Zobrazeno 1 - 10
of 958
pro vyhledávání: '"Nixon, James A."'
Autor:
Bury, Stephen
Publikováno v:
Benezit Dictionary of British Graphic Artists and Illustrators, 1 ed., 2013.
Externí odkaz:
http://www.oxfordreference.com/view/10.1093/acref/9780199923052.001.0001/acref-9780199923052-e-2008
Autor:
Nixon, James David
In this report we construct a family of holomorphic functions $\beta_{\lambda,\mu} (s)$ which behave asymptotically like iterated exponentials as $|s| \to \infty$ in the right half plane. Each $\beta_{\lambda,\mu}$ satisfies a convenient functional r
Externí odkaz:
http://arxiv.org/abs/2208.05328
Autor:
Nixon, James David
Using infinite compositions, we solve the general equations $P(\lambda w) = p(w)f(P(w))$ for holomorphic functions $p$ and $f$. We describe the situations in which this equation is palpable; and their effectiveness at describing dynamical properties
Externí odkaz:
http://arxiv.org/abs/2108.13519
Autor:
Nixon, James David
This is a summation of research done in the author's second and third year of undergraduate mathematics at The University of Toronto. As the previous details were largely scattered and disorganized; the author decided to rewrite the cumulative resear
Externí odkaz:
http://arxiv.org/abs/2106.03935
Autor:
Nixon, James David
In this paper we construct a family of holomorphic functions $\beta_\lambda (s)$ which are solutions to the asymptotic tetration equation. Each $\beta_\lambda$ satisfies the functional relationship ${\displaystyle \beta_\lambda(s+1) = \frac{e^{\beta_
Externí odkaz:
http://arxiv.org/abs/2104.01990
Autor:
Nixon, James David
The author provides a solution to the equation $ y(s+2) = \mathcal{T}^2 y = F(s,y,\mathcal{T} y) = F(s,y(s),y(s+1))$; where $y$ is holomorphic; and $F$ is a holomorphic function with specific decay conditions. This result is provided using infinite c
Externí odkaz:
http://arxiv.org/abs/2103.09292
Autor:
Nixon, James David
The author makes use of infinite compositions and a limiting function to construct a $\mathcal{C}^\infty$ tetration function $\mathcal{F}(t) = e \tet t$. As a tetration function, $\mathcal{F}$ satisfies $e^{\mathcal{F}(t)} = \mathcal{F}(t+1)$. Of it,
Externí odkaz:
http://arxiv.org/abs/2101.03021
Autor:
Nixon, James David
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at recovering
Externí odkaz:
http://arxiv.org/abs/2003.05280
Autor:
Nixon, James David
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief notice ai
Externí odkaz:
http://arxiv.org/abs/2001.04248
Autor:
Nixon, James David
For a nice holomorphic function $f(s, z)$ in two variables, a respective holomorphic Gamma function $\Gamma = \Gamma_f$ is constructed, such that $f(s, \Gamma(s)) = \Gamma(s + 1)$. Along the way, we fall through a rabbit hole of infinite compositions
Externí odkaz:
http://arxiv.org/abs/1910.05111