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Projects and Publications of the Applied Projects and Publications of the NATIONAL APPLIED MATHEMATICS LABORATORIES A QUARTERLY REPORT April through June 1950 ( NATIONAL APPLIED MATHEMATICS LABORATORIES of the NATIONAL BUREAU OF STANDARDS : t NATIONAL APPLIED MATHEMATICS LABORATORIES April 1 through June 30, 1950 ADMINISTRATIVE OFFICE John H. Curtiss, Ph.D., Chief Edward W. Cannon, Ph.D., Assistant Chief Olga Taussky-Todd, Ph.D., Mathematics Consultant Myrtle R. Kellington, M.A., Technical Aid Luis 0. Rodriguez, M.A. , Chief Clerk John B. Tallerico, B.C.S., Assistant Chief Clerk Jacqueline Y. Barch, Secretary Esther M. Castleman, Secretary Bora P. Cornwell, Secretary Esther McCraw, Secretary Esther L. Turner, Secretary INSTITUTE FOR NUMERICAL ANALYSIS COMPUTATION LABORATORY Los Angeles, California J. Barkley Rosser, Ph.D Director of Research John Todd, B.S Chief Albert S. Cahn, Jr., M.S. ... Assistant to Director Franz L. Alt, Ph.D Assistant Chief Research Staff Edward W. Barankin, Ph.D. .. Consultant Forman S. Acton, D. Sc Mathematician Stefan Bergman, Ph.D Consultant Aryeh Dvoretzky, Ph.D UCLA Associate Arnold N. Lowan, Ph.D Consultant George E. Forsythe, Ph.D Mathematician J.C.P. Miller, Ph.D Consultant Magnus R. Hestenes, Ph.D Mathematician Milton Abramowitz, Ph.D. ... Mathematician Mark Kac, Ph.D Mathematician Donald O. Larson, B.S Mathematician William Karush, Ph.D Mathematician Joseph K. Levin, Ph.D Mathematician Cornelius Lanczos, Ph.D ^ Mathematician Robert R. Reynolds, M.S. ... Mathematician Raymond P. Peterson, Jr., Ph.D Mathematician Herbert E. Salzer, M.A Mathematician Otto Szasz, Ph.D Mathematician Leland W. Sprinkle, B.A. ... Mathematician Wolfgang R. WasOw, Ph.D Mathematician Irene A. Stegun, M.A Mathematician Gradua te Fell ows Norman A. Wiegmann, Ph.D. .. Mathematician Richard E. Cutkosky, M.S. Harold Gruen, M.A. Compu t in g Staff: Stuart L. Fletcher, B.A. Lloyd K. Jackson, M.A. Oneida L. Baylor Lionel Levinson, B.M.E. George E. Gourrich, M.A. Marvin L. Stein, M.A. Joseph Blum, M.A. D avid S. Liepman Machine Development Unit Ruth E. Capuano Michael S. Montalbano, B.A. Harry D. Huskey, Ph.D Mathematician Natalie Coplan, B.A. Kermit C. Nelson Victor A. Oswald, Jr. , Ph.D Consultant Josephine C. Diggs Malcolm W. Oliphant, M.A. Roselyn Siegel Lipkis, B.A Mathematician Mary M. Dunlap, B.S. Mary Orr Harold Luxenberg, M.A Mathematician Elizabeth F. Godefroy B. Stanley Prusch Biagio F. Ambrosio, B.S Electronic Engineer Lester H. Gordon Andress 0. Ridgway, B.S. Edward L. Lacey, M.S Electronic Engineer Wanda P. Gordon, B.A. Max Rosenberg, B.A. David F. Rutland, M.S Electronic Scientist Louis Greenberg, M.S. Rose L. Rowen, B.A. Laboratory Electronic Staff: Benjamin F. Handy, Jr., M.S. Ruth C. Shepherd, B.S. Brent H. Alford Harry T. Larson, B.S. Bernard Heindish, B.E.E. Jack Singer Charles M. Brauer Michael J. Markakis, B.E. Harley A. Hill, B.S. Milton Stein Arnold Dolmatz, B.S. John L. Newberger, B.A. Viola D. Hovsepian, B.S. Gretchen Stolle, M.A. Blanche C. Eidem Geraldine Orr Joseph B. Jordan, B.A. Bertha H. Walter Sidney S. Green, B.S. James W. Walsh Henry B. Juenemann, B.A. Charles Ziperstein, B.A. Compu ta t i on Un i Kenneth Levenberg, M.S. Ruth Zucker , B.A. .' Gertrude Blanch, Ph.D . Mathematician Florence C. Pettepit Secretary Elliot T. Benedikt, Ph.D. .. UCIA Associate Lillian Sloane Secretary Marvin Howard, M.S Mathematician William C. Randels , Ph.D. .. UCLA Associate Everett C. Yowell, Ph.D. ... Mathematician STATISTICAL ENGINEERING LABORATORY Compu ting S ta ff: Patricia Burton Bremer, B.A. Gerald W. Kimbal, B.A. Churchill Eisenhart, Ph.D Chief Michael Cohen Thomas D. Lakin W. J. Youden, Ph.D Assistant Chief Leola Cutler, B.A. Norma Logel, B.S. Lola S. Deming, M.A Technical Aid Lillian Forthal, B.A. Nancy Robbins Mann, M.A. Joseph M. Cameron, M.S Mathematician Gladys P. Franklin, B.S. Shirley L. Marks, M.A. Gerald J. Lieberman, M.A Mathematical Statistician Fannie M. Gordon, M.B.A. William O. Paine, Jr. Julius Lieblein, M.A Mathematician Robert M. Hayes, M.A. John A. Post ley, B.A. Eugene Lukacs, Ph.D Mathematical Statistician Donald E. Henley, B.A. Albert H. Rosenthal Celia S. Martin, B.A Mathematical Statistician Ruth B. Horgan, B.A. M. Winifred Smith i Mary G. Natrella, B.A Mathematician Lindley S. Wilson, M.A. Marion T. Carson Computer Admin is tra ti 1 Uni t Vivian M. Frye, B.A. Secretary M. Evelyn Michaud+ ... Administrative Officer Helen M. Herbert Secretary F. Patricia K. Peed Librarian Ellma Frantz, B.S Library Assistant Velma R. Huskey, B.A . Physical Science Editor MACHINE DEVELOPMENT LABORATORY Dora Kaplan Procurement Clerk Earle W. Kimball Stock Clerk Edward W. Cannon, Ph.D Chief Secretarial Staff: Merle M. Andrew, Ph.D Mathematician Elsie E. Aho Elsie L. Husman Ira C. Diehm, B.S Mathematician Irene M. Everett Cecilia R. Leonard Ethel C. Marden, B.A Mathematician Margaret W. Gould Tess D. Mazer Edith T. Norris, B.A Mathematician Eleanore J. Harris Sata Ohashi Ida Rhodes, M.A Mathematician Dorothy M. Hibbard Gertrude Z. Reider Otto T. Steiner, B.A Mathematician Reve J. Vineyard Leta S. Marks Secretary U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS Charles Sawyer, Secretary E. U. Condon, Director Projects and Publications of the NATIONAL APPLIED MATHEMATICS LABORATORIES April through June 1950 Contents Page Index ill Announcement: National Bureau of Standards Eastern Auto- matic Computer (SEAC) .... 1 Status of Projects as of June 30, 1950 4 Institute for Numerical Analysis (NBS Section 11. l). 4 Computation Laboratory (NBS Section 11.2) 28 Statistical Engineering Laboratory (NBS Section 11.3) • 47 Machine Development Laboratory (NBS Section 11.4) .. 57 Lectures and Symposia 62 Publication Activities 66 National Applied Mathematics Laboratories of the National Bureau of Standards Preface This is a report on the activities of Division 11 of the National Bureau of Standards for the period from April 1, 1950 through June 50 , 1950. Division 11 is known as the National Applied Mathematics Laboratories. It is the mission of the Laboratories to perform research and to provide services in various quantitative branches of mathe- matics, placing special emphasis on the development and exploitation of high-speed numerical analysis and modern statistical methodology. The Labora- tories maintain an expert computing service of large capacity, and provide consulting services in classical applied mathematics and In mathematical statistics. These services are available primarily to other federal agencies, but under certain cir- cumstances it is possible to perform work for industrial laboratories and universities. Inquiries concerning the availability of the services of the National Applied Mathematics Labora- tories, or concerning further details of any of the projects described in this report, should be ad- dressed to the National Applied Mathematics Labora- tories, 415 South Building, National Bureau of Standards, Washington 25, D. C. A H Chief Director National Bureau of Standards 9 July 15, 1950 . Index of Active Research and Devel opment Projects NOTE: This index is not intended to cover the numerous special problem solutions, statistical analyses, and other ad hoc services to Government agencies which form an important part of the work of the National Applied Mathematics Laboratories. These services are, however, fully represented in the body of the report A. Research: Pure Mathematics Miscellaneous studies in pure mathematics. .... 8, 30 B. Research: Numerical Analysis Classical numerical analysis. Research in 28 Conformal mapping. Numerical methods in 5 Convergence of series. Studies in methods of improving the. 31 Critical points. Determination of 7 Dirichlet problem f-or certain multiply connected domains. In- vestigation of Bergman's method for the solution of the. 29 Eigenvalues, eigenvectors, and eigenfunctions of linear oper- ators, Calculation of 7 Extremals of functionals. Determination of 7 Fredholm's integral equation. An iterative solution of 10 Matrices, Condition of 30 Network analysis. Integral transforms and 10 Ordinary differential equations. Studies in numerical integra- tion of 5 Partial differential equations and integro-diff erential equa- tions, Sampling techniques for solving 6 Partial differential equations. Studies in numerical integra- tion of 6 *Riemann zeta-function. Computation of the imaginary zeros of the 13 Solution of sets of simultaneous algebraic equations and techniques for the inversion and iteration of matrices .... 4 C. Research: Applied Mathematics, Physics, Astronomy, and Automatic Translation * Language translation study 11 Linear programing. Research in 32 Orbits of comets, minor planets, and satellies. Determination of 22 Periods and amplitudes of the light variations of the stars £ Scuti and 12 Lacertae, The determination of the 22 *Program planning. Research in the mathematical theory of ... 12 D. Mathematical Statistics Extreme -value theory and applications 51 Location and scale parameters, Estimation of 48 ^Mathematical statistics. Studies in 12 Order statistics. Moments of 23 Probability theory of a certain double branching system .... 52 Samples of three observations. Statistical properties of . 47 Stochastic processes, Elementary theory of 47 *New projects Index of Active Research and Development Projects E. Mathematical Tables Antilogarithms, Table of 33 Bessel functions. Special table of. ... 14 Chebyshev polynomials. Table of 35 Coulomb wave functions. Tables of 33 E]_(z), second quadrant, Tables of 14 = E]_( z), (z x + iy) , Tables of 32 Fermi function II 38 Gamma function for complex arguments. Table of the 33 Gases, Table of thermodynamic properties of 37 Hermite polynomials. Zeros and weight factors of the first sixteen 34 l ( x c Tables of (see project 11.2/33-49-13) n > v)> 38 Lagrangian coefficients for sexagesimal interpolation. Table of. 34 Logarithms to many places, Radix table for calculating 34 Mathieu functions II 14 *n! and f (n+|) , Table of 36 Percentage points of the arithmetic mean in random samples from the sech and sech^ distributions 39 Probability tables for extreme values 35 Punched card library 15 Rocket navigation tables.
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