Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction

In this paper, we establish several theorems for the explicit evaluations of Ramanujan-G?llnitz-Gordon continued fraction by using some parameterizations of Ramanujan’s theta-functions. Nayandeep Deka Baruah, Corresponding author. Research partially supported by grant SR/FTP/MA-02/2002 from DST, Govt. of India. Authors’ address: Nayandeep Deka Baruah and Nipen Saikia, Department of Mathematical Sciences, Tezpur University, Napaam-784028, Assam, India     

Enhanced magneto-optic activity of magnetite-based ferrofluids subjected to gamma irradiation

We report here the effect of γ-irradiation on the particle size and size distribution dependent spectroscopic and magneto-optic properties of ferrofluids, synthesized by a co-precipitation method. The X-ray diffraction (XRD) study exhibits magnetite (Fe₃O₄) phase of the particles while electron microscopic and dynamic light scattering (DLS) studies have predicted particle growth upon γ-irradiation. Further, Fourier transform infrared (FT-IR) spectroscopy studies ensured that no dissociation has occurred due to irradiation effect. As a consequence of magneto-optic behavior reflected in the Faraday rotation (FR) measurement, the Verdet constant increased from a value of 0.64×10⁻² for the pristine sample to 5.6×10⁻² deg/Gauss-cm for the sample irradiated with the highest dose (2.635 kGy). The substantial enhancement in the FR is assigned to the improvement in associated chaining effect owing to adequate particle growth where an increased stoichiometry variation of Fe²⁺/Fe³⁺ is assured.     

Manganese Doped Zinc Sulfide Quantum Dots for Detection of Escherichia coli

A novel biocompatible chitosan passivated manganese doped zinc sulfide (Mn doped ZnS) nanophosphor has been synthesized through a simple aqueous precipitation reaction. Upon excitation with ultraviolet light, the quantum dots (QDs) emit an orange luminescence peaking at 590 nm, which is visible to the naked eye. These chitosan coated Mn doped ZnS QDs can have potential applications in bio-labeling, particularly in fluorescence-based imaging. One of the envisioned applications of these QDs is in improving the conventional, organic dye-reliant Fluorescence in situ Hybridization (FISH) technique, a widely used method for microbial detection. Here we demonstrate that the chitosan-capped Mn doped ZnS QDs are suitable for this purpose.     

When is water not water? Exploring water confined in large reverse micelles using a highly charged inorganic molecular probe

The interior water pool of aerosol OT (AOT) reverse micelles tends toward bulk water properties as the micelle size increases. Thus, deviations from bulk water behavior in large reverse micelles are less expected than in small reverse micelles. Probing the interior water pool of AOT reverse micelles with a highly charged decavanadate (V(10)) oligomer using (51)V NMR spectroscopy shows distinct changes in solute environment. For example, when an acidic stock solution of protonated V(10) is placed in a reverse micelle, the (51)V chemical shifts show that the V(10) is deprotonated consistent with a decreased proton concentration in the intramicellar water pool. Results indicate that a proton gradient exists inside the reverse micelles, leaving the interior neutral while the interfacial region is acidic.     

An analysis of lasing without inversion in a three level system in terms of vector representation

In the present work, we show that the problem of Λ-type three level systems and lasing without inversion can be understood in terms of evolution of vectors. The time evolutions of these vectors have been worked out using the transition probabilities and detuning. One of the salient features of the work is that Glauber-Sudershan’s p-function can be visualized with this approach. We also present a comparative study between different vector models representing three level Λ-type lasers.     

Rational design, synthesis, and spectroscopic and photophysical properties of a visible-light-excitable, ratiometric, fluorescent near-neutral pH indicator based on BODIPY

A visible-light-excitable, ratiometric, brightly fluorescent pH indicator for measurements in the pH range 5-7 has been designed and synthesized by conjugatively linking the BODIPY fluorophore at the 3-position to the pH-sensitive ligand imidazole through an ethenyl bridge. The probe is available as cell membrane permeable methyl ester 8-(4-carbomethoxyphenyl)-4,4-difluoro-3-[2-(1H-imidazol-4-yl)ethenyl]-1,5,7-trimethyl-3a,4a-diaza-4-bora-s-indacene (I) and corresponding water-soluble sodium carboxylate, sodium 8-(4-carboxylatophenyl)-4,4-difluoro-3-[2-(1H-imidazol-4-yl)ethenyl]-1,5,7-trimethyl-3a,4a-diaza-4-bora-s-indacene (II). The fluorescence quantum yield Φ(f) of ester I is very high (0.8-1.0) in the organic solvents tested. The fluorescence lifetime (ca. 4 ns) of I in organic solvents with varying polarity/polarizability (from cyclohexane to acetonitrile) is independent of the solvent with a fluorescence rate constant k(f) of 2.4×10(8) s(-1). Probe I is readily loaded in the cytosol of live cells, where its high fluorescence intensity remains nearly constant over an extended time period. Water-soluble indicator II exhibits two acid-base equilibria in aqueous solution, characterized by pK(a) values of 6.0 and 12.6. The Φ(f) value of II in aqueous solution is high: 0.6 for the cationic and anionic forms of the imidazole ligand, and 0.8 for neutral imidazole. On protonation-deprotonation in the near-neutral pH range, UV/Vis absorption and fluorescence spectral shifts along with isosbestic and pseudo-isoemissive points are observed. This dual-excitation and dual-emission pH indicator emits intense green-yellow fluorescence at lower pH and intense orange fluorescence at higher pH. The influence of ionic strength and buffer concentration on the absorbance and steady-state fluorescence of II has also been investigated. The apparent pK(a) of the near-neutral acid-base equilibrium determined by spectrophotometric and fluorometric titration is nearly independent of the added buffer and salt concentration. In aqueous solution in the absence of buffer and in the pH range 5.20-7.45, dual exponential fluorescence decays are obtained with decay time τ(1)=4.3 ns for the cationic and τ(2)=3.3 ns for the neutral form of II. The excited-state proton exchange of II at near-neutral pH becomes reversible on addition of phosphate (H(2)PO(4)(-)/HPO(4)(2-)) buffer, and a pH-dependent change of the fluorescence decay times is induced. Global compartmental analysis of fluorescence decay traces collected as a function of pH and phosphate buffer concentration was used to recover values of the deactivation rate constants of the excited cationic (k(01)=2.4×10(8) s(-1)) and neutral (k(02)=3.0×10(8) s(-1)) forms of II.     

Crystal Structures of (2-oxo-2H-Quinaxalin-1-yl)-acetic Acid and its Cobalt and Nickel Complexes and Their Comparison with (1,3-Dioxo-1,3-dihydro-isoindol-2-yl)-acetic Acid

Abstract The crystal structures of (2-oxo-2H-quinaxalin-1-yl)-acetic acid and its cobalt and nickel complexes are determined. The (2-oxo-2H-quinaxalin-1-yl)-acetic acid (1) crystallizes in orthorhombic, Pbca, a = 12.8571(11) ?, b = 9.4267(8) ?, c = 15.0095(13) ?, the cobalt complex of (2-oxo-2H-quinaxalin-1-yl)-acetic acid (2) crystallizes as dihydrate in triclinic, P-1 space group with a = 4.81150(10) ?, b = 11.8631(2) ?, c = 12.4867(3) ?, α = 71.7800(10)°, β = 79.2490(10)°, γ = 84.9020(10)° whereas the nickel complex of (2-oxo-2H-quinaxalin-1-yl)-acetic acid (3) crystallizes in monoclinic, P2₁/c space group with a = 14.9210(5) ?, b = 4.81730(10) ?, c = 15.7672(5) ?. and β = 99.823(2)°. The crystal structure of the ligand and the complexes are compared with structures of (1,3-dioxo-1,3-dihydro-isoindol-2-yl)-acetic acid and its cobalt and nickel complexes. Index Abstract The crystal structures of (2-oxo-2H-quinaxalin-1-yl)-acetic acid and its nickel and cobalt complexes are compared with (1,3-dioxo-1,3-dihydro-isoindol-2-yl)-acetic acid and its corresponding complexes with nickel(II) and cobalt(II).      

Interaction of Polystyryl Radical with Tris Azido-Iron(III) Complex

The polymerization of styrene initiated by 2,2′-azobisisobutyro-nitrile (AIBN) had been studied in N, N-dimethylformamide (DMF) at 60°C in presence of tris azido-iron(III) complex. The complex was prepared in situ by mixing solid sodium azide with hexakis(N, N-dimethylformamide)iron(m) perchlorate, [Fe(DMF)₆] (ClO₄)₃, in the ratio 3:1. The nature of the complex formed was established by Job's method. The equilibrium constant for Fe³⁺ + 3N₃ ^? ? Fe(N₃)₃ determined by the limiting logarithmic method is 6.14 ± 10⁶ liter³/mole³. The velocity constant for the polystyryl radical towards the complex is 3.13 ± 10⁴ liter/mole-sec.     

Metallacycles of cadmium, mercury dicarboxylates

A series of linear coordination polymers, metallacycles of cadmium(II) and mercury(II) of flexible carboxylic acid ligands, RCH{3-CH(3)-,5-CH(3)-,6-(-OCH(2)CO(2)H)C(6)H(2)}(2), (when R = C(6)H(5), (H(2)L(1)); 2-NO(2)C(6)H(4)- (H(2)L(2)) and 3-NO(2)C(6)H(4)- (H(2)L(3))) are synthesized and characterized. [CdL(1) (py)(3)](n)·3nH(2)O (py = pyridine) is a linear coordination polymer, whereas [CdL(2)(py)(CH(3)OH)](2)·CH(3)OH is a dinuclear complex of cadmium with a Cd(2)O(2) type of core. The latter is obtained from reaction of cadmium(II) acetate with H(2)L(2) in methanol followed by reaction with pyridine. A similar reaction of cadmium(II) acetate with H(2)L(2) in dimethylformamide results in the formation of a cadmium metallacycle, namely [CdL(2) (py)(2)(H(2)O)](2)·H(2)O. The H(2)L(3) reacted with cadmium(II) acetate in the presence of pyridine to form a metallacycle [CdL(3)(py)(2)(H(2)O)](2)·3H(2)O. The ligand H(2)L(2) form mercury(II) metallacycle [HgL(2)(4-mepy)(2)](2) in the presence of 4-methylpyridine (4-mepy) and the ligand H(2)L(3) forms metallacycle [HgL(3)(3-mepy)(2)](2)·DMF in the presence of 3-methylpyridine (3-mepy). The potassium salts of H(2)L(1) and H(2)L(2) were found to be coordination polymers and these potassium coordination polymers were structurally characterized.