From a mathematical and physics treatment of Mach's Principle in conjunction with the RS Model of Brane dynamics one can conclude that while a quantum version of the Aether does exist such a frame is constrained by Mach's principle to always obey the parameters of the Mickelson-Morley Experiment...

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper...

This article starts with the mathematical definition, concrete description, and physical meaning of Cartan's torsion. I proceed with the argumentation that torsion is required for the description of intrinsic spin. Moreover I argue that the duality between curvature and torsion is analogous to...

Several years ago, I suggested a quantum field theory which has many attractive features. (1) It can explain the quantization of electric charge. (2) It describes symmetrized Maxwell equations. (3) It is manifestly covariant. (4) It describes local four-potentials. (5) It avoids the unphysical...

The Laplacian matrix, , of a weighted digraph is a generalization of the Laplacian (Kirchhoff, admittance) matrix of an ordinary graph. For a weighted digraph whose arc weights belong to [0, 1], the standardized Laplacian matrix ′ is divided by , the number of vertices. We show that the...

In an earlier paper of the author's, partial differential equations with constant coefficients have been studied. Under a certain (restrictive) assumption upon the equation, those initial conditions were characterized for which the normalized formal solution of a corresponding Cauchy problem is...

We study power series whose coefficients are holomorphic functions of another complex variable and a non-negative real parameter , and are given by a differential recursion equation. For positive integer , series of this form naturally occur as formal solutions of some partial differential...

The Minimum Message Length approach to inference has been expounded at length (Wallace and Freeman, 1987, 1992) but it has yet to be adopted with any great enthusiasm by the statistical community. A possible reason may be the complexity of the symbolic determinant calculations required to...

We use a new idea about the test-and-branch (TAB) operation, familiar to computer programmers, to justify a probabilistic approach to the Sieve of Eratosthenes. We use random variable methods to derive an ‘information distribution law' for the outputs of the Sieve