Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

关于非线性Schrodinger方程混合问题解的破裂和质量集中

本文讨论了一类非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程混合问题解的破裂现象，ｂｌｏｗ－ｕｐ时刻的估计和质量集中定理，并推广和改进了［ｌ～３］中的结果．     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

A model of adsorption at liquid-solid interface involving association in the bulk phase

A model of monolayer adsorption of binary liquid mixtures on homogeneous and heterogeneous solid surfaces involving association of one component in the bulk phase is discussed. Suitable model calculations, illustrating association and heterogeneity effects, have been performed according to an equation derived for adsorption excess. This equation has been examined by using the experimental data of adsorption of alcohols from benzene andn-heptane on silica gel.

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Adsorptionsmodell für die Grenzfläche Feststoff-Flüssigkeit unter Berücksichtigung der Assoziation in der Flüssigkeitsphase

Zusammenfassung Es wird ein Adsorptionsmodell binärer, flüssiger Mischungen an homogenen und heterogenen Oberflächen von Feststoffen unter Beachtung der Assoziation eines der Bestandteile in der Flüssigkeitsphase diskutiert. Mit der aus dem Oberflächenüberschuß abgeleiteten Gleichung wurden entsprechende Modellberechnungen durchgeführt, die die mit Assoziation und Heterogenität verbundenen Effekte illustrieren. Die Gleichung wurde für die experimentellen Daten der Alkoholadsorption aus Benzol undn-Heptan an Kieselgel überprüft.

     

Partial molal heat capacities of aqueous tetraalkylammonium bromides as functions of temperature

Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate for aqueous Bu₄NBr over a similar temperature range. These data, along with similar data for Me₄NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions.     

Microheterogeneity in aqueous-organic solutions: Heat capacities,volumes and expansibilities of some alcohols,aminoalcohol and tertiary amines in water

The heat capacities per unit volume and the densities of aqueous solutions of 2-propanol, neopentanol, tert-amylalcohol, 2-amino-2-methylpropanol, triethylamine and diethylmethylamine were measured, in many cases as a function of temperature, over the whole mole fraction or solubility range. Apparent and partial molal heat capacities, volumes and expansibilities were derived. The concentration dependence of these functions suggest the existence of transitions in some of these systems, in the water-rich region, qualitatively similar to micellization. The large relaxation contribution observed with some of the thermodynamic functions of hydrophobic alcohols and amines suggests a reinforcement of hydrophobic hydration due to strong hydrogen-bonding interactions of the polar groups with water.     

An application of the modified Poisson- Boltzmann equation in studies of osmotic properties of micellar solutions

The spherical cell model of colloidal solutions is applied in calculations of the osmotic pressure of micellar systems. The predictions of the nonlinear Poisson-Boltzmann equation (MPB) and of the Modified Poisson-Boltzmann equation (MPB) containing the leading terms of the fluctuation potential and the exclusion volume corrections to the mean potential acting on simple ions are compared with the results of recent computer simulations. Both PB and MPB seem satisfactory for solutions with monovalent counterions while the MPB is preferable for studies of the solutions containing divalent countenons.On leave from the University of Ljubljana, Ljubljana, Yugoslavia     

Vapor pressure,speciation, and chemical activities in highly concentrated sodium borate solutions at 277 and 317°C

The system H₂O-B₂O₃-Na₂O has been studied experimentally at 277 and 317°C. The activities of water and boric acid have been determined at mole ratios Na/B from 0 to 1.5, and total dissolved solids 3 to 80 weight percent. The activity of boric acid has been fitted to within experimental error using a speciation model with eight complex species. This model is consistent with the model previously published by Mesmer et al. The electrolyte properties of the liquid are modeled using the Pitzer-Simonson model of very concentrated electrolyte solutions. The calculated values of water activity agree with experiment, and the activity of NaOH and pOH have also been calculated. The potassium borate system also was briefly studied at 317°C, and is adequately described by a model with five complex species. The potassium borate liquid is more alkaline at K/B= 1 than a sodium borate liquid at the same mole ratio, but pOH in the two systems is the same at lower mole ratios.