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Defining the Mean of a Real-Valued Function on an Arbitrary Metric Space
Kerry Michael Soileau
We show how a metric space induces a linear functional (a "mean") on real-valued functions with domains in that metric space. This immediately induces a "relative" measure on a col…
A parameterization of the Fermat curves satisfying x^(2N)+y^(2N)=1
Kerry M. Soileau
Note that the family of closed curves C_N={(x,y)\in R^2;x^(2N)+y^(2N)=1} for N=1,2,3,... approaches the boundary of [-1,1]^2 as N \to \infty. In this paper we exhibit a natural par…
The General Form Of Cyclic Orthonormal Generators In R^N
Kerry M. Soileau
In this paper we give a definition of cyclic orthonormal generators (cogs) in R^N. We give a general canonical form for their expression. Further, we give an explicit formula for c…
Representation Of Level Paths Of An Analytic Function
Kerry M. Soileau
We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly…