Applied Mathematics Commons^™

Composition Of Integers With Bounded Parts, Darren B. Glass

Math Faculty Publications

In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g.

Experiments On Surfactants And Thin Fluid Films, Peter Megson

HMC Senior Theses

We investigate the spatiotemporal dynamics of a surfactant monolayer on a thin fluid film spreading inward into a region devoid of surfactant, a system motivated by the alveolus of the human lung. We perform experiments that simultaneously measure the fluid height profile and the fluorescence intensity due to our fluorescent surfactant, NBD-PC. We perform experiments on both a Newtonian layer of glycerol and a shear-thinning fluid layer consisting of xanthan gum mixed with glycerol. We can very successfully extract height profiles on the xanthan gum fluid, although the simultaneous measurement of fluorescent intensity profiles proved problematic, as the laser tended …

Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented …

Data Mining Based Hybridization Of Meta-Raps, Fatemah Al-Duoli, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

Though metaheuristics have been frequently employed to improve the performance of data mining algorithms, the opposite is not true. This paper discusses the process of employing a data mining algorithm to improve the performance of a metaheuristic algorithm. The targeted algorithms to be hybridized are the Meta-heuristic for Randomized Priority Search (Meta-RaPS) and an algorithm used to create an Inductive Decision Tree. This hybridization focuses on using a decision tree to perform on-line tuning of the parameters in Meta-RaPS. The process makes use of the information collected during the iterative construction and improvement phases Meta-RaPS performs. The data mining algorithm …

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

Szego Kernel Transformation Law For Proper Holomorphic Mappings, Michael Bolt

University Faculty Publications and Creative Works

Let ω1;ω2 be smoothly bounded doubly connected regions in the complex plane. We establish a transformation law for the Szego kernel under proper holomorphic mappings. This extends known results concerning biholomorphic mappings between multiply connected regions as well as proper holomorphic mappings from multiply connected regions to simply connected regions.

Experimental Validation Of Robotic Manifold Tracking In Gyre-Like Flows, Matthew Michini, M. Ani Hsieh, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper, we present a first attempt toward experimental validation of a multi-robot strategy for tracking manifolds and Lagrangian coherent structures (LCS) in flows. LCS exist in natural fluid flows at various scales, and they are time-varying extensions of stable and unstable manifolds of time invariant dynamical systems. In this work, we present the first steps toward experimentally validating our previously proposed real-time manifold and LCS tracking strategy that relies solely on local measurements. Although we have validated the strategy in simulations using analytical flow models, experimental flow data, and actual ocean data, the strategy has never been implemented …

Transportation Of Perishable And Refrigerated Foods In Mylar Foil Bags And Insulated Containers: A Time-Temperature Study, Yanyan Li, John P. Schrade, Haiyan Su, John Specchio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Data are lacking on the temperature changes of food during transport without the use of refrigerated trucks. The purpose of this study was to evaluate the ability of several insulated and noninsulated containers with or without frozen gel packs to keep perishable and refrigerated foods within the temperature safe zone in relationship to duration of transport. The study was designed to duplicate the practices exhibited by customers purchasing perishable food products from a cash-and-carry business. Approximately 40 perishable food items were evaluated. Four types of containers were tested: a mylar foil bag, a commercial insulated bag, a generic insulated bag, …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

Predicting Propylene Loss With Inferential Model Development Using Design Of Experiments (Doe) And Historical Data, Jeffrey Allen Wheeler

Open Access Theses & Dissertations

Inferential models are a highly researched topic as the science of digital automation becomes more prevalent as information is in abundance. Welldeveloped inferred models can augment the use of analyzers in steady state processing and highly correlated ones can even replace online analytics. The use of design of experiments (DOE) inferred models with historical process data and a rigorous plant simulator can reduce the case study duration while achieving a high degree of accuracy. This paper uses surface response and full factorial models as the first step in model development, and then uses actual historical plant data to create a …

A Linearised Singularly Perturbed Convection-Diffusion Problem With An Interior Layer, Eugene O'Riordan, Jason Quinn

Articles

A linear time dependent singularly perturbed convection-diffusion problem is examined. The convective coefficient contains an interior layer (with a hyperbolic tangent profile), which in turn induces an interior layer in the solution. A numerical method consisting of a monotone finite difference operator and a piecewise-uniform Shishkin mesh is constructed and analysed. Neglecting logarithmic factors, first order parameter uniform convergence is established.

A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn

Articles

A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small …

Area Based Fan Beam Projection Model For Computed Tomography, Phillip J. Stevens

Phi Kappa Phi Research Symposium (Archived)

Computed tomography (CT) is image reconstruction of objects using computer processed transmission or reflection data, usually referred to as projection data, from x-ray scanning. This projection data is often modeled using line integrals, but x-rays are of finite width in reality, so the accuracy of the projection data can be improved if an area based approach is used instead. In addition emitter beam shapes affect the reconstruction effectiveness and data collection efficiency, with the two main types of beam choice for 2-D scanning being fan beam and parallel beam. Fan beam scanning offers some advantages over parallel beam, such as …

The Geometry Of The Projective Joint Spectrum And The Commutativity Of Self-Adjoint Operators, Isaak Chagouel

Legacy Theses & Dissertations (2009 - 2024)

The theory of single operators is by now a very mature subject, with the notion of spectrum playing a key role in the theory. However, multivariate operator theory is only in its very early stages of development. There is not even wide agreement about how "the joint spectrum" of an n-tuple A = (A₁, · · · , A_n) of bounded linear operators on the same Hilbert space H should be defined.

Preservation Of A Convergence Of A Sequence To A Set, Akira Iwasa, Masaru Kada, Shizuo Kamo

Computer Science and Mathematics Faculty Publications

We say that a sequence of points converges to a set if every open set containing the set contains all but finitely many terms of the sequence. We investigate preservation of convergence of a sequence to a set in forcing extensions.

Block Kaczmarz Method With Inequalities, Jonathan Briskman

CMC Senior Theses

The Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equalities. This paper studies a system of linear equalities and inequalities. We use the block version of the Kaczmarz method applied towards the equalities with the simple randomized Kaczmarz scheme for the inequalities. This primarily involves combining Needell and Tropp's work on the block Kaczmarz method with the application of a randomized Kaczmarz approach towards a system of equalities and inequalities performed by Leventhal and Lewis. We give an expected linear rate of convergence for this kind of system and find that using the block Kaczmarz scheme …

A Posteriori Estimates Using Auxiliary Subspace Techniques, Harri Hakula, Michael Neilan, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show …

Regularity Of Mediatrices In Surfaces, Pilar Herreros, Mario Ponce, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves …

Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion, Mark A. Mckibben, Micah Webster

Mathematics Faculty Publications

We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownianmotion in a real separable Hilbert space.Global existence results concerningmild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.

A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho

Theses and Dissertations--Mathematics

Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.

In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△_Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …