Some inequalities for the polar derivative of a polynomial

LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin.     

Numerical calculations of temperature distribution of double layer metallic surface treated by laser beams

A mathematical model of laser beam treatment of double layer alloys (Ni/Fe, Al/Fe and Cr/Fe systems) describing the effect of laser beam on different physical and geometrical parameters of coated layer system has been adapted. The numerical solutions of the non-homogeneous heat-transport differential equation could estimate the temperature of the treated region.The suggested model allows investigation of the temperature distribution as a function of treated surface and laser parameters. The physical parameters of the treated materials were taken as functions of temperature due to the change in the temperature of the treated double layer materials.     

A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations [1] was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in differentη-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

Polymer blends—I. Mechanical and morphological behaviour of polyethylene/polyvinyl chloride blends

As part of a fundamental study of the behaviour of mixed plastics during reprocessing and in service, blends of low density polyethylene (LDPE) and polyvinyl chloride (PVC) have been investigated. It was found that Young's modulus increased steadily from pure LDPE to pure PVC whereas both tensile strength at break and elongation at break passed through a minimum at about 5% PVC. Optical and scanning electron microscope studies have related this mechanical behaviour to morphological changes in the two phase system under stress.     

Antimicrobial triterpenes from Debregeasia salicifolia

New triterpene, 3beta-(trans-cinnamoyloxy)-19alpha-hydroxy-urs-12-ene (1) has been isolated from the methanolic fraction of Debregeasia salicifolia, along with uvaol (2), 3beta,19alpha-dihydroxy-urs-12-ene (3), ursolic acid (4), pomolic acid (5), pomolic acid methyl ester (6) and tormentic acid (7) reported for the first time from this species. The compounds (1), (3) and (6) showed significant antimicrobial activity. The structure elucidation was made with the help of extensive 2D NMR spectroscopic techniques.     

Potentiometric titration of permanganate with resacetophenone oxime

Milligram amounts of permanganate can be titrated with resacetophenone oxime (4-acetylresorcinol oxime) as a reducing titrant in the presence of phosphoric acid (0.5 M). The stoichiometry between permanganate and the oxime is 3:1 (MnO₄^-:oxime). The titration is successful in the presence of large amounts of dichromate or vanadate or moderate amounts of cerium(IV).     

Gas-phase on-line generation and infrared spectroscopic investigations of polyphosphazenes, (NPX2)3 where X=F, Cl and Br

Gas-phase infrared spectra of polyphosphazenes (phosphonitrilic halides trimer), (NPX2)3 where X=F, Cl and Br have been recorded. The molecules were generated for the first time by an on-line process using solid (NPCl2)3 as a precursor passed over heated sodium fluoride and potassium bromide at about 550 and 700 degrees C for (NPF2)3 and (NPBr2)3 production, respectively. The products were characterized by the infrared spectra of their vapors. The low-resolution gas-phase Fourier transform infrared spectra reported for the first time show strong bands centered at 1295, 1215 and 1200 cm-1, assigned to nu7(E'), in plane PN stretching mode of (NPX2)3, where X=F, Cl and Br, respectively.     

Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Effect of Erosive Agents on Surface Characteristics of Nano-Fluorapatite Ceramic: An In-Vitro Study

Erosive beverages cause dissolution of natural teeth and intra-oral restorations, resulting in surface characteristic changes, particularly roughness and degradation. The purpose of this study was to evaluate the surface roughness and topography of a dental ceramic following immersion in locally available erosive solutions. A total of 160 disc specimens of a nano-fluorapatite type ceramic (12 mm diameter and 2 mm thickness) were fabricated and equally distributed into two groups (n = 80) and then evenly distributed among the following five testing groups (n = 16): lemon juice, citrate buffer solution, 4% acetic acid, soft cola drink, and distilled water which served as a control. The surface roughness (Ra) and topography were evaluated using a profilometer and scanning electron microscope at baseline, 24 h, 96 h, and 168 h respectively. Data were analyzed using ANOVA and Tukey’s multiple comparisons (p ≤ 0.05). Surface changes were observed upon exposure to all acidic beverages except distilled water. Amongst all immersion media, 4% acetic acid produced the most severe surface roughness across all time periods (i.e., baseline, 24 h, 96 h, and 168 h). A statistically significant difference in the surface roughness values between all immersion media and across all four time intervals was observed. Erosive agents had a negative effect on the surface roughness and topography of the tested ceramic. The surface roughness increased with increased storage time intervals.