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.

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.

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.

During the past five years, potentialities of space travel have greatly increased and new knowledge has become available regarding the nature of cosmic radiation. In the present article the knowledge pertinent to dose evaluation is reviewed for conditions of flight in space in the vicinity of the earth but away from the influence of its atmosphere or magnetic field. Certain properties of the heavy nuclei are also discussed as well as some of the available information on their actual biological effects. Development and completion of the new Heavy Ion Linear Accelerator allows extension of quantitative biological work with these particles. Finally, the statistical nature of the hazard from cosmic radiations and the limitations of space flight due to such rays are discussed.

The problem of photosynthesis is the problem of defining the way in which green plants are able to convert electromagnetic energy into chemical potential in the form of reduced carbon, usually as carbohydrate, and molecular oxygen. The use of tracer carbon, as carbon-14, has made possible considerable progress in the mapping of the routes taken by the carbon atom from CO2 into plant substances. The techniques of separation and identification that have made this progress possible lie largely in the region of chromatography and radioautography involving fractional-gamma amounts of material. A number of proposals have been made about the photochemical act itself. These proposals have led to the development of direct physical tests of their validity, and some results of these will be described.

Apparent [Sigma] hyperon decay events in a large emulsion stack of 240 9" x 12" pellicles have been classified into those judged to have occurred at rest and those in flight. Of 36 decay events at rest, 21 secondaries were observed to be protons of about 1675 microns range. Of the events decaying in flight, 23 were decays into protons and 46 were decays into near-minimum secondaries. Attempts have been made to trace the tracks of 35 of the lightly ionizing secondaries; the results of this effort are summarized in a table.

This is an attempt to summarize and relate at least some of the material presented in four talks during a symposium on radiobiological studies on yeast, and in addition discuss some related experimental results. The discussion will be divided into two sections: I) a discussion of the various manifestations of radiation damage in yeast; and II) a consideration of modification of these damages by variations of physico-chemical and biological parameters.

The basic investigation of transistor feedback amplifiers has proven mathematically simple and of great practical value. The behavior of single-stage common-emitter amplifiers is described and provides a building block with which cascaded feedback amplifiers can be analyzed and designed. From the results of this analysis the conditions for minimum drift for cascaded single-stages and cascaded loops have been derived.

The method of detecting unpaired electrons in liquid and solid systems by electron spin resonance is discussed. The significance of the hyperfine structure in electron spin resonance is discussed and the possible use of these structural features of the electron spin resonance spectrum to elucidate the nature of the photoproduced unpaired electrons in photosynthesizing systems is introduced.

This report is a comparative cost study of radioactive waste disposal for the Lawrence Radiation Laboratory (UCRL). In particular, it compares the costs of sea disposal in depths of 1000 fathoms and of 2000 fathoms off the California coast with land burial of the wastes at the Hanford Atomic Products Operation (HAPO), Richland, Washington, at the National Reactor Testing Station (NRTS), Idaho Falls, Idaho, or at the Nevada Test Site (NTS), Nevada. In the comparison, the cost of utilizing a commercial waste-disposal firm is also shown as well as a tentative cost of using the Military Sea Transport Service (MSTS).