NATIONAL BUREAU OF STANDARDS REPORT

10343

PROJECTS and PUBLICATIONS

of the

APPLIED MATHEMATICS DIVISION

A Semi-Annual Report

July through December 1969

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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10343

IMPORTANT NOTICE NATIONAL BUREAU OF

for use within the Governmei and review. For this reason whole or in part, is net eu Bureau of Standards, vVashi the Report ha: been specific

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

)gress accour.ting documents intended

it is subjected to additional evaluation

tore listing of this Report, (jither in the Office of the Director, Nation.il

or, by the Government agency for which

tal copies for its ov/ii use.

U.S, DEPARTMENT OF COMMERCE

NATiOKAl. OUREAll OF STANDARDS

A.PPLIED MATHEMATICS DIVISION FUNCTIONS

Conduct research and provide consulting services to the Bureau and other Federal agencies

Jn various fields of mathematics important to phy.sical an.d engineering sciences, automatic

data processing, and operations research with emphasis on statistical, numerical and

comhinatorial analysis, and mathematical physics. Develop tools for mathematical work such

as mathematical tables, handbooks, manuai.s, mathematical models and computational methods,

and advise on their use. Provide training in disciplines related to these functions.

NUMI’.RICAL ANALYSIS SECTION: The advancement of computation and the theory

of munerical analysis, particularly in the development of computing algi,rithm

approximations to functions, end methods to facilitate the use of high sp'-^-d electronic computers by subject matter specialists. Design of mathematical

tables; exploratory calculations on automatic machines. Consulting services

and training, and preparation of manuals in these fields. Research in

underlying branches of pure and applied mathematics, such as matjix algebra,

combinatorial analysis, and number theory.

OPERATIONS RESEARCH SECTION; Development and application of mathematical and

computational techniques for the analysis, improvement or optimization >f complex systems or activity-patterns. This includes (l) research in specific

relevant areas of mathematics, such as linear programming, the theory of line

graphs, and the theory of strategic contests, (2) investigations in the art of constructing useful mathematical models of complex systems, and of obtaining information about the system by applying analytic or simulation

methods, and ( 3 ) application of these techniques to selected problems,

of general methodological significance, arising in the work of the Bureau

or of other Government agencies lacking specialized pei'sonncl in this field.

STATISTICAL EJCINEERIMG SECTION: Consulting services in the application

of mathematical statistics to physical science expei'iments and engineering

tests, particularly in the design of experiments and in the analysis and

interpretation of data. Research on pertinent topics in probability

and mathematical statistics. Preparation of reports, manuals, tables,

studies of computational methods and other aids to the application ef modern statistical methods .

SYSTEI-IS DYNAMICS SECTION; Research and consulting in applied mathematics

basic to physics and engineering, with emphasis on analysis of the dynamic

behavior of complex physical systems. This involves, primarily, the

develop.ment and application of techniques foi’ solving linear and non- linear system.s of differential equations and integral equations, or combinations of both. Of concern also is simulation of the behavior ;f physical systems by means of electronic computers using approximation

techniques and semi-analytic methods. Attention is given to problems in

plasma dynamics and the behavior of solid matter and multi compone.'nt liquid

syste.ms, with emphasis on developing matliematical methods of wide range of applicability beyond the scope of the immediate problem. Invcstig.atl nis are carried out on the special functions encountered in the analysis and

algpritliras for their evaluation are prepared.

II

Contents

Status of Pi’ojects° as of Becembei' 31,1969 ^

1. Numerical analysis 1

2. Operations research ‘i3- Probability and mathematical statistics 8

4. Statistical engineering services 10

5 . Systems dynamics

Lectures and technical meetings 1?

Publications activities 19

°0nly unclassified material is included in this report.

Ill

APPLIED MATHEMATICS DIVISION

Jjly 1, 1S69 through Dacernber 31, 1969

TECHNICAL ADVISORY PANEL

Marvin L» Minsky, Massachusetts Institute of Technology

Carl A, Bennett, Battelle Hsmorial Institute Murray S. Klamkin, Ford Scientific Laboratory

Charles R. DsPrima, California Inst, of Technology M. Ho Martin, University of Maryland

H, Oo Hartley, Texas A & M University John Riordan, The Rockefeller University

John Todd, California Institute of Technology

DIVISION OFFICE

Edward W, Cannon, Ph,D,, Chief

Catherine Hartsfleld, Secretary Molly F, Hevonor, Admin. Officer, B.S." Yates S. Bladen, Admin, Officer®

Russell A. Kirsch, M.S. A.nne A. Holston, B.A. Irene A. Stegun, M.A. Margaret L. Dean Gertrude V, Thompson Ruth Zuclcer, B.A.

Ida I. Rhodes, M.A. , Consultant

NlRklERICAJ. ANALYSIS SECTION, Morris Newman, Ph,D., Chief

Doris M, Burrell, Secretary Joseph Lehner, PhtD,"*" Karl Goldberg, Ph.D, Russell L. Merris, Ph.D. Seymour )!aber, Ph.D.

Frank W, o. Olver, D.Sc. Stephen J. Pierce, Ph.D,

Justin C. Schaffert*

STATISTICAL ENGINEERING lABQPJlT'OPY, Joan R, Rosenblatt, Ph.D,, Chief

Hslou K, liu, PhcD., Ase‘t Chief

Raj Cliandra Bose, Pli.D,, Consultant

Shirley G, Bremer, B.A.>''' Eleanor S, Brown

Veronica Connor, Secretary

James J. Filliben, Ph.D.

David Hogben, Ph.D,

Brian L, Joiner, Ph.D. Mary G, Natrella, B,A,>!‘ Sally T. Peavy, B.A.'^^

SYSTEMS DYNAMICS SECTION, Hans J. Oser, Ph.D,, Chief

Jeffrey T. Fong, Ph.D. Regina Kopec, Secretary

S, Richard Kraft, Ph.D,

Daniel W. Lozlei', M.Ai,

Malcolm S. Scott, M.S.’’' Janace , Speckman , M.S. Ruth N. Varner, B.A.*

Roy H. Wampler, M.A. William H. Youden, Ph.D.^+*

Zol]a G, Ruthberg, M.S.’f' Walter L. Sadowskl, Ph.D.

OPERATIONS RESEARCH SECTION, Alan J. Goldm.ati, Ph.D., Chief

Jack Edmonds, M,A,°

Judith F. Gilsinn, M.S. William C. Hall, B.A. Dolores F, Harrison, Secretary

William A. Horn, Ph.D,

liSmbort S. Joel, B.A,

David Klavan, B.A.’i’ David S, Lfibovitz, B.A, “S' Jeffery C. Lagarlns

Joel l,0 vy, M.A.

Pliilip Meyers, Ph.D.t

Martin H. Pearl, Ph.D.*

Patsy L, Saunders, B.S. Roger D, Traub, B.A,*

*Part-t imo ^^Postdoctoral Research Associate

***Guest Worker

°On Leave of Absence

^E.O.D, November 5, 1969 ^Retired October 31, 1969
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Status oi Projects

1 . NUMERICAL ANALYSIS

RESEARCH IN NUMERICAL ANALYSIS AND RELATED FIELDS

Task 20501-12-2050110/55-55

11540

Origin: NBS Manager: Morris Nevanan Full task description: July - September 1954 issue, p. 1

Authorized 8/29/54

Status: CONTINUED. M. Nev.mian has proved that if 77 is a unit in the cyclotomic number field

R(C) > where ^ is a primitive pth root of unity and p is a prime > 3 , then Tj is the rrh

power of another unit only if 1 rj < log N/log(2 cos

-^ ) , where N is the maximum of the absolute

values of 17 and its conjugates. This result was applied to prove that a number of diophantine

equations involving cyclotomic units had only trivial solutions.

M. Newman and L. Greenberg have proved that the density (in a well-defined sense) of solvable groups generated by elements of odd order is zero.

M. Nc^'/man has prepared several versions of his "exact solutions" program using only basic FORTRAN. These can be used immediately on any machine with a word length of 36 or more bits. Some dozen copies of this program have been distributed by request.

S. Haber completed vjriting a survey of the literature on numerical evaluation of m.ultiple

integrals

.

F.W.J. Olver has continued the study of the method of .stationary phase for the asymptotic

expansions of oscillatory iiAtegrals. An improved form of error analysis has been constructed and i being tested on illustrative examples.

K. Goldberg extended his results on similarity for formal power series over fields,

substituting a matrix equation for the determinant equation previously found.

K. Goldberg extended his tables of the coefficients in formal power series for various

operations including product, iteration, inversion, and the related power series L^(z) defined

by L^(f(z)) = L^(z) • f'(z) .'

S. Pierce has determined all multiplicative maps of the 2X2 matrices over a Dedekind

ring which do not send all singular matrices to 0 .

S, Pierce has proved that all members of the orthogonal group of a real positive multilinear form have only eigenvalues of modulus 1 and only linear elementary divisors.

1

Status of Projects

S, Pierce and K. Merris have shora that associated transformat ioiiw on higher degree

symmetry desses of tensors regarded as representations of the full linear group are always

reducible. Investigations for the case of degree one symmetry classes arc continuing.

S. Pierce has given a short proof using the Hilbert reciprocity law that -] is a simi of tv;o squares in any cyclotoralc field of order m when in is divisible by a prime

p s 3 or 5 (mod B)

R. Merris discovered a generalisation, T , of the trace of a matrix. If A and B are complex mXn matrice.s, (A,B) “ T(B'''A) is a positive semidefinite hen.nltian (psdh) form . Suppose H = (H^j) is an mnXmn block psdh matrix where is niXm . Then (T(l'^^)) is [)cdh .

R. Merris and S. Pierce proved the space of mXn matrices with the generalized trace form is regular on].y if T is the trace. Research in this area is continuing.

S, Pierce and R. Merris proved that if A is a complex matrix of sufficiently large

rank and if all the elementary divisors of K(A) are linear then all the elementary divisors of

A are linear. Here K(A) is an as.soclated transformation based on a group and an irreducible

character of arbitrary degree.

R. Merris and U. Watkins discovered some conditions forcing isomorphism between symmetry

classes of tensors.

R. Merris discovered an inequality for generalized matrix functions and block herndtian

matrices

.

Pub lications :

(1) Stochastic quadrature formulas, S. Haber. To appear in Math. Comp.

(2) Sequences of numbers that are approximately completely equidistrlbuted . S. Halier. Submitted

to a technical journal,

(3) On the sum £< C n >

^ and numerical integration. S. Haber and C.F, Osgood. To appear in Pacific Jour, of Math.

(4) Numerical evaluation of multiple integrals. S. Haber, Submitted to a technical- journal,

(5) Lectures on modular forms. J. Lehner. IiMS 61 of the NBS

.

(6) AuLomorphic Integrals vjith preassigned periods. .1, Lehne.r , J. of Re.^carch NBS, 73.B, 153-161

(1969)

.

(7) On the multipliers of the Dedekind modular function. J. Lehner. J. of Research NBS, 72B , No. 4,

253-261 (1968) ,

(5) Subgroups oi SL(t,z). M, Newman. J. of Research N8S, 73B, 143-146(1969).

(9) Some results on unitary matrix groups. M. Newmtm and M. Marcus. To appear in J. of Linear

Algebra

.

(10) Some results on roots of unity, with an application to a diophantlne problem, M, Newman. Aequationes Hath. 2, 163-166 (1969).

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(11) Isometric circles of congruence groups, M. Ncx'nnnn, Amer. ,1. Matn. 91, 648-656 (1969).

(12) Principal ideals in matrix rings (v;ith S. Pierce). M. Mewman. J. of Research tlBS, 733,

211-213 (1969).

(13) Normal subgroups of the modular group. L. Greenberg and 11. liewman. Submitted to a technical

journal .

(14) A diophantine equation, M. Kevtman. J. London Math. Soc . , 43, 105-107(1968).

(15) A table of the first factor for prime cyclotomic fields. M. Nevroan. To appear in Math, of Computation

.

(16) Some results on solvable groups. L. Greenberg and M. Newman. To appear in Arch.der Math.

(17) On Riemann surfaces with raaxim.al automorphism groups. J. Lehner and M. Newman. Glasgow

Mathematical Journal, Vol. 8, Part 2, 102-112 (1967).

(18) An enumeration problem for a congruence equation. M. Ne’-tman and R. Brualdi. To appear in

J. of Research NBS

,

(19) Why steepest de.scents? F.W.J, Olver, To appear in Proceedings of 1969 SIAM National Meeting,

June 10-12, 1969.

(20) Bounded matrix groups. M. Net'/mari and S. Pierce. To appear in Journal of Linear Algebra.

(21) Orthogonal groups of positive definite multilinear functionals. S. Pierce. To appear in Pacific Jour, of Math.

(22) Multiplicative maps of matrix semigroups over Dedeklnd rings. S. Pierce. Submitted to a technical journal.

(23) Orthogonal decompositions of tensors spaces. S. Pierce. To appear in J. of Research NBS.

(24) Trace functions I . R. Kerris. Submitted to a technical journal.

(25) Elementary divisors of higher degree associated transformations. R. Merris and S. Pierce.

Submitted to a technical journal.

(26) A class of representations of the full linear group. R, Merris and S. Pierce. Submitted to

a technical journal.

(27) Isomorphic symmetry classes of tensors. R. Merris and W. Watkins. Submitted to a technical

journal .

'

(28) Partitioned herraitian matrices. R. Merris. To appear in J. of Re.searc,h NBS.

3

2. OPKRyVnOKS RESEARCH

CONSULTATION IN ILViTlEMATICAL OJ'ERATIONS RESEARCl;

Task 205-12-2050151

Origin and Sponsor: NBS 11570 Authori:^ed 12/30/60

Manager: A.J. Goldman

Full task description: October-December 1960 issue, p.3

Status: CONTINUED.

(1) Demand for miscellaneous consulting and advisory services remained heavy. Section staff provided such services in 99 recorded instances, 96 involving assistance to NBS staff. The 99 ins(;ances totalled to 695 recorded man-hours. Cither agencies assisted included the Civil Service

Coiirmission, National Science Foundation, Office of Emergency Planning, Maritime Administration, Law Enforcement Assistance Agency, and Bureau of the Budget. Requests from universities, industry,

professional groups and journals v;ere also met.

(2) J. Gllsinn continued collaboration with the Information Processing Technology Division

in a study, for the Federal Aviation Authority, to improve air traffic designation procedures. A

previously-X";ritten simulation program was documented and applied to test an initial scheme for assigning radar beacon codes to airplane flights; the results were analyzed and documented. (Reported

here for convenience; supported under Project 6505453.)

(3) A.J. Goldman, W.A. Horn, J. Levy and M.H. Pearl completed a collaborative effort with the Technical Analysis Division on another study for the FAA, this one to analy.ze a proposed nevj "capacity" concept for an airport runway and the associated final-approach airspace. For a single stream of customers, the concept w’as shown (using tl'.e theory of Markov renev.iai process) to be re- presentable by a simple formula useful for planning and analysis purposes. The theoretical development and illustrative calculations were documented, and also presented orally at several briefings

for interested FAA personnel. (Reported here for convenience; supported under Project 4314449.)

(4) W.G. Hall continued helping the Army Data Field Systems Command in planning, design and numerical-analysis aspects of a new tactical artillery-fire control system. Efforts included contractor monitoring, and design and testing of a short course in basic computer programming and numerical analysis for tho Fort Sill Artillery Training School. (Reported here for convenience;

supported under Project 6505425.)

(5) Goldman, Hall, Horn, and L.S. Joel continued assistance to the Post Office Department's

Bureau of Research and Engineering in technical Interfacing v;ith contractors concerning computerized

models and data analysis. P. Saunders began assistance to the Technical Anaiysl.s Division in a simulation study of Coast Guard search and rescue operations. (Reported here for convenience;

supported under Project 4314561.)

(6) A.J. Goldman began service as Associate Editor of tlie Operations Researcli Society's

"Transportation Science" journal, and Vice-Chairman of the Society's Transportation Science Section.

Publications

(1) M. Aronoff (Dlv. 43]), A.J. Goldman al^. Analysis of a capacity concept for runway and final-approach path airspace. NBS Report 10 111, 11/69.

(2) R.D. Elbourn (Div. 650) and J.F. Gilsinn. Sin:ulation of Air Traffic Control radar beacon code

assignment plans (final report on Phase 1). NBS Report 10 117.

(3) A.J. Goldman and P.R. Meyers. Slmultane ous contractif ication. Journal of Research NBS, 73B (1969), pp. 301-305.

(4) A.J. Goldman. Systems analysis and urban problems (Discussion). To appear in Prcc. Sjnnposium on Systems Analysis for Social Problems, 5/69,
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W.A. Horn. Some fixed point theorems for compact maps and flows In Banach spaces,

in Trans. Ainer. Hath. Soc.

C3) To appear

(6) W.A. Horn

(7). W.A. Horn

Convex homotopy. Submitted to a technical journal.

Optimal design of sorting networks. NBS Report 10 146 (1/70).

COMBINATORIAL MliTHODS

Task 205-12-2050152

Origin and Sponsor: NBS 11540 Authorized 12/10/60

Manager: A.J. Goldman

Full task description: October-December 1964 issue, p.3; April-Jur.e 1962 , p.l5

Status: CONTINUED

(1) J. Gilsinn (and C. Witzgall of Boeing Scientific Research Labs) continued experiments

and documentation on the comparison of shor test-path algorithms.

(2) A.J. Goldman continued studies relating to the optimal location of facilities in networks. He and C. Witzgall generalized the theorem that a single node, which produces half or more of the total flow, must itself be an optimal location.

(3) L.S. Joel initiated computer implementation of J. Edmonds' algorithm for minimum-cardinality

partition of a matroid into independent sets. The program "frame" for general matroids, and the subroutine to make it applicable to graphical matroids, were programmed.

Publications

(1) J. Edmonds and D.R. Fulkerson (RAND). Bottleneck extrema. To appear in J. Combinatorial Theory.

(2) J. Edmonds and 0. Shisha (Wright-Pat terson A.F.B.). Acute bijections. To appear in J. Combinatorial Theory.

(3) A.J. Goldman. Optimal locations for centers in a network. Transportation Science 3 (1969),

pp. 352-360.

LINEAR AND NON-LINEAR PROGRAMMING

Task 205-12-2050153

Origin and Sponsor: NBS 11540 Authorized 12/30/60

Manager: W.G. Hall

Full task description: October-December 1960 issue, p.3

Status: CONTINUED

i| (1) W.G. Hall and P. Saunders continued work to improve the capabilities for linear programming

:| calculations at NBS. Testing has revealed flaws in several proposed programs; particularly hazardous

[ are those in which an erroneous solution (or an incorrect "no solution" indicator) arc given v.Mthout warning.

! (2) A.J. Goldman continued studying the minimax error selection of incom.pleteiy specified

? discrete probability distributions, examining the problem of disaggregating an exactly or

|[ approximately "given" distribution.

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Pub llc.Tt tons

(1) A.J. Goldman. Minlinay. error selection of a univariate distribution '.»'itli pre.scrjbcd

componentwise bounds and ranking. Journal of Research HBS, 73B (1969), pp. 225-210.

(2) A.J. Goldman. Minimax adjustment of a univariate, distribution tc saci.sfy componentwise bounds

and/or ranking. Journal of Research KBG, 7 3B (1969), pp. ^3]-239.

(3) W.A. Horn. A theorem on convex hulls. Journal Research NBS , 73B (1969), pp . 307-308.

SCHEDULING .5ND ROUTING IN INTEK-URB/W TRANSPORT

Task 205-12-2058656

Origin: Technical Analysis Division, NBS 21550

Sponsor: Northeast Corridor Transportation Project, Dept, of Transportation

Manager: P.B. Saunders

Full task description: This is one of three projects into which our wor.k for the Northeast Corridor

Transportetion project has been split. .Its objective Is to cont.inue the development, computer impl craentetlori and nppl Icution of metj-iods i,o c/Dt;-iri "good" operating rules for transport systems.

Status: NEW

(1) P. Saunders continued work on integrating rail scheduling a.lgorichms and demand forecasting

models. Contractor reports on rail and air-flight scheduling were reviewed.

(2) D. Klavan programmed and debugged the algorithm developed by G. Nemhauser (Johns Hopkins U.) for jointly optimal scheduling of local and express service along a line of stations. A slightly

revised version, to liandle two "locals" which compete over some Interior links of the line, was also developed.

Puhl

i

c ation

(1) D.R. Young (now of Stanford U,). Passenger transportation scheduling. NBS Report 10 069 (6/69).

PASSENGER DEMAND MODELS FOR INTER-URBAN TRANSPORT

Task 205-12-2050657

Origin: Technical Analysis Division, NBS 21550

Sponsor: Northeast Corridor Transportation Project, Dept, of Transportation

Manager: A.J. Goldman

Full task description: This is one of three projects into which our work for the Northeast

Corridor Transportation Project has been split. Its objective is to develop,

calibrate and prototype-test improved passenger-demand forecasting models.

Status: NEW

(11 L.S. Joel began an analysis of the promise for niodel use of various additional explanatory

variables describing characteristics of the transport system. He and .1. Lagarias initiatoil an investigation of the relationship between intercity passenger trip volumes and telephone-call

volumes

.

6

(2) A.J. Goldman and R. Ku (Division 431) examined tv;o mo’del inodif icaLion:; : one reflecting

the idea that auto-driver fatigue increases more than linearly -with trip time, the other revising

the modal-split submodel to incorporate a probabilistic lower limit on acceptable conductance.

Neither change significantly Improved the fit to the present da(:a set.

(3) J. Gilsinn, A.J. Goldman and R. Traub revie\;ed contractor reports and related literature.

Ku completed a summary ch.apter on the model cui rently used by the Corridor Project; Goldman (with

li. Cheslow of DOT) began a more extensive documen tu t ion

.

Publication

(1)

J. Gilsinn. Roles of demand models in the Northeast Corridor Transportation Project. NBS-NDCTP Working Paper No. 12, 7/69.

MISCELLANEOUS 1-LATH SERVICES CONCEPaNING INTER-URBAN TPvANSPORT

Task 205-12-2058458

Origin: Technical Analysis Division, NBS 21550

Sponsor: Northeast Corridor Project, Department of Transportation

Manager: A. .J. Goldman

Full task description: This is one of three projects into which our work for the Northeast

Corridor Transportation Project lias been split. Its objective is to provide

miscellaneous mathematical services and exploratory research for the Northeast Corridor Transportation Project (NECTP)

.

Status: NEW

(1) J. Levy and M.H. Pearl continued developing methods for evaluating feedback vs. non- feedback flow regulation at a merge point in a transport network. A comparison of the performance

of non-feedback, feedback, and "prophesying" control v:as begun.

(2) VI. A. Korn completed studying an approach to the design of transport networks when

minimizing the number of access points is of prime concern. He also assisted in review of contractor documents

.

(3) A.J. Goldman assisted in editing the first draft of the NECTP 12/69 Report.

Publications

(1) J. Levy and M.K. Pearl. Feedback regulation of traffic at an_ intersection of two streams. NBS-NECTP Working Paper No. 11 (9/69).

(2) M. Krakowski (Tulane U.). Adaptive svritching and routing in transport networks. NBS-NECTP

Working Paper No. 13 (10/69)'.

(3) W.A. Horn. Optimal Networks Joining N Points in the Plane. Strassenbau und Strassenverkehrstechnik, ^ (i969), (Beitrage zur Theorie des Verkehrsf losses) , pp . 161-166.

3. rnOP.ABILITY AKD I'OTfDiJ.lATICAI, STATISTICS

RESEAIiCH IK PROE/>EILITi' .ARD MATHEMATICAL STATISTICS

Tasic 201j03-]2-20'^0131/63-I2>9

1150

Origin: NBS Authorized 10/]/62

Manager; Joan Raup RoaenLla.tt Pull tasK description: July - December I962

Status; COlWIl'IUED. Brian L. Joiner and Eleanor S. Brown, in coDlaboration with Bert Levy (Harry

Diamond labs.) and N. F. Laubscher (National Research Inst, for Math. Sciences, South A.frica),

completed the preparation of a co;nhined author and permuted title index for seven statistics journals,

Including articles published since the most recent cumulative subject index to each of the journals.

The index V'as premred using a computer program vn’itten by the late V. W. Youden (NBS Center for Computer Sciences and Technology).

James J. Filliben is completing a study of the nature of the percent point function (ppf)--the inverse

cumulative distribution function. It is sliown that a nuniber of statistical procedures liave a simpler

and more natural expression in terras of the ppf rather than in terms of the cumulative distribution

function. Various simplifications in probability theory and order statistic theory are presented.

The use of the ppf in random number generation and probability plots is discussed. An alternative

set of measures of distributional characteristics based on the ppf, rather than on the mom.ents, is Introduced. The heliavior of the ppf under various tj'pes of transformations is considered. The use of the ppf in generating distributions with pre -.'specified tail lengtli is demonstrated.

Publi cat ions:

(1) The median significance level and other small sample measures of test efficacy. B. L. Joiner.

J. Amer. Statist. Assoc., ^ (1969), 9T1-985-

(2) Student-t deviate corresponding to a given normal deviate. B. L. Joiner

J. Res. MBS - C. Engineering and Instrumentation, 75C (1969)? 15-16.

(3) Some properties of the range in samples from Tukey's symmetric lambda distributions.

Brian L. Joiner and Joan R. Rosenblatt. Submitted to a technical journal.

(^) An author and permuted title index to selected statistical journals. Brian I,. Joiner,

N. F. Laubscher (Nat'l. Res. Inst, for Math. Sciences, S. Africa), Eleanor S. Brown, and Bert Levy (Harry Diamond Labs., IJ. S. Amy). To appear as NBS Special Pub, 321.

(5) Approximating discrete probability distributions. H. H. Ku and S. Kullback. (G.H.'j.). IEEE Transactions on Information Theory, IT-1 5 (19d9)>

(6) Analysis of multi -dimensional contingency tables. H. H. Ku, R, N. Varner and S. Kullback

(George Washington Unlv.). To appear in Free. l4tli Conf. on Design of Experiments in Army

Research Development and Testing. ,

(7) An application of minimum discrimination information estimatiojn to a problem of Grizzle and

Bei'Kson on the test of "no interaction" lOTothesis. H. H. Ku and S. Kullback (G.W.U.).

Submitted to a technical journal.

(8) Symmetry and marginal homogeneity of an r x r contingency' table. C. T. Ireland, S. Kullbaci,

(G.V’.LI.), aivi H. H. Ku. To appear in J, Araer. Statist. Assoc,

(9) An evaluation of linear least square.? computer programs, Roy H. Wampler.

J. Res. KBS-B. Math. Sciences, 73B (1969), 59-90*

(10) An evaluation of linear least squares computer programs: A sumuary report. Roy il. Wampler. To appear in Proc. l4th Conf. on Design cf Experiments in Army Researcli Development and Testing.

(11) A report on tlie accuracy of some widely used least squares computer programs. Roy H. V/ampler. To appear in J. Amar. Stati.st. Assoc.

6
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Task 20503-12-2050131

11550

Origin and Sponsor: KBS Authorized II/1/68

Managers: David Hogben, Sally T. Pcavy

Pull task description: July - December I968

Status; CONTIIiUED. David Hogben, Sa]jy T. Peavy, Ruth N, Varner and Shirley G. Bremer continued

trork on the development of the OMNITAB system. M. Stuart Scott developed a comiriand for correlation analysis detailed autonatic printing. Fight new versions have been implemented

successively. Details of the changes made appeared in the t'nree Newsletters issued. A set of

tvrelve instructions for perforniing operations on magnetic tape vrare added to the system.

R. C. McClennon (Office of Standard Reference Data-) contributed two conunands for array operations.

Other commands were added for printing data, and Gauss quadrature.

Many improvements were made in the printing and curve fitting commands. Results are now' normally

printed according to the "readable" format. The automatic printing for the least squares instructions has many valuabi.e additions, in particular, one page containing four different plots

of standardized residuals.

An important change W'as made in the word length of alpha/numeric data so that ONiNITAB is now' as machine independent as the state of the art will pennit.

Publications:

(1) The use of OMNITAB for statistical analysis of tabular data. Joan R. Rosenblatt,

Brian L. Joiner, and David Hogben. To appear in Census Tract Papers: Papers Presented

at the Conference on Small-Area Statistics, Aunerican Statistical A.ssociation, New York,

August 21, 1969
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COLLABOMTIOM ON GTATISTIOAJ. AGPECL'S Or'

NBS RESEARCH AMD TESTE'IG

Task 13911-612050950/5.1-J.

99500

Origin; NBS Authorised 7/1/5O

Mauagei’S; H. il. ?ai. J. R, Rosenblatt

Full task description: July - September 1950 issue, p. 60

Status: COMTINIIED. This is a continuing project involving cooperaticn VTitli other Bureau scientists

on the statistical aspects of their investigations. These services vary from short (one-hour)

sessions to extended collaborations involving several ina.n-monthsj and are concerned prlmariDy with

stetistical design of experiments, analysis and interpretation of data, and the use of cornpiuters in statistical analysis of data. Typical examples of the services performed are the following.

B;riaa L. Joiner is on detail to the Boulder Jjaboratories for one year, at the request of the NBS

Office of Measurement Services. His primary mission is to heip them establish cooperative calibration

progratas and to provide better inforination to support the uncertainty statements on the reports of calibration. So far effort lias concentrated on the analysis of existing data and the planning of experiments to obtain f'urtlier data on oo8,xlal and microvfave bolometers.

Brian I,. Joiner presented a talk on "Error Analysis" ac a Iteser Povrer and Energy Measurement Seminar

sponsored by the Quantum Electronics Section of the Radio Standards Physics Division.

Brian L. Joiner assisted Johi: Dean and Douglas Mann (Cryogenic Metrology Section) in the planning and

analysis of experiments to evaluate cryogenic flow meters.

Th.r Statistical Engineering Laboratory continues to distribute within the Bureau occasional notes on useful subroutines and documentation aids, for computer users who are not primarily computer

•pecialists. Three recent notes, for example, describe and give details for using plotting subrcjutines and programs applicable with equijjmerit available at the Bureau, Sally T. Peavy and

PvUth N. Varner are the chief contributors to the series, but notes have also been ’.nritten by other

(ijembers of the Statistical Engineering Laboratory and by persons in other Btireau divisions.

Roy K. V/ampler and Joan R. Rosenblatt are collaborating with G. L. Hov.'ett (NBS Office of Color: ruetry) on the analysis of the latest in a series of cooperative paired comparison experiments conducted by

the Committee oi: Uniform Color Scales of the Optical Society of America.

Joan R. Rosenblatt collaborated v.'ith M. A. Bond, Jr. (NBS Library) to develop and execute a simple

sam'ole design to estimate the distribution by publ.icat 1 on date of the library's books (not including

journals)

.

G. llatrella presented three lectures on "Statistics of Measurement" for senior tecimicians from

ihe State Weights and Measures Departments of Havra.ii, Ca li.foriiia, and TiUnois, Staff meiiibers of the

;iBS Office of 'Weights and Measures also attended tlie lectures.

lar.ies J. Fllliben collaborated with George Hicho (312.0j)and Harvey Yal.owltz (312,03) in the

pneT'aration and testing design of specimens for X-ray diffraction standards -- about 1000 pellets

compected from 5 vreight percent 310 stainless steel powder and 95 weight percent 430 stainless steel pevder

.

pjrii cations;

(l) Iriteriaboi-atory comparison of the potential heat test methed, D. Gross (Fire Research Section)

and M. G. Natrella. Submitted to a technical journal.

10
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BTATISTJCAL SERVICES

Task 20503-^0-2050132/58-3^6

11550

Origin and Sponsors; Various Agencies Authorized 3/31/58

Manager: J. R. Rosenblatt

Full task description: January - March 1958 issue, p. h’y

Status: CONTINUED. This is a continuing project which involves providing, upon request, statistica.l services to other governinental agencies, universities, industrial organizations, and otlier non- governmental agencies. Approximately jO such requests are lie.ndled per month langing frcm short conferences to coi.laboration involving several da,ys vorK,

Janace A. Speckraan used OMIITAB to perform l44 least soiiares straight line fits to data on the

Federal Court of A.ppeals workload, in response to a request from James A. McCafferty of the Division

of Procedural Studies and Statistics, Administrative Office of the United States Courts. Projections for 1970 to 1975 were computed and plotted for all 11 circuits combined and for each

circuit separately for 6 variables -- (total nuniber of appeals, numbei* of prisoner petitions, etc.)

using data from i960 to 1969. Projections vrere also made using only the data from I965 to I969 to

see if the trends have changed.

The Statistical Engineering laboratory vras asked by the NBS Center for Computer Sciences and

Technology to participate in one of a series of orientation meetings for a group of foreign trainees

(sponsored by the Agency for International Development) from the Census Bureau's Office of Inter- national Statistical Programs. The group included several computer prograinmers with i^articulai’ interest in statistical computations.

In response to requests, twenty-two copies of the OMNITAB program were distributed.

SYS'l'i'MS UYNAMLCS

rese«jk;h lij’ sYS'i'-W'is /rayu-iicf.!

A!MD RliLATED PMEI/iJG

Taek ?05)i0-12-20i)0l)^l/55-57

Oi’igin: IJBS Authorli-;cd 9/l/|;)4

Manager; H. J. Oser Full taslc description: July-geptemler 195^i- issue, p. 2"{

In consultation with Hr. J. A. Siiaaons of the Metallurgy i)iviBion (312-05) and Jlr'. E. A. K'’>i2-cley of the Mechanics Di\^slon (213-05), J- T. Fong proved tliai the problem of tlie finite defonaation of a memory-dependent .material continuum of the Bernstein-Kenrsley-Zapas tj^ic-: (Trans. Soc. Rheology, 7, 391“^10 ( 1963 ) is equ.ivelent to a variational problem for a rlieonomic system, i.c;. the local Lagrangion

depends on the time t explicitly. A manuscript entitled "On the existence of an action principle fer a dissipative continuum" is hoing prepared for review and di.scussJon.

In collaboration with Mr. L. J. ZapjiS of the Mechanics ilivision ( 213 . 05 ), J. T. Fong showed thot the

classical theory of plasticity in which the time t is not a physical variable but a maihcmiatlcal

parameter, can be modeled a.-fter the Bernstein-Kearsl cy-Zapas ' theory cf a memory -dependent material

provided tlie elastic potential of the EKZ theory Ic a homogeneous fujict ion of the vculable t ' of degree -1, where t' is the difference between the current time and some time in the past. Work is

C'.ontinviing to derive some basic features of a special pl.a,£;ticity theory from a cla.es of the memorydependent elastic potentials of the bKZ. theory.

Progress is al.so being made in a long-tcrTu project to find Ih.e necessary end sufficient conditions I'or the equivalence of the geometric theory of an "imperfect" material continuum due t.o Kondo, Eilby,

Kroner, etc. and the history-dependent kineii'.atic theory of a "sljnple" material due to Truesdell, Hell,

Kang, etc. To discuss some of his f.lndings, J. T. Fong visited Professor Y. C. Wong of the De-part.me.nt of Mathematics, Uni.versixy of Horxg Kong, as a guest worker with the title of Vlslcing Research Fellow

from July 5 to July 12, I.969 during which J. T, Fong also delivered the following two talhs

;

"Microscopic Theories of Engineering Material.s" - University of Hong Kong;

Department of Civil Engineering Seminar, July E, I969 ; "Applications of Differential Geometry in Continuum Physics" - University

of Kong Kong: Dept, of Mathematics Seminar, July 9» 1969-

R. S. Kraft obtained a constructive existence proof for a pure initial-velue prol.lem associated witli a .linear transport equation. A paper cn tlJ.s subjecc i.s b^ing prepa,red. Ideas fci' deriving a-priori

boimds for an approximation scheme associated with a bouirinry-lniTlal problem for a linear transport

equation have been obts.ined.

Tlie -study of a finite-difference scheme for the Kemst-Planck equations is continuing. Tecimlqucs for eDUablishing the positivity and convergence cf the non-lincar luerates are being examined.

R. S. Kraft discovered also a possibility for generalizing a method of reflecting solutions of elliptic

systems. The method, if feasible, would allow continuation across an analytic hcuncKu'y whon the solution of the system satisfies very general condi.tions on the boundary.

H. J. Oser completed, joi.ntly with J. E- McKinney of the Rheology Section (213-05), two manuscripts

deali.ng v,’ith acoustic propagation in viscous and inviscid, heat-conducting media. The authors show

that certain solutions of the underlying fourth-order i)ai-tial differential equation are not stable, a result which has not been I'epcrted heretofore in the ^Litci'abure. In viscous fluids the instability

does not occur if tlie vises;- Ivy exceeds a certain critical, value wliich depends on the ratio of the

specific heats, the Prandtl number, and the viscosity.

12

Continuing his effort to provide au :l-Mproved autoicatic nincerlcnl intcgratio:i routine for OilinTAB,

D. V;, Lozier produced end chocked out a Fortran program that uaca on adaptive Simijcon procedure. He also completed and submitted to American University a paper entitled "Frechet Ill.fferential Calculus"

as the finaJ. req^ulrement for the MA degree, which vas awarded in August. In another project, he de- veloped an algorit)m, and produced an Iniplementlng Fortran program, to determine v/itli a iiigh degree

of precision the volume of a nearly perfect si^here from experimental data taken by measuring deviations from roundnecs of great circles on the sphere. This work was done for P. E. Pontius and H. A. Bovnoan of 213.31 (Mass and Volume Section, Metrology Pivlslon). Several test cases were run to check

out both the algorithm a;id the program. Finally, he provided jnatheraatical e,nd computer programming

support for W. L. Sadowski and other staff members of UBS.

Z. G. Ruthberg compai'ed the efficiencies of several matrix inversion programs and two programs for

finding roots of polynominals . This effort is intended to involve the Section mere deeply in the

program for algorithm testing and development.

Z. G. Ruthherg also continued work on the binomi.ai operator [a(x,y) ^ + h(x,y) • A FORTRAN program is now avaJ.lable that produces the successive powers n of this operator. Tliis new program

is fai* more efficient (concerning the storage requirement) and faster than the earlier LISP program.

Consultations to and cooperative activities with other Bui*eau units continued throughout the period.

These involved contacts with the Metrology ilLvision (now a part of the Atomic Physics Mvision), the

Mechanics Division, the Electronic Technology rivlsicn and the Meat Division. The Mass and Volume

Section of the Metrology Di.vision Js concerned with determining with high precision the volume of almost perfect spheres . A method vas developed with that group to determine the volume corrections

numerlcal].y from a suitable number of traces along approximate great circles of the pseudo sphere.

Tlie results appear to offer a nev; and considerably more economical way of obtaining precise volumes for

pui'poses of density and el?.ss determinations.

Anothei’ effort for the Laser group in the Metrology U’.vision le devoted to checking whether anomalous

light propagation may take plr.ee in cerbaln laser optical arrangements . There is some speculation

that such might he the case. The investigations are not conclusive so far.

Work with J. E, McKinney ( 213. 05) was completed on the propagation of sound in viscous and inviscid

media. A paper dealing with viscous case will appear in Jour, of Acoustical Society of America in

the January 1970 issue. . The paper on the inviscid case was subriiitted to the V/ashington Editorial

Review Board for approval to appear in the KBS Journal of Research.

Shorter consultations with mejnbers of the Heat Division and the Electronic Technology Division involved

the solution of Integral equations and bo-ondary vad.ue problems

.

H. J. Oser sei-vcd as editor and trons]iitor of a book on the theoi-y and computation of hoimdary layers,

published by M.I.T. Press Inc.

Publications :

(1) Stability of Acoustic Waves witkin a Viscous, Coraprossible. Heat-Conductirjg Fluid. J. E. McKinney

and H. J. Oser. To appear in the Jour, of Acoustical- Society- of America, Vol. 47, Wo. 1. Jan. 1970.

(2) A. V/alz (edi.ted and transljated by H. J. Oser): Boundary Layers of Flow and Temperature. M.I.T.

Press, Inc., October 19d9-
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M/O’IffiliATICAL m'HOEG HI FUSKA PHYSICS

Task 20504-12-205014o/59-M(-2

II5I1O

Origin: KBS /luthorized 10/].3/6l

Mejiager: VJalter L. Sadovski

Full task description; October-Eeceiater I96I issue, p. 12

A hlgh-ordor Taylor series expenslon in the time vsxiable for the numerical solution of the Vlasov

equation has been developed. The expansion pei'nlts the use of a smaller number of Hemlte poljTiomlnals

and has a very' sma^J. truncation error. The error is expllcltely' calculated. In addition to the

higher speed, the algorithm makes it possible to study truncation errors in both Fourier ar/d Hermlte

space

.

The results show that the use of the electric field as 0 ci'iterion for numerical stability' is wholly'

Inadequate, numerically' unstable runs giving substantially the same value of the electric field as stable runs. This Indicates that nujnerical studies of processes that are highly dependent on kinetic

effects in plasma, such as hump on tall, must he re-examined to Insure that the results obtal.ned were numerically accurate.

Work is in progress to determine the ridnlmum size of eigenfunction expansion sets for various values of parameters. A paper on this topic is in preparation.

A one-day vrorkshop was held at I'lBS on October 15, 19^9 • The 'workshop dealt with the numerical solution

of the Vlasov equation. Amorg the topics discussed were the relative merits of the different methods

of solving the equation, reliability of results, numerical difficulties encountered and ways of dealing

with these.

Biring this conference the paidiclpaivts decided that a file of preprints should be held at HB3 and a newsletter be sent out to the participants to keep thera Informed on wliat the various groups aroimd the

country are doing. Ho agreement on Intercomporison of results has been reached, but a t’wo-v.ieek working

session, possibly at I'fflS, has been suggested for the summer of 1970 and the matter will be taken up again.

Publications

(1) Temperature Renormalization in the Non-Linear Vlasov Equation. W. L. Sadovski and Z. G. Ruthberg.

J. of Reseai’ch NBS, Vol. 73B, pp. 28I-29I, Dec. I969.

(2) Selective E>:citatlon of Harmonics in a CoUisionless Plasma by Two Countorstreajnlng Electron Beams.

W. L. Sadovski and Z. G. Ruthberg. J. of Reseta'ch NBS, Vol. 73B, pp. 293-300, Dec. I969.
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51560

Origin: NBS Sponsor: National Institutes of Health

Manager: Russell A. Kirscli Full task description: January-June 196A issue. 19

Autliorized 1/21 /6A

Status: CORTpiUED, The general procedure developed on the Q32 computer for automatic segmentation

of quantized images which yields as output a partial ordering (induced by the inclusion relation)

of all morphological objects in an image was continued as elements of this partial ordering served

as inputs for a higher level syntactic analysis. These procedures were applied to optical serial

section photographs of a double neuron which v/ere made using a progr'r.mmablc microscope stage and focus connected to the LINC-FDP-8 computer. The sections v;ere the’.i reconstructed and the morphologic

analyzer was also used to reconstruct an optical intensity photograph of two c’aromosomes

.

SCANNING MICROSCOPE PROCESSING

Task 20500-2050408

51560

Origin: NIiS Authorized 6/18/68

Sponsor: National Institutes of Health

Manager: Russell A. Kirsch

Full task description: July-December 1968 issue, p. 14

Status: CONIINITED. Progress was made in the study of the use of a programmable scanning microscope

controlled by a PDP-8 digital computer.

CHEMICAL BIOLOGICAL INFORMATION PROCESSING

Task 20500-2050410

51560

Origin: NBS Authorized 6/27/68

Sponsor: National Institutes of Health

Manager; Russell A. Kirscli Full task description: July-December' 1968 issue, p. 14

Status: CONTINUED. Further efforts v;ere made to coordinate the use of remote computers in communicating pharmacological information regarding chemical structure and biological activity among a group

of collaborating pharmacologists. Advisory work continued on Chemiccl Biological Information Handlin

techniques

.

15
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Task PO5OO-I1O-205O] 2.1 / 57-216

11550

Origin end Sponsor; NBS

Manager: I. A. Stegun

Full task description: July -Pecern’oer 196)4 issue, p. )4

.

Stetus; COHTU'TUED. Consultation continued with the steff of KBS, other government agencies, Industr-y

and universities. The topics covered were tables of specie! functions, general computing techniques

end compute tional pitfalls,

I. A. Stegun end R. Zucker, with emphasis on specie! functions, have conblnued(l ) the file maintenance

of available algorithms, spproximetlons and programs (2) the critical exemlnetlon of available

algorithms end opiproxlraations (3) the testing of the implementing subroutines. A paper has been

prepared on automatic computing methods for special functions- in particular- the error and com- plementary error function, The FORTRAN program yielding full machine accuracy for both functions

over the entire range will be presented together \;ith the test program and sample results.

In the course of the testing of subroutines, hardware and software errors have lieen detected, in particular, double precision mul tiplicetJ.on yielded incorrect single precision results under certain

conditions; the compiler set up the computation of an external factor as an internal factor in

'a suriimation. In collaboration with the Center foi' Computer Sciences and Technology, the hardware error was corrected end the software error is being further analysed.

1 6
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Oav/son, J.

Armstrong, T,

Feix, Iih

Danov i 1 1 , J

.

Mere I', H.

Kruskal, M.

Symoii, K.

Sadov,-ski, W„

Sliero, Kenneth D.

Gilsinu, David

Marlin, Monroe H.

ilOGBEN, D,

WALKER, J. C.

OLVER, F, W. ,J.

SADO’.VSKI, W. L.

JOEI., L. S.

Lectures jchnical Mr *' rra

Workshop on Vlasov Equations

October 15, 19G9

discussed were as follows

:

(Princeton University) Pi'.rticle v,s. distribution function inodojs

(University of Kansas) Interconiparison of eigenfunction oxjiansion with the Los Alamos codes

(University of Nancy, France) Tlio waterbag inodel

(NRL) Fourier-Fourier transform niothod for the solution of the Vlasov equation

(Oak Kidge i^aboratory) On some aspects of truncation in Fourier-Fourior

transforms of the Vlasov equation

(Princeton University) Some remarks on the f;tability

(Madison, Wisconsin) Bit pushing for simulation of particle models

(Systems Dynamics Section) Setting up of a coordination center and the problc-;-. of intercomparison of numerical lesults

Systems Dynamics Seminal'

NASA-Goddard Space Flight Center and University of Nebraska, Lincoln, Nebraska.

Oscillation Theorems for a Class of Delay Equations. July 23.

Melpar, Inc. (A Division of .American Standai-d Co,), Falls Church, Va . Domains

of Stability of Integral Manifolds for Some Nonlinear Differential Equations.

•Nov. 12,

Institute for Fluid Dynamics, University of !\!arylar.d. A Now Method for Finding

Exact Solutions of the Navicr-Stokes Equations. Doc. tO.

Mathomatics Division Expository L.c t nj_e_s

Computing for the Countless. July 23.

(Center for Computer Sciences and Teclmology) Categorical Algebra as a New Approach to Mathematics. September 17.

Tlie Method of Chester, Friedman and Urseli Asymptotic E.ypansion oi Definite

Integi'als Having Two Neai’ly Coincident Sand lo -Poi n ts . October 22.

The Numerical Solution of Differential Equations uy an Nth-Oixler Ku.nge- Ju t ta Method. Deceinber 3.

Loose Ends in tlie Tlieory of Games. Deterabei' IV.

NBS G raduate School , Fall .Semester

PEAtCf, S. T. Fortran Programming for Beginners
I

y..- -r-rg A

I

,

c-

*
-

D<tJ''or.s and Invited Talks Pi-esentori hy Mcinbca's of tlio Elafi at Meetinc.s ol Outside Oi'ganizations

FILLIBE'N, James J. .Simple and rob>i<it estimation of Die location parameter of a .syimnelric distri

bution. Institute of Mathematical Statistics, New York, August R).

FONG, J. T. Microscopic tlieories of ciiKineering materials. University of Hong Kong,

Departmciit of Matliemalies semiiiar. July 9.

GOLDMAN, A. J. The adequacy of itinnageinent science technology for i:on-i:ii 1 i tary a pi)l iea t i ons

in the I’oderal Goveritnien t . American Society Xoi' Public Admi n is t ra tiun , seminar on Management Science in the Federal Civilian Government. Sei>t. 18.

HOGBEN, David Computing for Die countless. American Statistical Association, New Y'ork, August 19.

JOINER, Brian L. The use of OMNITAB foi- statistical analysis of tabular data. Amei'icau Statistical Association, Conierence on Small Area Statistics, New Yoi-k, August 21,

KIRSCM, R. A. Using Computers as Visual rather than verbal devices. D, C. Teachers'

College, October 16.

KIRSCII, R. A. Computer determination of the constituent structure of biological images.

Computer Science colloquium, Rutger.s University, December 5.

KRAFT, R. S. Convergence of semi-discrete approximations of linear tr.ansport equations.

University of Oregon, Eugene, Oregon, August 29,

KU, H. H Analysis of multidimensional contingency tables: An inforruation theoretic

approach. International Statistical Institute, London, September 5.

NEWMAN, M. Number theoretic subroutines lor high speed digital com])uters, O.xfoi-d, England, August 20.

Computational problems connected with certain matrix groups, Oxford,

England, August 21.

Normal subgroups of the modular group, Madison, Wisconsin, October 28.

VARNER, Ruth N. OMNITAB. Washington Statistical Society and Urban Regional Information

Systems Association, Septcml)er 30.

18

PUBLICATIONS ACTF/ITIUS

1.0 PUOLICATIONS .THAT APPEARED DURING THIS PERIOD

1.2 Monograph

Lr;ctures on Modular Forms. J. Lehner, AMS 61.

l.H Technical Papers

Minimax Error Selection of a Univariate Distribution witli Prescribed Componentwise Hounds and Hanking. A. J. Goldman. J. of Research KBS, 73B 0939), pp. 225-2.:-l0.

Minimax Adjustnicnt of a Univariate Distribution to Satisfy Cornpohentwiso Bounds and/or Ranking.

A. J. Goldman. J. of Research NES, 73B (19G9), pp, 231-239.

Simultaneous Contractification. A. J. Gol<3man and P. R. Meyers, J. of Research NBS, 73U

(1969), pp. 301-305.

Optimal Locations for Centers inaNetwork. A. J. Goldman. Transportation Science 3, (19G9),

pp. 352-360.

A Theorem on Convex Hulls. W. A. Horn. J. of Research NBS, 7^ (1969), pp, 307-30S.

Optimal Networks Joining N Points in tlie Plane. W. A. Korn. Strasseubau und S I rassenvo rkela’S' teclmik, 80 (1969), (Beitrage zur Theorie des Verkehrsf iusses ) , pp. 161-166.

The Median Significance Level and Other Small Sample Measures of Test Efficacy. B, L. Joiner.

J, Amei’. Statist. Assoc., ^ (1969), 971-985.

Student-t Deviate Corresponding to a Given normal Deviate, H. L. Joiner. J. of Re;-earch NBS, 73C (1969), pp, 15-16,

Approximating Discrete Probability Distributions. H, H. Ku and S. Kullback (G.W.U.) IEEE Transactions on Information Tlieory, lT-15 (1969), 44-±~447,

Automorphio Integrals with Preassigned Periods. J. Lehner. J, of Research NBS, 73B , 153-161 (1969).

On the Multipliers of the Dedekind Modular Function. J. Lehner. J. of Research NBS, 72B , No. 4, 253-261 (1968).

On Riemann Surfaces with Maximal Automorphism Groups. J. I_ehner and M. Newinan, Glasgow

Matliematical Journal, Vol. 8, Part 2, 102-112 (1967).

Some Results on Roots of Unity with an Application to a Diophantine Problem. M. Newman. Aequationes Math. 163-166 (1969).

Subgroups of Si,(t,z). M. Newinan. J. of Researcli NBS, 73B . 143-144 (1969),

Isometric Circles of Congruence G.roups. M, Nev.inan. Amei-. J. Math., 91_, 648-656 (1969),

Principal Ideals in Mali'ix Rings. M. Newman and S. Pierce. J. of Research NBS, 7^B,

211-213 (1969).

Teinperalu;-e Renormalization in the Non-Linear Vlasov Equation, V>. L. Sadowski and 2, G. Hutlibcr

J. of Research NBS, Vol. 7^. No. 4, pp. 281-291 , (Dec . 1969).

Selective Excitation of Harmonics in a Col 1 is i onless Plasma by Two Counterstrcariing Electron

Beams. W. L. Sadowski and Z. G. Uutliberg. J. of Research NBS. Vol. 73D , No. 4, pp. 293-300,

(Dec. 1969).

An Evaluation of Linear Least Squares Computer Programs. Roy H. Wampler, J. of Researcli NES, 7^ (1969) 59-90.

19

1 » 5 Books

A. Walz (oditocl and IransJatod by li. J. Osor) : BovnuUiry Bayers o.t Flow and Temperature.

M.l.T. Press, Inc. Octolier ]969.

2.0 mNuseniPTs in tup process of publication

' 2.3 Technical Papers

I Normal Subgroups of the Modular Group, I.. Greenberg and M. Nev/man, Submitted to a leelmicnj

I journal,

i; Some Results on Solvable Groups. L, Grcenbe)-g and M, Newman. To ajjpear in Arcli. der MaUi.

/ Sequences of Numbers that are Approximately Completely Equi dis tribu t cd . S, Haber. To ai)neai- in J. of Assoc, for Computing Machinery.

I Niunerical Evaluation of Multiple Integrals. S. Haljer. Submitted to a tcclinieal jouj-nal .

s y -t

' On the Sum L<nr/.> and Numerical Integration. S. Haber and C. F. Osgood. To appea:- in Pacific J. of Math.

Symn,ctry and luarginal Homogeneity of an r x r Contir.gency Talilo, C. T. Ireland, S. Kuilba<.k (G.W.U.), and II, H. Ku. To appear in J. Amer. Statist. Assoc. Some Prope)-ties of the- R.ange in Samples from Tul-.ey's Symmetric Lnaubda Distributions.

Brian L, Joiner and Joan R. Rosenblatt , Submitted to a lochnical journ.al . On the Analysis of Multi-Dimensional Contingency Tables. H. H Ku, R. N. Varner and S. Kullliack (George Washington Univ,). To appear in Proc , 14th Coni, on Design of Experiments in Army

Research Development and Testing.

Stability of Acoustic Waves within a Viscous, Compressible, Heat-Conducting Fluid.

J. E. McKinney and H, J. Oser. To ai^peai’ in the J. of Acoustical Society oX America.

Vol . 47, No. 1, January 1970,

Trace Functions I. R. Merris. Submitted to a fCclinical journal.

Partitioned Hermetian Matrices. R. Merris. To aiqieav in J. of Ueseareh, NBS

,

Elementary Divisors of Higher Degree Associated Transformations. R. Merris and S. PiciTc.

Submitted to a technical journal.

A Class of Representations of ilie Full Linear Grou]). R. Merris and S. Pierce. Submitted to a teclinical journal ,

Isomorphic SynDiiotry Classes of Tensors, R. Morris and W. Watkins. Submitted to a technical

journal

.

A Table ol the First Factor for Prime Cyclotomic Fields. M. Newman , 'To appeal- in Matli.oi Computation

.

An Enumeration Problem for a Congruence Equation. M. Newman and R. Brualdi. To appeal- in J, of Keseai-ch NBS.

Bounded Mati-ix Groups. M. NewTiian and S. Pierce. To aj-ipear in J. oi Linear Algeln-a.

Why Steepest Descents? F. W. J. Olver, To appyar in Proc. of 1969 SIAM National Meeting,

Jime 10-12, 19G9.

Orthogonal Groups of Positive Deiinite Mu 1 t i 1 ,i nea r Fum- 1 j ona Is , . Piei-ce. To appear in Pac.ific J. of Matli.

Multiplicative Maps of Matrix Se'iiigroups ovci- Dedekind Ri.igs. S. Pierce, Submitted to a technical journal.

Ol- tliogonal Decompo.s i 1 ions of Tensors Siinces, S. Pierce. To appear in J. oi Researeli NBS.

Tiie Use of OMNITAB for Statistical •''.nalysis of Tabular Data. Joan R. Uosenlil ;i it , Brian 1,. Joiner,

and David Hogben. To appear in Census Tract Papi^rsr Papers Presented at the ConUri'nce on Small-Area Statistics, American Statistical Assor., Kov- York, August 2J, 19(59.
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An I'.v'al ua I ion oX Li.noar Least Squares '’A)ini>u ter Progi'ams : A suiiimaiy ioi>ort. lioy li. IVaiiiplei-. To apjiear in Pjoc . 14th Conf , on Desit;n of Experiments in Army Researcli Development and Testing..

A Report on the Accuracy of Some Widely Used I<;asl Squares Computer Programs. Roy H. Wampler.

To appear in J. Amer. Statist. Assoc.

2.4 Notes, Reviews

Systems Analysis and Urban Problems (Discussion). A. J. Goldman. To aijpoar in Proc. Symposium

on Systems Analysis lor Social Problems, 5/69.

2 . 5 Books

An Author and Permuted Title Index to Selected Statistical Journais. Brian L. Joiner,

.

N. F. Laubscher (Nat'l. Res. Inst, for Math, Sciences, S. Africa), Eleanor S. Brown, and Bert Levy (llai-ry Diamond Labs., U. S. Army). To appear as NBS Special Pub. 321.

21
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