Cycle-to-cycle Variations

Large-eddy simulation (LES) has been performed for a single-cylinder, two-valve, four-stroke-cycle piston engine through 70 consecutive motored cycles. Initial comparisons of ensemble-averaged velocity fields have been made between LES and experiment, and proper orthogonal decomposition (POD) has been used to analyze the complex in-cylinder turbulent flows. Convergence of POD modes has been quantified, several POD variants have been explored, and sensitivity of results to analyzing different subsets of engine cycles has been studied. In general, it has been found that conclusions that were drawn earlier from POD analysis of a simplified non-compressing piston-cylinder assembly with a fixed valve carry over to the much more complex flow in this motored four-stroke-cycle engine. For the cases that have been examined, the first POD mode essentially corresponds to the ensemble-averaged mean velocity. The number of engine cycles required to extract converged POD modes increases with mode number, and varies with phase (piston position). There is little change in the lower-order phase-invariant POD modes when as few as 24 phases per cycle (30° between samples) are used, and complex 3-D time-dependent in-cylinder velocity fields through full engine cycles can be reconstructed using a relatively small number of POD modes. Quantification of cycle-to-cycle variations and insight into in-cylinder flow dynamics can be extracted through analysis of phase-invariant POD modes and coefficients.     

Displacement-Based Experimental Stress Analysis of a Circularly-Perforated Asymmetrical Isotropic Structure

This paper demonstrates the ability to determine the individual full-field components of stress, strain and displacement in finite asymmetrical engineering structures from recorded values of a single displacement component while not necessitating differentiation of the measured displacement data; a process which can be ill-conditioned and adversely influenced by data noise and quality. While the present approach of processing recorded displacements with a stress function is not new, previous cases have been restricted to symmetrical scenarios. Full-field displacements are measured here using the digital image correlation (DIC) method. As well as satisfying load equilibrium, the experimental results agree with those predicted using the finite element method (FEM).