Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Applied Mathematics (32)
- Other Mathematics (22)
- Discrete Mathematics and Combinatorics (20)
- Computer Sciences (19)
- Education (15)
-
- Engineering (15)
- Statistics and Probability (14)
- Analysis (13)
- Algebra (12)
- Geometry and Topology (9)
- Data Science (8)
- Dynamical Systems (8)
- Medicine and Health Sciences (7)
- Science and Mathematics Education (7)
- Theory and Algorithms (7)
- Aerospace Engineering (6)
- Artificial Intelligence and Robotics (6)
- Numerical Analysis and Computation (6)
- Physics (6)
- Other Applied Mathematics (5)
- Statistical Models (5)
- Applied Statistics (4)
- Astrophysics and Astronomy (4)
- Curriculum and Instruction (4)
- Dynamic Systems (4)
- Partial Differential Equations (4)
- Secondary Education (4)
- Biostatistics (3)
- Institution
-
- Brigham Young University (167)
- University of South Carolina (113)
- University of Texas Rio Grande Valley (103)
- Air Force Institute of Technology (40)
- Virginia Commonwealth University (38)
-
- Florida Institute of Technology (28)
- Illinois State University (23)
- Rowan University (7)
- University of Arkansas Little Rock (7)
- Mississippi State University (6)
- Columbus State University (4)
- City University of New York (CUNY) (3)
- SASTRA Deemed to be University (3)
- Nova Southeastern University (2)
- Texas A&M International University (2)
- University of North Dakota (2)
- Keyword
-
- Physical Sciences and Mathematics, Mathematics (29)
- Pure sciences (23)
- Mathematics (21)
- Graph theory (14)
- Algebra (9)
-
- Congruences (8)
- Graph (8)
- Modular forms (8)
- Combinatorics (7)
- Differential equations (7)
- Graph Theory (6)
- Minimum rank (6)
- Algebraic geometry (5)
- Classification (5)
- Galois representations (5)
- Machine learning (5)
- Number theory (5)
- Polynomials (5)
- Topology (5)
- Algebraic Geometry (4)
- Differential geometry (4)
- Entropy (4)
- FJRW theory (4)
- Generating functions (4)
- Geometry (4)
- Graphs (4)
- Health and environmental sciences (4)
- Hypergraphs (4)
- Inverse limit (4)
- Matrix (4)
- Publication Year
Articles 451 - 480 of 548
Full-Text Articles in Mathematics
Phase History Decomposition For Efficient Scatterer Classification In Sar Imagery, Dane F. Fuller
Phase History Decomposition For Efficient Scatterer Classification In Sar Imagery, Dane F. Fuller
Theses and Dissertations
A new theory and algorithm for scatterer classification in SAR imagery is presented. The automated classification process is operationally efficient compared to existing image segmentation methods requiring human supervision. The algorithm reconstructs coarse resolution subimages from subdomains of the SAR phase history. It analyzes local peaks in the subimages to determine locations and geometric shapes of scatterers in the scene. Scatterer locations are indicated by the presence of a stable peak in all subimages for a given subaperture, while scatterer shapes are indicated by changes in pixel intensity. A new multi-peak model is developed from physical models of electromagnetic scattering …
Crouzeix's Conjecture And The Gmres Algorithm, Sarah Mcbride Luo
Crouzeix's Conjecture And The Gmres Algorithm, Sarah Mcbride Luo
Theses and Dissertations
This thesis explores the connection between Crouzeix's conjecture and the convergence of the GMRES algorithm. GMRES is a popular iterative method for solving linear systems and is one of the many Krylov methods. Despite its popularity, the convergence of GMRES is not completely understood. While the spectrum can in some cases be a good indicator of convergence, it has been shown that in general, the spectrum does not provide sufficient information to fully explain the behavior of GMRES iterations. Other sets associated with a matrix that can also help predict convergence are the pseudospectrum and the numerical range. This …
3d Image Reconstruction And Level Set Methods, Spencer R. Patty
3d Image Reconstruction And Level Set Methods, Spencer R. Patty
Theses and Dissertations
We give a concise explication of the theory of level set methods for modeling motion of an interface as well as the numerical implementation of these methods. We then introduce the geometry of a camera and the mathematical models for 3D reconstruction with a few examples both simulated and from a real camera. We finally describe the model for 3D surface reconstruction from n-camera views using level set methods.
Stability For Traveling Waves, Joshua W. Lytle
Stability For Traveling Waves, Joshua W. Lytle
Theses and Dissertations
In this work we present some of the general theory of shock waves and their stability properties. We examine the concepts of nonlinear stability and spectral stability, noting that for certain classes of equations the study of nonlinear stability is reduced to the analysis of the spectra of the linearized eigenvalue problem. A useful tool in the study of spectral stability is the Evans function, an analytic function whose zeros correspond to the eigenvalues of the linearized eigenvalue problem. We discuss techniques for numerical Evans function computation that ensure analyticity, allowing standard winding number arguments and rootfinding methods to be …
The Constrained Isoperimetric Problem, Minh Nhat Vo Do
The Constrained Isoperimetric Problem, Minh Nhat Vo Do
Theses and Dissertations
Let X be a space and let S ⊂ X with a measure of set size |S| and boundary size |∂S|. Fix a set C ⊂ X called the constraining set. The constrained isoperimetric problem asks when we can find a subset S of C that maximizes the Følner ratio FR(S) = |S|/|∂S|. We consider different measures for subsets of R^2,R^3,Z^2,Z^3 and describe the properties that must be satisfied for sets S that maximize the Folner ratio. We give explicit examples.
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
Theses and Dissertations
Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. …
Maximal Unramified Extensions Of Cyclic Cubic Fields, Ka Lun Wong
Maximal Unramified Extensions Of Cyclic Cubic Fields, Ka Lun Wong
Theses and Dissertations
Maximal unramified extensions of quadratic number fields have been well studied. This thesis focuses on maximal unramified extensions of cyclic cubic fields. We use the unconditional discriminant bounds of Moreno to determine cyclic cubic fields having no non-solvable unramified extensions. We also use a theorem of Roquette, developed from the method of Golod-Shafarevich, and some results by Cohen to construct cyclic cubic fields in which the unramified extension is of infinite degree.
A Multi-Frequency Inverse Source Problem For The Helmholtz Equation, Sebastian Ignacio Acosta
A Multi-Frequency Inverse Source Problem For The Helmholtz Equation, Sebastian Ignacio Acosta
Theses and Dissertations
The inverse source problem for the Helmholtz equation is studied. An unknown source is to be identified from the knowledge of its radiated wave. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, we prove that data obtained from finitely many frequencies is not sufficient. On the other hand, if the frequency varies within an open interval of the positive real line, then the source is determined uniquely. An algorithm is based on an incomplete Fourier transform of the measured data and we establish an error estimate under certain regularity assumptions on the …
Three-Dimensional Galois Representations And A Conjecture Of Ash, Doud, And Pollack, Vinh Xuan Dang
Three-Dimensional Galois Representations And A Conjecture Of Ash, Doud, And Pollack, Vinh Xuan Dang
Theses and Dissertations
In the 1970s and 1980s, Jean-Pierre Serre formulated a conjecture connecting two-dimensional Galois representations and modular forms. The conjecture came to be known as Serre's modularity conjecture. It was recently proved by Khare and Wintenberger in 2008. Serre's conjecture has various important consequences in number theory. Most notably, it played a key role in the proof of Fermat's last theorem. A natural question is, what is the analogue of Serre's conjecture for higher dimensional Galois representations? In 2002, Ash, Doud and Pollack formulated a precise statement for a higher dimensional analogue of Serre's conjecture. They also provided numerous computational examples …
The Weak Cayley Table And The Relative Weak Cayley Table, Melissa Anne Mitchell
The Weak Cayley Table And The Relative Weak Cayley Table, Melissa Anne Mitchell
Theses and Dissertations
In 1896, Frobenius began the study of character theory while factoring the group determinant. Later in 1963, Brauer pointed out that the relationship between characters and their groups was still not fully understood. He published a series of questions that he felt would be important to resolve. In response to these questions, Johnson, Mattarei, and Sehgal developed the idea of a weak Cayley table map between groups. The set of all weak Cayley table maps from one group to itself also has a group structure, which we will call the weak Cayley table group. We will examine the weak Cayley …
Three Channel Polarimetric Based Data Deconvolution, Kurtis G. Engelson
Three Channel Polarimetric Based Data Deconvolution, Kurtis G. Engelson
Theses and Dissertations
A three channel polarimetric deconvolution algorithm was developed to mitigate the degrading effects of atmospheric turbulence in astronomical imagery. Tests were executed using both simulation and laboratory data. The resulting efficacy of the three channel algorithm was compared to a recently developed two channel approach under identical conditions ensuring a fair comparison amongst both algorithms. Two types of simulations were performed. The first was a binary star simulation to compare resulting resolutions between the three and two channel algorithms. The second simulation measured how effective both algorithms could deconvolve a blurred satellite image. The simulation environment assumed the key parameters …
Comparison Of Development Test And Evaluation And Overall Program Estimate At Completion, William R. Rosado
Comparison Of Development Test And Evaluation And Overall Program Estimate At Completion, William R. Rosado
Theses and Dissertations
Historically, cost growth regression models analyze aggregate, program-level information. Initiatives by the Office of Secretary of Defense, Cost Assessment and Program Evaluation (OSD CAPE) require direct, centralized reporting of the complete Work Breakdown Structure (WBS) Earned Value (EV) data. Centralized reporting allows access to unfiltered, unaltered, EV data for multiple programs. Using regression, we evaluate if WBS element Development Test and Evaluation (DT&E) EV data is related to program estimate at completion (EAC). Identifying a relationship provides evidence validating pertinence and reliability of low level EV data. Additionally, a relationship between a specific WBS element and program EAC establishes a …
Mean Square Estimate For Primitive Lattice Points In Convex Planar Domains, Ryan D. Coatney
Mean Square Estimate For Primitive Lattice Points In Convex Planar Domains, Ryan D. Coatney
Theses and Dissertations
The Gauss circle problem in classical number theory concerns the estimation of N(x) = { (m1;m2) in ZxZ : m1^2 + m2^2 <= x }, the number of integer lattice points inside a circle of radius sqrt(x). Gauss showed that P(x) = N(x)- pi * x satisfi es P(x) = O(sqrt(x)). Later Hardy and Landau independently proved that P(x) = Omega_(x1=4(log x)1=4). It is conjectured that inf{e in R : P(x) = O(x^e )}= 1/4. I. K atai showed that the integral from 0 to X of |P(x)|^2 dx = X^(3/2) + O(X(logX)^2). Similar results to those of the circle have been obtained for regions D in R^2 which contain the origin and whose boundary dD satis fies suff cient smoothness conditions. Denote by P_D(x) the similar error term to P(x) only for the domain D. W. G. Nowak showed that, under appropriate conditions on dD, P_D(x) = Omega_(x1=4(log x)1=4) and that the integral from 0 to X of |P_D(x)|^2 dx = O(X^(3/2)). A result similar to Nowak's mean square estimate is given in the case where only "primitive" lattice points, {(m1;m2) in Z^2 : gcd(m1;m2) = 1 }, are counted in a region D, on assumption of the Riemann Hypothesis.
3-D Computational Investigation Of Viscoelastic Biofilms Using Gpus, Paisa Seeluangsawat
3-D Computational Investigation Of Viscoelastic Biofilms Using Gpus, Paisa Seeluangsawat
Theses and Dissertations
A biofilm is a slimy colony of bacteria and the materials they secrete, collectively called “extracellular polymeric substances (EPS)”. The EPS consists mostly of bio-polymers, which cross link into a network that behave viscoelastically under deformation. We propose a single-fluid multi-component phase field model of biofilms that captures this behavior, then use numerical simulations on GPUs to investigate the biofilm’s growth and its hydrodynamics properties.
Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills
Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills
Theses and Dissertations
Growth curves are used to model various processes, and are often seen in biological and agricultural studies. Underlying assumptions of many studies are that the process may be sampled forever, and that samples are statistically independent. We instead consider the case where sampling occurs in a finite domain, so that increased sampling forces samples closer together, and also assume a distance-based covariance function. We first prove that, under certain conditions, the mean parameter of a fixed-mean model cannot be estimated within a finite domain. We then numerically consider more complex growth curves, examining sample sizes, sample spacing, and quality of …
A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert
A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert
Theses and Dissertations
Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into 3-dimensional space and can be very complicated. Twist and bitwist are simple constructions that provide an easy path to both creating and understanding closed, orientable 3-manifolds. By starting with simple face pairings on a 3-ball, a myriad of 3-manifolds can be easily constructed. In fact, all closed, connected, orientable 3-manifolds can be developed in this manner. We call this work a tool kit to emphasize the …
The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton
The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton
Theses and Dissertations
For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.
Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup
Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup
Theses and Dissertations
In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study many non-locally connected spaces and show that some have periodic structure either identical or related to Sharkovskii's result, while others have essentially no restrictions on the periodic structure. We next consider embeddings of solenoids together with their complements in three space. We differentiate solenoid complements via both algebraic and geometric means, and show that every solenoid has an unknotted embedding …
A Lift Of Cohomology Eigenclasses Of Hecke Operators, Brian Francis Hansen
A Lift Of Cohomology Eigenclasses Of Hecke Operators, Brian Francis Hansen
Theses and Dissertations
A considerable amount of evidence has shown that for every prime p &neq; N observed, a simultaneous eigenvector v_0 of Hecke operators T(l,i), i=1,2, in H^3(Γ_0(N),F(0,0,0)) has a “lift” v in H^3(Γ_0(N),F(p−1,0,0)) — i.e., a simultaneous eigenvector v of Hecke operators having the same system of eigenvalues that v_0 has. For each prime p>3 and N=11 and 17, we construct a vector v that is in the cohomology group H^3(Γ_0(N),F(p−1,0,0)). This is the first construction of an element of infinitely many different cohomology groups, other than modulo p reductions of characteristic zero objects. We proceed to show that v …
Applications Of Descriptive Set Theory In Homotopy Theory, Samuel M. Corson
Applications Of Descriptive Set Theory In Homotopy Theory, Samuel M. Corson
Theses and Dissertations
This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.
Planar Cat(K) Subspaces, Russell M. Ricks
Planar Cat(K) Subspaces, Russell M. Ricks
Theses and Dissertations
Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Theses and Dissertations
This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Theses and Dissertations
A parametric study was performed to determine optimal geometries to allow the successful transition of a detonation from a pre-detonator into the thrust tube of a pulse detonation engine. The study was performed using a two-dimensional Euler solver with progress variables to model the chemistry. The geometrical configurations for the simulations look at the effect of shock reflections, flow obstructions, and detonation diffraction to determine successful geometries. It was observed that there are success and failure rates associated with pre-detonators. These success rates appear to be determined by the transverse wave structure of a stably propagating detonation wave and must …
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Theses and Dissertations
A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …
Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett
Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett
Theses and Dissertations
This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. The three level system consists of an alkali metal vapor, typically Rb or Cs, pumped by a diode from the 2S1/2 state to the 2P3/2 , a collisional relaxation from 2P3/2 to 2P1/ 2 , and then lasing from 2P1/2 to 2S1/2 . The hyperfine absorption and emission cross sections for these transitions are developed in detail. Differential equations for intra-gain pump attenuation …
Asian Spread Option Pricing Models And Computation, Sijin Chen
Asian Spread Option Pricing Models And Computation, Sijin Chen
Theses and Dissertations
In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal with average price risk. But when those two risks are combined together, then we need to consider Asian spread options and Asian-European spread options for hedging purposes. For an Asian or Asian-European spread call option, its payoff depends on the difference of two underlyings' average price or of one average price and …
Midwave Infrared Imaging Fourier Transform Spectrometry Of Combustion Plumes, Kenneth C. Bradley
Midwave Infrared Imaging Fourier Transform Spectrometry Of Combustion Plumes, Kenneth C. Bradley
Theses and Dissertations
A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a flow rate of 300 cm3/min was collected at 1 cm−1 resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of water, CO, and CO2 were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature …
Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz
Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz
Theses and Dissertations
In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. …
Growth And Geodesics Of Thompson's Group F, Jennifer L. Schofield
Growth And Geodesics Of Thompson's Group F, Jennifer L. Schofield
Theses and Dissertations
In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some …
Application Of Dual-Tree Complex Wavelet Transforms To Burst Detection And Rf Fingerprint Classification, Randall W. Klein
Application Of Dual-Tree Complex Wavelet Transforms To Burst Detection And Rf Fingerprint Classification, Randall W. Klein
Theses and Dissertations
This work addresses various Open Systems Interconnection (OSI) Physical (PHY) layer mechanisms to extract and exploit RF waveform features (”fingerprints”) that are inherently unique to specific devices and that may be used to provide hardware specific identification (manufacturer, model, and/or serial number). This is addressed by applying a Dual-Tree Complex Wavelet Transform (DT-CWT) to improve burst detection and RF fingerprint classification. A ”Denoised VT” technique is introduced to improve performance at lower SNRs, with denoising implemented using a DT-CWT decomposition prior to Traditional VT processing. A newly developed Wavelet Domain (WD) fingerprinting technique is presented using statistical WD fingerprints with …