Nonequispaced Fast Fourier Transform,
2017
University of South Carolina
Nonequispaced Fast Fourier Transform, David Hughey
Theses and Dissertations
Two algorithms for fast and accurate evaluation of high degree trigonometric polynomials at many scattered points are presented. Both methods rely on highly localized kernels and the Fast Fourier Transform. The first algorithm uses the function values at uniformly distributed grid points and kernels that reproduce trigonometric polynomials, while the second method uses kernels that approximate well the function on the frequency side. Both algorithm are termed Nonequispaced Fast Fourier Transform. The first algorithm is coded in MATLAB and shown to approximate well the function to be evaluated.
Subdivision Of Measures Of Squares,
2017
University of South Carolina
Subdivision Of Measures Of Squares, Dylan Bates
Theses and Dissertations
The primary goal of our work is to establish a method to relate simple measures to a given set of moments. We calculate the moments of squares via linear polynomial weight measures and straight line cuts and use this to calculate the centre of mass of the square. The one-to-one correspondence that is found is needed to represent surfaces with gaps, which can estimate arbitrary measures on squares. From this, a subdivision scheme is developed, which successively quadrisects squares and uses the relation to estimate the new measures in order to provide a good representation of the original surface. One …
Multiple Solutions With Constant Sign Of A Dirichlet Problem For A Class Of Elliptic Systems With Variable Exponent Growth,
2017
Henan Agriculture University
Multiple Solutions With Constant Sign Of A Dirichlet Problem For A Class Of Elliptic Systems With Variable Exponent Growth, Li Yin, Jinghua Yao, Qihu Zhang, Chunshan Zhao
Mathematical Sciences: Faculty Publications
We present here, in the system setting, a new set of growth conditions under which we manage to use a novel method to verify the Cerami compactness condition. By localization argument, decomposition technique and variational methods, we are able to show the existence of multiple solutions with constant sign for the problem without the well-known Ambrosetti--Rabinowitz type growth condition. More precisely, we manage to show that the problem admits four, six and infinitely many solutions respectively.
Gorenstein Injective Envelopes And Covers Over Two Sided Noetherian Rings,
2017
Georgia Southern University
Gorenstein Injective Envelopes And Covers Over Two Sided Noetherian Rings, Alina Iacob
Mathematical Sciences: Faculty Publications
We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.
A Zariski-Local Notion Of F-Total Acyclicity For Complexes Of Sheaves,
2017
Texas Tech University
A Zariski-Local Notion Of F-Total Acyclicity For Complexes Of Sheaves, Lars Winther Christensen, Sergio Estrada, Alina Iacob
Mathematical Sciences: Faculty Publications
We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local—i.e. it can be verified on any open affine covering of the scheme—and for sheaves over a quasi-compact semi-separated scheme it agrees with the categorical notion. In particular, it agrees, in their setting, with the notion studied by Murfet and Salarian for sheaves over a noetherian semi-separated scheme. As part of the study we recover, and in several cases extend the validity of, recent results on existence of covers and precovers in categories of sheaves. One consequence is the existence of an adjoint …
Gorenstein Flat And Projective (Pre)Covers,
2017
Universidad de Murcia
Gorenstein Flat And Projective (Pre)Covers, Sergio Estrada, Alina Iacob, Sinem Odabasi
Mathematical Sciences: Faculty Publications
We consider a right coherent ring R. We prove that the class of Gorenstein flat complexes is covering in the category of complexes of left R-modules Ch(R). When R is also left n-perfect, we prove that the class of Gorenstein projective complexes is special precovering in Ch(R).
An Early Semester Mastery Activity And Intervention In First-Year Calculus,
2017
University of Nebraska-Lincoln
An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield
Department of Mathematics: Faculty Publications
Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …
Group Divisible Designs With Two Groups And Three Associate Classes,
2017
Faculty of Science
Group Divisible Designs With Two Groups And Three Associate Classes, Ladamas Saiphet
Chulalongkorn University Theses and Dissertations (Chula ETD)
No abstract provided.
Selection Problems In O-Minimal Structures,
2017
Faculty of Science
Selection Problems In O-Minimal Structures, Saronsad Sokantika
Chulalongkorn University Theses and Dissertations (Chula ETD)
In this dissertation, we improve the Definable Michael's Selection Theorem in o-minimal expansions of real closed fields. Then applications of this theorem are established; for instance, we prove the following statement: Let be an o-minimal expansion of and T be a definable set-valued map where n = 1 or m=1. If T has a continuous selection, then T has a definable continuous selection. Moreover, we prove the statement: Let be an o-minimal expansion of a real closed field and be a closed subset of Rn. If T: E --> Rm is a definable continuous set-valued map and T is bounded …
Designing Packing Boxes To Minimize Number Of Box Types,
2017
Faculty of Science
Designing Packing Boxes To Minimize Number Of Box Types, Teeradech Laisupannawong
Chulalongkorn University Theses and Dissertations (Chula ETD)
In a product packing procedure, many types of packing boxes may be used if a factory has several kinds of goods or products. The cost spent for many types of boxes is added to the manufacturing cost. However, it would be more efficient in the aspects of the cost reduction and the production management if we can design reasonable box sizes and can minimize the number of box types for packing goods. In this work, we propose a heuristic rectangular box design algorithm for packing each kind of rectangular goods when the number of goods per box is given. The …
Positive Solutions Of A Singular Fractional Boundary Value Problem With A Fractional Boundary Condition,
2017
Nova Southeastern University
Positive Solutions Of A Singular Fractional Boundary Value Problem With A Fractional Boundary Condition, Jeffrey W. Lyons, Jeffrey T. Neugebauer
EKU Faculty and Staff Scholarship
For \(\alpha\in(1,2]\), the singular fractional boundary value problem \[D^{\alpha}_{0^+}x+f\left(t,x,D^{\mu}_{0^+}x\right)=0,\quad 0\lt t\lt 1,\] satisfying the boundary conditions \(x(0)=D^{\beta}_{0^+}x(1)=0\), where \(\beta\in(0,\alpha-1]\), \(\mu\in(0,\alpha-1]\), and \(D^{\alpha}_{0^+}\), \(D^{\beta}_{0^+}\) and \(D^{\mu}_{0^+}\) are Riemann-Liouville derivatives of order \(\alpha\), \(\beta\) and \(\mu\) respectively, is considered. Here \(f\) satisfies a local Carathéodory condition, and \(f(t,x,y)\) may be singular at the value 0 in its space variable \(x\). Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
Electric Ion Dispersion As A New Type Of Mass Spectrometer,
2017
The University of Texas Rio Grande Valley
Electric Ion Dispersion As A New Type Of Mass Spectrometer, Michael R. Lindstrom, Iain Moyles, Kevin Ryczko
School of Mathematical & Statistical Sciences Faculty Publications
At the 2014 Fields-MPrime Industrial Problem Solving Workshop, PerkinElmer presented a design problem for mass spectrometry. Traditionally, mass spectrometry is done via three methods: using magnetic fields to deflect charged particles whereby different masses bend differently; using a time-of-flight procedure where particles of different mass arrive at different times at a target; and using an electric quadrupole that filters out all masses except for one very narrow band. The challenge posed in the problem was to come up with a new design for mass spectrometry that did not involve magnetic fields and where mass fractions could be measured in an …
Using Technology To Determine Factorability Or Non-Factorability Of Quadratic Algebraic Trinomials,
2017
The University of Texas Rio Grande Valley
Using Technology To Determine Factorability Or Non-Factorability Of Quadratic Algebraic Trinomials, John E. T. Bernard, Olga Ramirez, Cristina Villalobos
School of Mathematical & Statistical Sciences Faculty Publications
This paper is aimed for mathematics educators who teach algebra, more specifically, the factoring of quadratic algebraic expressions, and who want to enhance student learning of this topic using technology in conjunction with the Middle Term Splitting Method (Donnell, 2010; MTSM 2016a; MTSM 2016b). We will use technology-based algebra and geometry connections to help determine factorability or nonfactorability of quadratic algebraic trinomials over the integers, over the real numbers, and over the complex numbers, both with clarity, certainty and with understanding by using two equations, one derived from the coefficients of the outer terms and the other from the middle …
An Intrinsic Characterization Of Bonnet Surfaces Based On A Closed Differential Ideal,
2017
The University of Texas Rio Grande Valley
An Intrinsic Characterization Of Bonnet Surfaces Based On A Closed Differential Ideal, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The structure equations for a two-dimensional manifold are introduced and two results based on the Codazzi equations pertinent to the study of isometric surfaces are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem due to Bonnet is obtained. A transformation for the connection forms is developed. It is proved that the angle of deformation must be harmonic, and that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations, and these results can …
An Introduction To Ricci Flow For Two-Dimensional Manifolds,
2017
The University of Texas Rio Grande Valley
An Introduction To Ricci Flow For Two-Dimensional Manifolds, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The study of diferentiable manifolds is a deep an extensive area of mathematics. A technique such as the study of the Ricci flow turns out to be a very useful tool in this regard. This flow is an evolution of a Riemannian metric driven by a parabolic type of partial differential equation. It has attracted great interest recently due to its important achievements in geometry such as Perelman's proof of the geometrization conjecture and Brendle-Schoen's proof of the differentiable sphere theorem. It is the purpose here to give a comprehensive introduction to the Ricci flow on manifolds of dimension two …
Coloring Graphs With Forbidden Minors,
2017
University of Central Florida
Coloring Graphs With Forbidden Minors, Martin Rolek
Electronic Theses and Dissertations
A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. My research is motivated by the famous Hadwiger's Conjecture from 1943 which states that every graph with no Kt-minor is (t − 1)-colorable. This conjecture has been proved true for t ≤ 6, but remains open for all t ≥ 7. For t = 7, it is not even yet known if a graph with no K7-minor is 7-colorable. We begin by showing that every graph with no Kt-minor is (2t − 6)- colorable for t = …
Filtering Problems In Stochastic Tomography,
2017
University of Central Florida
Filtering Problems In Stochastic Tomography, Tyler Gomez
Electronic Theses and Dissertations
Distinguishing signal from noise has always been a major goal in probabilistic analysis of data. Such is no less the case in the field of medical imaging, where both the processes of photon emission and their rate of absorption by the body behave as random variables. We explore methods by which to extricate solid conclusions from noisy data involving an X-ray transform, long the mathematical mainstay of such tools as computed axial tomography (CAT scans). Working on the assumption of having some prior probabilities assigned to various states a body can be found in, we introduce and make rigorous an …
Global Stability Of Higher Dimensional Monotone Maps,
2017
Trinity University
Global Stability Of Higher Dimensional Monotone Maps, Eduardo C. Balreira, Saber Elaydi, Rafael Luís
Mathematics Faculty Research
We develop a notion of monotonicity for maps defined on Euclidean spaces Rk+, of arbitrary dimension k. This is a geometric approach that extends the classical notion of planar monotone maps or planar competitive difference equations. For planar maps, we show that our notion and the classical notion of monotonicity are equivalent. In higher dimensions, we establish certain verifiable conditions under which Kolmogorov monotone maps on Rk+ have a globally asymptotically stable fixed point. We apply our results to two competition population models, the Leslie–Gower and the Ricker models of two- and three-species. It …
Network Analytics For The Mirna Regulome And Mirna-Disease Interactions,
2017
Virginia Commonwealth University
Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri
Theses and Dissertations
miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …
Functions Of The Infinitesimal Generator Of A Strongly Continuous Quaternionic Group,
2017
Chapman University
Functions Of The Infinitesimal Generator Of A Strongly Continuous Quaternionic Group, Daniel Alpay, Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
Mathematics, Physics, and Computer Science Faculty Articles and Research
The analogue of the Riesz-Dunford functional calculus has been introduced and studied recently as well as the theory of semigroups and groups of linear quaternionic operators. In this paper we suppose that T is the infinitesimal generator of a strongly continuous group of operators (ZT (t))t2R and we show how we can define bounded operators f(T ), where f belongs to a class of functions which is larger than the class of slice regular functions, using the quaternionic Laplace-Stieltjes transform. This class will include functions that are slice regular on the S-spectrum of T but not necessarily at infinity. Moreover, …
