The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Indirect fluorometric determination of diclofenac sodium.

A simple and easy method of analysis for diclofenac sodium is reported. A spectrofluorometric method for the microdetermination of diclofenac sodium has been developed through its reaction with cerium(IV) in an acidic solution and measurement of the fluorescence of the Ce(III) ions produced. Under the optimum experimental conditions for the oxidation reaction, 1.0 M H2SO4 with 90 min of heating time (100 degrees C), the range of application is 124.3-600 ng mL(-1) and the limit of detection is 72.7 ng mL(-1). The proposed method was applied to the determination of diclofenac sodium in pharmaceutical tablets. The results of the analysis show a good agreement with those obtained by the official USP 27 HPLC method.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Synthesis and hydrolysis of substituted tetrahydropyrimidinium salts. Behaviour of the degradation products on varying pH

Reaction of 1,2-diaryl-3-methyl-1,4,5,6-tetrahydropyrimidinium iodides 1a-i with alkaline solutions afforded N-aroyl-N-aryl-N'-methyltrimethylenediamines 2a-i . Compounds 2 are stable under acid conditions but in neutral or alkaline media spontaneously rearrange giving N-aroyl-N'-aryl-N-methyltrimethylenediamines 3a-i . Treating compounds 3 with concentrated acids reverse reaction takes place. Kinetic studies were performed on this intramolecular N → N' aroyl transfer over the H_o-pH range -0.9 to 2.30. Compounds 3 undergo acyl transfer to give 2 by a mechanism which involves a change in the rate determining step from formation to acid-catalysed decomposition of a six-membered heterocyclic intermediate on going from H_o to pH values. The existence of maxima in the pH rate profile allow to determine apparent pKa values of the hexahydropyrimidine intermediates which gave good correlation with the Swain F substituent constants. Stability of these heterocycles was also predicted by determination of thermodinamic parameters. Comparisons are made with the behaviour of five-membered heterocyclic intermediates (imidazolidine derivatives) which were studied in an earlier paper.     

Complex emulsion inversion pattern associated with the partitioning of nonionic surfactant mixtures in the presence of alcohol cosurfactant

Commercial ethoxylated nonionic surfactant mixtures containing alcohol cosurfactant exhibit a three-phase behavior whose formulation strongly varies with the water/oil ratio. As a consequence, a change in water/oil ratio can result in a sequence of up to three different emulsion inversion processes, through a combination of formulation and composition effects.     

About compensation effect by thermal decomposition of some catalyst precursors

Summary In order to obtain catalysts, the thermal decomposition of the precursors is a compulsory step. However, kinetic analysis of the decomposition data obtained under non-isothermal conditions lead very seldom to the intimate reaction mechanism. There is also a lack of information because in non-isothermal kinetics, the compensation effect, is rather a rule and unfortunately a source of debate. In order to discriminate between these processes, and the influence of conversion, respectively temperature on the reaction rate, the NPK (non-parametric kinetic - Sempere and Nomen) method was used. This method is based on the singular value decomposition algorithm (SVD) applied on the matrix of reaction rate at corresponding conversion and temperature. This method allows a less speculative determination of the conversion functions and of the kinetic parameters.     

Five-component food-grade microemulsions: structural characterization by SANS

In this paper we present the structural characterization of a five-component food-grade microemulsion containing Tween 80, R(+)-limonene, ethanol, glycerol, and water. Our main approach to investigating the microstructure of dense microemulsions, and how it can be influenced by the various components, was to employ small-angle neutron scattering and the new evaluation technique for dense, interacting systems, the Generalized Indirect Fourier Transformation. We started our investigation with the impact of glycerol and ethanol on Tween 80 micelles in water. We found that glycerol increases the aggregation number and withdraws the hydrating agents from the headgroup region of the surfactant, resulting in a higher packing density of molecules in a micelle at slightly increasing size. The same trend holds when the micelles are oil swollen and/or ethanol is present. Ethanol, on the other hand, redistributes mainly between water and the interface-headgroup region of the surfactant. Part of it replaces surfactant molecules in the micelles, which increases the available interface and results in a higher number of micelles with shrinking size. The same trend holds when the micelles are oil swollen and/or glycerol is present in the aqueous phase. We also investigated samples along the dilution of a mixture of surfactant and oil phase (R(+)-limonene and ethanol), which can be diluted with aqueous phase (mixture of water and glycerol) without the occurrence of phase separation. In some samples of this dilution most probably bicontinuous structures are present. To elucidate this point, we also employed dynamic light scattering, viscosity, and conductivity measurements.