Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.     

Ferrocenyl-nitrogen donor ligands. Synthesis and characterization of rhodium(I) complexes of ferrocenylpyridine and related ligands

The preparation of a series of complexes of the types [RhCl(CO)₂(L)], [RhCl(cod)(L)] and [Rh(cod)(L)₂]ClO₄, where L is a ligand incorporating a ferrocenyl group and a pyridine ring is described. Complexes were characterized using NMR, IR and electronic spectroscopy. The electrochemical behaviour of the complexes was examined using cyclic voltammetry. The X-ray structures of three of the complexes, [RhCl(CO)₂{NC₅H₄CNC₆H₄(η⁵-C₅H₄)Fe(η⁵-C₅H₅)}], [RhCl(cod)(3-Fcpy)] and [RhCl(cod){3-Fc(C₆H₄)py}], were determined.     

UV Excited‐State Photoresponse of Biochromophore Negative Ions

Members of the green fluorescent protein (GFP) family may undergo irreversible phototransformation upon irradiation with UV light. This provides clear evidence for the importance of the higher‐energy photophysics of the chromophore, which remains essentially unexplored. By using time‐resolved action and photoelectron spectroscopy together with high‐level electronic structure theory, we directly probe and identify higher electronically excited singlet states of the isolated para‐ and meta‐chromophore anions of GFP. These molecular resonances are found to serve as a doorway for very efficient electron detachment in the gas phase. Inside the protein, this band is found to be resonant with the quasicontinuum of a solvated electron, thus enhancing electron transfer from the GFP to the solvent. This suggests a photophysical pathway for photoconversion of the protein, where GFP resonant photooxidation in solution triggers radical redox reactions inside these proteins.     

Investigating structural aspects to understand the putative/claimed non‐toxicity of the Hg‐based Ayurvedic drug Rasasindura using XAFS

XANES‐ and EXAFS‐based analysis of the Ayurvedic Hg‐based nano‐drug Rasasindura has been performed to seek evidence of its non‐toxicity. Rasasindura is determined to be composed of single‐phase α‐HgS nanoparticles (size ～24 nm), free of Hg⁰ or organic molecules; its structure is determined to be robust (<3% defects). The non‐existence of Hg⁰ implies the absence of Hg‐based toxicity and establishes that chemical form, rather than content of heavy metals, is the correct parameter for evaluating the toxicity in these drugs. The stable α‐HgS form (strong Hg—S covalent bond and robust particle character) ensures the integrity of the drug during delivery and prevention of its reduction to Hg⁰ within the human body. Further, these comparative studies establish that structural parameters (size dispersion, coordination configuration) are better controlled in Rasasindura. This places the Ayurvedic synthesis method on par with contemporary techniques of nanoparticle synthesis.     

Bandwidth enhancement of transformation optics-based cloak with reduced parameters

In this paper, dispersive cloak design with broad bandwidth and minimal scattering cross section is proposed by appropriately selecting a radial permeability for each shell in a discretized reduced cloak. The dispersive medium is constructed by artificially varying the inner radius of the cloak with frequency, and this variation results into unique material properties at every frequency. The variation of inner radius of the cloak with frequency is artificial since the actual physical dimension of inner radius remains invariant. The relation between bandwidth and geometrical parameters of cloak is obtained by ensuring that transformation media must satisfy the condition that group velocity must remain less than the speed of light along every direction for a finite frequency range. The proposed cloak provides \(8.9\,\%\) bandwidth with respect to the center frequency for \(50\,\%\) reduction in total scattering cross section, and at the design frequency, the minimum scattering cross section obtained is \(0.266\). The proposed dispersive cloak design is verified by numerical full-wave simulations results which also confirm good cloaking performance.     

Design and synthesis of coordination networks containing amide,pyridine and carboxylate functionalities

The reactions of bis(pyridinecarboxamido)alkane with copper(II) in the presence of mono or dicarboxylic acids resulted in discrete species, one-dimensional and two-dimensional networks. The carboxylates considered for this study include m-nitrobenzoic acid, isophthalic acid and succinic acid. In the presence of m-nitrobenzoic acid the ligands with Cu(II) form 1D coordination networks which include m-nitrobenzoic acid and water molecules as guests. The use of isophthalic acid resulted in discrete species while the use of succinic acid resulted in a two-dimensional layer containing rectangular grids of dimension 9.7 × 16.5 Å². The 2D layers in this complex exhibit inclined 2-fold interpenetration. Further, all these coordination networks are assembled via hydrogen bonding interactions between the amides and water molecules. The Cu(II) centre exhibits a unique octahedral coordination geometry, for the complexes reported here, as it coordinates with two each of pyridine moieties, water molecules and carboxylates.     

Crosslinked styrene‐maleic acid copolymer complexes of some transition metals and their adsorption behavior

Transition metal complexes of linear and crosslinked styrene‐maleic acid copolymer were prepared in ethyl alcohol. The complexes appear as micro clusters fairly uniformly distributed in the copolymer matrix. Vapor adsorption–desorption studies of the complex beads with methyl isobutyl ketone (MIBK), toluene and ethyl alcohol show initial fast release followed by a steady and slow release. Hydrogen adsorption at room temperature was studied for a few complexes up to about 650 torr, which showed initial slow adsorption followed by a rapid increase at about 550 torr. Copyright © 2005 John Wiley & Sons, Ltd.     

RP-HPLC method for simultaneous determination of butenafine hydrochloride and betamethasone dipropionate in a cream formulation

An RP-HPLC method has been developed for the simultaneous determination of butenafine hydrochloride and betamethasone dipropionate on an Inertsil C18 column (250 x 4.6 mm id) using a mobile phase gradient consisting of methanol and water at a flow rate of 1 mL/min. Detection was carried out at 254 nm. Retention times of betamethasone dipropionate and butenafine hydrochloride were 4.82 (+/- 0.80) and 16.18 (+/- 0.17) min, respectively. The method was validated with respect to specificity, linearity, accuracy, precision, ruggedness, and robustness. This method is simple, precise, and sensitive, and applicable for the simultaneous quantification of butenafine hydrochloride and betamethasone dipropionate in a cream formulation.     

Silicotungstic acid catalysed Claisen Schmidt condensation reaction: an efficient protocol for synthesis of 1,3-diaryl-2-propenones

An efficient and clean synthesis of 1,3-diaryl-2-propenones has been carried out by Claisen Schmidt condensation reaction of aryl methyl ketones with a series of aromatic aldehydes at room temperature in the presence of the catalyst silicotungstic acid (STA). This method provides an ecofriendly, chemoselective, efficient and green synthesis of 1,3-diaryl-2-propenones in excellent yields.