We define the eigenderivatives of a linear operator on any real or complex Banach space, and give a sufficient condition for their existence.
We generalize the concept of disjunction.
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?
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.
If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
In this paper we show how to approximate ("learn") a function f, where X and Y are metric spaces.
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.
In this paper, we exhibit the creation of the maximal integral domain mid(R) generated by a nonzero commutative ring R.
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.
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.