A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

The smallest simple Moufang loop

We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Simple components of the center of FG/J(FG)

Let G be a finite group, F a field, FG the group ring of G over F, and J(FG) the Jacobson radical of FG. Using a result of Berman and Witt, we give a method to determine the structure of the center of FG/J(FG), provided that F satisfies a field theoretical condition.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Gas-Phase Nucleophilic and Elimination Reactions in Simple Alkyl Nitrates

There has been increasing interest in the gas-phase reactivity of alkyl nitrates because of their well-known applications as explosives and because of then role in atmospheric and in marine processes This manuscript describes an experimental study by FT-ICR techniques of the gas-phase reactions of OH(-) and F(-) with methyl and ethyl Innate For methyl nitrate, the main reaction channel is found to be an elimination process promoted by abstraction of an a proton from the methyl group. Nucleophilic displacement of nitrate anion through an S(N)2 process at the carbon center Is also found to he an important reaction channel with methyl nitrate In ethyl nitrate, Ruination of NO(3)(-) is greatly enhanced and this is attributed to the ease of an E2-type elimination process promoted by proton abstraction at the beta position of the ethyl group. Theoretical calculations at the MP2/6-311+G(3df,2p)//MP2/6-31+G(d) level of theory ale consistent with the relative importance of the reaction channels and suggest that these reactions proceed through a double well potential The calculations also predict that nucleophilic attack by OH(-) at the nitrogen center (Sn2@N) is energetically the rueful ad pathway but experiments with (18)OH(-) showed no evidence for this channel. Single-point calculations reveal a strong preference for approach to the emboli center and may explain the lack of reactivity at the nitrogen center. Calculations were also carried out or NH(2)(-) and SH(-) to establish the reactivity pattern to provide a better understanding of environmentally relevant nitrate esters.

Simple method for determination of cocaine and main metabolites in urine by CE coupled to MS

in this work, a simple method for the simultaneous determination of cocaine (COC) and five COC metabolites (benzoylecgonine, cocaethylene (CET), anhydroecgonine, anhydroecgonine methyl ester and ecgonine methyl ester) in human urine using CE coupled to MS via electrospray ionization (CE-ESI-MS) was developed and validated. Formic acid at 1 mol/L concentration was used as electrolyte whereas formic acid at 0.05 mol/L concentration in 1:1 methanol:water composed the coaxial sheath liquid at the ESI nozzle. The developed method presented good linearity in the dynamic range from 250 ng/mL to 5000 ng/mL (coefficient of determination greater than 0.98 for all compounds). LODs (signal-to-noise ratio of 3) were 100 ng/mL for COC and CET and 250 ng/mL for the other studied metabolites whereas LOQ`s (signal-to-noise ratio of 10) were 250 ng/mL for COC and CET and 500 ng/mL for all other compounds. Intra-day precision and recovery tests estimated at three different concentration levels (500, 1500 and 5000 ng/mL) provided RSD lower than 10% (except anhydroecgonine, 18% RSD) and recoveries from 83-109% for all analytes. The method was successfully applied to real cases. For the positive urine samples, the presence of COC and its` metabolites was further confirmed by MS/MS experiments.

Stereoselective Nucleophilic Addition of Potassium Alkyltrifluoroborates to Cyclic N-Acyliminium Ions: a Simple and Mild Approach to Chiral 5-Alkyl-pyrrolidin-2-ones

The stereoselective nucleophilic addition of potassium alkyltrifluoroborates to cyclic N-acyliminium ions derived from N-benzyl-3,4,5-triacetoxy-pyrrolidin-2-one, which affords 5-substituted-pyrrolidin-2-ones, is described. The products are obtained in moderate to good yields and are produced predominantly as the anti diastereomer.

Spectrophotometric determination of zinc in pharmaceutical and biological samples with di-2-pyridyl ketone benzoylhydrazone: A simple, fast, accurate and sensitive method

A simple, fast, accurate, and sensitive spectrophotometric method was developed to determine zinc(II). This method is based on the reaction of Zn(II) with di-2-pyridyl ketone benzoylhydrazone (DPKBH), at pH=5.5 and 50% (v/v) ethanol. Beers law was obeyed in the range 0.020-1.82 mu g mL(-1) with a molar apsorptivity of 3.64 x 10(4) L mol(-1) cm(-1), and a detection limit (3) of 2.29 mu g L-1. The action of some interfering ions was verified and the developed method applied to pharmaceutical and biological samples. The results were then compared with those obtained by using a flame atomic absorption technique.

Simple Method to Evaluate and to Predict Flash Points of Organic Compounds

Flash points (T(FP)) of organic compounds are calculated from their flash point numbers, N(FP), with the relationship T(FP) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901. In turn, the N(FP) values can be predicted from boiling point numbers (Y(BP)) and functional group counts with the equation N(FP) = 0.974Y(BP) + Sigma(i)n(i)G(i) + 0.095 where G(i) is a functional group-specific contribution to the value of N(FP) and n(i) is the number of such functional groups in the structure. For a data set consisting of 1000 diverse organic compounds, the average absolute deviation between reported and predicted flash points was less than 2.5 K.

Microwave-Assisted Derivatization of Cellulose in an Ionic Liquid: An Efficient, Expedient Synthesis of Simple and Mixed Carboxylic Esters

Microwave (MW)-assisted cellulose dissolution in ionic liquids (ILs) has routinely led either to incomplete biopolymer solubilization, or its degradation. We show that these problems can be avoided by use of low-energy MW heating, coupled with efficient stirring. Dissolution of microcrystalline cellulose in the IL 1-allyl-3-methylimidazolium chloride has been achieved without changing its degree of polymerization; regenerated cellulose showed pronounced changes in its index of crystallinity, surface area, and morphology. MW-assisted functionalization of MCC by ethanoic, propanoic, butanoic, pentanoic, and hexanoic anhydrides has been studied. Compared with conventional heating, MW irradiation has resulted in considerable decrease in dissolution and reaction times. The value of the degree of substitution (DS) was found to be DS(ethanoate) > DS(propanoate) > DS(butanoate). The values of DS(pentanoate) and DS(hexanoate) were found to be slightly higher than DS(ethanoate). This surprising dependence on the chain length of the acylating agent has been reported before, but not rationalized. On the basis of the rate constants and activation parameters of the hydrolysis of ethanoic, butanoic, and hexanoic anhydrides in aqueous acetonitrile (a model acyl transfer reaction), we suggest that this result may be attributed to the balance between two opposing effects, namely, steric crowding and (cooperative) hydrophobic interactions between the anhydride and the cellulosic surface, whose lipophilicity has increased, due to its partial acylation. Four ethanoate-based mixed esters were synthesized by the reaction with a mixture of the two anhydrides; the ethanoate moiety predominated in all products. The DS is reproducible and the IL is easily recycled. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 134-143, 2010