Physical Sciences and Mathematics Commons^™

Computer Simulation And Homogenization In Heating Design Optimization, Daniel K. Balls

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The ability to ensure uniformity of temperature within a given finite physical region is an essential element in the success of many scientific processes, especially those that involve extreme fluctuation in temperature. Such a process is performed in an instrument called the LightTyper developed by Idaho Technology, Inc. of Salt Lake City Utah. This paper details the development and results of a scheme intended to obtain a heating design that ensures a high degree of temperature uniformity within the Idaho Technology instrument. Due to the experiments performed during this project, we were able to answer many questions that concerned finding …

Predicting Mountain Pine Beetle Development With The Extended Von Foerster Model, Jeffrey Tullis Leek

Undergraduate Honors Capstone Projects

The mountain pine beetle (Dendroctonus ponderosae Hopkins) represents a significant threat to ponderosa pine and lodgepole pine stands in the western United States, and has the potential to threaten commercially valuable jack pine in both the United States and Canada. The success of the mountain pine beetle is based on synchronization of developmental events to time cold-hardened life stages for extreme winter temperatures and to facilitate mass attack and overwhelm the defenses of the host. This paper presents a solution methodology for an extended McKendrick - von Foerster model for the development of the mountain pine beetle in varying …

Applications Of List Decoding To Tracing Traitors, Alice Silverberg, Jessica Staddon, Judy L. Walker

Department of Mathematics: Faculty Publications

We apply results from algebraic coding theory to solve problems in cryptography, by using recent results on list decoding of error-correcting codes to efficiently find traitors who collude to create pirates. We produce schemes for which the TA (traceability) traitor tracing algorithm is very fast. We compare the TA and IPP (identifiable parent property) traitor tracing algorithms, and give evidence that when using an algebraic structure, the ability to trace traitors with the IPP algorithm implies the ability to trace with the TA algorithm. We also demonstrate that list decoding techniques can be used to find all possible pirate coalitions. …

Identification Of Optimal Conditions For Dry Drilling (Analytical Approach To Prediction Of The Occurrence Of Bue), Prasad Gali

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Lubrication is used during the drilling of aluminum to counter the formation of a built-up-edge (BUE), among other reasons. The elimination of the use of lubricants in drilling of aluminum is important because of the associated high costs of cleaning and disassembly involved in lubrication. The optimal conditions sought in this work include the elimination of the use of lubricants along with the possible attainment of a high material removal rate, which could help in reduction of cost and increase productivity at the same time. BUE has been found to be almost always present in the process of metal cutting …

Taking The Sting Out Of Wasp Nests: A Dialogue On Modeling In Mathematical Biology, Jennifer C. Klein, Thomas Q. Sibley

Mathematics Faculty Publications

Wasps in hot climates build elongated nests, while in colder areas they tend to be circular. Mathematics cannot explain that, but there are questions about numbers of cells that can be answered.

Bootstrap Unit Root Tests For Heavy-Tailed Observations, Andrejus Parfionovas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We explore the application of the bootstrap unit root test to time series with heavy-tailed errors. The size and power of the tests are estimated for two different autoregressive models (AR(1)) using computer simulated data. Real-data examples are also presented. Two different bootstrap methods and the subsampling approach are compared. Conclusions on the optimal bootstrap parameters, the range of applicability, and the performance of the tests are made.

Discovering Properties Of Complex Numbers By Starting With Known Properties Of Real Numbers, Esther D. Hatch

Honors College

No abstract provided.

An Individual- Based Model For The Toxic Algae Species Pseudo-Nitzschia Multiseries, Maria Siopsis

Doctoral Dissertations

In 1987 an outbreak of a previously unobserved disease occurred in Canada and was traced back to the toxin domoic acid produced by the diatom Pseudo-nitzschia multiseries. Since then, fisheries closures due to domoic acid have occurred worldwide. Pseudo-nitzschia species produce domoic acid under nutrient stress, including low silicon or phosphorus under high nitrogen conditions. However, it is still unclear what conditions cause the dangerously high levels that have sometimes been observed. We present an individual-based algae model detailing the physiology of an algal cell with a focus on nutrient and energy flows to delineate the causes of domoic acid …

The Least Square Values And The Shapley Value For Cooperative Tu Games, Irinel C. Dragan

Mathematics Technical Papers

The Least Square Values (briefly LS-values), represent a family of values for cooperative transferable utility games, introduced by L. Ruiz. F. Valenciano and J.Zarzuelo (1998). For a fixed set of players N, a set of weights [see pdf for notation], and any TU-game v , M.Keane (1968) has defined and solved a quadratic programming problem: minimize the sum of weighted squares of deviations of the excesses from their average, on the preimputation set. He has shown that this problem has a unique solution which depends on the weights and has also given the new computational formula. Further, Ruiz/Valenciano/Zarzuelo have called …

Investigations Of Nonstandard, Mickens-Type, Finite-Difference Schemes For Singular Boundary Value Problems In Cylindrical Or Spherical Coordinates, Ron Buckmire

Ron Buckmire

No abstract provided.

On A Conjecture Of Auslander And Reiten, Craig Huneke, Graham J. Leuschke

Mathematics - All Scholarship

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Extⁱ_Lambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen-Macaulay normal domains containing the rational numbers, and slightly more generally.

Local Rings Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand

Mathematics - All Scholarship

Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent …

Hypersurfaces Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand

Mathematics - All Scholarship

Let R = k[[x₀, . . . , x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x₀, . . . , x_d]]. We investigate the question of which rings of this form have bounded Cohen–Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen–Macaulaymodules. As with finite Cohen–Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen–Macaulay type if and only if R ∼= k …

Local Spectra Of Operator Weighted Shifts, Abdellatif Bourhim

Mathematics - All Scholarship

In this paper, we study the local spectral properties of unilateral operator weighted shifts.

Subdifferential And Superdifferential Optimality Conditions In Nonsmooth Minimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called subdifferential and superdifferential optimality conditions. The former ones involve basic/limiting subgradients of cost functions, while the latter conditions are expressed via Frechet superdifferentials provided that they are not empty. All the superdifferential and major subdifferential optimality conditions obtained in the paper are new even in finite dimensions. We give applications of general optimality conditions to mathematical programs with equilibrium constraints.

Paths Of Length Four, Béla Bollobás, Amites Sarkar

Mathematics Faculty Publications

For each sufficiently large m, we determine the unique graph of size m with the maximum number of paths of length four. If m is even, this is the complete bipartite graph K(m/2,2).

Difference Equations From Discretization Of A Continuous Epidemic Model With Immigration Of Infectives, Sophia Jang, Saber Elaydi

Mathematics Faculty Research

A continuous-time epidemic model with immigration of infectives is introduced. Systems of difference equations obtained from the continuous-time model by using nonstandard discretization technique are presented. Comparisons between the continuous-time model and its discrete counter-part are made.

The Symbolic Dynamics Of Multidimensional Tiling Systems, E. M. Coven, Aimee S.A. Johnson, N. Jonoska, K. Madden

Mathematics & Statistics Faculty Works

We prove a multidimensional version of the theorem that every shift of finite type has a power that can be realized as the same power of a tiling system. We also show that the set of entropies of tiling systems equals the set of entropies of shifts of finite type.

Cause-Effect Relationships In Analytical Surveys: An Illustration Of Statistical Issues, Gary L. Gadbury, Hans T. Schreuder

Mathematics and Statistics Faculty Research & Creative Works

Establishing cause-effect is critical in the field of natural resources where one may want to know the impact of management practices, wildfires, drought, etc. on water quality and quantity, wildlife, growth and survival of desirable trees for timber production, etc. Yet, key obstacles exist when trying to establish cause-effect in such contexts. Issues involved with identifying a causal hypothesis, and conditions needed to estimate a causal effect or to establish cause-effect are considered. Ideally one conducts an experiment and follows with a survey, or vice versa. in an experiment, the population of inference may be quite limited and in surveys, …

Multiobjective Optimal Control Problems With Endpoint And State Constraints, Kirsty J. Eisenhart

Dissertations

In this thesis we consider nonsmooth multiobjective optimal control problems in terms of a general preference on [Special characters omitted.]. The optimal control problems considered involve differential inclusion, endpoint constraints and state constraints. No convexity assumption is needed on the differential inclusion. Examples of common preferences are given, and the idea of approximating a preference is introduced. Euler-Lagrange necessary conditions and a form of the maximum principle are developed for closed preferences (and those that can be approximated by closed preferences) in terms of the limiting subdifferential. As a consequence, this is the first result in the literature for lexicographical …

Intensional Logic And Topology, Andrew Scott Buchanan

Student Work

This thesis is concerned with mathematical logic, in particular it is an investigation of a branch of mathematical logic called modal logic. This branch of mathematical logic extends the propositional calculus by adding two unary operators □ and 0 to the standard set of logical operators. This extension of classical logic has many interpretations; traditionally it is said to be the logic of necessity, denoted by the box operator, and possibility, denoted by the diamond operator. The notion of necessity within modal logic is ubiquitous and lends itself to a vast sea of metaphysics. For example, if X is necessarily …

Multi-Symplectic Integrators For Nonlinear Wave Equations, Alvaro Lucas Islas

Mathematics & Statistics Theses & Dissertations

Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of multi-symplectic partial differential equations (PDEs). In particular, we show that multi-symplectic PDEs have an underlying spatio-temporal multi-symplectic structure characterized by a multi-symplectic conservation law MSCL). Then multi-symplectic integrators (MSIs) are numerical schemes that preserve exactly the MSCL. Remarkably, we demonstrate that, although not designed to do so, MSIs preserve very well other associated local conservation laws and global invariants, such as …

Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza

MPP Published Research

In this paper we investigate two problems concerning the theory of power series in 18th-century mathematics: the development of a given function into a power series and the inverse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular on the conception of a series as the result of a formal transformation of a function. After describing the procedures considered acceptable by 18th-century mathematicians, we examine in detail the different strategies—both direct and …

Sandwich Theorem And Calculation Of The Theta Function For Several Graphs, Marcia Ling Riddle

Theses and Dissertations

This paper includes some basic ideas about the computation of a function theta(G), the theta number of a graph G, which is known as the Lovasz number of G. theta(G^c) lies between two hard-to-compute graph numbers omega(G), the size of the largest lique in a graph G, and chi(G), the minimum number of colors need to properly color the vertices of G. Lovasz and Grotschel called this the "Sandwich Theorem". Donald E. Knuth gives four additional definitions of theta, theta_1, theta_2, theta_3, theta_4 and proves that they are all equal.

First I am going to describe the proof of the …

Balanced Configurations Of Lattice Vectors And Gkz-Rational Toric Fourfolds In P^6, Eduardo Cattani, Alicia Dickenstein

Eduardo Cattani

We introduce a notion of balanced configurations of vectors. This is motivated by the study of rational A-hypergeometric functions in the sense of Gelfand, Kapranov and Zelevinsky. We classify balanced configurations of seven plane vectors up to GL(2,R)-equivalence and deduce that the only gkz-rational toric four-folds in P6 are those varieties associated with an essential Cayley configuration. We show that in this case, all rational A-hypergeometric functions may be described in terms of toric residues. This follows from studying a suitable hyperplane arrangement.

On The Local Spectral Properties Of Weighted Shift Operators, Abdellatif Bourhim

Mathematics - All Scholarship

In this paper, we study the local spectral properties for both unilateral and bilateral weighted shift operators.

Radius Of Convergence Of A Power Series, Todor D. Todorov

Mathematics

We derive two simple and memorizable formulas for the radius of convergence of a power series which seem to be appropriate for teaching in an introductory calculus course.

Pareto Optimal Allocations In Nonconvex Models Of Welfare Economics, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational analysis to the study of Pareto (as well as weak and strong Pareto) optimal allocations in nonconvex models of welfare economics with infinite-dimensional commodity spaces. Our basic tool is the extremal principle of variational analysis that provides necessary conditions for set extremality and may be viewed as a variational extension of the classical convex separation principle to the case of nonconvex sets. In this way we obtain new versions of the generalized second welfare theorem for nonconvex economies in terms of appropriate concepts of normal cones.

Stochastic Differential Systems With Memory (Spring School On Stochastic Delay Differential Equations), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Evaluating The Performance Of Multiple Classifier Systems: A Matrix Algebra Representation Of Boolean Fusion Rules, Justin M. Hill

Theses and Dissertations

Given a finite collection of classifiers one might wish to combine, or fuse, the classifiers in hopes that the multiple classifier system (MCS) will perform better than the individuals. One method of fusing classifiers is to combine their final decision using Boolean rules (e.g., a logical OR, AND, or a majority vote of the classifiers in the system). An established method for evaluating a classifier is measuring some aspect of its Receiver Operating Characteristic (ROC) curve, which graphs the trade-off between the conditional probabilities of detection and false alarm. This work presents a unique method of estimating the performance of …