Procedures for determining the sample sizes to use in comparing the rates of two Poisson populations in order to achieve a pre-specified power at a given ratio of the rates are proposed. The first method relies on a conditional uniformly most powerful test (CUMPT) which leads to sample sizes...

We present a near complete solution of the GWP in braid groups for cyclic subgroups and arbitrary subgroups. We generalise the GWP and give solutions of this generalisation. This open problem on the discrete logarithm was proposed in [2]. In this paper we point out that the discrete logarithm...

The preference of bacterial genes for the leading strand of DNA is like the alignment of magnetic dipoles with an applied field as transcriptional polarity is entrained in the direction of replication. A one-dimensional Ising model formalizes this analogy and reduces the nucleotide sequences of...

By invoking known constraints on Brane Models in general that follow current Standard Model requirements of Supersymmetry I will show that some of the more recent modification to the Randall-Sundrum Model do not actual predict the ability to exist off the brane into hyperspace at all, but rather...

In this paper, we consider the existence and non-existence of non-trivial solution to a Brezis-Nirenberg type problem with singular weights. First, we obtain a compact imbedding theorem which is an extension of the classical Rellich-Kondrachov compact imbedding theorem, and consider the...

Two and three-dimensional finite volume extensions of the Lax-Friedrichs (LF) and Nessyahu-Tadmor (NT) one-dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems, and in particular to typical test cases for both...

Let R be a four-sided convex polygon in the xy plane and let M1 and M2 be the midpoints of the diagonals of R. It is well-known that if E is an ellipse inscribed in R, then the center of E must lie on Z, the open line segment connecting M1 and M2. We prove the converse: If (h,k) lies in Z, then...