Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, 2020 The University of Southern Mississippi

#### Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, Subagya Perera

*Master's Theses*

In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few ...

A Dynamic F5 Algorithm, 2020 The University of Southern Mississippi

#### A Dynamic F5 Algorithm, Candice Mitchell

*Dissertations*

Gröbner bases are a “nice” representation for nonlinear systems of polynomials, where by “nice” we mean they have good computation properties. They have many useful applications, including decidability (whether the system has a solution or not), ideal membership (whether a given polynomial is in the system or not), and cryptography. Traditional Gröbner basis algorithms require as input an ideal and an admissible term ordering. They then determine a Gröbner basis with respect to the given ordering. Some term orderings lead to a smaller basis, but finding them traditionally requires testing many orderings and hoping for better results. A dynamic algorithm ...

Written Reflections And Discussion Forums-- Math For Elementary School Teachers (Q2s-Ep: Math 301aqbr And Math 301bqbr ), 2020 California State University, San Bernardino

#### Written Reflections And Discussion Forums-- Math For Elementary School Teachers (Q2s-Ep: Math 301aqbr And Math 301bqbr ), Stephanie Creswell

*Q2S Enhancing Pedagogy*

Preparing for the transition from quarters to semesters, instructors of the mathematics sequence for future elementary teachers (Math 301ABC, Math 308 and their semester equivalents 3011, 3012 and 3013) applied research about best practices for online learning in mathematics to the quarter bridge courses Math 301AQBR and 301BQBR that each include 0.5 units of online activities. Successful activities piloted in the quarter bridge courses may be implemented in the 3011-3012-3013 semester sequence and their associated lab courses 3011L-3012L-3013L. This paper focuses on written reflections and group discussion forums associated with the class textbook Powerful Problem Solving by Max Ray.

Syllabus For Semester Bridge Course: Fundamental Concepts Of Math For Educators: Fundamental Concepts Of Algebra And Geometry & Problem Solving Through Theory And Practice (Math 301a Qbr), 2020 California State University, San Bernardino

#### Syllabus For Semester Bridge Course: Fundamental Concepts Of Math For Educators: Fundamental Concepts Of Algebra And Geometry & Problem Solving Through Theory And Practice (Math 301a Qbr), Lamies Nazzal, Joyce Ahlgren

*Q2S Enhancing Pedagogy*

The Quarter-to-Semester transition at CSUSB brought a number of challenges for many courses or course series. One of those included the math requirement for Liberal Studies series, Math 30x courses. The challenge here is that the 30x series includes four courses, yet the transition to semesters will yield three courses. In the Fall of 2020, the fourth 2-unit course in the series, Math 308 (Problem Solving Through Theory and Practice), will no longer be offered. Instead, it will be embedded into the first three courses. Students beginning the series after Fall 2019, will not have enough time to complete the ...

Mathematical And Physical Description Of Conical Intersections, 2020 Grand Valley State University

#### Mathematical And Physical Description Of Conical Intersections, Nicholas Dewey

*Honors Projects*

Conical intersections (CIs) are points of degeneracy between two or more potential energy surfaces. Due to the intersection point, it is much easier for molecules to transition their electronic, vibrational, and rotational energies between surfaces. Therefore, CIs are critical to the study of excited states, particularly in the context of photochemistry. However, they are difficult to study because they interfere with traditional thermodynamics and deviate from the Born-Oppenheimer approximation. The purpose of this review is to explain why that is the case by exploring the foundation for the mathematics and physics behind CIs. Also included is an application of how ...

Using Machine Learning Tools To Predict The Severity Of Osteoarthritis Based On Knee X-Ray Data, 2020 Marquette University

#### Using Machine Learning Tools To Predict The Severity Of Osteoarthritis Based On Knee X-Ray Data, Yaorong Xiao

*Master's Theses (2009 -)*

Knee osteoarthritis(OA) is a very general joint disease that disturb many people especially people over 60. The severity of pain caused by knee OA is the most important portent to disable. Until now, the bad impact of osteoarthritis on health care and public health systems is still increasing.In this paper, we will build a machine learning model to detect the edge of the knee based on the X-ray image and predict the severity of OA. We use a clustering algorithm and machine learning tools to predict the severity of OA in knee X-ray images. The data is coming ...

Local-Global Principles For Diophantine Equations, 2020 Liberty University

#### Local-Global Principles For Diophantine Equations, Benjamin Barham

*Senior Honors Theses*

The real number field, denoted **ℝ**, is the most well-known extension field of ℚ, the field of rational numbers, but it is not the only one. For each prime *p*, there exists an extension field ℚ* _{p}* of ℚ, and these fields, known as the

*p*-adic fields, have some properties substantially different from

**ℝ**. In this paper, we construct the

*p*-adic numbers from the ground up and discuss the local-global principle, which concerns connections between solutions of equations found in ℚ and in ℚ

*. We state the Hasse-Minkowski theorem, which addresses a type of Diophantine equation to ...*

_{p}Analysis Of The Homeless Population Of Three Major Cities, 2020 Merrimack College

#### Analysis Of The Homeless Population Of Three Major Cities, Katherine Ferrara

*Honors Senior Capstone Projects*

No abstract provided.

Nonnegative Matrix Factorization Problem, 2020 William & Mary

#### Nonnegative Matrix Factorization Problem, Junda An

*Undergraduate Honors Theses*

The Nonnegative Matrix Factorization (NMF) problem has been widely used to analyze high-dimensional nonnegative data and extract important features. In this paper, I review major concepts regarding NMF, some NMF algorithms and related problems including initialization strategies and near separable NMF. Finally I will implement algorithms on generated and real data to compare their performances.

Recursive Formulas For Beans Functions Of Graphs, 2020 Yokohama National University

#### Recursive Formulas For Beans Functions Of Graphs, Kengo Enami, Seiya Negami

*Theory and Applications of Graphs*

In this paper, we regard each edge of a connected graph $G$ as a line segment having a unit length, and focus on not only the "vertices" but also any "point" lying along such a line segment. So we can define the distance between two points on $G$ as the length of a shortest curve joining them along $G$. The *beans function* $B_G(x)$ of a connected graph $G$ is defined as the maximum number of points on $G$ such that any pair of points have distance at least $x>0$. We shall show a recursive formula for $B_G(x ...

Compactifications Of Cluster Varieties Associated To Root Systems, 2020 University of Massachusetts Amherst

#### Compactifications Of Cluster Varieties Associated To Root Systems, Feifei Xie

*Doctoral Dissertations*

In this thesis we identify certain cluster varieties with the complement of a union of closures of hypertori in a toric variety. We prove the existence of a compactification $Z$ of the Fock--Goncharov $\mathcal{X}$-cluster variety for a root system $\Phi$ satisfying some conditions, and study the geometric properties of $Z$. We give a relation of the cluster variety to the toric variety for the fan of Weyl chambers and use a modular interpretation of $X(A_n)$ to give another compactification of the $\mathcal{X}$-cluster variety for the root system $A_n$.

On Selected Subclasses Of Matroids, 2020 Louisiana State University at Baton Rouge

#### On Selected Subclasses Of Matroids, Tara Elizabeth Fife

*LSU Doctoral Dissertations*

Matroids were introduced by Whitney to provide an abstract notion of independence.

In this work, after giving a brief survey of matroid theory, we describe structural results for various classes of matroids. A connected matroid $M$ is unbreakable if, for each of its flats $F$, the matroid $M/F$ is connected%or, equivalently, if $M^*$ has no two skew circuits. . Pfeil showed that a simple graphic matroid $M(G)$ is unbreakable exactly when $G$ is either a cycle or a complete graph. We extend this result to describe which graphs are the underlying graphs of unbreakable frame matroids. A laminar ...

Renewal Redundant Systems Under The Marshall–Olkin Failure Model. A Probability Analysis, 2020 Kettering University

#### Renewal Redundant Systems Under The Marshall–Olkin Failure Model. A Probability Analysis, Boyan Dimitrov, Vladimir Rykov, Tatiana Milovanova

*Mathematics Publications*

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical ...

Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, 2020 University of Technology, Iraq

#### Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, Raghad Kadhim Salih

*Emirates Journal for Engineering Research*

A proposed method is presented to solve n^{th} order linear retarded Volterra integro-differential equations (RVIDE's) numerically by using fourth-order block and Weddle methods. Comparison between numerical and exact results has been given in numerical examples for conciliated the accuracy of the results of the proposed scheme.

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, 2020 University of Technology, Iraq

#### Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

*Emirates Journal for Engineering Research*

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.

Memory-Modulated Cir Process With Discrete Delay Coefficients, 2020 University of Indianapolis, Indianapolis, IN 46227, USA

#### Memory-Modulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa

*Journal of Stochastic Analysis*

No abstract provided.

Alternating Connectivity In Random Graphs, 2020 Western Michigan University

#### Alternating Connectivity In Random Graphs, Patrick Bennett, Ryan Cushman, Andrzej Dudek

*Faculty Research and Creative Activities Award (FRACAA)*

Many problems in graph theory are so hard in general that they seem hopeless. So sometimes mathematicians lower our expectations a bit, and try to prove that a statement is true for "almost all graphs" (for some reasonable interpretation of what that means) rather than insisting on proving it for all graphs. One way to address questions about about almost all graphs to use a random graph model, the first of which is due to Erdos, Rényi and Gilbert in the 1950's. Since then many more models have been introduced, but they all generate graphs according to the outcome ...

Some Exit Time Estimates For Super-Brownian Motion And Fleming-Viot Process, 2020 University of Pittsburgh, Pittsburgh, PA 15260, USA

#### Some Exit Time Estimates For Super-Brownian Motion And Fleming-Viot Process, Parisa Fatheddin

*Journal of Stochastic Analysis*

No abstract provided.

Triangles In Ks-Saturated Graphs With Minimum Degree T, 2020 California State University, Sacramento

#### Triangles In Ks-Saturated Graphs With Minimum Degree T, Craig Timmons, Benjamin Cole, Albert Curry, David Davini

*Theory and Applications of Graphs*

For $n \geq 15$, we prove that the minimum number of triangles in an $n$-vertex

$K_4$-saturated graph with minimum degree 4 is exactly $2n-4$, and that there is a unique extremal

graph.

This is a triangle version of a result of

Alon, Erd\H{o}s, Holzman, and Krivelevich from 1996.

Additionally, we show that for any $s > r \geq 3$ and $t \geq 2 (s-2)+1$, there

is a $K_s$-saturated $n$-vertex graph with minimum degree $t$ that has

$\binom{ s-2}{r-1}2^{r-1} n + c_{s,r,t}$ copies of $K_r$. This shows that

unlike ...

Groups Of Divisibility, 2020 University of South Dakota

#### Groups Of Divisibility, Seth J. Gerberding

*Honors Thesis*

In this thesis, we examine a part of abstract algebra known as Groups of Divisibility. We construct these special groups from basic concepts. We begin with partially-ordered sets, then build our way into groups, rings, and even structures akin to rings of polynomials. In particular, we explore how elementary algebra evolves when an ordering is included with the operations. Our results follow the work done by Anderson and Feil, however we include more explicit proofs and constructions. Our primary results include proving that a group of divisibility can be provided with an order to make it a partially-ordered group; that ...