Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions

We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius r, as . For the planar Gaussian analytic function, , we show that this probability is asymptotic to . For the hyperbolic Gaussian analytic functions, , we show that this probability decays like .In the planar case, we also consider the problem posed by Mikhail Sodin² on moderate and very large deviations in a disk of radius r, as . We partially solve the problem by showing that there is a qualitative change in the asymptotics of the probability as we move from the large deviation regime to the moderate.Research supported by NSF grant #DMS-0104073 and NSF-FRG grant #DMS-0244479.     

Synthesis of Novel 4‐Substituted Coumarins,Docking Studies,and DHODH Inhibitory Activity

Coumarins are the important class of naturally occurring heterocyclic compounds. Activities like antioxidant, antibacterial, anti‐inflammatory, and anticancer have been reported for coumarin derivatives. Present work details the synthesis of substituted coumarin‐4‐pyrrolones as well as coumarin‐4‐acetyl amino acids and their DHODH inhibitory activity, which is a dual target for malaria and cancer. Coumarin‐4‐acetic acids ( 2a – c ) were coupled with different methyl esters of α‐amino acids ( 3 ) giving rise to corresponding coumarin‐4‐acetyl amino acid methyl esters ( 4a – o ), which on hydrolysis under basic condition underwent cyclization forming substituted dihydropyrrole‐2‐ones ( 5a – i ), dihydroindolizine‐3‐ones ( 5j – l ), and dihydropyrrolizin‐3‐one ( 5m – o ). Acidic hydrolysis of the compounds ( 4a – o ) yielded corresponding coumarin‐4‐acetyl amino acids ( 6a – f ). The docking study was performed with the protein 4IGH (obtained from PDB) using Surflex–Dock module. The newly synthesized compounds were tested for DHODH inhibitory activity using Brequinar as the standard. Compound 6b showed remarkable inhibition compared with the standard, and the other compounds with terminal COOH showed moderate inhibition.     

Mesoporous Foam TiO2 Nanomaterials for Effective Hydrogen Production

Hydrolysis of TiCl₄ in a diether‐functionalized imidazolium ionic liquid (IL), namely 1‐methyl‐3‐[2‐(2‐methoxy(ethoxy)ethyl]imidazolium methane sulfonate (M(MEE)I ? CH₃SO₃), results in a heterostructured organic/inorganic and sponge‐like porous TiO₂ material. The thermal treatment (300 °C) followed by calcination (500 °C) affords highly porous TiO₂. The characterization of the obtained samples (with and without IL, before and after calcination) by XRD, SEM, and TEM reveals TiO₂ anatase crystalline phases and irregular‐shaped particles with different porous structures. These hierarchical‐structured mesoporous TiO₂ nanomaterials were employed as efficient photocatalysts in the water‐splitting process, yielding up to 1304 μmol g^?1 on hydrogen production.     

Self-image (autoidolon) techniques for the realisation of optical computing type operations

Self-images of a number of spatially periodic (e.g., gratings) and quasiperiodic (e.g., halftone picture) objects have been systematically studied. These studies indicate that self-imaging techniques could be useful in optical computing type operations. It is also established that the Rayleigh relation in the context of self-imaging is quantitatively in error.     

Thin film processing of axially modified phthalocyanine derivatives

A new class of hydroxyl terminated silicon phthalocyanine (SiPc) derivatives was prepared by capping dihydroxy SiPc with a variety of compounds containing two or more hydroxyl groups. The unique feature of these polyhydroxy SiPc derivatives is their function as crosslinkers that allows their processability into polyurethane films on reacting with isophorone diisocyanate. The films possess high impact resistance, thermostability at 125°C for over 10 h, and low absorption in the visible region. Solid polymeric films incorporating over 20% (w/w) of Pc rings were prepared without phase segregation. The kinetic parameters of polymerization, such as reaction conversion versus time and temperature, heat of reaction (ΔH), activation energy (ΔE), and reaction order (n) were investigated. Some of the polyhydroxy SiPc derivatives exhibit very high solubility in common organic solvents and possess adequate optical transparency for use as nonlinear optical materials in vision protection against laser light. © 1996 John Wiley & Sons, Inc.     

Variation of long periodicity in blends of styrene butadiene,styrene copolymer/polyaniline using small angle X-ray scattering data

Small angle X-ray scattering data have been recorded for the blends of styrene butadiene, styrene copolymer/polyaniline using the beamline of the LNLS (Laboratorio Nacional de Luz sincroton-Campinas, Brazil). Employing one-dimensional Hosemann’s paracrystalline model, we have simulated the meridional reflections of these blends in order to compute the long periodicity and hence to find the variation with concentrations of the blends. Within the region of available experimental data we observe that there is a linear relationship between long periodicity and concentration of blends. These parameters are compared with physical measurements like tensile strength to find the structure-property relation in these blends.      

Total Synthesis of Myceliothermophins C,D, and E

The total synthesis of cytotoxic polyketides myceliothermophins E ( 1 ), C ( 2 ), and D ( 3 ) through a cascade‐based cyclization to form the trans‐fused decalin system is described. The convergent synthesis delivered all three natural products through late‐stage divergence and facilitated unambiguous C21 structural assignments for 2 and 3 through X‐ray crystallographic analysis, which revealed an interesting dimeric structure between its enantiomeric forms.