An observed event being composed of simple events of the same kind and of which the possibility is unknown, to determine the probability that this possibility is comprehended within some given limits. Expression of this probability. Formula in order to determine it by a very convergent series, when the observed event is composed of a great number of these simple events. Extension of this formul...

When the Gaussian HJM model is recast in terms of simple forwards, it becomes dual to the LogNormal Forward model in the sense that for almost every formula in one model there is a similar formula in the other which can be obtained by simple transformation or substitution.

Abstract. We derive some Hodge integral identities by taking various limits of the Mariño-Vafa formula using the cut-and-join equation. These identities include the formula of general λg-integrals, the formula of λg−1-integrals on Mg,1, the formula of cubic λ integrals on Mg, and the ELSV formula relating Hurwitz numbers and Hodge integrals. In particular, our proof of the MV formula by the cut...

BACKGROUND Bonett and Wright (2011) proposed a simple and accurate sample size planning formula for estimating a squared multiple correlation with desired relative precision. Shieh (2013) incorrectly evaluated the accuracy of the Bonett-Wright formula. METHOD To address a criticism of Shieh that the Bonett-Wright formula was not examined under a wider range of conditions, the accuracy of the ...

We modify the recent analytic formula given by Allen and Casper [1] for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate momentum. The resulting formula (which is exact when the effects of gravitational back-reaction are neglected) is a sum of O(N4) polynomial and log terms w...

An old conjecture of Graham stated that if [Formula: see text] is a prime and [Formula: see text] is a sequence of [Formula: see text] terms from the cyclic group [Formula: see text] such that all (nontrivial) zero-sum subsequences have the same length, then [Formula: see text] must contain at most two distinct terms. In 1976, Erdős and Szemerédi gave a proof of the conjecture for sufficiently ...