Mathematics Commons^™

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

Covering Subsets Of The Integers And A Result On Digits Of Fibonacci Numbers, Wilson Andrew Harvey

Theses and Dissertations

A covering system of the integers is a finite system of congruences where each integer satisfies at least one of the congruences. Two questions in covering systems have been of particular interest in the mathematical literature. First is the minimum modulus problem, whether the minimum modulus of a covering system of the integers with distinct moduli can be arbitrarily large, and the second is the odd covering problem, whether a covering system of the integers with distinct moduli can be constructed with all moduli odd. We consider these and similar questions for subsets of the integers, such as the set …

Deep Learning: An Exposition, Ryan Kingery

Theses and Dissertations

In this paper we describe and survey the field of deep learning, a type of machine learning that has seen tremendous growth and popularity over the past decade for its ability to substantially outperform other learning methods at important tasks. We focus on the problem of supervised learning with feedforward neural networks. After describing what these are we give an overview of the essential algorithms of deep learning, backpropagation and stochastic gradient descent. We then survey some of the issues that occur when applying deep learning in practice. Last, we conclude with an important application of deep learning to the …

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, 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, 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, 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, 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, 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).

Teachers' Theories Of Teaching And Learning And The Use Of Math Interventions, Nicole P. Jones

Walden Dissertations and Doctoral Studies

Despite the academic gap between students with learning disabilities (LD) and their nondisabled peers, schools continue to educate students with LD in regular education classrooms. In secondary math classes, such as Algebra 1, students with LD have high percentages of failure. The purpose of this cross-sectional study was to examine the relationship between teachers' personal theories of teaching and learning and their use of math interventions. Fox's (1983) theoretical framework of teaching and learning was used as a conceptual lens. Surveys were administered to 20 high school math teachers in an urban Northeastern U.S. school district. An ordinal logistic regression …

Group Divisible Designs With Two Groups And Three Associate Classes, Ladamas Saiphet

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Explicit Formula For Conditional Expectations Of Product Of Polynomial And Exponential Function Of Affine Transform Of Extended Cox-Ingersoll-Ross Process, Phiraphat Sutthimat

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis an explicit formula for conditional expectations of the product of polynomial and exponential function of an affine transform is derived under the extended function of an transform is derived under the extended Cox-Ingersoll-Ross (ECIR) process. By applying the Feynman-Kac theorem, the explicit formula is revealed from the solution of the corresponding partial differential equation. To support the validity of the obtained results, we, herein, conduct Monte Carlo simulations to investigate the accuracy of the explicit formula.

Cuckoo Search And Enhanced Artificial Bee Colony Heuristic Methods For Vehicle Routing Problem With Backhaul And Time Window Constraints, Tanawat Worawattawechai

Chulalongkorn University Theses and Dissertations (Chula ETD)

The vehicle routing problem with backhauls and time windows (VRPBTW) aims to find a feasible vehicle route that minimizes the total traveling distance while imposing capacity, backhaul, and time-window constraints. In this dissertation, a mathematical model of VRPBTW is introduced to obtain an optimal solution. The heuristics, namely the nearest urgent candidate (NUC), which applies the urgency priority and candidate techniques, and the nearest neighbor with roulette wheel selection (NNRW) which is a combination of a roulette wheel selection method and the improved nearest neighbor heuristic, are also presented to solve this problem. Moreover, two metaheuristic methods are presented to …

การวิเคราะห์การคำนวณเมคสแปนสำหรับปัญหาการจัดตารางการผลิตแบบตามสั่ง, วันเฉลิม โฮชิน

Chulalongkorn University Theses and Dissertations (Chula ETD)

เมคสแปนในปัญหาการจัดตารางการผลิตแบบตามสั่งเป็นค่าที่สำคัญในการหาค่าผลเฉลยใกล้เคียงของการค้นหาแบบทาบู อย่างไรก็ตามขั้นตอนการหาค่าผลเฉลยใกล้เคียงเป็นส่วนที่ใช้เวลาประมวลผลนานที่สุด วิทยานิพนธ์เล่มนี้ทำการปรับปรุงเทคนิคการหาค่าผลเฉลยใกล้เคียงด้วยค่าเมคสแปนที่ถูกเสนอโดย Nowicki และ Smutnicki (2005) และเปรียบเทียบความซับซ้อนของเวลาของวิธีการหาค่าผลเฉลยใกล้เคียง ระหว่างวิธีการของ Nowicki และ Smutnicki และวิธีการที่ได้ปรับปรุงขึ้น ความแตกต่างที่สำคัญของทั้งสองวิธีการคือการหาตำแหน่งสำคัญบางตำแหน่งบนลำดับโทโพโลยีของผลเฉลยเมล็ดพันธุ์ ทั้งสองวิธีการใช้ปัญหามาตรฐานที่มีจำนวนโอเปอเรชันไม่เกิน 400 โอเปอเรชัน ในการทดสอบ ผลการทดลองพบว่า ขั้นตอนวิธีการค้นหาแบบทาบูที่ใช้ขั้นตอนการหาค่าผลเฉลยใกล้เคียงด้วยวิธีการที่ได้ปรับปรุงขึ้น ใช้เวลาประมวลผลน้อยกว่าวิธีการค้นหาแบบทาบูที่ใช้ขั้นตอนการหาค่าผลเฉลยใกล้เคียงด้วยวิธีการของ Nowicki และ Smutnicki

Boundedness Of Green Operators For Nonlocal Equations On Weighted Lebesgue Spaces, Itthinat Nuntajittanond

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this research. we establish the local existence and uniqueness of solutions for the Cauchy problem of the nonlocal equation of the form ∂ₜU(x.t) = ∫R n J(x.Y)U(Y,t)dY – U (x.t) + (In(e + I x I2)) U p (x,t) where p > 1 and ∂ > 0 are constants. In this research, the kernel / of the nonlocal term may not radially symmetric. We investigate the Cauchy problem on weighted Lebesgue spaces with a logarithmic weight. One of the most important results in this thesis is the boundedness of the corresponding Green operator on the weight Lebesgue spaces. We also establish …

Anomalous Assemblage Detection Using Nearest Neighbor Distance, Kayyasit Singkarn

Chulalongkorn University Theses and Dissertations (Chula ETD)

The outlierness of an instance in this thesis is defined based on the distance between two instances. For some datasets, outliers may not be isolated and formed small clusters. C-anomalous assemblage is a group of associated outliers having the number of instances less than or equal to C percent of the total instances. This thesis presents the anomalous assemblage detection algorithm called CND using a nearest neighbor distance for an anomalous score. The algorithm computes the index k equal to floor function of C percent times the total number of instances and uses the k-nearest neighbor distance for representing an …

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 …

Measurement For Disordered Proteins Affecting Scale-Free Network, Satanat Kitsiranuwat

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Clifford Algebra-Valued Segal-Bargmann Transform, Sorawit Eaknipitsari

Chulalongkorn University Theses and Dissertations (Chula ETD)

A classical Segal-Bargmann transform maps square-integrable functions on R to holomorphic square-integrable functions on C with respect to some Gaussian measure. In this work, we extend the classical Segal-Bargmann transform to functions taking values in a Clifford algebra. We establish that in this setting, the generalized Segal-Bargmann transform is a unitary isomorphism mapping Clifford algebra-valued square-integrable functions on Rⁿ with respect to some Gaussian measure to monogenic square-integrable functions on Rⁿ⁺¹ with respect to another Gaussian measure. We also discuss about the differential and multiplication operators in the monogenic functions space as well as certain properties of their domains.

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 …

Complete Convergence For Sequences Of Coordinatewise Widely Orthant Dependent Random Vectors In Hilbert Spaces, Teerayut Phutthanukool

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce a new dependence concept for a sequence of random vectors taking values in real separable Hilbert spaces called coordinate-wise widely orthant dependence and extend the Baum-Katz Theorem to obtain complete convergence and complete moment convergence for a sequence of co-ordinatewise widely orthant dependent random vectors taking values in Hilbert spaces.

Unconditionally Energy Stable Numerical Schemes For Hydrodynamics Coupled Fluids Systems, Alexander Yuryevich Brylev

Theses and Dissertations

The thesis consists of two parts. In the first part we propose several second order in time, fully discrete, linear and nonlinear numerical schemes to solve the phase-field model of two-phase incompressible flows in the framework of finite element method. The schemes are based on the second order Crank-Nicolson method for time disretizations, projection method for Navier-Stokes equations, as well as several implicit-explicit treatments for phase-field equations. The energy stability, solvability, and uniqueness for numerical solutions of proposed schemes are further proved. Ample numerical experiments are performed to validate the accuracy and efficiency of the proposed schemes thereafter.

In the …

Convergence And Rate Of Convergence Of Approximate Greedy-Type Algorithms, Anton Dereventsov

Theses and Dissertations

In this dissertation we study the questions of convergence and rate of convergence of greedy-type algorithms under imprecise step evaluations. Such algorithms are in demand as the issue of calculation errors appears naturally in applications.

We address the question of strong convergence of the Chebyshev Greedy Algorithm (CGA), which is a generalization of the Orthogonal Greedy Algorithm (also known as the Orthogonal Matching Pursuit), and show that the class of Banach spaces for which the CGA converges for all dictionaries and objective elements is strictly between smooth and uniformly smooth Banach spaces.

We analyze an application-oriented modification of the CGA, …

Polynomials Of Small Mahler Measure With No Newman Multiples, Spencer Victoria Saunders

Theses and Dissertations

A Newman polynomial is a polynomial with coefficients in f0;1g and with constant term 1. It is known that the roots of a Newman polynomial must lie in the slit annulus fz 2C: f��1 1 such that if a polynomial f (z) 2 Z[z] has Mahler measure less than s and has no nonnegative real roots, then it must divide a Newman polynomial. In this thesis, we present a new upper bound on such a s if it exists. We also show that there are infinitely many monic polynomials that have distinct Mahler measures which all lie below f, have …

Simulation Study On Jleic High Energy Bunched Electron Cooling, H. Zhang, Y. Roblin, Y. Zhang, Ya. Derbenev, S. Benson, R. Li, J. Chen, H. Huang, L. Luo

Mathematics & Statistics Faculty Publications

In the JLab Electron Ion Collider (JLEIC) project the traditional electron cooling technique is used to reduce the ion beam emittance at the booster ring, and to compensate the intrabeam scattering effect and maintain the ion beam emittance during the collision at the collider ring. Different with other electron coolers using DC electron beam, the proposed electron cooler at the JLEIC ion collider ring uses high energy bunched electron beam, provided by an ERL. In this paper, we report some recent simulation study on how the electron cooling rate will be affected by the bunched electron beam properties, such as …

An Example Of Nature's Mathematics: The Rainbow, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Orientable ℤ < Inf> N -Distance Magic Labeling Of The Cartesian Product Of Many Cycles, Bryan Freyberg, Melissa S. Keranen

Michigan Tech Publications, Part 1

The following generalization of distance magic graphs was introduced in [2]. A directed ℤn- distance magic labeling of an oriented graph G = (V,A) of order n is a bijection ℓ: V → ℤn with the property that there is a μ ∈ ℤn (called the magic constant) such that If for a graph G there exists an orientation G such that there is a directed ℤn-distance magic labeling ℓ for G, we say that G is orientable ℤn-distance magic and the directed ℤn-distance magic labeling ℓ we call an orientable ℤn-distance magic labeling. In this paper, we find orientable …

Investigating The Role Of The Written Curriculum On Lesson Planning For First-Year Elementary Mathematics Teachers, Anna Kron

Honors Program Theses

While studies have previously explored aspects of lesson planning from the perspective of experienced teachers, there is a lack of research investigating how this process is different for brand new educators. The researcher, a preservice elementary teacher studying at the University of Northern Iowa, wanted to learn more about the available resources and how she would utilize them when planning for mathematics instruction in her first elementary classroom. At the completion of this project, the researcher hoped to have a better understanding of the process first-year elementary teachers experience when transforming written textbook materials into a mathematics lesson plan. The …

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 …

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 = …