An isomorphism theorem for henselian algebraic extensions of valued fields

In general, the value groups and the residue fields do not suffice to classify the algebraic henselian extensions of a valued fieldK, up to isomorphism overK. We define a stronger, yet natural structure which carries information about additive and multiplicative congruences in the valued field, extending the information carried by value groups and residue fields. We discuss the cases where these “mixed structures” give a solution of the classification problem.     

On the Tzitzeica–Johnson configuration

Working in the context of Hilbert’s axiomatic system, we prove that the generic Tzitzeica–Johnson configuration presents an equivalent to the determination of the metric of an absolute plane.     

The Lebesgue decomposition of the free additive convolution of two probability distributions

We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular continuous with respect to the Lebesgue measure on ${\mathbb{R}}$ only if one of the two measures is a point mass. The density of the absolutely continuous part with respect to the Lebesgue measure is shown to be analytic wherever positive and finite. The atoms of the free additive convolution of Borel probability measures on the real line have been described by Bercovici and Voiculescu in a previous paper.     

Phase Ratio and Equilibrium Constant in RP-HPLC Obtained from Octanol/Water Partition Constant Through Solvophobic Theory

The experimentally known dependence in RP-HPLC of the retention factor k′ on octanol/water partition coefficient (K _ow) has been examined based on solvophobic theory. The result showed that the dependence provides a means for the evaluation of phase ratio (Φ) of RP-HPLC columns, and of the equilibrium constant for a given compound and mobile phase. Using this theory, the phase ratio was evaluated for a set of seven different C18 columns (five having fully porous particles and two core–shell particles), and the equilibrium constants were calculated for four homologous series of compounds in two mobile phase systems. One mobile phase was methanol/aqueous solution of 0.1% H₃PO₄, and the other was acetonitrile/aqueous solution of 0.1% H₃PO₄. Besides providing the values for Φ for the evaluated columns, the results of the study indicated that for a specific composition of the mobile phase and for a given compound displaying only hydrophobic interactions, the equilibrium constant K(X) for different C-18 columns is basically the same. The data were further used to provide guidance in the selection of a chromatographic column for a specific separation based on K _ow values and chemical structure of the analytes. The study indicated that the separation of compounds with identical polar groups (or no polar groups) and with very close values for the K _ow cannot be achieved based only on hydrophobic interactions that dominate the separation on RP-type columns. Only column that displays polar interactions may provide a solution to such separations. For hydrocarbons with close K _ow values, the separation cannot be achieved even on columns with some polarity. On the other hand, even compounds with equal K _ow values, but with different functionalities can be separated on RP-HPLC columns without involving polar interactions. The compounds with different K _ow values are expected to be easily separated on RP-HPLC columns.     

Four new topological indices based on the molecular path code

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

Recent Applications of Fourier Transform Infrared Spectrophotometry in Herbal Medicine Analysis

Abstract

Fourier transform infrared spectroscopy (FTIR) is a fast and nondestructive analytical method. Associated with chemometrics, it is a powerful tool for the pharmaceutical industry. It is becoming a suitable technique for analysis of herbal medicine. This review focuses on the recent developments and updates for the qualitative and quantitative analysis of herbal medicine using FTIR. Moreover, it can be implemented during herbal drug development, in production for process monitoring, or in quality control laboratories.     

Iterative solution of inconsistent systems of linear inequalities

In 1980 S.P. Han proposed a finitely terminating (in exact arithmetic) algorithm for solving an inconsistent system of linear inequalities in a least squares sense. This algorithm uses a singular value decomposition of a submatrix of the problem matrix on each iteration, making it impractical for all but only smaller problems. In this paper we show that a modification of Han's algorithm allows us to introduce an iterative approximation to the singular value decomposition solution. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)