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cally before the detailed analysis by use of predictions begins. This technique will greatly increase the speed of translation through the proper placement of subject and predicate in the syntactic analysis.

Mathematical Tables. The main concentration in mathematical tables during the year has been on the completion of the Handbook of Mathematical Functions. All chapters of the Handbook now exist in manuscript form. A modest amount of revision of expository text and updating of bibliographies remain. The Chapters in press comprise about one-quarter of the volume.

Digital Computation. Digital computers were applied in both the scientific and data processing fields. Scientific computing was centered. about measurement and calibration, i.e., primarily concerned with problems on gage blocks, thermometers, bead sizing, heat pump capacity, transistor aging, etc. Problems such as those arising in studies of crystal structure, the thermodynamic properties of gases, spectrum analysis, and colorimetry also required extensive computing techniques. Significant computations were performed on problems related to radiation patterns of antennas, light scattering, heat transfer in crystals, and the radiative envelopes of model stars. Important problems in data processing included the assignment of radio frequencies, traffic studies, mathematical investigations related to postal operations, analysis of electrocardiograms, airline traffic surveys, and the simulation of military engagements.

Extensive research was continued in the field of automatic programing, where the primary objective is to render easy, fast, and inexpensive communication between electronic computers and human users. The Bureau pursued this objective with direct practical applications as well as through research and long-range development. The Black Box Computer-a tool devised to speed a problem from originator to machine-was improved and its applications expanded. By use of this tool, Bureau laboratory workers. can prepare their problems for direct introduction into electronic computers to produce least-square fits, numerical integration and interpolation, compilation of physical tables, evaluation of certain desired statistics, such as the mean or the standard deviation, etc.

The Bureau has performed research in the area of artificial languages and their translation by machine. It participated during the year in the establishment of programer-oriented languages-ALGOL for scientific applications and COBOL for business or data-processing problems. Significant contributions were made, also, to the program on standardization of symbols. languages, and equipment of the Office Equipment Manufacturers Institute. Experiment Designs. Work on the mathematics of experiment design resulted during the year in the substantial revision and preparation for publication of the "catalog" of fractional factorial designs for the 2" 3" series developed during the preceding year in preliminary form. A special class of "weighing" designs of the fractional factorial type was studied. These designs approach the classical weighing designs with respect to the small numbers of observations required, but still permit identification of

two-factor interactions and thus are particularly appropriate for use in experiments on the determination of fundamental physical constants. In addition, they are applicable to the evaluation of routine calibration and testing procedures. Explicit construction and "cataloging" of a series of magic rectangles for use as trend-elimination designs were accomplished. These rectangles provide orders for running the "treatment" combinations in a twoway classification so that comparisons of the resulting "main effects" of the respective "treatments" are not upset by linear trends or drifts in the measurements. A special operational calculus for symmetrical and asymmetrical factorial arrangements was developed.

Life Testing and Reliability. The intensive investigations of the measurement of reliability conducted by the Bureau were summarized to show the possible weaknesses of current life-testing procedures being applied when the assumptions on which they are based are not valid. New and improved results were obtained, including excellent approximations to the distribution of a sum of Weibull-distributed random variables and to the OC-curves and average-sample-size expressions for sequential tests based on sums of Weibull-distributed random variables.

Studies in probability and

Probability and Mathematical Statistics. mathematical statistics took various forms. Work was resumed on the NBS tables of power points of the noncentral F- and x2-distributions. A detailed numerical investigation was initiated of properties of a special family of probability distributions derived from the uniform distribution on (0, 1) by a transformation suggested by J. W. Tukey. Information theory was applied to the analysis of a four-way contingency table. The fourth in a Bureau series of selected bibliographies of statistical literature for the period 1930-1957 was completed.

Mathematical Physics. Research in mathematical physics emphasized the formulation of mathematical theories basic to the development of theoretical physics and engineering science. Investigations included research in the kinetic theory of plasmas and magnetohydrodynamics, in which the previously developed theory for homogeneous plasma was generalized to include the long-range collective behavior, the effect of memory in oscillations, and the expansion wave problem in neutral gases.

Investigations concerning satellite orbits were continued. Emphasis was placed on the central problem of satellite astronomy, namely, the determination of the motion of an artificial satellite around an axially symmetric but oblate planet. The method developed reduces the relevant Hamilton-Jacobi equation to separable form, and provides for the application of well-known techniques in successive approximation to the problem of satellite motion.

Other work in mathematical physics included studies of Brownian motion, as governed by the Chapman-Kolmogoroff functional equation; elliptic boundary-value problems, in which important bounds for the deflection of elastic plates were derived; the deflection of circular plates with radially varying thickness under a radially symmetric traverse load and edge conditions; and the flexure of elastic beams.

Operations Research. General areas of investigation during the year included game theory, graph theory, weapon simulation, Boolean functions, and mathematical models of distribution networks.

The problem of optimal frequency allocations for a network of radio transmitters is similar to that of finding a minimum point-cover of a linear graph. Graph-theoretic algorithms were investigated. A significant development was that of a general algorithm, suggesting characterization for optimal coverings of a set, providing promising alternatives to known algorithms, and specializing to the minimum point-cover problem.

Three major areas were explored in connection with the analysis of mathematical problems related to postal operations. These areas were: (1) a longrange study of mathematical models of distribution networks, with a view to optimizing the location of distribution centers and the degree of system centralization; (2) determination of the appropriate parameters for a specified mail-sorting device; and (3) studies concerning procedures in existent, partly automated post offices.

Other significant activities in operations research during the year included the analysis and computer simplification of Boolean functions (important in network and circuit theory), the analysis and simulation of missile system. operation, a study of optimal radar site distribution, and the analysis and simulation of electronic countermeasures.

2.3.2. DATA PROCESSING SYSTEMS

The Bureau has been conducting a broad program of research and development in analog and digital technology and in application techniques needed to foster effective use of data processing systems by the many agencies of the Government. A major purpose was to extend the areas of application beyond conventional "paperwork" as well as to expedite the data handling problems of the experimental sciences and the storage, search, and retrieval of information. The Bureau's data processing systems laboratory acts as a centrally available technical facility for providing assistance and advisory services for such purposes within the Bureau and to other government agencies.

Some present areas of activity include research, design, and evaluation of improved circuitry; logical organization of data processing and control systems; automated collection, transmission, and presentation of experimental data; and techniques for machine processing of syntactic and graphic forms. of data. Of particular significance is the continued expansion of the program of assistance to the Bureau's own research laboratories in identifying problem areas particularly adaptable to automatic data processing techniques and demonstrating the feasibility of preparing experimental data in acceptable form for input to and output displays from a central high-speed automatic data processing facility. The range of data processing applications both for NBS and for other government agencies increased materially during the past year.

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The PILOT data processor, now nearing completion, will provide a highly flexible research facility for new and unusual Government data processing problems (page 112).

PILOT Data Processor. The engineering design and physical structure of the NBS PILOT Data Processor, a highly flexible research tool developed for investigating new and unusual data processing problems for the Government, was completed. Power distribution, clock distribution, circuit protection, and logical wiring for all parts of the machine were installed. The secondary diode-capacitor memory is already functioning as a part of the PILOT system, while the completed primary diode-capacitor memory is ready to be mated to the central machine. Performance tests were completed on the logical wiring of the system and on 7,000 individual stages of the system.

The peripheral equipment presently attached includes an automatic typewriter, magnetic wire handler, magnetic tape handler, and high-speed paper tape reader. Initial service programs were prepared, and specifications were established for the preliminary compiler for the main computer. The first set of training courses in both programing and maintenance and operation was conducted in preparation for routine operation.

Technical Assistance for Data Processing. The continuing aid and assistance to the laboratory operations throughout the Bureau led to the identification of a considerable number of potential areas for automatic data recording and processing, many of which had special data-conversion problems. Technical assistance was provided through study of the problem to determine whether analog and/or digital techniques were applicable and

through demonstration of the feasibility of such applications. Additional assistance was given in the form of design and development of special datalogging equipment, some of which was constructed by the "user" laboratories with advice in the utilization of packaged circuitry provided by the data processing systems laboratory in order to convert the data to input form acceptable to the computer.

Typical problems on which assistance was provided included gas analysis by infrared spectrometry, plasma traverse, transmission of data from radiation physics, coulometric titration, heat transfer by radiation, concentration of near-saturated solutions, separation of signals from noise, radial distribution of plasma properties, search of atomic nuclei in crystal structures, model loop for process control with dead time, stability constants of complex ions, nuclear reactor transients, probability of convoluted probability functions, theory of reflection from metallic surfaces, processing metallurgical photomicrographs, plotting of continuous curves by interpolation of discrete data on magnetic tape, storage and examination of 1,000 points in the focal plane of a lens, and handling of data from an electron paramagnetic resonance unit. Components and Techniques. The development of faster, more complex, and more reliable computers and data processors has led to the study of new components and further investigation of existing ones. Measurement of the properties of these components is fundamental. Several significant contributions were made to the theoretical analysis of solid-state semiconductor devices operating as circuit elements.

A large-signal junction transistor equivalent circuit and switching theory study was completed. This study produced a new large-signal junction transistor equivalent circuit that is valid for all modes of circuit operation. The physical charge-concept approach to semiconductor devices was bridged mathematically to the area of device application, resulting in nonlinear differential equations that could be solved by graphical, analytic, and computer techniques. These equations made possible analytic solution of modes of junction transistor operation which were previously untractable. The use of new time domain measuring techniques was incorporated into the study as a means of evaluating elements of the equivalent circuit. The study also resulted in a characterization of the transient input base current of the junction transistor for all driving conditions. The static base-to-emitter voltage-current characteristic and a unique time constant factor were shown to be the principal data required for the large signal switching analysis.

A tunnel diode large-signal simulation study was undertaken which involved the development of an analytic approximation to the static voltagecurrent characteristics of the tunnel diode that displayed the required negative-resistance region. A complex second-order nonlinear differential equation and techniques for its solution by analog computer and graphical analy sis methods were developed. These equations are of considerable value in determining the large-signal switching response of the tunnel diode in digital circuitry.

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