Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra
Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra
Publications and Research
No abstract provided.
An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou
An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou
Publications and Research
We will study and prove important results on primes of the shape ��2 + ��2 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.
A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens
A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens
Publications and Research
We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster’s small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster’s small MCM conjecture.
An In-Depth Look At P-Adic Numbers, Xiaona Zhou
An In-Depth Look At P-Adic Numbers, Xiaona Zhou
Publications and Research
In this study, we consider $p$-adic numbers. We will also study the $p$-adic norm representation of real number, which is defined as $\mathbb{Q}_p = \{\sum_{j=m}^{\infty }a_j p^j: a_j \in \mathbb{D}_p, m\in\mathbb{Z}, a_m\neq 0\} \cup \{0\}$, where $p$ is a prime number. We explore properties of the $p$-adics by using examples. In particular, we will show that $\sqrt{6},i \in \mathbb{Q}_5$ and $\sqrt{2} \in \mathbb{Q}_7 $. $p$-adic numbers have a wide range of applicationsnin fields such as string theory, quantum mechanics, and transportation in porous disordered media in geology.
Winding Numbers And Full Extendability In Holomorphic Motions, Yunping Jiang
Winding Numbers And Full Extendability In Holomorphic Motions, Yunping Jiang
Publications and Research
We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.
Estimating Population Immunity Without Serological Testing, Andrew Lesniewski
Estimating Population Immunity Without Serological Testing, Andrew Lesniewski
Publications and Research
We propose an approximate methodology for estimating the overall level of immunity against COVID-19 in a population that has been affected by the recent epidemic. The methodology relies on the currently available mortality data and utilizes the properties of the SIR model. We illustrate the application of the method by estimating the recent levels of immunity in 10 US states with highest case numbers of COVID-19.
The Tsukano Conjectures On Exponential Sums, Brad Isaacson
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.