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Definition and Existence of the Eigenderivative

Soileau Kerry M.
15 Sep 2011 math.GM arxiv.org/abs/1109.4025

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

Soileau Kerry M.
13 Jul 2010 math.GM arxiv.org/abs/1007.3440

We generalize the concept of disjunction.

Consistency Spaces

Soileau Kerry M.
09 Dec 2008 math.GM arxiv.org/abs/0812.1728

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 consistent, is it possible to reconstruct their lattice structure?

Linearizing a certain family of nonlinear differential equations

Soileau Kerry M.
10 Jun 2008 math.GM arxiv.org/abs/0806.1721

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

Soileau Kerry M.
14 Nov 2007 math.GM arxiv.org/abs/0711.2241

If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.

A general learning algorithm for functions between metric spaces

Soileau Kerry M.
13 Sep 2007 math.FA math.GM arxiv.org/abs/0709.2155

In this paper we show how to approximate ("learn") a function f, where X and Y are metric spaces.

A parameterization of the Fermat curves satisfying x^(2N)+y^(2N)=1

Soileau Kerry M.
20 Jul 2007 math.GM arxiv.org/abs/0707.3143

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 parameterization of these curves and generalize to a larger class of equations.

The Maximal Integral Domain Generated By A Commutative Ring

Soileau Kerry M.
14 May 2007 math.RA math.AC arxiv.org/abs/0705.2063

In this paper, we exhibit the creation of the maximal integral domain mid(R) generated by a nonzero commutative ring R.

A homotopy method for finding eigenvalues and eigenvectors

Soileau Kerry M.
11 May 2007 math.FA math.SP arxiv.org/abs/0705.1708

Suppose we want to find the eigenvalues and eigenvectors for the linear operator L, and suppose that we have solved this problem for some other "nearby" operator K. In this paper we show how to represent the eigenvalues and eigenvectors of L in terms of the corresponding properties of K.

State Vector Determination By A Single Tracking Satellite

Soileau Kerry M.
08 May 2007 astro-ph arxiv.org/abs/0705.1155

Using only a single tracking satellite capable of only range measurements to an orbiting object in an unknown Keplerian orbit, it is theoretically possible to calculate the orbit and a current state vector. In this paper we derive an algorithm that can perform this calculation.