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Full-Text Articles in Physical Sciences and Mathematics
An Introduction To Shape Dynamics, Patrick R. Kerrigan
An Introduction To Shape Dynamics, Patrick R. Kerrigan
Physics
Shape Dynamics (SD) is a new fundamental framework of physics which seeks to remove any non-relational notions from its methodology. importantly it does away with a background space-time and replaces it with a conceptual framework meant to reflect direct observables and recognize how measurements are taken. It is a theory of pure relationalism, and is based on different first principles then General Relativity (GR). This paper investigates how SD assertions affect dynamics of the three body problem, then outlines the shape reduction framework in a general setting.
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
Master's Theses
In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Mathematics
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier (Proc Symp Pure Math 54(3):37–44, 1993).
Computing Homology Of Hypergraphs, Jackson Earl
Computing Homology Of Hypergraphs, Jackson Earl
STAR Program Research Presentations
In the modern age of data science, the necessity for efficient and insightful analytical tools that enable us to interpret large data structures inherently presents itself. With the increasing utility of metrics offered by the mathematics of hypergraph theory and algebraic topology, we are able to explore multi-way relational datasets and actively develop such tools. Throughout this research endeavor, one of the primary goals has been to contribute to the development of computational algorithms pertaining to the homology of hypergraphs. More specifically, coding in python to compute the homology groups of a given hypergraph, as well as their Betti numbers …