Discrete Morse Theory By Vector Fields: A Survey And New Directions,
2020
Minnesota State University, Mankato
Discrete Morse Theory By Vector Fields: A Survey And New Directions, Matthew Nemitz
All Graduate Theses, Dissertations, and Other Capstone Projects
We synthesize some of the main tools in discrete Morse theory from various sources. We do this in regards to abstract simplicial complexes with an emphasis on vector fields and use this as a building block to achieve our main result which is to investigate the relationship between simplicial maps and homotopy. We use the discrete vector field as a catalyst to build a chain homotopy between chain maps induced by simplicial maps.
Classification Of The Real Roots Of The Quartic Equation And Their Pythagorean Tunes,
2020
Technological University Dublin
Classification Of The Real Roots Of The Quartic Equation And Their Pythagorean Tunes, Emil Prodanov
Articles
Presented is a two-tier analysis of the location of the real roots of the general quartic equation x4+ax3+bx2+cx+d=0 with real coefficients and the classification of the roots in terms of a, b, c, and d, without using any numerical approximations. Associated with the general quartic, there is a number of subsidiary quadratic equations (resolvent quadratic equations) whose roots allow this systematization as well as the determination of the bounds of the individual roots of the quartic. In many cases the root isolation intervals are found. The second tier of the analysis uses two subsidiary cubic equations (auxiliary cubic equations) and …
Model-Based Cluster Analysis Of Indiana Social Security Beneficiary Data,
2020
Butler University
Model-Based Cluster Analysis Of Indiana Social Security Beneficiary Data, Gwendolyn Spencer
Undergraduate Honors Thesis Collection
Annual reports of the U.S. Old-Age, Survivors, and Disability Insurance (OASDI) program, published by the Social Security Administration, detail the aggregate information about the program for each U.S. Postal ZIP code. This information includes the types of beneficiaries and monthly benefits received. These reports present the opportunity for contemporary analysis of the aggregate information about the OASDI program. To better capture the significance of the most-recent report for 2018, this project will use model-based cluster analysis, the unsupervised machine-learning process of grouping similar data points, to compare the 2017 and 2018 data. Due to the large amount of data, the …
Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model,
2020
University of Gujrat
Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman
Mathematics Faculty Publications
In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …
The Relative Gromov Width Of Lagrangian Cobordisms Between Legendrians,
2020
Haverford College
The Relative Gromov Width Of Lagrangian Cobordisms Between Legendrians, Sabloff M. Joshua, Lisa Traynor
Mathematics Faculty Research and Scholarship
We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of J-holomorphic disks with boundary on the Lagrangian cobordism that pass through the center of a given symplectically embedded ball. The areas of these disks - and hence the sizes of these balls - are controlled by a real-valued fundamental capacity, a quantity derived from the algebraic structure of filtered linearized Legendrian Contact Homology of the Legendrian at the top of the cobordism. Lower bounds come from explicit constructions that use neighborhoods of Reeb chords in the …
The Tsukano Conjectures On Exponential Sums,
2020
CUNY New York City College of Technology
The Tsukano Conjectures On Exponential Sums, Brad Isaacson
Publications and Research
We prove three conjectures of Tsukano about exponential sums stated in his Master’s thesis written at Osaka University. These conjectures are variations of earlier conjectures made by Lee and Weintraub which were first proved by Ibukiyama and Saito.
Saperi: Approaching Gender Gap Using Spatial Ability Training Week In High-School Context,
2020
Politecnico di Torino
Saperi: Approaching Gender Gap Using Spatial Ability Training Week In High-School Context, Maria Giulia Ballatore, Gavin Duffy, Sheryl Sorby, Anita Tabacco
Articles
Maria Giulia Ballatore, Gavin Duffy, Sheryl Sorby, and Anita Tabacco. 2020. SAperI: approaching gender gap using Spatial Ability training week in high-school context. In Eighth International Conference on Technological Ecosystems for Enhancing Multiculturality (TEEM’20), October 21–23, 2020, Salamanca, Spain. ACM, New York, NY, USA, 7 pages. https://doi.org/10.1145/3434780.3436577
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability,
2020
Technological University Dublin
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze
Articles
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …
Designing A National Blended Learning Program For “Out‑Of‑Field” Mathematics Teacher Professional Development,
2020
The University of Queensland, Australia
Designing A National Blended Learning Program For “Out‑Of‑Field” Mathematics Teacher Professional Development, Merrilyn Goos, John O’Donoghue, Máire Ní Ríordáin, Fiona Faulkner, Tony Hall, Niamh O'Meara
Articles
“Out-of-field” teaching refers to the practice of assigning secondary school teachers to teach subjects that do not match their training or education. This practice is an issue of concern in many countries around the world, and seems particularly prevalent in the teaching of mathematics. The aim of this paper is to analyse the design principles underpinning the development and delivery of a blended learning program of professional development for out-of-field teachers of secondary school mathematics in Ireland. Three theoretical frameworks inform our analysis of the blended learning design. The first identifies critical dimensions of blended learning environments as a boundary …
A Mosquito Population Model With Four Positive Equilibrium Points And Sterile Insect Release,
2020
University of Alabama in Huntsville
A Mosquito Population Model With Four Positive Equilibrium Points And Sterile Insect Release, Maxwell Fox
Summer Community of Scholars Posters (RCEU and HCR Combined Programs)
No abstract provided.
Kähler Metrics Via Lorentzian Geometry In Dimension Four,
2020
Clark University
Kähler Metrics Via Lorentzian Geometry In Dimension Four, Amir Babak Aazami, Gideon Maschler
Mathematics
Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under certain conditions g and gK share various properties, such as a Killing vector field or a vector field with a geodesic flow. In some cases the Kähler metrics are complete. The Ricci and scalar curvatures of gK are computed under certain assumptions in terms of data associated to g. Many examples are described, …
The Adjunction Inequality For Weyl-Harmonic Maps,
2020
Clark University
The Adjunction Inequality For Weyl-Harmonic Maps, Robert Ream
Mathematics
In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical '1-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality. The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well …
Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives,
2020
University at Albany, State University of New York
Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives, Sachin Munshi
Legacy Theses & Dissertations (2009 - 2024)
Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.
The Unrolled Quantum Group Of Sl(2) With Connections To Topological Quantum Field Theory And Vertex Operator Algebras,
2020
University at Albany, State University of New York
The Unrolled Quantum Group Of Sl(2) With Connections To Topological Quantum Field Theory And Vertex Operator Algebras, James F. Clark
Legacy Theses & Dissertations (2009 - 2024)
This dissertation expands on the work of Constantino, Geer, and Patureau-Mirand \cite{CGP}, as well as Creutzig, Milas, and Rupert \cite{CMR} on exploring the unrolled quantum group of $\mathfrak{sl}(2)$ (denoted by $\overline{U_q}^H(\mathfrak{sl}_2)$) and the category of finite dimensional weight $\overline{U_q}^H(\mathfrak{sl}_2)$-modules (denoted by $\mathscr{C}$) for any $p$\textsuperscript{th} root of unity where $p>2$. This unrolled quantum group and category has connections to topological quantum field theory (TQFT) and to vertex operator algebras (VOAs). Significant results of this dissertation include proving that the $\mathscr{C}$ is a ribbon category, finding all simple and projective modules of $\mathscr{C}$ and proving that they form a full …
An Exploration Of The Use Of The Fibonacci Sequence In Unrelated Mathematics Disciplines,
2020
University of New Hampshire, Durham
An Exploration Of The Use Of The Fibonacci Sequence In Unrelated Mathematics Disciplines, Molly E. Boodey
Honors Theses and Capstones
No abstract provided.
Asymptotic Properties Of Solutions To Second-Order Difference Equations,
2020
TÜBİTAK
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.
Submanifolds Of Almost Poly-Norden Riemannian Manifolds,
2020
TÜBİTAK
Submanifolds Of Almost Poly-Norden Riemannian Manifolds, Selcen Yüksel Perktaş
Turkish Journal of Mathematics
Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannian manifold, which is a new type of manifold first introduced by Şahin [17]. We give fundamental properties of submanifolds equipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditions for such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-Norden Riemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface of almost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components of the structure …
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category,
2020
TÜBİTAK
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an Eilenberg-MacLane-type description for the first, second and third spaces of the spectrum defined by a symmetric monoidal category.
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions,
2020
TÜBİTAK
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions, Şuayi̇p Yüzbaşi, Murat Karaçayir
Turkish Journal of Mathematics
In this paper, we present a weighted residual Galerkin method to solve linear functional differential equations. We consider the problem with variable coefficients under initial conditions. Assuming the exact solution of the problem has a Taylor series expansion convergent in the relevant domain, we seek a solution of the given problem in the form of a polynomial having degree $N$ of our choice. Substituting this polynomial with unknown coefficients in the given equation yields an expression linear in these coefficients. We then proceed as in the weighted residual method and take inner product of this expression with monomials up to …
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc,
2020
TÜBİTAK
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Turkish Journal of Mathematics
In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.
