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Radial Singular Solutions To Semilinear Partial Differential Equations, Marcelo A. Almora RIos 2021 Claremont Colleges 81818app手机版下载

Radial Singular Solutions To Semilinear Partial Differential Equations, Marcelo A. Almora Rios

HMC Senior Theses

We show the existence of countably many non-degenerate continua of singular radial solutions to a p-subcritical, p-Laplacian Dirichlet problem on the unit ball in R^N. This result generalizes those for the 2-Laplacian to any value p and extends recent work on the p-Laplacian by considering solutions both radial and singular.


Geometric Unified Method In 3d Object Classification, Mengyi Shan 2021 Claremont Colleges

Geometric Unified Method In 3d Object Classification, Mengyi Shan

HMC Senior Theses

81818app手机版下载3D object classification is one of the most popular topics in the field of computer vision and computational geometry. Currently, the most popular state-of-the-art algorithm is the so-called Convolutional Neural Network (CNN) models with various representations that capture different features of the given 3D data, including voxels, local features, multi-view 2D features, and so on. With CNN as a holistic approach, researches focus on improving the accuracy and efficiency by designing the neural network architecture. This thesis aims to examine the existing work on 3D object classification and explore the underlying theory by integrating geometric approaches. By using geometric algorithms ...


An Enticing Study Of Prime Numbers Of The Shape 𝑝 = 𝑥^2 + 𝑦^2, Xiaona Zhou 2020 CUNY New York City College of Technology

An Enticing Study Of Prime Numbers Of The Shape 𝑝 = 𝑥^2 + 𝑦^2, Xiaona Zhou

Publications and Research

We will study and prove important results on primes of the shape 𝑥2 + 𝑦281818app手机版下载 using number theoretic techniques. Our analysis involves maps, actions over sets, fixed points and involutions. This presentation is readily accessible to an advanced undergraduate student and lay the groundwork for future studies.


Sum Of Cubes Of The First N Integers, Obiamaka L. Agu 2020 California State University, San Bernardino

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

81818app手机版下载In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at ...


Delta Hedging Of Financial Options Using Reinforcement Learning And An Impossibility Hypothesis, Ronak Tali 2020 Utah State University 81818app手机版下载

Delta Hedging Of Financial Options Using Reinforcement Learning And An Impossibility Hypothesis, Ronak Tali

All Graduate Theses and Dissertations

81818app手机版下载In this thesis we take a fresh perspective on delta hedging of financial options as undertaken by market makers. The current industry standard of delta hedging relies on the famous Black Scholes formulation that prescribes continuous time hedging in a way that allows the market maker to remain risk neutral at all times. But the Black Scholes formulation is a deterministic model that comes with several strict assumptions such as zero transaction costs, log normal distribution of the underlying stock prices, etc. In this paper we employ Reinforcement Learning to redesign the delta hedging problem in way that allows us ...


Classification Of Jacobian Elliptic Fibrations On A Special Family Of K3 Surfaces Of Picard Rank Sixteen, Thomas Hill 2020 Utah State University 81818app手机版下载

Classification Of Jacobian Elliptic Fibrations On A Special Family Of K3 Surfaces Of Picard Rank Sixteen, Thomas Hill

All Graduate Theses and Dissertations

K3 surfaces are an important tool used to understand the symmetries in physics that link different string theories, called string dualities. For example, heterotic string theory compactified on an elliptic curve describes a theory physically equivalent to (dual to) F-theory compactified on a K3 surface. In fact, M-theory, the type IIA string, the type IIB string, the Spin(32)/Z2 heterotic string, and the E8 x E8 heterotic string are all related by compactification on Calabi-Yau manifolds.

We study a special family of K3 surfaces, namely a family of rank sixteen K3 surfaces polarized by the lattice ...


Weather Derivatives And The Market Price Of Risk, Julius Esunge, James J. Njong 2020 University of Mary Washington, Fredericksburg, Virginia USA 81818app手机版下载

Weather Derivatives And The Market Price Of Risk, Julius Esunge, James J. Njong

Journal of Stochastic Analysis

No abstract provided.


Use Of Mathematics In Costume Design And Construction, Ryan DiPaola 2020 State University of New York College at Brockport

Use Of Mathematics In Costume Design And Construction, Ryan Dipaola

Senior Honors Theses

My journey at Brockport did not follow the typical mathematics major’s path; as a student in the adolescent education program, I focused on topics of mathematical literacy, including conceptual understanding, procedural fluency, and mathematical reasoning. As an Honors student, I supplemented my learning experience by contracting courses in stage makeup and costume construction. This thesis combines what I’ve learned across the disciplines, and demonstrates the importance of teaching for mathematical literacy, and the benefits of recognizing underlying mathematical concepts and making informed decisions based on them.


Spectral Properties Of Quaternionic Unit Gain Cycles, Nolan J. Coble 2020 State University of New York College at Brockport

Spectral Properties Of Quaternionic Unit Gain Cycles, Nolan J. Coble

Senior Honors Theses

81818app手机版下载The quaternions are a non-commutative division ring that extends the complex numbers. A gain graph is a simple graph together with a gain function that assigns a value from an arbitrary group to each edge of the graph. We can define certain concepts on these graphs such as adjacency and Laplacian matrices, gains of paths, and more. If we restrict ourselves to the unit norm quaternions, we can define quaternionic unit gain graphs, or U(H)-gain graphs, as gain graphs where the domain of the gain function is the unit quaternions. Traditional methods from spectral graph theory are not ...


Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth 2020 Wentworth Institute of Technology

Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth

CODEE Journal

Specifications-based grading (SBG) is an assessment scheme in which student grades are based on demonstrated understanding of known specifications which are tied to course learning outcomes. Typically with SBG, students are given multiple opportunities to demonstrate such understanding. In undergraduate-level introductory ordinary differential equations courses at two institutions, SBG has been found to markedly decrease students’ self-reported anxiety related to the course as compared to traditionally graded courses.


Simulating Phase Transitions And Control Measures For Network Epidemics Caused By Infections With Presymptomatic, Asymptomatic, And Symptomatic Stages, Benjamin Braun, Başak Taraktaş, Brian Beckage, Jane Molofsky 2020 University of Kentucky

Simulating Phase Transitions And Control Measures For Network Epidemics Caused By Infections With Presymptomatic, Asymptomatic, And Symptomatic Stages, Benjamin Braun, Başak Taraktaş, Brian Beckage, Jane Molofsky

Mathematics Faculty Publications

We investigate phase transitions associated with three control methods for epidemics on small world networks. Motivated by the behavior of SARS-CoV-2, we construct a theoretical SIR model of a virus that exhibits presymptomatic, asymptomatic, and symptomatic stages in two possible pathways. Using agent-based simulations on small world networks, we observe phase transitions for epidemic spread related to: 1) Global social distancing with a fixed probability of adherence. 2) Individually initiated social isolation when a threshold number of contacts are infected. 3) Viral shedding rate. The primary driver of total number of infections is the viral shedding rate, with probability of ...


Exchangeably Weighted Bootstraps Of Martingale Difference Arrays Under The Uniformly Integrable Entropy, Salim Bouzebda, Nikolaos Limnios 2020 Alliance Sorbonne Universités, Université de Technologie de Compiègne, L.M.A.C., Compiègne, France

Exchangeably Weighted Bootstraps Of Martingale Difference Arrays Under The Uniformly Integrable Entropy, Salim Bouzebda, Nikolaos Limnios

Journal of Stochastic Analysis

No abstract provided.


On An Asset Model Of Hobson-Rogers Type, Narn-Rueih Shieh 2020 4F Astro-Math Building, National Taiwan University, Taipei 10617, Taiwan

On An Asset Model Of Hobson-Rogers Type, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.


Tile Based Self-Assembly Of The Rook's Graph, Ernesto Gonzalez 2020 California State University, San Bernardino 81818app手机版下载

Tile Based Self-Assembly Of The Rook's Graph, Ernesto Gonzalez

Electronic Theses, Projects, and Dissertations

81818app手机版下载The properties of DNA make it a useful tool for designing self-assembling nanostructures. Branched junction molecules provide the molecular building blocks for creating target complexes. We model the underlying structure of a DNA complex with a graph and we use tools from linear algebra to optimize the self-assembling process. Some standard classes of graphs have been studied in the context of DNA self-assembly, but there are many open questions about other families of graphs. In this work, we study the rook's graph and its related design strategies.


Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo 2020 The Graduate Center, City University of New York 81818app手机版下载

Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo

Dissertations, Theses, and Capstone Projects

In this thesis we obtain the growth rates for conjugacy classes of reciprocal words for triangle groups of the form G = Z2 ∗ H where H is finitely generated and does not contain an order 2 element. We explore cases where H is infinite cyclic and finite cyclic. The quotient O = H/G is an orbifold and contains a cone point of order 2, due to the first factor Z2 in the free product G. The reciprocal words in G correspond to geodesics on O which pass through the order 2 cone point on O. We use methods from analytic combinatorics ...


Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, Corey B. Switzer 2020 The Graduate Center, City University of New York 81818app手机版下载

Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, Corey B. Switzer

Dissertations, Theses, and Capstone Projects

81818app手机版下载This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from Baire space to Baire space ...


Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner 2020 Gettysburg College 81818app手机版下载

Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner

Math Faculty Publications

81818app手机版下载An arithmetical structure on a graph is given by a labeling of the vertices that satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical structures for graphs in these families.


Nonparametric Recursive Method For Kernel-Type Function Estimators For Censored Data, Salim Bouzebda, Yousri Slaoui 2020 Alliance Sorbonne Universités, Université de Technologie de Compiègne, L.M.A.C., Compiègne, France

Nonparametric Recursive Method For Kernel-Type Function Estimators For Censored Data, Salim Bouzebda, Yousri Slaoui

Journal of Stochastic Analysis

81818app手机版下载No abstract provided.


Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss 2020 Marshall University

Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss

Mathematics Faculty Research

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of ...


General Product Formula Of Multiple Integrals Of Lévy Process, Nishant Agrawal, Yaozhong Hu, Neha Sharma 2020 University of Alberta, Edmonton, Alberta, T6G 2R3, Canada

General Product Formula Of Multiple Integrals Of Lévy Process, Nishant Agrawal, Yaozhong Hu, Neha Sharma

Journal of Stochastic Analysis

No abstract provided.