The Artin-Stafford gap theorem

Let be an algebraically closed field, and let be a finitely graded -algebra which is a domain. We show that cannot have Gelfand-Kirillov dimension strictly between and .

     

On a Pump

We examine the Navier–Stokes equations in a two space dimensional time dependent domain. The system is considered with nonhomogeneous slip boundary conditions. The main result shows that under a certain geometrical constraint on deformations of the domain, it is possible to prove existence of solutions globally in time for arbitrary flows across the boundary with a new time independent bound on the vorticity. The geometrical restriction does not imply simply connectedness of the domain. Our model may be treated as a simple model of a pump.Mathematics Subject Classifications (2000) 35Q30, 75D03, 76D05.     

Clement-type interpolation on spherical domains--interpolation error estimates and application to a posteriori error estimation

In this paper, a mixed boundary value problem for the Laplace–Beltramioperator is considered for spherical domains in R³, i.e. fordomains on the unit sphere. These domains are parametrized byspherical coordinates (, ). A suitable finite element spaceis introduced. It corresponds to an isotropic triangulationof the underlying domain on the unit sphere. Error estimatesare proven for a Clément-type interpolation operator,where appropriate weighted norms are used. The estimates areapplied to the derivation of a reliable and efficient residualerror estimator for the Laplace–Beltrami operator.     

Interpolating hereditarily indecomposable Banach spaces

The following dichotomy is proved.

Every Banach space either contains a subspace isomorphic to , or it has an infinite-dimensional closed subspace which is a quotient of a Hereditarily Indecomposable (H.I.) separable Banach space.

In the particular case of , it is shown that the space itself is a quotient of a H.I. space. The factorization of certain classes of operators, acting between Banach spaces, through H.I. spaces is also investigated. Among others it is shown that the identity operator admits a factorization through a H.I. space. The same result holds for every strictly singular operator .

Interpolation methods and the geometric concept of thin convex sets together with the techniques concerning the construction of Hereditarily Indecomposable spaces are used to obtain the above mentioned results.     

A characterization of Möbius transformations

Let be an integer and let be a domain of . Let be an injective mapping which takes hyperspheres whose interior is contained in to hyperspheres in . Then is the restriction of a Möbius transformation.

     

Thermal stability of bovine serum albumin DSC study

A calorimetric study of thermal denaturation of bovine serum albumin in aqueous solutions has shown essential differences in stability of fatty acid containing and defatted albumin. The first one shows a single endotherm peak in DSC curve near 69°C with enthalpy change about 1000 kJ mol^-1. Defated albumin melts in two different temperature ranges: near 56 and 69°C with enthalpy changes about 300 and 200 kJ mol^-1 respectively. Deconvolution analysis shows that the single endotherm is well approximated as the sum of three independent two-state transitions. Two transitions of bimodal DSC curve for defatted albumin are not of a two-state type. This molecule melts probably as two structurally independent parts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Derivatives of regularly varying functions in Rd and domains of attraction of stable distributions

In R² the integral of a regularly varying (RV) function f is regularly varying only if f is monotone. Generalization to R² of the one-dimensional result on regular variation of the derivative of an RV-function however is straightforward. Applications are given to limit theory for partial sums of i.i.d. positive random vectors in R²₊.     

On the effect of an elastic shear stress upon the magnetization of ferromagnetic sheets

When an elastic shear stress and a cyclical magnetic field, parallel to each other, are applied in the plane of a ferromagnetic sheet, magnetization changes perpendicular to the field are induced in the sample. “Transverse” hysteresis loops, i.e. transverse magnetization plotted as a function of the longitudinal field, were studied in various materials. The characteristic shape of the loop and the differences in sign and magnitude of the “transverse” magnetization have been qualitatively explained in terms of magnetic domain theory. Work supported by G.N.S.M. (CNR).     

Projection Theorems for Harmonic Measure in NTA Domains

Suppose D is an NTA domain, E D is any closed set, and P ^x ₀(E) is the projection with respect to a point x ₀D of the set E onto the boundary of D. The projection P ^x ₀ satisfies certain geometric properties so that it is a generalization of the notion of radial projection with respect to a point x ₀ onto a boundary of a domain. It is shown that the harmonic measure of E with respect to the domain DE evaluated at the point x ₀ is bounded below by a constant times the harmonic measure of the set P ^x ₀(E) with respect to the domain D evaluated at the point x ₀. The constant is independent of the set E but it may depend upon x ₀.