A general form of Green's theorem

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

General form of a cooperative gradual maximal covering location problem

Cooperative and gradual covering are two new methods for developing covering location models. In this paper, a cooperative maximal covering location–allocation model is developed (CMCLAP). In addition, both cooperative and gradual covering concepts are applied to the maximal covering location simultaneously (CGMCLP). Then, we develop an integrated form of a cooperative gradual maximal covering ...

A General Correlation Theorem

A general ballot theorem

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.

A Dual Form of Ramsey’s Theorem

Let k E w, where w is the set of all natural numbers. Ramsey’s Theorem deals with colorings of the k-element subsets of w. Our dual form deals with colorings of the k-element partitions of w. Let (o)lr (respectively (w)“) be the set of all partitions of w having exactly k (respectively infinitely many) blocks. Given X E (w)” let (X)k be the set of all YE (w)” such that Y is coarser than X. Dual...