Delta Function for an Affine Subspace

The Kubo–Yokoi and Donsker delta functions are well known generalized functions in infinite dimensional distribution theory. In this paper we develop the delta function for an affine subspace and show that it is a generalization of the Kubo–Yokoi and Donsker delta functions. The Wiener– Itˆo expansion of the delta function for an affine subspace is also given

Extending the Support Theorem to Infinite Dimensions

The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.Comment: 22 page

Extension of Shor\u27s period-finding algorithm to infinite dimensional Hilbert spaces

Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, including the main relevant results. Inspired by a generalized function in the algorithm, we develop a new distribution, the delta function for a subspace of an infinite dimensional Hilbert space. We then use this distribution to rigorously prove one of the main identities needed for the algorithm. Finally we provide a rigorous formulation of the hidden subspace algorithm in infinite dimensions

Ultra deep SU-8 manufacturing and characterization for MEMS applications

The Micro Systems Engineering Team (mSET) at Louisiana State University (LSU) utilizes microfabrication for a number of heat and mass transfer devices. These include cross flow heat exchangers, mechanical seals with integrated micro heat exchangers, catalytic converters, and micro reactors. In all of these applications, micro honeycomb arrays provide increased surface area per unit volume which significantly enhances heat and mass transfer. In the past, it was only possible to fabricate SU-8 structures approximately 1.5 mm tall. Furthermore, qualitatively, it is much more difficult to fabricate close packed feature arrays than sparse arrays. For many of the previously mentioned applications, it is important to both increase the height of the features and to produce considerably more closely packed features. The goal of this research is to develop a greatly enhanced capability to lithographically define SU-8 features with heights that are on the order of 2-3 mm, with characteristic widths that are on the order of a few hundred micrometers, and, equally important, close packed. The major discovery that was ascertained in an attempt to achieve this goal was the diffusion of acid into unexposed regions prior to and during post bake is THE important physical parameter that governs all SU-8 processing steps. From this central idea, all SU-8 processing steps were altered to limit diffusion. The main process modification that allowed for this accomplishment was the new casting procedure that permitted for low uniform solvent content. The resulting new processing procedure led to SU-8 samples with heights between 2-4.5 mm and with a high density of SU-8 structures

A History Of The Louisiana Shrimp Industry, 1867-1961

In the latter half of the nineteenth century the Louisiana shrimp industry began in Barataria Bay when canning and drying operations raised shrimping from a local business venture to a small-scale localized industry. The purpose of this study is to trace the economic development of the industry from 1867 through its various stages of growth to the present. Publications of federal and state conservation agencies and personal interviews provided the principal sources of information for this study. Eighty-six years after its founding the shrimp industry became the most import United States fishery. This was due largely to technological improvements in the production of shrimp and the corresponding growth of initial processed shrimp forms to utilize the increased catch in expanding markets. Shortly after the trawl replaced the seine and led to larger catches, the marketing of shrimp in headless form created new outlets. When offshore discoveries of shrimp expanded production, frozen shrimp became an important marketing form to supply the growing demand throughout the United States. The key to the industry’s future seems to be expansion into new fishing grounds, revitalization of the grounds which have produced sparingly in recent years, and curbing growing imports

Teaching Group Counseling in an Online Intensive Format

Abstract Online education continues to grow in popularity each year. Although more counselor education programs offer online coursework, few articles discuss teaching strategies for online group work courses. We proposed, developed, and piloted a model for teaching group work in an online intensive format. In this article, we discuss the structure, components, and rationale of this model as well as the perceived benefits and challenges. We also provide recommendations for those who want to teach group work online

A Limiting Process to Invert the Gauss-Radon Transform

In this work we extend the finite dimensional Radon transform [23] to the Gaussian measure. We develop an inversion formula for this GaussRadon transform by way of Fourier inversion formula. We then proceed to extend these results to the infinite dimensional setting