Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Single-column ion-chromatographic determination of chromium(VI) in aqueous soil and sludge extracts

Single-column ion-chromatography (SCIC) was investigated as a routine, rapid, precise and selective analytical method for the determination of chromium(VI) in aqueous extracts of soil and sewage sludge. Chromatographic parameters were optimized for determination of Cr(VI), NO(-)(3) and SO(2-)(4). A low-capacity resin-based column was used for the separation and the anions were determined by conductometric detection. p-Hydroxybenzoic acid (5mM) at pH 8.5 was used as the eluent. The limit of detection, defined as S/N = 3, was 92 mug/l. The resolution between Cr(VI) and SO(2-)(4) was 2.8, the precision ranged from 0.9% for NO(-)(3) to 2.0% for Cr(VI) with a 500-mul injection. The SCIC results for Cr(VI) agreed closely with those obtained by inductively coupled argon-plasma emission and spectrophotometry.     

Reduction studies on benzaza[3.3.3]propellanc derivatives

Sodium borohydride reduction of 3-methyl-2,3-dioxo-7,8-benzo-3-aza[3.3.3]propellan-6-one (1b) gave 2,4-dioxo-3-methyl-7,8-benzo-3-aza[3.3.3]propellan-6-ol, while lithium aluminum hydride reduction gave 3-methyl-7,8-benzo-3-aza[3.3.3]propellan-6-ol, which on oxidation, gave the corresponding ketone. This ketone formed the corresponding thioketal upon reaction with 1,2-ethanedithiol. Raney nickel desulfurization of the thioketal provided 3-methyl-6,7-benzo-3-aza[3.3.3]propellane. The same compound was also obtained in poor yield by forming the thioketal of Ib followed by lithium aluminum hydride reduction and Raney nickel desulfurization of the product. Desulfurization of the thioketal of Ib gave 2,4-dioxo-6,7-Benzo-3-aza[3.3.3]propellane.     

Cyclization of ylidenemalononitriles. X. Synthesis of benzazapropellane derivatives from α-Cyano-β-chloroalkylcinnamonitriles

The reaction of nucleophilic and non-nucleophilic bases wtih 2-carbamoyl-3-(γ-chloropropyl)-1-indenone ( 5 ) have been investigated. Condensation of γ-chlorobutyrophenone with malono-nitrile afforded α-cyano-β-(3-ehloropropyl)cinnamonitrile which was cyclized in concentrated sulfurie acid to produce 5 . Two other products obtained from the cyclization reaction were 2-carbamoyl-3-(γ-ehloropropylidene)-1-indanone ( 4 ) and α-carbamoyl-β-(3-chloropropyl)cinnam-amide. Treatment of a solution of 4 in ethyl acetate with piperidine resulted in cyclization of the γ-chloropropyl side chain to give 2-carbamoyl-3-cycIopropyl-1-indanone. The same compound was obtained in improved yield by the treatment of 4 or 5 with sodium hydroxide solution. The reaction of dirnethylamine with 5 in benzene gave initial Michael addition of the amine followed by internal alkylation of the carbanion so formed to yield 3a-dimethylamino-2,3,3a,8-tetrahydro-8-oxoeyclopent[a]indene-8a(lH)earboxamide ( 7a ). Similarly addition of ammonia, pyrrolidine, piperidine, benzenethiol, p-toluenethiol, 2-naphthalenethiol and nitromethane to the indenone I gave respective analogs of type 7 . Treatment of 5 with sodium cyanide in aqueous t-butyl alcohol resulted in a similar Michael addition followed by internal alkylation. In addition, cyclization between the nitrile and the carbamoyl functions occurred in the same step to give 2-oxo-4-imino-7,8-benzo-3-aza[3.3.3]-propellan-6-one ( 13a ). Hydrolysis of the iminopyrrolido ring in 13a to the corresponding suecin-irnide gave 2,4-dioxo-7,8-benzo-3-aza[3.3.3]propellan-6-one ( 13b ). Reactión of 13b with methyl iodide, allyl bromide, benzyl bromide, and diethyluminoethyl chloride afforded the corresponding N-alkylated products. A similar sequence starling with δ-ehlorovalerophenone led to 5,6-fused ring systems, including a [4.3.3]propellane. 2,9-Dioxo-4-methyl-7,8-benzo-3-aza[4.3.3]propell-4-ene was obtained by the reaction of 5 with acetone in dilute alkali.     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

Electrical conduction mechanism in a polycrystalline Sb35Se65 sample

Localized state conduction through a variable-range hopping mechanism in the low-temperature region (～180–270 K) and thermally activated phonon-assisted tunneling in the higher-temperature region (～270–320 K) has been observed in a polycrystalline Sb₃₅Se₆₅ sample.     

Static charged gas spheres in general relativity

In the present paper the field equations of general relativity have been solved to obtain the different solutions for the static charged gas sphere. These solutions are free from singularities and satisfy the necessary physical conditions.     

Planck's Half-Quanta: A History of the Concept of Zero-Point Energy

Max Planck introduced the concept of zero-point energy in spring 1911. In the early struggles to establish the concept of the energy-quantum, it provided a helpful heuristic principle, to guide as well as supplement the efforts of some leading physicists in understanding the laws that applied in the atomic domain. The history and growth of this concept, and its application in the general development of quantum theory during the past many decades are studied under three principal headings: (1) The Birth of the Concept of zero-Point Energy; (2) Does Zero-Point Energy Really Exist? and (3) The Ground State of Quantum Systems.