Differential geometry of atomic structure and the binding energy of atoms

The geometric theory of partial differential equations due to E. Cartan is applied to atomic systems in order to solve the many-body problems and to obtain the binding energies of electrons in an atom. The procedure consists in defining a Schrödinger equation over an Euclidean patch which overlaps with other Euclidean patches in a specified way to form a manifold. If the energy of the system has to be a minimum, it is shown using the Dirichlet principle that the coordinate systems are related by the Cauchy-Riemann relations. The invariance of the Schrödinger equations in the overlapping region leads to a nonlinear second-order equation which is invariant to automorphic transformations and whose solutions are doubly periodic functions. There are only two possible single-valued solutions to this nonlinear partial differential equation and these correspond to lattices of points in the complex space, which are (a) corners of an array of equilateral triangles, and (b) corners of an array of isosceles right-angled triangles. The first solution was used in an earlier work to derive many static properties of nuclei. In this paper it is shown that the second solution gives binding energies of atoms in agreement of about 3% for the few experimental points that are available and also in good agreement with the binding energies of atoms obtained by the perturbation theory. It is also shown that this lattice under certain approximations is equivalent to a pure Coulomb law and the Bohr orbits of the hydrogen atom are correctly predicted. In obtaining the binding energies of atoms, no free parameters are required in the theory, except for the value of the binding energy of the He atom, as the theory is developed only for spinless systems. All other constants turn out to be fundamental constants.     

Soliton stability in a square lattice model of an inhomogeneous helimagnet

In this paper, we propose a square lattice model to study the nonlinear spin excitationsof an inhomogeneous helimagnet with bilinear, twist and anisotropic interactions in thesemi classical limit. The dynamics is found to be governed by a nonlinear partialdifferential equation (pde) in (2 +1) dimensions. The nonlinear excitations and the influence of differenttypes of interactions are investigated using a perturbation technique. The effect ofinhomogeneities in the system is demonstrated graphically in terms of solitonstability.     

Aluminum phosphate [AlPO4(H)]: A mild and efficient recyclable catalyst for one‐pot synthesis of polyhydroquinoline via the Hantzsch reaction under solvent‐free conditions

Polyhydroquinolines have been synthesized in good to excellent yields (80–90%) and short reaction times (15–30 min) in the presence of aluminum phosphate [AlPO₄] as heterogeneous catalyst at 90°C; the reaction workup is simple and the catalyst aluminum phosphate [AlPO₄] can be easily separated from the product and reused. J. Heterocyclic Chem., (2012).     

Preconcentration of Cu(II) and Ni(II) ions in edible fish organs by solid phase extraction using triton X-100 resin

An enrichment separation procedure for the atomic absorption spectrophotometric determinations of Cu(II) and Ni(II) ions in common edible fishes was established. The 2-[(2-hydroxynaphthalen-1-yl)diazenyl]-5-methylbenzene-1,3-diol (HNDMD) complexes of the analyte ions at pH 6.0 were adsorbed on the p-octylpolyethylene glycolphenylether (Triton X-100) column and then desorbed with 10 mL of acetone. Under optimized conditions, the recovery values were above 95%. The developed preconcentration methods were successfully applied to the determination of Cu(II) and Ni(II) ion concentrations in common edible fishes from the local market. The precision and accuracy of the method are very good.     

Ruthenium(III) Catalyzed Oxidative Degradation of Amitriptyline-A Tricyclic Antidepressant Drug by Permanganate in Aqueous Acidic Medium

The oxidation of amitriptyline by potassium permanganate has been investigated spectrophotometrically in the presence of ruthenium(III) as catalyst in aqueous acidic medium at a constant ionic strength of 0.20 mol⋅dm⁻³. The stoichiometry was found to be 1:1 in terms of the mole ratio of amitriptyline and permanganate ions consumed. The order of the reaction with respect to manganese(VII) and ruthenium(III) concentration was unity while the order with respect to amitriptyline was less than unity over the concentration range studied. The rate increased with an increase in acid concentration. The reaction rates revealed that the Ru(III) catalyzed reaction was about eight-fold faster than the uncatalyzed reaction. The oxidation products were identified by spectral analysis. A tentative mechanism consistent with the kinetics has been proposed. The reaction constants involved in the different steps of the reaction mechanism were calculated. Kinetic experiments suggest that HMnO₄ is the reactive permanganate species and [Ru(H₂O)₆]³⁺ is the reactive Ru(III) species.     

Ab-initio prediction and reliability of protein structural genomics by PROPAINOR algorithm

We have formulated the ab-initio prediction of the 3D-structure of proteins as a probabilistic programming problem where the inter-residue 3D-distances are treated as random variables. Lower and upper bounds for these random variables and the corresponding probabilities are estimated by nonparametric statistical methods and knowledge-based heuristics. In this paper we focus on the probabilistic computation of the 3D-structure using these distance interval estimates. Validation of the predicted structures shows our method to be more accurate than other computational methods reported so far. Our method is also found to be computationally more efficient than other existing ab-initio structure prediction methods. Moreover, we provide a reliability index for the predicted structures too. Because of its computational simplicity and its applicability to any random sequence, our algorithm called PROPAINOR (PROtein structure Prediction by AI an Nonparametric Regression) has significant scope in computational protein structural genomics.     

Electrical, structural and surface morphological properties of thermally stable low-resistance W/Ti/Au multilayer ohmic contacts to n-type GaN

A W/Ti/Au multilayer scheme has been fabricated for achieving thermally stable low-resistance ohmic contact to n-type GaN (4.0 × 10¹⁸ cm⁻³). It is shown that the as-deposited W/Ti/Au contact exhibits near linear I-V behaviour. However, annealing at temperature below 800 °C the contacts exhibit non-linear behaviour. After annealing at a temperature in excess of 850 °C, the W/Ti/Au contact showed ohmic behaviour. The W/Ti/Au contact produced specific contact resistance as low as 6.7 × 10⁻⁶ Ω cm² after annealing at 900 °C for 1 min in a N₂ ambient. It is noted that the specific contact resistance decreases with increase in annealing temperature. It is also noted that annealing the contacts at 900 °C for 30 min causes insignificant degradation of the electrical and thermal properties. It is further shown that the overall surface morphology of the W/Ti/Au stayed fairly smooth even after annealing at 900 °C. The W/Ti/Au ohmic contact showed good edge sharpness after annealing at 900 °C for 30 min. Based on the Auger electron spectroscopy and glancing angle X-ray diffraction results, possible explanation for the annealing dependence of the specific contact resistance of the W/Ti/Au contacts are described and discussed.     

Synthesis,spectral characterization,molecular docking studies,biological activity of (E)-2-((E)-3-(3,4,5-trimethoxyphenyl)allylidene) and (E)-N-phenyl 2-((E)-3-(3,4,5-trimethoxyphenyl)allylidene)hydrazinecarbothioamides and their Cu(II) complexes

Two slightly distorted octahedral complexes of copper(II) with (E)-2-((E)-3-(3,4,5-trimethoxyphenyl)allylidene)hydrazinecarbothioamide (L1) common name 3,4,5-trimethoxy-cinnamaldehydethiosemicarbazone and (E)-N-phenyl-2-((E)-3-(3,4,5-trimethoxyphenyl)-allylidene)hydrazinecarbothioamide (L2) common name 3,4,5-trimethoxycinnamaldehyde-4-phenylthiosemicarbazone have been synthesized. The two free ligands and their copper(II) complexes were characterized by spectroscopic techniques like FT-IR, FT-Raman, UV, EPR, Powder X-ray diffraction and cyclic voltammetry. The EPR spectra evidenced a rhombically distorted octahedron geometry for both the copper(II) complexes. The band gap calculations for the ligands L1, L2 and their complexes Cu(L1)₂Cl₂ and Cu(L2)₂Cl₂ were found to be 2.98, 2.61, 2.66 and 2.50 eV respectively. Cu(L1)₂Cl₂ and Cu(L2)₂Cl₂ have shown 50% of viability at 80 μg/ml and 60 μg/ml. The anti-oxidant activity study revealed that the compounds are good reductants of DPPH radical. Moderate to good anti-bacterial activity is shown by the compounds against the Gram-positive and Gram-negative bacteria. Molecular docking studies have been carried out to predict the orientation and binding mode of analysis in the active site. The synthesized ligand and complex well occupy (catalytic triad and adenine-binding site) in the active site of β-ketoacyl-acyl carrier protein synthase III enzyme, and also well occupy in helix 11 (in the DCS complex) of human estrogen receptor. Moreover they form water mediated hydrogen bond and hydrogen bond with Cys530 residue.