A hierarchical method for obtaining eigenvalue enclosures

We introduce a new method of obtaining guaranteed enclosures of the eigenvalues of a variety of self-adjoint differential and difference operators with discrete spectrum. The method is based upon subdividing the region into a number of simpler regions for which eigenvalue enclosures are already available.

     

Brown-Booth-Tillotson theory for classes of exponentiable spaces

Brown, Booth and Tillotson introduced the C-product, or the BBT C-product, for any class C of topological spaces. It is proved that any topological space is exponentiable with respect to the BBT C-product if and only if C is a subclass of the class of exponentiable spaces. The topology of the function space is induced by a canonical manner making use of the exponential topology for the spaces in C. It is not the C-open topology in general. The function space defined by this method enjoys good properties for algebraic topology. A necessary and sufficient condition on the class C is obtained for the exponential function to be a homeomorphism with the BBT C-product.     

Noetherian Maxwell spaces and Bessel-Hagen factors

We obtain conditions for some classes of Maxwell spaces to be Noetherian. We also find Bessel-Hagen factors for some subgroups of the Poincaré group.     

A method for obtaining approximate solutions for two-dimensional estuaries

An approximate model for the steady flow in a slightly stratified two- dimensional estuary is considered. The method consists of assuming an approximate form of the salinity which satisfies the boundary conditions and which contains two unknown constants. The stream function is calculated from the equation of motion. Two nonlinear equations for the two constants are obtained by applying Galerkin's method to the salt continuity equation and by insisting that there is zero salt flux across some vertical section.     

Canonical representatives in strict isomorphism classes of formal groups

The aim of the present paper is to explicitly construct canonical representatives in every strict isomorphism class of commutative formal groups over an arbitrary torsion-free ring. The case of an Z(p) -algebra is treated separately. We prove that, under natural conditions on a subring, the canonical representatives of formal groups over the subring agree with the representatives for the ring. Necessary and sufficient conditions for a mapping induced on strict isomorphism classes of formal groups by a homomorphism of torsion-free rings to be injective and surjective are established.     

A method for obtaining iterative formulas of order three

An improved method for the order of convergence of iterative formulas of order two is given. Using this method, new third-order modifications of Newton’s method are derived. A comparison with other methods is given.     

A finite element method for approximating the time-harmonic Maxwell equations

Summary In this paper we study the use of Nédélec's curl conforming finite elements to approximate the time-harmonic Maxwell equations on a bounded domain. The analysis is complicated by the fact that the bilinear form is not coercive, and the principle part has a very large null-space. This difficulty is circumvented by using a discrete Helmholtz decomposition of the error vector. Numerical results are presented that compare two different linear elements.Research supported in part by grants from AFOSR and NSF     

Some new classes of Banach-Mackey spaces

Some weakenings of property (K) of Antosik for locally convex spaces are introduced: local property (K) and, for spaces with Schauder-type decompositions, two variants of property (K) defined in terms of block- and tail-sequences. It is shown that if a space enjoys any of these new properties, then it is Banach-Mackey. An application to the barrelledness of the spaces of Pettis integrable functions is given, and examples are provided to distinguish between the various K-type properties.