An approximate Boltzmann equation, known as the single relaxation model is studied here. This equation is linearized and the fundamental solution is considered. Following N. Grad, the solution, asymptotic in small values of the ratio of mean-free-path to distance from the origin, is sought. It can be shown that the fundamental solution itself gives the asymptotic description of the flow field past an object. This solution gives the asymptotic description when the distance from the origin is much greater than either the mean-free-path or the body size. This is true independently of the Knudsen number.

"The problem of a steady boundary layer or sheath between a plasma and a magnetic field is considered. A self-consistent transition layer is found which joins a uniform magnetic field at plus infinity with a collisionless field-free plasma region with arbitrary velocity distribution at minus infinity, i.e., a magnetic field profile is found such that the exact particle orbits in this field produce a current which gives rise to this field. An interesting feature of the solution is that, with any nonsingular velocity distribution at minus infinity, the magnetic field the plasma extends to infinity, exponentially attenuated, into the magnetic field region. The scale of length is the Larmor radius. Electric fields arising from charge separation in the case of particles of different mass are ignored."

"Mesic decay of hyperfragments is discussed systematically on the basis of a previous model for hyperfragments. The general formalism for the two-body and three-body mesic decay was developed. The polarization-direction correlation and the angular correlation for the two-body and the three-body decays are discussed together with the decay probability. The formalism was developed so as to include the isotopic spin selection rule ( DELTA I = 1/2 and 3/2) for the mesic decays. The theory was applied especially for the low mass number hypergragments where it was found that the branching ratios of the two-body and the three-body mesic decays of /sup 3/H/sub i and /sup 4/H/sub i, (/sup 3/ H/sub i yields /sup 3/He + i/sup -/)/(/sup 3/H/sub i yields D + p+ pi /sup -/) and (/sup 4/H/sub i yields /sup 4/He + pi /sup -/)/(/sup 4/H/ sub i yields /sup 3/H + p + pi /sup -/), could be used for the determination of the spins of both hyperfragments. The fraction of the p-wave decay rate for the free LAMBDA decay obtained from the reaction /sup 5/He/sub i yields /sup 4/He + p + pi where the decay proceeds through two-resonant states (p/sub 3/2/ and p/sub 1/2/) …