A method of solution of the ornstein-zernike equation in one and three dimensions

An elegant analytic method is presented to derive a modified form of the Ornstein-Zernike equation which not only solves the statistical mechanical problem for hard rods and spheres but can be used to find solutions for arbitrary non-vanishing direct correlation functions.     

Integral sum rules and inequalities for ππ partial wave amplitudes

Exact integral relations on all ππ partial waves are derived from crossing symmetry. As a corollary we also derive an infinite number of inequalities fors-wave amplitudes.     

Simultaneous determination of metformin and glimepride in pharmaceutical dosage form by reverse-phase liquid chromatography

A simple, rapid, and precise reversed-phase liquid chromatographic method has been developed for the simultaneous determination of metformin in combination with glimepride. Under the developed conditions, good separation of the analytes was achieved in short analysis time. Several parameters affecting the separation of the analytes were studied, including pH and the concentration of SDS. The method is validated and shown to be linear in the range of 25 microg/mL to 150 microg/mL for metformin and 0.1 microg/mL to 0.6 microg/mL for glimepride. The method is applied for the analysis of these analytes in commercially available tablets.     

On the power of a perturbation for testing non-isomorphism of graphs

In this paper we prove an inverted version of A. J. Schwenk's result, which in turn is related to Ulam's reconstruction conjecture. Instead of deleting vertices from an undirected graphG, we add a new vertexv and join it to all other vertices ofG to get a perturbed graphG+v. We derive an expression for the characteristic polynomial of the perturbed graphG+v in terms of the characteristic polynomial of the original graphG. We then show the extent to which the characteristic polynomials of the perturbed graphs can be used in determining whether two graphs are non-isomorphic.This work was supported by the U.S. Army Research Office under Grant DAAG29-82-K-0107.     

An effective potential for heavy quark antiquark bound system

A heavy quark antiquark potential is suggested connecting asymptotic freedom and quark confinement in a unified way. Theα _g (q ²) calculated using Borel summation technique with three loop agrees with the two loopβ-function up tog ²/4π≅ 1.1 but changes appreciably afterg ²/4π=1.5. The potential so derived satisfactorily explains the and spectrum.     

Kinetics and mechanism of base hydrolysis of tris(3-(2-pyridyl)-5,6-diphenyl-1,2,4-triazine)iron(II) in aqueous and micellar media

The kinetics of base hydrolysis of tris(3-(2-pyridyl)-5,6-diphenyl-1,2,4-triazine)iron(II), \( {\text{Fe(PDT)}}_{ 3}^{2 + } \) has been studied in aqueous, cetyltrimethyl ammonium bromide (CTAB) and sodium dodecyl sulphate (SDS) media at 25, 35 and 45 °C under pseudo-first-order conditions, i.e. \( [ {\text{OH}}^{ - } ]\gg [{\text{Fe(PDT)}}_{ 3}^{2 + } ] \). The reactions are first order in both of substrate \( {\text{Fe(PDT)}}_{ 3}^{2 + } \) and hydroxide ion. The rates decrease with increasing ionic strength in aqueous and CTAB media, whereas SDS medium shows little ionic strength effect. The rate also increases with CTAB concentration but decreases with SDS. The specific rate constant, k and thermodynamic parameters (E _a, ΔH ^#, ΔS ^# and ΔG ^#) have also been evaluated. The near equal values of ΔG ^# obtained in aqueous and CTAB media suggest that these reactions occur essentially by the same mechanism such that \( {\text{Fe(PDT)}}_{ 3}^{2 + } \) reacts with OH^? in the rate-determining step. The ionic strength effect in SDS medium suggests that the rate-determining step involves an ion and a neutral species. The results in this study are compared with those obtained for other iron(II)-bipyridine complexes.     

Comparison of two- and three-dimensional modeling of invert trap for sewer solid management

In the present study, five different invert trap configurations （rectangular with and without lids on both sides; trapezoidal, trapezoidal with rectangular base and rectangular with trapezoidal base with lids on both sides） were simulated for both two-dimensional （2D） and three-dimensional （3D） flow conditions for three sediment types （sand, styrocell and plastic beads） at six flow rates （0.35, 0.70, 1.05, 1.35, 4.55 and 9.95 L/s） for each trap. Computational fluid dynamics （CFD）-based modeling using FLUENT software with Renormalization Group （RNG） k-e model along with discrete phase model （DPM） were used in the simulations. A hexagonal/tetrahedral and map-type non-uniform grid was chosen to discretize the entire computational domain and a control volume finite difference method was used to solve the governing equations. The flow rates selected in the present study cover the entire range of flow rate expected for dry weather and monsoon. The simulation is capable of differentiating between 2D and 3D modeling of particle trajectories, the effects of flow rate and trap geometry on flow patterns developed in the trap. The sediment retention ratio for 2D is higher than that for 3D modeling for all flow conditions, particle types and model geometry due to inclusion of lateral effects in 3D modeling. The invert trap having rectangular shape with trapezoidal base is found to be the most efficient configuration in both 2D and 3D modeling.