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.     

Synthesis and characterisation of some new stabilisers for polyvinylchloride

Some new stabilisers having a chelating polymeric structure were synthesised and characterised, i.e., 8-hydroxyquinoline-formaldehyde chelating resins of Cd, Zn, and Pb. The efficiency of these new stabilisers was studied with respect to PVC. The stabilised PVC samples showed outstanding thermal stability as studied by thermogravimetric techniques, i.e., the percentage of HCl evolved reduced remarkably with increasing polymer decomposition temperature.     

1‐Acetyl‐3′‐(4‐bromophenyl)‐3′‐chlorospiro[3H‐indole‐3,2′‐oxetan]‐2(1H)‐one

In the title compound, C₁₈H₁₃BrClNO₃, the heterocyclic ring of the indole is distorted from planarity towards an envelope conformation. The orientations of the indole, oxetane, chloro and bromo­phenyl substituents are conditioned by the sp³ states of the spiro‐junction and the Cl‐attached C atoms.     

Phosphinsubstituierte Chelatliganden. XVIII. Penta- und Tetracarbonylmetall-Komplexe des Chroms,Molybdäns und Wolframs mit sekundären und tertiären Phosphinothioformamid-Liganden

Phosphine Substituted Chelate Ligands. XVIII. Penta- and Tetracarbonylmetal Complexes of Chromium, Molybdenum, and Tungsten with Secondary and Tertiary Phosphinothioformamide Ligands Mono- and bidentately coordinated phosphinothioformamide complexes are obtained by photochemical substitution of the metal hexacarbonyls M(CO)₆ (M ? Cr ( a ), Mo ( b ), W ( c )). The M(CO)₅ · THF adducts react with secondary thioamides under exclusion of light to give the P-coordinate pentacarbonyl complexes [(CO)₅MPPh₂C(S)NHR¹] (R¹ ? Ph ( 1a – c ), Me ( 2a )). The photoreaction of M(CO)₅ · THF with secondary and tertiary thioamides at low temperatures leads to the formation of the P, S-chelate complexes . The corresponding N-silylated complexes 6a – c (R¹ ? Me₃Si, R² ? Ph) are obtained by direct photosubstitution of M(CO)₆ in cyclohexane solution. The labile bis(thioformamide) complexes [(CO)₄M(PPh₂C(S)NHMe)₂] ( 7a – c , cis-trans isomers) are synthesized in low yields according to the same procedure. The attempted alkylation of the chelate complexes 3a – c remains unsuccessful, whereas the secondary thioformamides react with n-BuLi/CH₂Br₂ to give the methylene bis(thioformirnidoesters) [Ph₂PC(NR¹)S]₂CH₂ (R¹ ? Ph (8), Me ( 9 )) in quantitative yields.     

Di‐2‐pyridyl ketone N4,N4‐(butane‐1,4‐diyl)thiosemicarbazone

The title compound, C₁₆H₁₇N₅S, is in the thione form and crystallizes with two independent mol­ecules in the asymmetric unit. In both mol­ecules, the penta­methyl­ene­imine five‐membered ring adopts an envelope conformation, and in one of the molecules this ring shows positional disorder. The thione S and hydrazine N atoms are in the Z configuration with respect to the C—N bond.     

Cobalt(II), nickel(II), copper(II) and zinc(II) complexes of conjugated 3-(benzylidene/salicylidene)-β-diketones (having no enolisable γ-carbon proton) and their reactions

Transition Metal Chemistry - The synthesis and structural characterization of new metal(II) chelates (M = CoII, NiII, CuII and ZnII) of neutral conjugated bidentate β-diketone ligands, having...     

Bis[1,1′‐bis(diphenylphosphino)ferrocenium] hexadecachlorotetraantimony(III) ethanol solvate

In the title compound, [Fe(C₁₇H₁₄P)₂]₂[Sb₄Cl₁₆]·C₂H₆O, the Fe atoms lie on inversion centres and the pairs of cyclopentadienyl rings are consequently in a fully staggered conformation. The centrosymmetric anionic clusters formed by [Sb₄Cl₁₆]^4? are surrounded by the cations and are held together by weak C—H?Cl interactions. These formations stack along the a axis to form columns, and the columns are interconnected by another weak C—H?Cl interaction along the b axis.