Refining adsorption parameters of n-butyl alcohol at the interface of mercury electrode with aqueous NaF and Na2SO4 solutions by correcting the adsorbate concentration

As an adjunct to the regression analysis of differential capacitance curves, which allows refining the adsorption parameters, a program, which takes into account possible errors in volume concentrations of organic substances, is developed. Using this procedure, the earlier data on the differential capacitance of a mercury electrode in aqueous solutions of normal butanol (1-BuOH) containing either 0.1 M NaF or 0.05 and 0.5 M Na₂SO₄ as the supporting electrolyte are analyzed. This allows obtaining the most accurate values of adsorption parameters for the systems mentioned above within the framework of the model of two parallel capacitors and the Frumkin isotherm. It is shown that, when a linear dependence of the intermolecular interaction parameter on the electrode potential is taken into account, the standard deviation of experimental capacitance values from those calculated using the mentioned model is 6.8–8.8%, which points to very high accuracy of this phenomenological model.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Meromorphic singular foliations on complex projective surfaces

Here we show that many numerical computations and bounds on the degrees of the algebraic leaves for singular meromorphic foliations on ² may be extended to large classes of foliations and complex projective surfaces.The author was partially supported by MURST and GNSAGA of CNR (Italy)     

Modeling of the relationship between electroosmotic flow and separation parameters in capillary zone electrophoresis using artificial neural networks and experimental design

The prediction of migration time of electroosmotic flow (EOF) marker was achieved by applying artificial neural networks (ANN) model based on principal component analysis (PCA) and standard normal distribution simulation to the input variables. The voltage of performance, the temperature in the capillary, the pH and the ionic strength of background electrolytes (BGE) were applied as the input variables to ANN. The range of the performance voltage studied was from 15 to 27 kV, and that of the temperature in the capillary was from 20 to 30 °C. For the pH values studied, the range was from 5.15 to 8.04. The range of the ionic strength investigated in this paper was from 0.040 to 0.097. The prediction abilities of ANN with different pre-processing procedure to the input variables were compared. Under the same performance conditions, the average prediction error of the migration time of the EOF marker was 5.46% with RSD = 1.76% according to 10 parallel runs of the optimized ANN structure by the proposed approach, and that of the 10 parallel predictions of the optimal ANN structure for the different performance conditions was 12.95% with RSD = 2.29% according to the proposed approach. The study showed that the proposed method could give better predicted results than other approaches discussed.     

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G) and nonlinear (N ₁) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively.This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse.For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.     

Resolution of (+/-)-ibuprofen using (-)-brucine as a chiral selector by thin layer chromatography

The enantiomeric resolution of (+/-)-ibuprofen into its enantiomers was achieved by TLC on silica gel plate using optically pure (-)-brucine as a chiral selector and acetonitrile-methanol (5:1, v/v) as the solvent system. Spots were located in an iodine chamber. The detection limit was 4.9 microg. The effect of concentration of the chiral selector, temperature and pH on resolution has been studied.     

A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.     

Vibrational spectra of 2-biphenylmethanol. Spectrum simulation and molecular structure

The vibrational spectra of a solid crystalline sample of 2-biphenylmethanol have been measured at room temperature. The IR absorption spectra were recorded in the range 400 cm^–1–3600 cm^–1; Raman spectra were measured in the range 10 cm^–1–1640 cm^–1. The direct mechanical and optoelectronic problems were solved using the fragment method realized as Lev-100 software; the intensity distribution in the IR spectrum of 2-biphenylmethanol was obtained by the same method. The experimental Raman and IR absorption spectra were interpreted by analyzing the calculated data on the frequencies and forms of normal vibrations and their intensities in the IR spectra. IR absorption spectra were simulated for several models of 2-biphenylmethanol conformers that differ in the mutual orientation of fragments. Based on the results of simulation and comparison of the calculated and experimental spectra of conformers we suggested a model for the conformer realized in the solid phase under normal conditions.Original Russian Text Copyright © 2004 by L. M. Babkov, J. Baran, N. A. Davydova, J. I. Kukielskii, and S. V. TrukhachevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 624–631, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

A class of multiple shrinkage estimators

Based on a sample of size n, we investigate a class of estimators of the mean of a p-variate normal distribution with independent components having unknown covariance. This class includes the James-Stein estimator and Lindley's estimator as special cases and was proposed by Stein. The mean squares error improves on that of the sample mean for p3. Simple approximations imations for this improvement are given for large n or p. Lindley's estimator improves on that of James and Stein if either n is large, and the coefficient of variation of is less than a certain increasing function of p, or if p is large. An adaptive estimator is given which for large samples always performs at least as well as these two estimators.