Applied Mathematics Commons^™

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.

A Way That Can Be Walked Is Not The Way And A Name That Can Be Named Is Not The Name: My Complex Crusade Through Systems, Nature, And Taoist Text For Solutions On Proper Leadership, Roy Leaf '12

Honor Scholar Theses

No abstract provided.

Derivation Of Hill's Equation From Scale Invariance, Andres Ortiz^, Vladik Kreinovich*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

Structure For Regular Inclusions, David R. Pitts

Department of Mathematics: Faculty Publications

We study pairs (C,D) of unital C∗-algebras where D is an abelian C∗-subalgebra of C which is regular in C in the sense that the span of {v 2 C : vDv∗ [ v∗Dv D} is dense in C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D whose restriction to D is the identity on D. We show that the left kernel of E, L(C,D), is the unique closed two-sided ideal of C maximal with respect to having trivial …

Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *

COURI Symposium Abstracts, Spring 2012

Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …

Negative Curves On Algebraic Surfaces, Thomas Bauer, Brian Harbourne, Andreas Leopold Knutsen, Alex Kuronya, Stefan Muller-Stach, Xavier Roulleau, Tomasz Szemberg

Department of Mathematics: Faculty Publications

We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any smooth complex projective surface X with a surjective non-isomorphic endomorphism has bounded negativity (i.e., that C2 is bounded below for prime divisors C on X). We prove the same statement for Shimura curves on Hilbert modular surfaces. As a byproduct we obtain that there exist only finitely many smooth Shimura curves on a given Hilbert modular surface. We. also show that any set of curves of bounded genus on a smooth complex projective surface must have bounded negativity

R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis

All HMC Faculty Publications and Research

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays …

Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao

Doctoral Dissertations

Underground pipeline systems play an indispensable role in transporting liquids in both developed and developing countries. The associated social and economic cost to repair a pipe upon abrupt failure is often unacceptable. Regular inspection is a preventative action that aims to monitor pipe conditions, catch abnormalities and reduce the chance of undesirable surprises. Robots with CCTV video cameras have been used for decades to inspect pipelines, yielding only qualitative information. It is becoming necessary and preferable for municipalities, project managers and engineers to also quantify the 3-D geometry of underground pipe networks. Existing robots equipped specialized hardware and software algorithms …

Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon

Doctoral Dissertations

As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.

In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …

The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown

Doctoral Dissertations

The use of computational methods for design and simulation of control systems allows for a cost-effective trial and error approach. In this work, we are concerned with the robust, real-time control of physical systems whose state space is infinite-dimensional. Such systems are known as Distributed Parameter Systems (DPS). A body whose state is heterogeneous is a distributed parameter. In particular, this work focuses on DPS systems that are governed by linear Partial Differential Equations, such as the heat equation. We specifically focus on the MinMax controller, which is regarded as being a very robust controller. The mathematical formulation of the …

Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo

Department of Mathematics: Dissertations, Theses, and Student Research

We consider the local and global well-posedness of the coupled nonlinear wave equations

u_tt – Δu + g₁(u_t) = f₁(u, v)

v_tt – Δv + g₂(v_t) = f₂(u, v);

in a bounded domain Ω subset of the real numbers (Rⁿ) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f₁(u, v) and f₂(u, v) are with supercritical exponents …

Random Number Generation: Types And Techniques, David F. Dicarlo

Senior Honors Theses

What does it mean to have random numbers? Without understanding where a group of numbers came from, it is impossible to know if they were randomly generated. However, common sense claims that if the process to generate these numbers is truly understood, then the numbers could not be random. Methods that are able to let their internal workings be known without sacrificing random results are what this paper sets out to describe. Beginning with a study of what it really means for something to be random, this paper dives into the topic of random number generators and summarizes the key …

Determining Angular Frequency From A Video With A Generalized Fast Fourier Transform, Lindsay N. Smith

Theses and Dissertations

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. …

Local Histograms For Per-Pixel Classification, Melody L. Massar

Theses and Dissertations

We introduce a rigorous mathematical theory for the analysis of local histograms, and study how they interact with textures that can be modeled as occlusions of simpler components. We first show how local histograms can be computed as a system of convolutions and discuss some basic local histogram properties. We then introduce a probabilistic, occlusion-based model for textures and formally demonstrate that local histogram transforms are natural tools for analyzing the textures produced by our model. Next, we characterize all nonlinear transforms which satisfy the three key properties of local histograms and consider the appropriateness of local histogram features in …

Preconditioning Visco-Resistive Mhd For Tokamak Plasmas, Daniel R. Reynolds, Ravi Samtaney, Hilari C. Tiedeman

Mathematics Research

No abstract provided.

On Soliton Interactions For A Hierarchy Of Generalized Heisenberg Ferromagnetic Models On Su(3)/S(U(1) $\Times$ U(2)) Symmetric Space, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valchev

Articles

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In …

Ball Remotality In Banach Spaces And Related Topics., Tanmoy Paul

Doctoral Theses

In this project we aim to study Ball Remotality and densely Ball Remotality of subspaces in Banach spaces. We study this property in many classical spaces of type c0, c,\\â„“p and C(K) where K is a compact Hausdorff space. The said problem also discussed for Banach spaces when considered as a subspace in its bidual. It is observed M-ideals in C(K) are densely ball remotal. It is shown that a particular type of M-ideal in A(K) where K is a Choquet simplex is densely ball remotal.

The Immersed Interface Method For Two-Fluid Problems, Miguel Uh, Sheng Xu

Mathematics Research

No abstract provided.

Numerical Solution Of Integral Equations In Solidification And Laser Melting, Elizabeth Case, Johannes Tausch

Mathematics Research

No abstract provided.