The internal state of a gas of particles with spin

A Hamiltonian theory of motion for particles with internal structure, based on a dynamical bracket algebra, serves to define a generalized phase space for axially symmetric particles. Hydrodynamics of a gas of particles are explored through Liouville's and Boltzmann's equations and the equilibrium distribution function is obtained. Some modification of the pressure and density are necessary because of the spin and for a cold Fermi gas in thermal equilibrium they are shown explicitly.This work is based on a Ph.D. thesis of Y. Feldman submitted to Tel Aviv University in 1979.     

Bounds on completely convergent Euclidean Feynman graphs

LetG be a Euclidean Feynman graph containingL(G) lines. We prove that ifG has massive propagators and does not contain any divergent subgraphs its value is bounded byK ^L(G). We also prove the infrared analogue of this bound.     

Effect of CO2 laser-pulse mode quality on multiple photon absorption in SF6

Unimolecular multiple-photon absorption cross sections are measured for SF₆ for both single and multiple longitudinal mode CO₂ laser pulses at three different frequencies over a four-decade range of energy fluence. The results indicate only a weak dependence on pulse mode structure for fluence levels corresponding to as little as 0.02 photons absorbed per molecule.     

On the continuity of the spectrum in certain Banach algebras

In this paper we describe some classes of linear operatorsTL(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hilbert spacesH such that the spectrum (T, L(H)) is continuous at the pointsT from these classes. We also describe some subalgebras of the algebras for which the spectrum (x,) becomes continuous at the pointsx when (x,) is restricted to the subalgebra . In particular, we show that the spectrum (x,) is continuous in Banach algebras with polynomial identities. Examples of such algebras are given.This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.     

On a characterization of convolutions of Gaussian and Haar distributions

We prove some analogues of the well‐known Skitovich–Darmois and Heyde characterization theorems for a second countable locally compact Abelian group X under the assumption that the distributions of the random variables have continuous positive densities with respect to a Haar measure on X and the coefficients in the linear forms considered are topological automorphisms of X.