Browsing Mathematics by Title
Now showing items 29-36 of 36
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A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
(East Carolina University, 2010)The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and ... -
Random Walks on Finite Fields and Heisenberg Groups
(East Carolina University, 2011)Let H be a finite group and [mu] a probability measure on H. This data determines an invariant random walk on H beginning from the identity element. The probability distribution for the state of the random walk after n ... -
Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms
(2022-07-07)For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this ... -
The Spectral Theorem for Self-Adjoint Operators
(East Carolina University, 2016-04-25)The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing ... -
Theorems in Visual Art: Art and Math Teacher Collaboration toward Creative Leadership
(2018)An artist and a mathematician meet. The authors of this article, one an art education professor and the other a mathematics professor, collaborated to conduct research as a team, examining perceptions of K-12 art ... -
Theoretical aspects and modelling of cellular decision making, cell killing and information-processing in photodynamic therapy of cancer
(2013)BACKGROUND: The aim of this report is to provide a mathematical model of the mechanism for making binary fate decisions about cell death or survival, during and after Photodynamic Therapy (PDT) treatment, and to supply ...