Some Basic Extensions of Gustafson-Rakha's Multivariate Basic Hypergeometric Series

In this paper we extend some special cases of the multivariate basic hypergeometric series associated to the roots system of type A_m A_m that has been established and proved in [8]. For both types of the series, we will prove that when m = 2n; n = 1 m = 2n; n =1 one of the series is equivalent to Jackson's ₈ Y₇ _8 \Psi _7 sum, while the other series is equivalent to the basic Gauss' sum.     

Anagostic Interactions under Pressure: Attractive or Repulsive?

Square‐planar d⁸‐ML₄ complexes might display subtle but noticeable local Lewis acidic sites in axial direction in the valence shell of the metal atom. These sites of local charge depletion provide the electronic prerequisites to establish weakly attractive 3c–2e M???H? C agostic interactions, in contrast to earlier assumptions. Furthermore, we show that the use of the sign of the ¹H NMR shifts as major criterion to classify M???H? C interactions as attractive (agostic) or repulsive (anagostic) can be dubious. We therefore suggest a new characterization method to probe the response of these M???H? C interactions under pressure by combined high pressure IR and diffraction studies.     

Raman Spectroscopy of Natural Bone and Synthetic Apatites

Abstract

Raman spectroscopy of natural bones and hydroxyapatites is described. In addition, how Raman spectroscopy has proved crucial in providing baseline data for the modification of synthetic apatite powders that are routinely used now as bone replacement materials is explained. It is important to understand the chemical structural properties of natural bone. Bone consists of two primary components: an inorganic or mineral phase, which is mainly a carbonated form of a nanoscale crystalline calcium phosphate, closely resembling hydroxyapatite, and an organic phase, which is composed largely of type I collagen fibers. Other constituents of bone tissue include water and organic molecules such as glycosaminoglycans, glycoproteins, lipids, and peptides. Ions such as sodium, magnesium, fluoride, and citrate are also present, as well as hydrogenophosphate. Hence, the mineral phase in bone may be characterized essentially as nonstoichiometric substituted apatite. Such a distinction is important in the development of synthetic calcium phosphates for application as skeletal implants. An understanding of bone function and its interfacial relationship to an implant clearly depends on the associated structure and composition. Therefore, it is essential to fully understand the chemical composition of bone, and Raman spectroscopy is an excellent technique for such an analysis.     

Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

In the view of viscous potential flow theory, the hydromagnetic stability of the interface between two infinitely conducting, incompressible plasmas, streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction will be considered. The plasmas are flowing through porous media between two rigid planes and surface tension is taken into account. A general dispersion relation is obtained analytically and solved numerically. For Kelvin-Helmholtz instability problem, the stability criterion is given by a critical value of the relative velocity. On the other hand, a comparison between inviscid and viscous potential flow solutions has been made and it has noticed that viscosity plays a dual role, destabilizing for Rayleigh-Taylor problem and stabilizing for Kelvin-Helmholtz. For Rayleigh-Taylor instability, a new dispersion relation has been obtained in terms of a critical wave number. It has been found that magnetic field, surface tension, and rigid planes have stabilizing effects, whereas critical wave number and porous media have destabilizing effects.     

Economic production quantity model with repair failure and limited capacity

We develop an economic production quantity (EPQ) model with random defective items and failure in repair. The existence of only one machine results with limited production capacity and shortages. The aim of this research is to derive the optimal cycle length, the optimal production quantity and the optimal back ordered quantity for each product so as to minimize the total expected cost (holding, shortage, production, setup, defective items and repair costs). The convexity of the model is derived and the objective function is proved convex. Two numerical examples illustrate the practical usage of the proposed method.     

A hybrid method of Pareto,TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments

Multi-periodic inventory control problems are mainly studied employing one of two assumptions. The first is the continuous review, where depending on the inventory level, orders can be placed at any time, and the other is the periodic review, where orders can be placed only at the beginning of each period. In this paper, we relax these assumptions and assume that the time-periods between two replenishments are random fuzzy variables. While in the model of the problem at hand the decision variables are of integer type and there are space and service level constraints, for the shortages we consider a combination of back-order and lost-sales. We show the model of this problem to be an integer-nonlinear-programming type and in order to solve it, a hybrid method of Pareto, TOPSIS and Genetic Algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology.     

<Emphasis Type="Italic">v</Emphasis>-Adic maximal extensions,spectral norms and absolute Galois groups

Let (K, v) be a perfect rank one valued field and let ([`(K<sub>v</sub>)],[`(v)]){(\overline{K_{v}},\overline{v})} be the canonical valued field obtained from (K, v) by the unique extension of the valuation [(v)\tilde]{\widetilde{v}} of K _v , the completion of K relative to v, to a fixed algebraic closure [`(K<sub>v</sub>)]{\overline{K_{v}}} of K <sub>v</sub> . Let [`(K)]{\overline{K}} be the algebraic closure of K in [`(K<sub>v</sub>)]{\overline {K_{v}}}. An algebraic extension L of K, L ì [`(K)]{L\subset\overline{K}}, is said to be a v-adic maximal extension, if [`(v)] | <sub>L</sub>{\overline{v}\mid_{L}} is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in connection with the v-adic spectral norm on [`(K)]{\overline{K}} and with the absolute Galois groups Gal([`(K)]/K){(\overline{K}/K)} and Gal([`(K_v)] /K_v){(\overline{K_{v}} /K_{v})}. Some other auxiliary results are given, which may be useful for other purposes.     

Effects of tilted congruence on spherical compact stars

The aim of this paper is to investigate physical characteristics of spherical stars for an observer moving relative to matter distribution in linear regime. We impose shear-free condition to explore numerical solution of the field equations for five well-known compact stars (PSR J1614-2230, PSR J1903+0327, Vela X-1, SMC X-1, Cen X-3) and examine their physical behavior. It is found that all considered compact stars are stable. We conclude that all expected physical features are present related to stellar fluid configuration.     

Efficacy of Phytochemicals Derived from Roots of Rondeletia odorata as Antioxidant,Antiulcer, Diuretic,Skin Brightening and Hemolytic Agents—A Comprehensive Biochemical and In Silico Study

Roots of Rondeletia odorata are a rich source of phytochemicals with high antioxidant potential and thus may possess health benefits. This study used the LC-MS technique to identify phytoconstituents in R. odorata roots extract/fractions. Results revealed that n-butanol fraction and ethanolic extract contained total phenolic and flavonoid contents with values of 155.64 ± 0.66 mgGAE/g DE and 194.94 ± 0.98 mgQE/g DE, respectively. Significant potential of antioxidants was observed by DPPH, CUPRAC and FRAP methods while the ABTS method showed moderate antioxidant potential. Maximum % inhibition for urease, tyrosinase and carbonic anhydrase was shown by ethanolic extract (73.39 ± 1.11%), n-butanol soluble fraction (80.26 ± 1.59%) and ethyl acetate soluble fraction (76.50 ± 0.67%) which were comparable with thiourea (standard) (98.07 ± 0.74%), kojic acid (standard) (98.59 ± 0.92%) and acetazolamide (standard) (95.51 ± 1.29%), respectively, while all other extract/fractions showed moderate inhibition activity against these three enzymes. Hemolytic activity was also observed to range from 18.80 ± 0.42 to 3.48 ± 0.69% using the standard (triton X-100) method. In total, 28 and 20 compounds were identified tentatively by LC-MS analysis of ethanolic extract and n-butanol soluble fraction, respectively. Furthermore, molecular docking was undertaken for major compounds identified by LC-MS for determining binding affinity between enzymes (urease, tyrosinase and carbonic anhydrase) and ligands. It was concluded that active phytochemicals were present in roots of R. odorata with potential for multiple pharmacological applications and as a latent source of pharmaceutically important compounds. This should be further explored to isolate important constituents that could be used in treating different diseases.