The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather t...

Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...

We show that if one takes into account Penrose’s conformal technique in the Einstein-Cartan gravity, it is possible to obtain a relation between Hubble’s expansion and Birch’s rotation of the Universe at spacelike infinity. This relation also leads to the final reduction of the gravitational coupling to a dimensionless quantity of order unity at spacelike infinity. Initial-value equations at sp...

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube Γ and on characteristic data on an outgoing null cone emanating from an initial cross-section of Γ. We present the details of a 3-dimensional computational algori...

In this paper we prove that under a lower bound on the Ricci curvature and an asymptotic assumption on the scalar curvature, a complete conformally compact manifold (M, g), with a pole p and with the conformal infinity in the conformal class of the round sphere, has to be the hyperbolic space.

Researchers designing experiments in which a sample of participants responds to a sample of stimuli are faced with difficult questions about optimal study design. The conventional procedures of statistical power analysis fail to provide appropriate answers to these questions because they are based on statistical models in which stimuli are not assumed to be a source of random variation in the d...

We give two proofs of a conjecture of Neumann [N1] that a reduced algebraic plane curve is regular at infinity if and only if its link at infinity is a regular toral link. This conjecture has also been proved by Ha H. V. [H] using Lojasiewicz numbers at infinity. Our first proof uses the polar invariant and the second proof uses linear systems of plane curve singularities. The second approach a...

We investigate a random proposer bargaining game with a dead line. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcome as the number of bargaining periods goes to infinity while the dead line is kept fixed. This limit is close to the Raiffa solution when the time horizon is very short. If the dead line goes...

We consider a simple model of an autocatalytic chemical reaction where a limit cycle rapidly increases to infinite period and amplitude, and disappears under variation of a parameter. We show that this bifurcation can be understood from seeing the system as a singular perturbation problem, and we find the bifurcation point by an asymptotic analysis. Scaling laws for period and amplitude are der...

In this note we consider the spectrum of the Laplacian acting on the space of (co-closed) differential forms on the quotient of /i-dimensional hyperbolic space by a co-compact Kleinian group. Using a result of P.-Y. Gaillard we relate these to currents on the sphere at infinity of hyperbolic space with distinctive transformation properties under the action of the group. We analyse these current...