Some questions concerning the ideal Bose-Einstein gas are reviewed and examined further.
The bulk behavior including the condensation phenomenon is characterized by the …

For a one‐dimensional fluid model where the pair interaction potential between the molecules
consists of a hard core and an exponential attraction, Kac has shown that the partition …

Statistical Mechanics of Assemblies of Coupled Oscillators * Page 1 504 OW GREENBERG
AND AML MESSIAH since in e(F)(l) the matrix element must be antisymmetric under …

Can One Hear the Shape of a Drum? Page 1 CAN ONE HEAR THE SHAPE OF A DRUM?
MARK KAC, The Rockefeller University, New York To George Eugene Uhlenbeck on the …

This book is an expanded version of twelve lectures delivered at the Seminar in Applied
Mathematics held in Boulder, Colorado, in the summer of 1957. Like the lectures, the book is …

A mathematical model, the spherical model, of a ferromagnet is described. The model is a
generalization of the Ising model; and one-, two-, and three-dimensional lattices of infinite …

The basic equation of the kinetic theory of dilute monatomic gases is the famous nonlinear
integro-differential equation of Boltzmann. In the simplest case when the molecules of the gas …

(1.1) Vixir)) dr J o where x (i) is an element of Wiener's space (OíS¿<<») and F (x) is subject
to certain restrictions. The most severe of these restrictions is that Vix) be nonnegative, or …

(1) Xo+ Xxx+ X2x2+•••+ In-i^" 1= 0, where the X's are independent random variables assuming
real values only, and denote by Nn= N (X0f•••, Xn-i) the number of real roots of (1). We …

Indeed, the first step will certainly take me a distance v At in the positive direction. Now I must
toss my coin and find what will happen to the velocity. It will change from v into€ ļt;, ie, it will …