Projects and Publications of the NATIONAL APPLIED MATHEMATICS LABORATORIES A QUARTERLY REPORT October through December 1950 NATIONAL APPLIED MATHEMATICS LABORATORIES of the NATIONAL BUREAU OF STANDARDS 1 NATIONAL AP P L T ED MATHEMATICS LABORATORIES October 1 through December 31, 1950 ADMINISTRATIVE OFFICE John li. 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, Chief Clerk M.A. , John B. Tallenco, B.C.S. , Assistant Chief Clerk Jacqueline Y. Barch, Secretary Dora P. Cornwell, Secretary Dolores M. Mayer, Secretary Esther McCraw, Secretary Esther L. Turner, Secretary INSTITUTE FOR NUMERICAL ANALYSIS COMPUTATION LABORATORY Los Angeles, California Fritz John, Ph.D Director of Research John Todd, B.S Magnus R. Hestenes, Ph.D Asst. Director and Franz L. Alt, Ph.D > UCLA Liaison Officer Leslie Fox, Ph.D Harry D. Huskey, Ph.D Asst. Director for Math’ J.C.P. Miller Ph.D Services Louis Rosenhead, Ph.D Gertrude Blanch, Ph.D Assistant to the Director Milton Abramowitz, Ph.D (Numerical Analysis) Albert S. Cahn, Jr., M.S Assistant to the Joseph H. Levin, Ph.D Director (Administrative Section) Herbert E. Salzer, M.A Research Staff Leland W. Sprinkle, B.A Forman S. Acton, D.Sc Mathematician Irene A. Stegun, M.A Milton Drandell, M.A UCLA Research Associate Computing Staff: Aryeh Dvoretzky, Ph.D UCLA Research Associate Oneida L. Baylor Joseph B. Jordan, B.A. George E. Forsythe, Ph.D.. Mathematician Joseph Blum, M.A. Henry B. Juenemann, B.A. Robert Fortet, Ph.D UCLA Research Associate Ruth E. Capuano Norman Levine, B.S. John W. Green, Ph.D Consultant Natalie Coplan, B.A. Lionel Levinson, B. M. E. William Karush, Ph.D Mathematician Melchoir J. DiCarlo-Cottone, B.S. David S. Liepman Cornelius Lanczos, Ph.D... Mathematician Bernard C. Dove, B.A. Samuel Mallos, M.A. Hans Lewy, Ph.D Consultant Mary M. Dunlap, B.S. Michael S. Montalbano, R.A. William E. Milne, Ph.D.... Mathematician Frances R. Froherger, R.A. Kermit C. Nelson Theodore S. Motzkin, Ph.D. UCLA Research Associate Leon Gainen, B.S. Peter J. O’Hara, B.S. David S. Saxon, Ph.D Physicist Lewis F. Garrett, B.A. Mary Orr Wolfgang R. Wasow, Ph.D... Mathematician Elizabeth F. Godefroy Donald S. Park, B.A. Graduate Fellows: Lester H. Gordon, B.A. R. Stanley Prusch Harold P. Edmundson, M.A. Robert M. Hayes, M.A. Wanda P. Gordon, B.A. Max Rosenberg, B.A. Robert K. Golden, M.S. William C. Hoffman, M.A. Helen V. Hammar, B.S. Rose L. Rowen, B.A. L. Stein, M.A. Harold Gruen, M.A. Marvin Benjamin F. Handy, Jr. , M.S. Ruth C. Shepard, B.S. James P. Wesley, M.A. Genevie Hawkins, B.S. Milton Stein Machine Development Unit Bernard Heindish, B. E. E. Gretchen Stolle, M.A. Biagio F. Ambrosio, B.S Electronic Engineer John Hershberger, M.S. George E. Turner, B.S. Edward Lacey, M.S Electronic Engineer Viola D. Hovsepian, B.S. Bertha H. Walter David F. Rutland, M.S Electronic Scientist Marlie E. Johnson, B.S. Marjorie 0. White Laboratory Electronic Staff: Ruth Zucker, B.A. Rrent H. Alford Norman F. Loretz, B.S. Florence C. Pettepit Arnold Dolmatz, B.S. Michael J. Markakis, B.E. Lillian Sloane Blanche C. Eidem Edward D. Martinolich Sidney S. Green, B.S. John L. Newberger, B.A. Harry T. Larson, B.S. James W. Walsh Ma thematical Services Unit Marvin Howard, M.S. ... Mathematician STATISTICAL ENGINEERING LABORATORY Roselyn S. Lipkis, B.A Mathematician Harold Luxenberg, Ph.D Mathematician Churchill Eisenhart, Ph.D. Chief Robert R. Reynolds, M.S. Mathematician W. J. Youden, Ph.D Assistant Chief Everett C. \owell, Ph.D Mathematician Lola S. Deming, M.A Technical Aid Computing Staff: Lakin Joseph M. Cameron, M.S.... Mathematician Patricia B. Bremer, B.A. Thomas D. Julius Lieblein, M.A Logel B. S. Mathematician Leola Cutler, B.A. Norma , M.A. Eugene Luckacs, Ph.D Mathematical Statistician Alexandra I. Forsythe, M.A. Shirley L. Marks, Mary G. Natrella, B.A Mathematician Lillian Forthal, B. A. William 0. Paine, Jr. Marion T. Carson Computer Gladys P. Franklin, B.S. John A. Post ley, B.A. Vivian M. Frye, B.A Secretary Fannie M. Gordon, B.A. Albert H. Rosenthal Smith Helen M. Herbert Secretary Ruth B. Horgan, B. A. M. Winifred M.A. Virginia E. Sweeny Secretary Gerald W. Kimble, A.B. Lindley S. Wilson, Admit ii s trati ve Uni t Dora K. Madoff Administrative Assistant Elsie E. Aho Administrative Clerk F. Patricia K. Peed Librarian Assistant Madeline V. Youll, B.A.., Library MACHINE DEVELOPMENT LABORATORY Clerk Velma R. Huskey, B.A Information and Editorial Stock Control Clerk Earle W. Kimball... .Property and Ph.D Secretarial Staff: Edward W. Cannon, Chief Husman Merle M. Andrew, Ph.D Jean S. Booth Elsie L. Mathematician Leonard Ira C. Diehm, B.S Gloria E. Bosowski Cecilia R. Mathematician Reider Ethel C. Marden, B.A Selma S. Doumani Gertrude Z. Mathematician Stafford Edith T. Norris, B.A Irene M. Everett Ruth A. Mathematician Vineyard Ida Rhodes, M.A Margaret W. Gould Reve J. Mathematician Warren Otto T. Steiner, B.A Dorothy M. Hibbard Katharine C. Mathematician 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 October through December 1950 Contents Page Index iv Status of Projects as of December J>±, 1950 1 Institute for Numerical Analysis (NBS Section 11. l). 1 Computation Laboratory (NBS Section 11.2) 24 Statistical Engineering Laboratory (NBS Section 11. 5). 44 Machine Development Laboratory (NBS Section 11.4). 49 Lectures and Symposia. ......... 55 Publication Activities ........... 58 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 October 1, 1950 to December yi, 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- Director National Bureau of Standards February 1, 1951 Index of Active Research and Development 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 9, 25 B. Research: Numerical Analysis Classical numerical analysis. Research in 24 Conformal mapping. Numerical methods in , 2 Convergence of series. Studies in methods of improving the. 26 Differential equations. Studies in numerical integration of . 3 Dirichlet problem for certain multiply connected domains. Investigation of Bergman's method for the solution of the . 24 Eigenvalues, eigenvectors, and eigenfunctions of linear operators. Calculation of 2 Matrices, Condition of. 25 Monte Carlo method. Solution of Laplace equation by 26 *Non-negative trigonometric polynomials 27 Riemann zeta-function, Computation of the imaginary zeros of the 10 Solution of sets of simultaneous algebraic equations and techniques for the inversion and iteration of matrices. ... 1 Variational methods 6 C. Research: Applied Mathematics, Physics, Astronomy, and Automatic Translation Applied mathematics. Studies in 7 Crystal structure. Analysis of 34 Crystal structure problem for point atoms 33 Language translation study 12 Linear programing. Research in 37 Orbits of comets, minor planets, and satellites. Determination of 18 Periods and amplitudes of the light variations of the stars S Scuti and 12 Lacertae, The determination of the 15 Program planning. Research in the mathematical theory of ... 10 Relative abundance of the elements Theoretical physics. Miscellaneous studies In . X-ray penetration problem. 34 D. Mathematical Statistics Extreme-value theory and applications. 45 Location and scale parameters. Estimation of 45 Miscellaneous studies in probability and statistics 46 NBS Research and testing. Collaboration on statistical aspects of 48 Research on application of theory of extreme values to Gust Load problems 48 * Sampling plans. Analysis of 28 Stochastic processes. Elementary theory of 45 New projects , Index of Active Research and Development Projects E. Mathematical Tables Anti logarithms, Table of 29 Bessel functions. Special table of 16 Chebyshev polynomials. Table of ....... 31 *Collected short mathematical tables of the Computation . Laboratory 32 Coulomb wave functions. Tables of 29 Ep(z), second quadrant. Tables of . 17 Ep(z), (z = x + iy) Tables of. ... 28 Fermi function II 30 Gamma function for complex arguments. Table of the 29 Gases, Table of thermodynamic properties of . 40 Hermite polynomials. Zeros and weight factors of the first sixteen. ..... ..... 30 In (x,c v ), Tables of (see task 1102-53-1106/49-13) 36 Lagrangian coefficients for sexagesimal interpolation. Table of. 30 Logarithms to many places. Radix table for calculating ..... 30 Mathieu functions II . 16 n! and P(n+-|-), Table of.