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.

The validity of the nuclear track emulsion technique for fast-neutron dosimetry is examined in the exposure of a human phantom to PuBe neutrons, Semiautomatic track scanning and high-speed data analysis obviate the major disadvantages of emulsion dosimetry, and allow the absolute differential proton track energy spectrum at various locations in the phantom to be obtained without a serious cost in time. From this are calculated the total absorbed local tissue dose due to proton recoils and the local thermal neutron intensity during irradiation.

The power of nuclear track research emulsion as a fast neutron dosimeter is examined in the exposure of a human phantom to PuBe neutrons. Semiautomatic track scanning and high-speed data analysis obviate the major disadvantages of this dosimeter, and allow the following basic information to be obtained without a serious cost in time: the rulative proton recoil energy spectrum, the absolute differential proton track den sity spectrum, and the average proton recoil energy at various locations in the phantom. From this are calculated the total absorbed local tissue doze due is proton recoils, the local thermal neutron intensity, and that portion of the tissue doze due to thermal [formula] tracks.

Quarterly report on the metabolic properties of various materials, biological studies of radiation effects, health chemistry, health physics.

The motivation for the measurement of the angular distribution of elastic scattering of medium energy protons and neutrons has been clearly presented by others. They have also listed the results obtained prior to their experiments at 31.5 Mev. This is a report on some results obtained with 30.6 Mev protons scattered from Be, C, and Al.

One of the techniques by which highly ionized plasmas can be generated in the laboratory makes use of strong, electromagnetically driven shock waves propagating into a cold gas. In this paper the phenomenon is analyzed as a one-dimensional single-fluid hydromagnetic problem, neglecting dissipation behind the wave.

In previous letters we have reported a Av resonance, called Y*1, observed through the study of the interaction of 1.15-Bev/c K* mesons in hydrogen in the Lawrence Radiation Laboratory 15-in. bubble chamber. We now wish to report the results of the study of the three reactions [formula](1), [formula](2) and [formula](3).

There is an active principle in heparinized plasma that may be studied in vitro with a prescribed lipoprotein-containing medium. To this end the interaction of this active principle or factor was studied with lipoprotein species isolated from egg yolk.

This paper describes the method developed and the results obtained in an extensive program of measurement of the masses of charged pions. Measurements were made of the total ranges in nuclear track emulsion and the momenta (obtained from the curving of the particle trajectory in the magnetic field of the 184-inch cyclotron) of pions and protons of nearly the same velocity.

The Bevatron requires an intense source of high energy protons. The machine should accept monoenergetic protons for a duration of approximately 500 microseconds once every 6 seconds. To satisfy the requirements of small loss due to scattering by the gas in the accelerating chamber, a 9.9-Mev linear accelerator has been built and operated.

A set of 69 pile yield curves for the production of plutonium, americium, and curium isotopes in a neutron flux of 5 x 10<sup>14 cm<sup>-2 sec<sup>-1 is given. The differential analyzer of the University of California Radiation Laboratory was used in obtaining the curves. The curves are given also on log-log plots for comparison.

Quarterly updates on nuclear chemistry, bio-organic chemistry, general chemistry, chemical engineering (process chemistry).

Our aerosol program employing monkeys has been initiated. A plutonium oxilate solution was introduced into the trachea. Preliminary results of the fecal and urinary determinations appear here.

Progress report on biological studies of radiation effects, metabolic properties of various materials, health chemistry, health physics.

A preliminary study of positive pion production from proton-nucleus collisions revealed that positive pion production cross sections agree more favorably with a Z 2/3 variation than with a variation proportional to the atomic number. A similar study on negative pion production has shown that negative pion yields from proton-nucleus collisions tend to vary in proportion to the number of neutrons in the nucleus. As a result an experiment was performed to investigate if there is a significant change in positive pion production with changing atomic number at two lower pion energies.

Progress report on programs in target research and in accelerator research.

The purpose of this report is to describe a method of obtaining deuterons from the 184-inch cyclotron of higher energy than can be achieved from direct acceleration.

An empirical relation is presented which represents a boundary between no vacuum sparking and possible vacuum sparking. Metal electrodes and r.f. or d.c. voltages are used. The criterion fits several orders of surface gradient, voltage, gap, and frequency. Current due to field emission is considered necessary for sparking but in addition, energetic particles are required to initiate a cascade process which increases the field emission currents to the point of sparking. An elementary cascade process is outlined, but the data upon which it is based is not fully stated.

Diffusion equations for a cascade shower which include an energy cutoff and energy parameters for each particle have not previously been studied. In this paper it is found that an inclusion of both permits collision loss to be represented as a discrete process by modifying the differential radiation cross section.

Certain isotopes in the region of the heaviest elements have been produced by cyclotron and pile bombardment techniques, and their nuclear decay properties have been investigated. The orbital electron capture decay of At210, At211, Np234, Np235, Pu234, Pu237, and Am242m has been studied and decay schemes have been proposed. In addition, the alpha spectra of Po211, At210, and At211 have been observed.

One of the oldest properties of electrons is their emission of x-rays (discrete and continuous spectra) when impinging on matter. Cloud-chamber tracks show light ionization, and considerable multiple scattering, except for fast electrons. Tracks are long and range indefinite.

The existing data on positive pion production resulting from the interaction of 340 Mev protons with complex nuclei indicate that the production cross-sections agree more closely with a 2/3 variation than with a variation proportional to z. A preliminary survey of negative pion production at two pion energies has been made for Be, C, Al, Cu, Ag and Po, using the externally deflected 340 Mev synchro-cyclotron proton beam.

Project Sherwood is a nation-wide attempt to produce a controlled thermo-nuclear fusion reaction. The Astron experiment, conceived by Nicholas Christofilos, will utilize the effects of a cylindrical layer of relativistic electrons to contain and heat the plasma. A high quality, 200-ampere, 5-Me V electron beam is required to form the electron layer. The electron beam is produced by a linear induction electron accelerator. Three hundred and thirty-three toroidal cores of magnetic material surround an evacuated ceramic accelerating column. The electrons are accelerated by the transverse electric field produced by the changing flux. The magnetic cores are tape-wound toroids of .001", 50% Ni - 50% Fe. Two hundred eighty-eight cores are 24" o.d. x 8-1/2" i. d. x 1/2" thick and the remaining forty-five are 33" o. d. x 18" i. d. x 1/2" thick. Each core is required to support 16 kG for 0.4 psec. The choice of magnetic material was made by testing all available material for the required parameters. Results of these tests are presented.

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.