College of Computer, Mathematical & Natural Sciences
http://hdl.handle.net/1903/12
2022-01-18T15:33:26ZUSING COMMERCIAL LIST INFORMATION IN SCREENING ELIGIBLE HOUSING UNITS
http://hdl.handle.net/1903/28296
USING COMMERCIAL LIST INFORMATION IN SCREENING ELIGIBLE HOUSING UNITS
Maze, Alena
When using commercial address lists to sample households, investigators spend considerable time and money on screening households for eligibility as well as locating certain subpopulations (to achieve target sample sizes). Utilizing the demographic information on these lists to target eligible persons and subgroups has the potential to lower costs and field workers workload. Unfortunately, the information attached to the lists is error prone. We propose to evaluate the use of demographic information available on commercial lists in multistage household sampling. Specifically, this research will study how to efficiently design a three-stage sample that involves screening of housing units to determine eligibility. This research will also examine more complex estimators than have been previously studied. The goals of this study are to (1) estimate the accuracy rates in which commercial lists can correctly identify households with certain characteristics (e.g., Hispanics, Non-Hispanic Blacks, etc.); (2) Derive a theoretical variance formula, including variance components, for estimated totals; (3) Estimate variance components and evaluate alternative variance component estimators (design-based ANOVA, anticipated variance (model + design)); (4) Determine how to allocate two and three stage samples supplemented with commercial lists accounting for inaccuracy of listings, costs at each stage of sampling, target sample sizes and coefficient of variations (CVs), stratification of SSUs, and stratification of HU’s by MSG characteristics (e.g., Race/Ethnicity, ages of persons in HU, etc.).
This research seeks to better understand the quality of demographic data attached to commercial lists and to use this information to increase sampling efficiency in the HRS by recovering more information for lower costs. This research potentially creates an improved sample design for HRS and similar surveys that is less costly and equally or more statistically efficient than the current design. In particular, the proposed design will help sample designers reduce the amount of housing unit screening needed to identify target subpopulations (e.g., Blacks, Hispanics, teenagers, and females). Furthermore, the results of this research will extend to other multistage household surveys that use commercial lists for sampling.
2021-01-01T00:00:00ZSubmaximal Function Algebras
http://hdl.handle.net/1903/28289
Submaximal Function Algebras
Van Meter, Garrett Oliver II
Let X be a compact Hausdorff space. A function
algebra on X is a complex Banach subalgebra of C(X) which
separates the points of X and contains the constants. Moreover,
a function algebra on X is maximal if it is contained
properly in no proper subalgebra of C(X). We mention that
maximal function algebras are large enough to have a goodly
amount of structure. In order that we be able to state the
ideas and results simply let us assume that for each algebra
A the underlying space X is so adjusted that A contains
no non-trivial ideals of C(X).
Generally if A is a maximal function algebra on X,
then the topological dimension of X is at most one. The
idea of this thesis is to extend the notion of maximal
function algebra so that on the one hand features of maximal
algebras would be retained, while on the other hand the
topological dimension of the underlying space could be forced
to be arbitrarily large. Thus our introduction of the notion
of submaximal function algebra.
We prove that all maximal algebras are submaximal. A
submaximal, non-maximal algebra is A(Tn), the completion of
the polynomials in n-complex variables on the unit n-torus in Cn. However, if A is submaximal on X, then each proper function algebra between A and C(X) is contained in a proper maximal function algebra on X. Moreover, we show by example that the converse to this last statement is false. If A is a submaximal function algebra on X, then every point in X has a compact neighborhood in X such that the algebra of restrictions of functions in A is dense in the continuous functions on the neighborhood. This is the (natural) analogue of the "pervasive" property of maximal function algebras.
It turns out that maximal function algebras are antisymmetric, which means that they contain no non-constant real-valued functions. This is not true in general for submaximal function algebras. However, if we render the antisymmetric property in the following way, then it holds true for submaximal algebras: if the real-valued continuous functions f1,...,fn on X along with A together generate a dense subalgebra of C(X), then the continuous real-valued functions h1,...,hn on X and A together generate a dense subalgebra of C(X), provided only that each hj is sufficiently close to fj. In addition, we show that if A is submaximal on X, then there are always exist finitely many real-valued continuous functions on X which together with A generate a dense subalgebra of C(X). Finally we discuss tensor products of submaximal algebras. In particular, we prove that under certain restrictions, the tensor product of two submaximal algebras is submaximal.
1971-01-01T00:00:00ZThe Photochemistry of Amides and Phthalimides
http://hdl.handle.net/1903/28284
The Photochemistry of Amides and Phthalimides
Bowen, Michael William
N-Alkyl amides undergo photodecomposition much slower
than their ketone, ester, and aldehyde analogs . The Norrish
Type II process in amides is also less important than in
these other classes of compounds due to electronic and geometric
effects. Type II products account for less than 10%
of the decomposed amides in all cases and usually less than
5%.
A 2% solution of amide in dioxane, when irradiated
through quartz with light >200 nm, did not decompose in the
Type II fashion to yield N-alkyl acetamides, alkenes, and
unsubstituted amides. The preferred reaction mode was the
Norrish Type I process where the O=C+N bond or the O=C+C
bond was cleaved to yield either an acyl radical and amine
radical or an acyl radical and alkyl radical. These photochemically
unstable radicals, once produced, rapidly underwent
secondary reactions to yield smaller molecules. These
molecules were detected, underwent further reactions (polymerization;
photoreduction), or interacted with the solvent .
The dimers of dioxane and cyclohexane, created via hydrogen
abstraction, were the main products of amide photodecomposition in these solvents. Small aldehydes and alkenes
produced as intermediates, underwent inefficient photoreductions
with solvent to afford alkyl dioxanes and cyclohexanes
and the two diastereomers of ( 2-p-dioxyl ) ethanol
as other major products. The alcohols were also produced
by photoreduction of acetaldehyde and hexanal as well as
by direct photodecomposition of dioxane .
Tertiary amides reacted faster than secondary amides.
The Type I reaction was accelerated by electronic (inductive)
factors. The Type II reaction was also more efficient due
to geometric and electronic factors. The Type I amine product, dihexylamine, was observed as an intermediate in the
photodecomposition of N, N-dihexylhexanoamide .
Unsymmetrical anilide imides photodecomposed in dioxane
to yield a wide variety of products. The Photo-Fries decomposition
mode was most favored where acyl groups migrated to
positions ortho and para to the amine substituent. For example, N-acetyl-butyranilide decomposed to yield o- and p-acetoaniline, o - and p-butyraniline , o- and p-acetobutyranilide,
and o- and p-butyracetanilide. Very little Type II
decomposition was observed, that is, N-acetyl-butyranilide
yielding N, N -diacetylaniline or o- and p-acetoacetanilide.
N-Alkylphthalimides were the sole group of amides or
imides reported in the literature to undergo efficient Y-hydrogen
abstraction. These compounds underwent initial
Y-hydrogen abstraction to yield a 1,4-biradical followed by
ring closure to form an azacyclobutanol intermediate. The intermediate then underwent retrotransannular ring opening
to yield various 3,4-benzo-6,7-dihydro(1H)azepine-2,5-diones.
Dihydrophthalimide alkenes were minor products in acetonitrile
which arose after the initial y-hydrogen abstraction
via subsequent δ-hydrogen transfer.
Quantum yield determination as well as mechanistic
investigation was conducted . The quantum yields varied
from 0.023 to 0.003. Photolysis of an optically active
phthalimide with an asymmetric Y-position to yield starting
material of the same activity proved that the initial
hydrogen abstraction was irreversible. A Type I cleavage
to yield phthalic anhydride on treatment with silica gel
and heat was important when they Y-position was tertiary.
A quenching study of these N-alkylphthalimides with
piperylene showed acceleration of starting material disappearance
but decrease in product formation. An additional
reaction process was interfering with the azepinedione formation.
Liquid chromatography showed formation of several
highly alkylated products which could not be isolated in
pure form.
N-Methylphthalimide, which could not ring expand, was
irradiated with various alkenes to produce analogous N-methylazepinediones. The mechanism involved a 2 + 2 cyclo-addition
of the double bond to the C-N bond to yield a dipolar
azacyclobutanc intermediate.
The intermediate with
a retrotransannular ring opening yielded the observed 3, 4-
benzo-6,7-dihydro-1-methylazepine-2,5-diones. These reactions prove that the C-N bond in phthalimide is of a substantial double bond character.
1977-01-01T00:00:00ZOn Numerical Analysis in Residue Number Systems
http://hdl.handle.net/1903/28283
On Numerical Analysis in Residue Number Systems
Lindamood, George Edward
Recent attempts to utilize residue number systems
in digital computers have raised numerous questions about
adapting the techniques of numerical analysis to residue
number systems. Among these questions are the fundamental
problems of how to compare the magnitudes of two numbers, how
to detect additive and multiplicative overflow, and how to
divide in residue number systems. These three problems are
treated in separate chapters of this thesis and methods are
developed therein whereby magnitude comparison, overflow
detection, and division can be performed in residue number
systems. In an additional chapter, the division method is
extended to provide an algorithm for the direct approximation
of square roots in residue number systems. Numerous
examples are provided illustrating the nature of the problems considered and showing the use of the solutions presented in
practical computations. In a final chapter are presented the
results of extensive trial calculations for which a conventional
digital computer was programmed to simulate the use
of the division and square root algorithms in approximating
quotients and square roots in residue number systems. These
results indicate that, in practice, these division and
square root algorithms usually converge to the quotient or
square root somewhat faster than is suggested by the theory.
1964-01-01T00:00:00Z