Mathematics Commons^™

Flow And Pressure Distributions In Vascular Networks Consisting Of Distensible Vessels, Gary S. Krenz, Christopher A. Dawson

Mathematics, Statistics and Computer Science Faculty Research and Publications

We examine the influence of vessel distensibility on the fraction of the total network flow passing through each vessel of a model vascular network. An exact computational methodology is developed yielding an analytic proof. For a class of structurally heterogeneous asymmetric vascular networks, if all the individual vessels share a common distensibility relation when the total network flow is changed, this methodology proves that each vessel will continue to receive the same fraction of the total network flow. This constant flow partitioning occurs despite a redistribution of pressures, which may result in a decrease in the diameter of one and …

Stage Based Interventions For Low Fat Diet With Middle School Students, Marilyn Frenn, Shelly Malin, Naveen K. Bansal

College of Nursing Faculty Research and Publications

Preventing obesity and cardiovascular disease at early ages is important; however, few effective interventions for early adolescents have been reported. In this study, low-income, culturally diverse students from an urban middle school (n = 60) received four classroom interventions with the use of a combined Health Promotion/Transtheoretical Model to control fat in diet and increase physical activity. A control group (n = 57) received the usual classroom education. Pretest percentage fat in diet was regressed on demographics, access to low-fat foods, perceived self-efficacy, benefits/barriers, and stage of change with results as proposed by the model [F(9,64) …

Modeling Nonintersective Adjectives Using Operator Logics, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Our topic is one that involves the interface between natural language and mathematical logic. First-order predicate language/logic does a good job approximating many parts of (English) speech, i.e., nouns, verbs and prepositions, but fails decidedly when it comes to, say, adjectives. In particular, it cannot account for the quite different ways in which the adjectives green and big modify a noun such as chair. In the former case, we can easily view a world in which the class of green chairs is the intersection of the class of green things with the class of chair-things. By contrast, the way …

L-Arginine Uptake And Metabolism Following In Vivo Silica Exposure In Rat Lungs, Leif D. Nelin, Gary S. Krenz, Louis G. Chicoine, Christopher A. Dawson, Ralph M. Schapira

Mathematics, Statistics and Computer Science Faculty Research and Publications

Pulmonary inflammation increases nitric oxide (NO) production via inducible nitric oxide synthase (iNOS). This study was performed to determine some of the factors that affect the availability of the NOS substrate, L-arginine (L-arg), in the intact lung subjected to silica-induced inflammation. Nitrate production, as an index of NO production, was significantly greater in silica-exposed lungs (53.5 ± 12.1 nmol/90 min) compared with controls (22.5 ±5.1 nmol/90 min, P < 0.05). This was accompanied by greater (P< 0.0001) 90-min [³H]L-arg uptake (62 ± 3% control, 82 ± 1% silica), a significantly (P < 0.005) increased permeability-surface area product for L-arg(0.28 ± 0.05 ml/min control, 0.63 ± 0.07 ml/min silica), and asignificantly (P < 0.001) increased urea production (1.16 ± 0.08µmol/90 min control, 1.77 ± 0.06 µmol/90 min silica). There was no difference in eNOS protein between groups and eNOS mRNA was not detectable in either group, whereas silica exposure resulted in the appearance of both iNOS protein and mRNA. Silica exposure increased CAT-1 and CAT-2 mRNA ~ 8-fold compared with controls. We conclude that the increase in NO production in silica-exposed lungs was associated with increased L-arg uptake from the vasculature, presumably resulting from increased CAT-1 and CAT-2, and by increased L-arg metabolism via arginase.

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …

Branching Exponent Heterogeneity And Wall Shear Stress Distribution In Vascular Trees, Kelly Lynn Karau, Gary S. Krenz, Christopher A. Dawson

Mathematics, Statistics and Computer Science Faculty Research and Publications

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D ₁)^z = (D ₂)^z + (D ₃)^z; D ₁ is the parent vessel diameter and D ₂ and D ₃ are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance …

Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.

A Hierarchy Of Maps Between Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev_≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev_≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …

Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato

Mathematics, Statistics and Computer Science Faculty Research and Publications

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5<HS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2¹⁰. A modified method is proposed to correct for …

Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan

Mathematics, Statistics and Computer Science Faculty Research and Publications

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …

Topologies Invariant Under A Group Action, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We study links between faithful group actions on a set and topologies on that set. In one direction, a group action has its invariant topologies (so we may regard members of the action to be homeomorphisms relative to those topologies); in the other direction, a topology has its preserving group actions (i.e., the subgroups of the homeomorphism group of the topology). This two-way passage allows us to discuss topological features of group actions as well as symmetry features of topologies.

Pseudobases In Direct Powers Of An Algebra, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A subset P of an abstract algebra A is a pseudobasis if every function from P into A extends uniquely to an endomorphism on A. A is called K-free has a pseudobasis of cardinality K; A is minimally free if A has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the 1-free groups are always abelian, and are precisely the additive groups of E-rings.) Our interest here is in the existence of pseudobases in direct powers A^I of an algebra A. On the positive side, if A is a rigid …

Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An error has been found in the cited paper; namely, Theorem 3.1 is false.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Taxonomies Of Model-Theoretically Defined Topological Properties, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y _{E …}

Reduced Coproducts Of Compact Hausdorff Spaces, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to …

Expressive Power In First Order Topology, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of …

Coarse Topologies In Nonstandard Extensions Via Separative Ultrafilters, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Topological Extensions And Subspaces Of Ηα-Sets, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The η_x-sets of Hausdorff have large compactifications (of cardinality ≽ exp(α); and of cardinality ≽ exp(exp(2^<α)) in the Stone-Čech case). If Q_α denotes the unique (when it exists) η_α -set of cardinality α, then Q_α can be decomposed (= partitioned) into homeomorphs of any prescribed nonempty subspace; moreover the subspaces of Q_α can be characterized as those which arc regular T₁, of cardinality and weight ≼ α, whose topologies are closed under < α intersections.

The Total Negation Of A Topological Property, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

The Fresnel Integrals, Jean Therese Powers

Master's Essays (1922 - )

In the study of complex analysis, and in particular in the area of complex integration, there arise a series of integrals whose evaluation require more than an thing else, a great deal of mathematical ingenuity. Among these classical integrals are two known as the Fresnel Integrals and it is the purpose of this paper to discuss one method of evaluation of this pair of functions.

Embedding A Ring Into A Ring With Identity, Richard F. Maruszewski Jr.

Master's Essays (1922 - )

The presentation of this paper is divided into three sections. The first or these sections is composed of proofs of different ways of embedding rings into rings with identity The material in this section, which constitutes pages 1 - 10 , is quite different from the material in the last two sections. Because of this difference I followed a different method of presentation in the first section. The method used is to present a lecture outline, that is to produce the material just as I would in class. The last two sections ·are presented in a more narrative fashion. In …

Equivalence Classes Of Fundamental Sequences Of Rational Numbers, M. Marlene Greatens

Master's Essays (1922 - )

No abstract provided.

The Uniform Right Ideals Of A Ring Of Matrices, Gerald Joseph Janusz

Bachelors’ Theses

The concept of uniform right ideals plays an important part in the structure tbeory of prime rings and semi-prime rings as developed by Goldie in [1] and (=[2]. Very few examples of uniform right ideals appear in the literature, however. In section one, we obtain the form of these right ideals in a matrix ring, I_n, where I is a right Ore domain with identity. The existence of the identity involves some loss of generality, but greatly simplifies the approach used in this paper.

The Tangent Surface To A Circular Helix, David Alan Rux

Bachelors’ Theses

The circular helix is a space curve which may be defined as the curve generated by a point on an element of a circular cylinder as the point moves along the element and the element moves around the cylinder, both at a constant rate. The circular helix may also be defined as the curve, on the surface of a circular cylinder, which cuts each element of the cylinder under the same angle.

A Test Of Richardson's Equation, Gerald J. Pyne

Bachelors’ Theses

The purpose of this work is the verification of the above relationship between saturated emission current and temperature, and especially, the evaluation of the current-temperature relating constants, A and theta.

Additional Equations For The Wigner_Seitz Model Of Solids, Alex Sharley Keene

Bachelors’ Theses

This report consists of an extension of the Wigner-Seitz equations to particular cases and boundary conditions. These equations are tools whereby energy bands and wave functions for a face centered lattice can be determined.

Certain Loci Associated With A One Parameter Family Of Conics In Three Dimensions, Raymond Francis Lausmann

Bachelors’ Theses

The conic sections and also the types of traces that might be obtained by the intersection of a plane with the ten real quadric surfaces have always been a source of great interest to me.

Lack of time has always been an obstacle to satisfying this curiosity. However, the opportunity for taking time was presented when the Department granted permission to write this thesis.

Families Of Circles, Mary Olive Norman

Bachelors’ Theses

No abstract provided.

A Problem In Reflection Of Light, M. Imogene Palen

Bachelors’ Theses

A circular mirror has a. ray of light from a source at one point on the circumference which is reflected twice. The first ray will by extension, if necessary, intersect the second reflected ray. Increasing the angle of reflection by revolving the source of light so that the first ray falls on all points of the circumference gives a locus, to the successive points made by the intersection of the first ray and the second reflected ray. The problem of this thesis is to picture the locus and find its equation.