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.     

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.     

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.     

Determination of the partition coefficients of the nonionic detergent C12E7 between lipid-detergent mixed membranes and water by means of Laurdan fluorescence spectroscopy

The membrane-water partition coefficient of the detergent C₁₂E₇ between water and C₁₂E₇/POPC mixed membranes has been determined by means of steady-state fluorescence spectroscopy. The emission spectra of the fluorescent probe Laurdan were used as an indicator of membrane composition at different membrane concentrations in the sample. The partition coefficient expressed as the ratio of the mole fractions of the detergent in the membrane and water phases is about 6^*10⁵ at low molar ratios of C₁₂E₇/POPC (R _c ) and decreases rapidly with increasingR _c . The limiting detergent content of the lamellar phase (R _c ^* >0.8) is indicated by a minimum ofP(R _c ).     

Preparation of USY zeolite VOx supported catalysts from V(AcAc)3 and NH4VO3. Catalytic properties for the dehydrogenation of n-butane in oxygen-free atmosphere

The preparation of different samples of vanadia supported on ultrastable zeolite (VO(x)/USY) is discussed. The samples were prepared in order to obtain highly dispersed V-species, avoiding the formation of crystalline vanadia and the destruction of the zeolite framework. Two methods were employed for preparing VO(x)/USY samples: an organic route using V(AcAc)3 and an inorganic route using NH4VO3. The characterization of the samples was performed with XRD, TPR, NH3-TPD, and N2 isotherms. From these results it is concluded that when VO(x) is supported on the surface of USY from acidic aqueous solution of ammonium metavanadate, the destruction of the zeolite framework is accomplished. For higher pH values in the impregnating solution, undesired V2O5 is formed on the USY surface. On the other hand, VO(x)/USY prepared from the organic precursor shows no destruction of the USY structure. In addition, highly dispersed VO(x) are formed, though for relatively high V loadings (6%) an obstruction of the zeolite windows takes place. The samples are tested as catalysts for gas phase dehydrogenation of n-butane to olefins. The catalysts prepared from NH4VO3 are almost inactive for the reaction. On the other hand, both samples prepared from V(AcAc)3 present initial conversion levels in the 8-12% range. However, the selectivity depends on the V loading, the catalysts with 6% loading being the most selective (75%). The catalytic patterns of the samples (activity and selectivity) are in agreement with the physicochemical features of the VO(x)/USY surface.     

Polymeric flocculants processing by accelerated electron beams and microwave heating

Results obtained by accelerated electron beam, microwave and simultaneous microwave and electron beam application in the chemistry of acrylamide and acrylic acid copolymers (polymeric flocculants used for wastewater treatment) are presented. Comparative results concerning the molecular weight and Huggins’ constant for the acrylamide and acrylic acid copolymers obtained by classical heating, microwave heating, electron beam irradiation and simultaneous microwave and electron beam treatment are reported. Microwave heating produces high water solubility of the polymeric flocculants but median molecular weight values. Electron beam irradiation gives high molecular weight values but associated with a cross-linked structure (poor water solubility) while microwave energy addition to electron beam energy gives simultaneously high molecular weight values and high water solubility.     

Spectroscopic investigation of the adsorption and oxidation of thiourea on polycrystalline Au and Au(111) in acidic media

In the present paper, a systematic electrochemical investigation on thiourea (TU) electrooxidation was developed on polycrystalline and (111) single-crystal gold electrodes in 0.1 M perchloric acid. The combination of cyclic voltammetry with in situ Fourier transform infrared spectroscopy (FTIRS) and differential electrochemical mass spectrometry techniques have allowed the nature of the species formed during the electroadsorption and electrooxidation of TU to be established. FTIRS experiments were performed in D2O to clean up the region of the H2O bending around 1600 cm(-1). It was concluded that TU adsorbs tilted on the surface in the 0.05-0.40 VRHE potential range. A dual-path reaction mechanism was evidenced in the oxidation process. The first pathway takes place from adsorbed TU at E > 0.40 VRHE and implies the formation of [Au(I)-(TU)2]+, which is oxidized to NH2CN and S0 at E > 0.80 VRHE. In a following oxidation step at E > 1.20 V, N2, CO2, and HSO4-/SO4(2-) were produced. The second parallel reaction occurs from TU in solution at E > 0.50 VRHE to form (TU)2(2+). All these species were characterized from the spectroscopic experiments. Similar results were obtained for both surfaces.