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A Necessary Condition on the Collatz Conjecture
Kerry M. Soileau
The Collatz conjecture implies that an iterated function sequence under a certain linear operator, beginning with a certain complex valued function, must converge to a certain comp…
Definition and Existence of the Eigenderivative
Kerry M. Soileau
We define the eigenderivatives of a linear operator on any real or complex Banach space, and give a sufficient condition for their existence.
A Generalization of the Idea of Disjunction
Kerry M. Soileau
We generalize the concept of disjunction.
Consistency Spaces
Kerry M. Soileau
We introduce the concept of a consistency space. The idea of the consistency space is motivated by the question, Given only the collection of sets of sentences which are logically…
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…
Linearizing a certain family of nonlinear differential equations
Kerry M. Soileau
We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.
Bounds on the cardinality of partition
Kerry M. Soileau
If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
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…
Implicit function density computation
Kerry Michael Soileau
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be comp…
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…