Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

The solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

子系统为S≥3的非线性大系统在近平衡区内的稳定性

本文采用文[1,2]中提出的平衡结构法研究子系统s≥3的非线性大系统在近平衡区内的稳定性;得到了判别这类大系统稳定性的两个一般性准则.     

The application of Hölder exponent to traffic congestion warning

In this paper, we applied multifractal modeling techniques to analyze the traffic data collected from the Beijing Yuquanying. The results indicated that multifractal characteristics obviously exist in the traffic system; the degree of fractality of these traffic data tends to increase as the traffic system becomes congested; the Hölder exponent that measures the local rate of fractality may be used as indicators to predict the presence of the traffic congestion.     

Radiation induced synthesis and swelling characterization of thermo-responsive N-isopropylacrylamide-co-ionic hydrogels

Two-component thermo-responsive hydrogels poly(N-isopropylacrylamide)-co-vinylbenzyltrimethylammonium chloride (NIPA-co-VBT) and poly(N-isopropylacrylamide)-co-p-sodium styrene sulphonate (NIPA-co-SSS) were prepared by using high energy gamma radiation. The gels were characterized by Fourier transformed infrared spectroscopy (FTIR), scanning electron microscopy (SEM) and sol-gel analysis. The presence of ionic monomers in NIPA leads to lower gel content. Introduction of ionic components in the matrix enhanced swelling extent but caused slower volume transition. The swelling studies in alcohol indicated that swelling extent was function of polarity of the swelling medium and all gels followed the order water > methanol > ethanol > iso-propanol. In mixed co-solvents (water-alcohol), they exhibit complex reentrant behavior. The co-polymer gels containing VBT swelled faster and to higher extent than those containing SSS. The dynamic swelling studies indicated that diffusion of water in PNIPA gel shifts from Fickian for PNIPA to anomalous for NIPA-co-ionic gels also the mean swelling time (MST) decreases for gels containing ionic monomers.     

Equilibrium studies of Mn(II), Mg(II), Ca(II), Sr(II) and Ba(II) withp-fluoro-,p-chloro-,p-bromo-,p-methyl-benzoylacetones and 1-(4-fluorophenyl)-1,3-pentanedione

The rawpH-data, obtained from the potentiometric titrations of the titled ligands with NaOH in 75% (v/v) dioxane-water mixture performed at 20, 30 and 40°C at constant ionic strength (=0.1M-NaClO₄), have been adequately corrected for dilution, and solvent effects in order to evaluate thermodynamic dissociation constants. Variance of the latter as a function of temperature has also been accounted for. The differing magnitudes of thermodynamic dissociation constants of the titled ligands have been explained on the basis of the non coplanar orientation of the phenyl ring in the ligands and a comparison has been made with those of unsubstituted benzoylacetone, dibenzoylmethane and acetylacetone.Following similar technique, thermodynamic stepwise and overall formation constants of the titled metal-ligand systems have been obtained and the results correlated with ligand basicity inverse metal crystal radii and second potentials of metals. Decrease in the free enthalpy (–G) of complexation reaction has also been evaluated.

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Untersuchung der Gleichgewichte von Mn(II), Mg(II), Ca(II), Sr(II) und Ba(II) mit p-Fluor-, p.-Chlor-, p-Brom-, p-Methyl-benzoylaceton und 1-(4-Fluorphenyl)-1,3-pentanedion

Zusammenfassung Aus der potenitometrischen Titration der Titelverbindungen mit NaOH in 75 (v/v) Dioxan—Wasser bei, 20, 30 und 40°C bei konstanter Ionenstärke (=0,1M-NaClO₄) wurden die thermodynamischen Dissoziationskonstanten ermittelt. Verdünnungs-, Lösungsmittel-und Temperatureffekte wurden berücksichtigt. Die unterschiedlichen Dissoziationskonstanten werden mit der Nichtplanarität des Phenylrings in den Liganden erklärt. Außerdem wurden die Komplexbildungskonstanten bestimmt; sie sind in die Diskussion miteinbezogen.

     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.