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 computed from the distribution of A.
If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
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 the coefficients of polynomials are selected by some random process, the zeros of the resulting polynomials are in some sense random. In this paper the author rephrases the above in more precise language, and calculates the joint conditional densi
ties of a random vector whose values determine almost surely the zeros of a random reduced cubic.
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 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 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 collection of subsets of the underlying set.
We consider bargaining problems which involve two participants, with a nonempty closed, bounded convex bargaining set of points in the real plane representing all realizable bargains. We also assume that there is no definite threat or disagreement po
int which will provide the default bargain if the players cannot agree on some point in the bargaining set. However, there is a nondeterministic threat: if the players fail to agree on a bargain, one of them will be chosen at random with equal probability, and that chosen player will select any realizable bargain as the solution, subject to a reasonable restriction.
In this paper we show how to approximate (learn) a function f, where X and Y are metric spaces.
