It is widely believed that the chemical master equation has no rigorous microphysical basis, and hence no a priori claim to validity. This view is challenged here through arguments purporting to show that the chemical master equation is exact for any gas-phase chemical system that is kept well stirred and thermally equilibrated.

A simple and general derivation of Josephson formulae for the tunneling currents is presented on the basis of Sewell’s general formulation of superconductivity in use of off-diagonal long range order (ODLRO).

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivatio...

A multi-parafermion basis of states for the Zk parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple-sum which enumerates partitions whose parts separated by the distance k− 1 differ by at least 2. Two analogous bases are derived for graded parafermions; one of these entails a new expression for their fermionic charac...

This paper is the first part of a two-part paper on maximum likelihood (ML) estimation of structure parameters from electron microscopy images. In principle, electron microscopy allows structure determination with a precision that is orders of magnitude better than the resolution of the microscope. This requires, however, a quantitative, model-based method. In our opinion, the ML method is the ...

The shrinkage estimate of a quantitative trait locus (QTL) effect is the posterior mean of the QTL effect when a normal prior distribution is assigned to the QTL. This note gives the derivation of the shrinkage estimate under the multivariate linear model. An important lemma regarding the posterior mean of a normal likelihood combined with a normal prior is introduced. The lemma is then used to...

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general «-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left ■EW*-algebra induced by an unbounded Hub...

Rabindra R. Bajracharya and John R. Thompson Department of Physics, 301 Weniger Hall, Oregon State University, Corvallis, Oregon 97331, USA Department of Physics and Astronomy, University of Maine, 5709 Bennett Hall, Orono, Maine 04469-5709, USA Maine Center for Research in STEM Education, University of Maine, 5727 Estabrooke Hall, Orono, Maine 04469-5727, USA (Received 24 July 2015; published ...

A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are ...