The Generalized Chazy Equation from the Self-Duality Equations

It is shown that classically known generalizations of the Chazy equation and Darboux–Halphen system are reductions of the self-dual Yang–Mills (SDYM) equations with an infinite-dimensional gauge algebra. The general ninth-order Darboux–Halphen system is reduced to a Schwarzian equation which governs conformal mappings of regions with piecewise circular sides. The generalized Chazy equation is shown to correspond to special mappings where either the triangles are equiangular or two of the angles are π/3.     

Separation of Clinical Grade 188Re from 188W Using Polymer Embedded Nanocrystalline Titania

Currently, ¹⁸⁸Re is obtained from ¹⁸⁸W/¹⁸⁸Re chromatographic generator containing alumina which has a limited capacity (~80 mg Wg⁻¹) for ¹⁸⁸W. This results in high bolus volumes of ¹⁸⁸Re, which often needs to be concentrated before radiolabeling. We have demonstrated the feasibility of using polymer embedded nano crystalline titania (TiP), a novel high capacity sorbent material (~300 mg Wg⁻¹), for developing a ¹⁸⁸W/¹⁸⁸Re chromatographic generator. A TiP based chromatographic ¹⁸⁸W/¹⁸⁸Re generator was developed in which ¹⁸⁸Re could be eluted with 0.9% saline solution. About 90% of the ¹⁸⁸Re could be recovered in the first 4–5 mL of total activity with more than 80% yield. The purity of ¹⁸⁸Re is adequate for clinical applications.

     

Numerical simulation of mass transfer to micropolar fluid flow past a stenosed artery

A mathematical model of unsteady non‐Newtonian blood flow together with the mass transfer through constricted arteries has been developed. The mass transport refers to the movement of atherogenic molecules, i.e. blood‐borne components, such as low‐density lipoproteins from flowing blood into the arterial walls or vice versa. The flowing blood is represented as the suspension of all erythrocytes assumed to be Eringen's micropolar fluid and the arterial wall is considered to be rigid having cosine‐shaped stenosis in its lumen. The mass transfer to blood is controlled by the convection–diffusion equation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell method and the results obtained are checked for numerical stability with the desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow‐field and the mass concentration along with their distributions over the entire arterial segment as well. The key factors, such as the wall shear stress and Sherwood number, are also examined for further quantitative insight into the flow and the mass transport phenomena through arterial stenosis. The present results show consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration. Copyright © 2010 John Wiley & Sons, Ltd.     

Iron(III) Catecholates for Cellular Imaging and Photocytotoxicity in Red Light

Iron(III) complexes [Fe( L )( L′ )(NO₃)]—in which L is phenyl‐N,N‐bis[(pyridin‐2‐yl)methyl]methanamine ( 1 ), (anthracen‐9‐yl)‐N,N‐bis[(pyridin‐2‐yl)methyl]methanamine ( 2 ), (pyreny‐1‐yl)‐N,N‐bis[(pyridin‐2‐yl)methyl]methanamine ( 3 – 5 ), and L′ is catecholate ( 1 – 3 ), 4‐tert‐butyl catecholate ( 4 ), and 4‐(2‐aminoethyl)‐benzene‐1,2‐diolate ( 5 )—were synthesized and their photocytotoxic properties examined. The five electron‐paramagnetic complexes displayed a Fe^III/Fe^II redox couple near ?0.4 V versus a saturated calomel electrode (SCE) in DMF/0.1 m tetrabutylammonium perchlorate (TBAP). They showed unprecedented photocytotoxicity in red light (600–720 nm) to give IC₅₀≈15 μM in various cell lines by means of apoptosis to generate reactive oxygen species. They were ingested in the nucleus of HeLa and HaCaT cells in 4 h, thereby interacting favorably with calf thymus (ct)‐DNA and photocleaving pUC19 DNA in red light of 785 nm to form hydroxyl radicals.     

The occurence of barium in the corneal surface of the barking deer, Muntiacus Muntjak (Zimmerman) as revealed by energy dispersive x-ray micro-analysis

Energy dispersive X-ray micro-analysis with simultaneous visual display by secondary electron emission mode of scanning electron microscopy reveals the occurrence of barium, in addition to silicon, phosphorus, sulphur, potassium and calcium in the corneal surface of the barking deer, Muntiacus muntjak. The lenticular surface on the other hand shows the presence of aluminium silicon, phosphorus and sulphur but no barium.Quantitative data obtained by using the ZAF-4/FLS programme (Link) shows that the relative percentage of barium is the highest of all the elements detected in the cornea, whereas in the lens-surface, sulphur constitutes the maximum percentage.     

Ultrasonic study of molecular interaction in binary liquid mixtures at 30°C

Densities ρ and ultrasonic speeds u of the binary mixtures of tetrahydrofuran (THF) with 1-butanol and tert-butanol, at 30°C, over the entire composition range were measured. From these data isentropic compressibility, K _s, intermolecular free length L _f, relative association R _A, acoustic impedance Z, molar sound speed R _m, deviations in isentropic compressibility ΔK _s, and excess volume V ^E were calculated. The variation of these parameters with composition of the mixture helps us in understanding the nature and extent of interaction between unlike molecules in the mixtures. Further, theoretical values of ultrasonic speed were evaluated using theories and empirical relations. The relative merits of these theories and relations were discussed.     

Rheology of semi-dilute solutions of calf-thymus DNA

We study the rheology of semi-dilute solutions of the sodium salt of calf-thymus DNA in the linear and nonlinear regimes. The frequency response data can be fitted very well to the hybrid model with two dominant relaxation times τ₀ and τ₁. The ratio (τ₀/τ₁) ∼5 is seen to be fairly constant on changing the temperature from 20 to 30°C. The shear rate dependence of viscosity can be fitted to the Carreau model.     

Double-strand DNA cleavage from photodecarboxylation of (micro-oxo)diiron(III) L-histidine complex in visible light

The oxo-bridged diiron(III) complex [{Fe(L-his)(dpq)}(2)(micro-O)](2+) having L-histidine (L-his) and dipyrido[3,2-d:2',3'-f]quinoxaline (dpq) bound to Fe(III) exemplifies an iron-based model photonuclease that shows visible light-induced DNA double-strand cleavage in a photodecarboxylation pathway and models iron-bleomycin activity.     

Multiwavelength ultralow-threshold lasing in quantum dot photonic crystal microcavities

We demonstrate multiwavelength lasing of resonant modes in linear (L3) microcavities in a triangular-lattice 2D photonic crystal (PC) slab. The broad spontaneous emission spectrum from coupled quantum dots, modified by the PC microcavity, is studied as a function of the intensity of incident optical excitation. We observe lasing with an ultralow-threshold power of approximately 600 nW and an output efficiency of approximately 3% at threshold. Two other resonant modes exhibit weaker turnon characteristics and thresholds of approximately 2.5 and 200 microW, respectively.     

Parameterizations of the Chazy Equation

The Chazy equation y?= 2yy″? 3y′² is derived from the automorphic properties of Schwarz triangle functions S(α, β, γ; z) . It is shown that solutions y which are analytic in the fundamental domain of these triangle functions, only correspond to certain values of α, β, γ . The solutions are then systematically constructed. These analytic solutions provide all known and one new parameterization of the Eisenstein series P, Q, R introduced by Ramanujan in his modular theories of signature 2, 3, 4, and 6.