Physical Sciences and Mathematics Commons^™

(A Note On)(2) The Shape Of The Erythrocyte, J. A. Adam

Mathematics & Statistics Faculty Publications

A note on the shape of the red blood cell is revisited, utilizing variational calculus to to find an extremum for the surface area of such a cell, using the volume as a constraint. A fairly significant error in the value of the volume is corrected, and the note concludes with a discussion of measures of cell shape (such as the sphericity index) which are more appropriate than the dimensional surface area to volume ratio.

The Adjoint Alternative For Matrix Operators, C. H. Cooke

Mathematics & Statistics Faculty Publications

The following inverse problem is considered: given a matrix B of rank r, does there exist a matrix A such that

B = T(A) = adjoint (A)

where the classical adjoint operation is intended? Conditions are determined on the rank of B which decides whether or not B lies in the range of the matrix adjoint operator.

Steady Incompressible Magnetohydrodynamic Flow Near A Point Of Reattachment, J. M. Dorrepaal, S. Moosavizadeh

Mathematics & Statistics Faculty Publications

The oblique stagnation-point flow of an electrically conducting fluid in the presence of a magnetic field is a highly nonlinear problem whose solution is of interest even in the simplest of geometries. The problem models the flow of a viscous conducting fluid near a point where a separation vortex reattaches itself to a rigid boundary. A similarity solution exists which reduces the problem to a coupled system of four ordinary differential equations which can be integrated numerically. The problem has two independent parameters, the conductivity of the fluid and the strength of the magnetic field. Solutions are tabulated for a …

Uniform Lipschitz Continuity Of Best L(P)-Approximations By Polyhedral Sets, Martina Finzel, Wu Li

Mathematics & Statistics Faculty Publications

In this paper we prove that the metric projection Π_{k, p} onto a polyhedral subset K of ℝⁿ, endowed with the p-norm, is uniformly Lipschitz continuous with respect to p,1 , p , ∞. As a consequence the strict best approximation and the natural best approximation are Lipschitz continuous selections for the metric projections Π_k, _∞ and Π_k,1, respectively. This extends a recent analogous result in Berens et al. [J.Math. Anal. Appl. 213 1997, 183-201] on linear subspaces.

Error Correcting Codes Associated With Complex Hadamard Matrices, I. Heng, C. H. Cooke

Mathematics & Statistics Faculty Publications

For primes p > 2, the generalized Hadamard matrix H(p,pt) can be expressed as H = x^A, where the notation means h_ij = x^aij. It is shown that the row vectors of A represent a p-ary error correcting code. Depending upon the value of t, either linear or nonlinear codes emerge. Code words are equidistant and have minimum Hamming distance d = (p − 1)t. The code can be extended so as to possess N = p²t code words of length pt …

Characterization Of Generalized Haar Spaces, M. Bartelt, W. Li

Mathematics & Statistics Faculty Publications

We say that a subset G of C₀(T, ℝ^k) is rotation-invariant if [Qg: g ∈ G]=G for any k x k orthogonal matrix Q. Let G be a rotation-invariant finite-dimensional subspace of C₀(T, ℝ^k) on a connected, locally compact, metric space T. We prove that G is a generalized Haar subspace if and only if P_G(ƒ) is strongly unique of order 2 whenever P_G(ƒ) is a singleton.