On the possibility of an unusual extension of the minimax theorem

Summary A natural extension of the minimax theorem for cooperative games is considered.This work was prepared at the Econometric Research Program of Princeton University and it has been partially supported by the Office of Naval Research under contract No. 1958 (16).     

Properties of solution-grown crystals of fractions of isotactic polypropylene with different degrees of stereoregularity

Solution-grown crystals of fractions of isotactic polypropylene (IPP) with different degrees of stereoregularity have been obtained by isothermal crystallization from α-chloronaphthalene, using a self-seeding technique. Electron micrographs of samples, crystallized under the same undercooling, show that, with decreasing fraction of isotactic pentads, the perfect rectangular shape of the single crystal is lost and the presence of more complex morphologies is increasingly observed. The equilibrium dissolution temperature T_d of IPP fractions, from polymers prepared with a titanium based catalyst, decreases linearly with decreasing percentage of isotactic pentads. An extrapolated value of 171°C is obtained for the equilibrium dissolution temperature of a crystal of IPP with 100% isotactic pentads, i.e., an IPP crystal free of configurational defects. The melting temperature T′_m and the apparent enthalpy of fusion ΔH of crystallized and annealed crystal aggregates have been determined by differential calorimetry. The equilibrium melting temperature T_m also depends greatly upon the isotactic pentad concentration. For 100% concentration the extrapolated value of T_m is 181°C. T_m decreases about 1°C per 1% decrease in the isotactic pentad population. The observed equilibrium melting and dissolution temperature depression does not follow the predictions of the Flory equation for copolymer crystallization. In fact, the effect of decreasing probability of isotactic sequence propagation is to depress T_d and T_m much more rapidly. The apparent enthalpy of fusion of both solution-grown crystals and melt-recrystallized samples decreases with an increase in the number of configurational impurities along the chain. For the most stereoregular fraction the average length of isotactic stereoblocks has been compared with the lamellar thickness of solution-grown lath-shaped single crystals.     

Codimension two submanifolds with 2-nonnegative curvature operator

In this paper we obtain a classification of compact n-submanifolds of the Euclidean space with 2-nonnegative curvature operator. Received: 4 April 2007     

On the numerical evaluation of Cauchy transforms

In this paper we consider simple methods for the reconstruction of the Cauchy transform over a curve when an explicit parametrization of the latter is not provided. The methods consist of replacing the parametrization of the curve by piecewise polynomial interpolation followed by the use of Newton-Cotes type formulae for the integration. The order of convergence of the resulting quadrature is higher than would be expected on the basis of considerations involving just interpolation theory, provided that the Cauchy transform is evaluated at known nodes on the curve. These results allow the calculation of the Cauchy transform at other points with the same accuracy if this scheme is followed by an interpolatory formula of sufficiently high accuracy.     

Well‐posedness,positivity, and time asymptotics properties for a reaction–diffusion model of plankton communities,involving a rational nonlinearity with singularity

In this work, we consider a reaction–diffusion system, modeling the interaction between nutrients, phytoplankton, and zooplankton. Using a semigroup approach in , we prove global existence, uniqueness, and positivity of the solutions. The nonlinearity is handled by providing estimates in , allowing to deal with most of the functional responses that describe predator/prey interactions (Holling I, II, III, Ivlev) in ecology. The paper finally exhibits some time asymptotic properties of the solutions.     

A Leslie-Gower Holling-type II ecoepidemic model

The modified Leslie-Gower and Holling-type II predator-prey model is generalized in the context of ecoepidemiology, with disease spreading only among the prey species. A new feature is introduced, the intraspecific competition of infected prey. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibrium is shown.     

Perspective in polymer science and technology

Scientific, and technological developments of polymers will tend to increase their attitude to substitute different materials (ceramics, metals, glasses. wood). Substitution and penetration process of polymers will follow different routes mostly having as objective the realization of systems specific functions suitable then to be more and more market oriented. The possibilities to realize these goals will require strong efforts of basic and applied research.     

Purification and stability of glutaryl-7-ACA acylase from pseudomonas sp.

The enzyme glutaryl-7-ACA acylase fromPseudomonas sp. NCIMB 40474, produced by a recombinantEscherichia coli host, was purified to homogeneity. The enzyme is a tetramer composed of two couples of asymmetric dimers, each of them constituted of two subunits of mol wt 18 and 52 kDa, respectively. It was found that glutaric acid, one of the products of the substrate hydrolysis, is an effective acylase inhibitor. Between pH 6.0 and pH 10.0, the enzymatic activity is almost constant, but below pH 6.0 it progressively declines. The acylase activity decreased sharply as a function of guanidine HC1 concentration. The loss is significant even at concentrations of denaturant lower than those causing unfolding, as suggested by UV spectroscopy and fluorescence emission studies. In these conditions (low denaturant concentration and low pH) the inactivation of the enzyme is caused by the tetramer dissociation into dimers. The lability of the quaternary structure of the enzyme is a key feature that must be taken into account for the improvement of the catalyst stability.