Normalized Matching in Direct Products of Partial Orders

In this paper we investigate the question: When does the direct product of partial orders each satisfying the normalized matching condition also satisfy it? A proof of Harper's result that a sufficient condition for this is that factor partial orders have rank populations that are multiplicatively convex, is presented. A general necessary and sufficient condition is described, and conditions which occur when one factor is a chain are obtained. In particular we show that under these circumstances it is necessary that the product order have multiplicatively convex population rank.     

Shell-model studies of the 90Y, 91Zr, 92Nb and 93Mo nuclei

A shell-model calculation of the N = 51, 39 ≦ Z ≦ 42 nuclei is presented. The ⁸⁸Sr nucleus is assumed to be an inert closed core. The extra-core protons are restricted to the ($\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$) configurations, and the active neutron is allowed to occupy the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbits. The proton-proton effective interaction is directly taken from the previous analysis on the energy levels for N = 50 isotones by Ball et al. The proton-neutron effective interaction is assumed to be of the form of the surface δ-interaction. The energy spectra are calculated from a least-squares fit to the experimental data, varying the T = 0 and T = 1 strengths of the surface δ-interaction. Spectroscopic factors, E2 transition rates and two-body matrix elements are also calculated and compared with the observed values and the previous theoretical results.     

Tetracyclines Communication 22. Stereochemistry of 2- and 3-substituted 10-oxo-9-hydroxy-9-methyl-1,2,3,4,4a,9,9a,10-octahydroanthracenes

Summary Intramolecular cyclization reactions were investigated, and the configurations were proved of 2- and 3-substituted 10-oxo-9-hydroxy-9-methyl-1,2,3,4a,9,9a.10-octahydroanthracenes of type (I), which are possible intermediaries for the synthesis of tetracyclines and their analogs.Translated from Izvestiya Akademii Nauk SSSR, Setiya Khimicheskaya, No. 6, pp. 1024–1035, June, 1964     

Determination of components in propolis by capillary electrophoresis and photodiode array detection

The capillary electrophoretic separation of components in propolis, a commonly used natural medicine, was investigated. Optimum conditions for the separation were established. Photodiode-array detection permitted the rapid identification of the components in the samples analysed. The determination of these components, including caffeic acid, dimethylcaffeic acid, isoferulic acid and quercetin, was performed on a commercial propolis sample.     

Deviations from linearity in statistical evaluation of linearity in assay validation

Linearity and linear range are the key evaluations of the accuracy in assay validation. The average deviation from linearity (ADL) and the sum of squares of deviations from linearity (SSDL) have been proposed for assessment of the linearity. However, both ADL and SSDL do no consider the variability of the assay for evaluation of linearity. Therefore, we proposed the coefficient of variation of deviations from linearity (CVDL) as an alternative measure for the linearity assessment. For the inference of evaluation of linearity, we proposed testing procedures based on generalized pivotal quantities (GPQ) of ADL and CVDL for evaluation of linearity. The simulation studies were conducted to empirically investigate the size and power between the three methods. The simulation results show that all three methods adequately control size. However, the ADL method is uniformly more powerful than the other two methods. A numeric example illustrates the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Mathematical modeling of interrelationships among cutting angles,setting angles and working angles of single-point cutting tools

The angles of a cutting tool play a key role in determining its cutting efficiency. However, once the tool has been mounted on a machine tool, setting errors inevitably cause the working angles of the tool to deviate slightly from the designed cutting angles. Accordingly, this study develops mathematical models to analyze the interrelationships among the tool angles, the setting angles and the working angles. In the proposed approach, a process of homogeneous coordinate transformation is employed to develop a kinematic model of the cutting tool such that the working angles can be derived given the tool angles and setting angles. Mathematical formulae are then developed to inversely derive the tool angles required to generate the specified working angles given prior knowledge of the setting angles. An illustrative numerical example is presented to demonstrate the validity of the proposed approach. Overall, the numerical results confirm that the methodology presented in this study provides a comprehensive, simple and versatile means of modeling a variety of conventional single-point cutting tools.     

Robustness of Tail Index Estimation

Abstract

The implementation of the Hill estimator, which estimates the heaviness of the tail of a distribution, requires a choice of the number of extreme observations in the tails, r from a sample of size n where 2 ≤ r + 1 ≤ n. This article is concerned with a robust procedure of choosing an optimal r. Thus, an estimation procedure, δ _s , based on the idea of spacing statistics, H^(r) is developed. The proposed decision rule for choosing r under the squared error loss is found to be a simple function of the sample size. The proposed rule is then illustrated across a wide range of data, including insurance claims, currency exchange rate returns, and city size.