Consider an orthogonal series [formula] where [formula] is an arbitrary orthonormal system for the interval (a, b) and [formula] is a sequence of real numbers. This report is a collection of theorems which give sufficient conditions for the convergence almost everywhere in (a, b) and summability a. e. in (a, b) of the above series.

Five isotopes of bismuth occur in nature. Using particle accelerators providing helium ions up to 40 Mev in energy and deuterons up to 20 Mev in energy, it was possible to produce and identify two artificial radioactive isotopes. With the advent of the 184-inch Berkeley syncho-cyclotron and its hundreds of Mev energies, it was possible to form highly neutron-deficient bismuth isotopes extending more than ten mass units below stable Bi(209).

Calculations presented were done to determine what maximum temperature gradients and stresses would be in typical designs of flat thorium plates, 100 mils thick and coolled on both sides by NaK.

A phase shift analysis is an attempt to translate experimental measurements (observables) into well-determined scattering amplitudes, since these are the quantities that can be readily compared with theoretical predictions, In this sense, the phase shift analysis should contain as little theory as possible. The scattering amplitudes (or phase shifts) constitute an experimental statement, and the phase shift analysis should logically be done by the experimental groups who measure the observables.

A fraction of the energy released by the underground detonation of nuclear explosives is locally deposited as residual thermal energy. An accurate prediction of this usable fraction of the energy released is necessary to evaluate the feasibility of several of the proposed projects in the Plowshare Program. This paper will present a summary of the available data on residual thermal energy from nuclear detonations in three different geological media: tuff, halite, and granodiorite.

Certain aspects of mating behavior in two different types of Drosophila melanogaster females (Basc and Bv) and wildtype males (Samarkand) have been investigated and compared.

The pion-pion interaction is of great theoretical importance and must be understood before the other and more familiar interactions can be systematically analyzed. Therefore, various experiments to verify the existence of a P resonance in the w w system are proposed.

The increasing exponential function e-at [a > 0] characterizes such natural events as gas discharges, neutron multiplication, and the transistor avalanche phenomenon. This report describes an instrument for measuring the rate of rise, a, of an increasing electrical exponential signal.