Mathematics Commons^™

An Embedding Of Schwartz Distributions In The Algebra Of Asymptotic Functions, Michael Oberguggenberger, Todor D. Todorov

Mathematics

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper "asymptotic function," similar to but different from J. F Colombeau's algebras of new generalized functions.

A Tour Of Mistakes, Paul H. Edelman

Vanderbilt Law School Faculty Publications

In these pages, Steven Lubet recently reviewed A Tour of the Calculus, by David Berlinski. Inspired by both the beauty of calculus and Berlinski's description of it, Lubet waxes poetic on the many parallels between the law and calculus. It is completely understandable--even admirable that one might be led to ruminations on the relationship between calculus and one's own discipline. There is little doubt that the subject of calculus stands as one of the great intellectual feats of Western thought. It has had profound implications for physics, engineering, economics and many other disciplines-so why not law? Alas, these philosophical musings …

A Comparison Of Advanced Time Series Models For Environmental Dependent Stock Recruitment Of The Western Rock Lobster, Saarah A. Farag

Theses: Doctorates and Masters

Time series models have been applied in many areas including economics, stuck recruitment and the environment. Most environmental time series involve highly correlated dependent variables, which makes it difficult to apply conventional regression analysis, Traditionally, regression analysis has been applied to the environmental dependent stock and recruitment relationships for crustacean species in Western Australian fisheries. Alternative models, such as transfer function models and state space models have the potential to provide unproved forecasts for these types of data sets. This dissertation will explore the application of regression models, transfer function models, and state space models to modelling the puerulus stage …

Isospectral Deformations Of Closed Riemannian Manifolds With Different Scalar Curvature, Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb

Dartmouth Scholarship

No abstract provided.

Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups, Iem H. Heng

Mathematics & Statistics Theses & Dissertations

Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon this communication technology.

The concept of Hadamard matrices with elements drawn from an Abelian group is a natural generalization of the concept. For the case in which the dimension of the matrix is q and the group consists of the p-th roots of unity, these generalized Hadamard matrices are called “Butson Hadamard Matrices BH(p, q)”, …

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.