Robert Hermann introduced the concept of tangent vector fields on the space of functions from one manifold to another. He applied these to give a new proof of the Cartan-Kahler theorem. An example of such vector fields are maps from the jet space to the tangent bundle of the target space which commute with projections. It is this class of vector fields which we study here. Using prolongations a Lie bracket operation is defined and justified on the grounds that it agrees with the primitive...

Topics: DTIC Archive, Johnson, Harold H, WASHINGTON UNIV SEATTLE, *GROUP DYNAMICS, TAYLORS SERIES, VECTOR...

A procedure for estimating the parameters of a time series is proposed. The estimate minimizes a criterion function which is the weighted sum of squares of the distances between the periodograms and the spectrum of the series. Under mild conditions, the estimate is shown to be strongly consistent. The asymptotic distribution of the estimate is also obtained. With a proper choice of weighting function, the estimate has the same asymptotic distribution as the one for the maximum likelihood...

Topics: DTIC Archive, Chiu, Shean-Tsong, *TIME SERIES ANALYSIS, *WEIGHTING FUNCTIONS, *LEAST SQUARES...

In the present report, a method is illustrated of obtaining more precise values of shock wave angle, pressure, Mach number, and drag coefficient from a given cone angle and velocity past the cone. From the Rankine-Hugoniot shock wave equations a single equation is obtained which fixes the position of the shock wave. Another term is obtained in Maccoll's Taylor expansion about the surface of the cone which permits the use of a larger integral of integration with the same degree of smoothness and...

Topics: DTIC Archive, Turetsky, Raymond A, ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD, *CONICAL...

While it is well-known that every purely nondeterministic full rank q- variate weakly stationary stochastic process (X sub n) with the spectral density W has an (infinite order) one-sided moving average representation, not every such process can have a mean convergent (infinite order) autoregressive representation (ARR) and the problem of ARR of such processes has not received the attention which it deserves. Due to the importance of ARR in prediction theory, and particularly in the statistical...

Topics: DTIC Archive, Pourahmadi,M, NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES,...

Procedures are presented for estimating desired and undesired receiver mixer responses. Computer models, developed using the Taylor-Fourier series method to analyze double-balanced-diode and single-diode mixers, are described. (Author)

Topics: DTIC Archive, Maiuzzo,Michael A, IIT RESEARCH INST ANNAPOLIS MD, *COMPUTERIZED SIMULATION,...

The usual method of testing the response of an accelerometer is to orient the instrument so as to pick up varying components of the earth's gravitational field along the instrument's sensitive axis. This method is limited because a maximum of only one gravity unit of acceleration is available and also because the component of acceleration normal to the sensitive axis cannot be varied independently. However, with present techniques the precision obtainable far surpasses other methods such as the...

Topics: DTIC Archive, TRW SPACE TECHNOLOGY LABS LOS ANGELES CA, *ACCELEROMETERS, TEST METHODS, SENSITIVITY,...

Statistical variance has been widely used in propagation studies associated with radio direction finding for many years. With the advent at this laboratory of high speed digital computing machinery, it is advisable to explore methods of on and off line calculation of variance, with particular emphasis placed on on-line computations. It is not the purpose of this note to judge whether or not variance is the correct parameter to use, but to find ways for calcu lating it.

Topics: DTIC Archive, Smith, Robert S, ILLINOIS UNIV AT URBANA-CHAMAPIGN, *RADIO DIRECTION FINDERS, DIGITAL...

The nearly nonstationary first order autoregression is a sequence of processes where the autoregressive coefficient tends to 1 as n approaches infinity. M-estimates of the autoregressive coefficient are considered. The process is allowed to be nongaussian, but a 2 + delta moment condition is assumed. The limiting distribution is not the usual normal limit but is characterized as a ratio of two stochastic integrals. The asymptotically most efficient M-estimate is not given by maximum likelihood....

Topics: DTIC Archive, Cox,Dennis D, WASHINGTON UNIV SEATTLE DEPT OF STATISTICS, *TIME SERIES ANALYSIS,...

The asymptotic distribution of a finite set of autocorrelations is obtained for a time series from a linear stochastic process. The disturbances (or innovations) are martingale differences with bounded variances and bounded mixed fourth-order moments satisfying a uniform conditional square integrability condition. The conditions are weaker than those used previously for such asymptotic distributions. Specific topics include: autocorrelations, asymptotic distributions, martingale differences,...

Topics: DTIC Archive, Anderson, T W, STANFORD UNIV CA DEPT OF STATISTICS, *LINEAR SYSTEMS, TIME SERIES...

It is shown that Percus' method can be used to write down explicitly integral equations for the two-body correlation function which generalizes the PY and HNC equation. A first test of the fitness of such equations was given in the case of the hard cube gas. Further information will be provided in a future paper where the equations given in the present paper will be applied to the case of the lattice gas.

Topics: DTIC Archive, Verlet, Loup, ECOLE NORMALE SUPERIEURE PARIS (FRANCE), *INTEGRAL EQUATIONS,...

This document proposes a test for detecting serial dependence among multivariate observations. The test statistic is the maximum absolute value of the lag 1 correlation obtainable from a linear combination of the observations. The authors express the statistic in terms of two eigenvalues and then obtain the asymptotic null distribution. Asymptotic power is examined for sequences of local alternatives in a multivariate normal autoregressive process. An explicit expression is obtained for the...

Topics: DTIC Archive, Johnson, Richard A., WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...

Topics: DTIC Archive, Lewis, S H, AEROSPACE CORP EL SEGUNDO CA, *GUIDED MISSILES, *SIMULATION, *COMPUTERS,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Asymptotic distributions of EDF statistics - goodness-of-fit statistics based on the empirical distribution function - can be obtained by expanding a related function in a series of orthogonal functions. This method was given by Watson and developed especially in this connection by Durbin and Knott and by the author. an earlier approach by Anderson and Darling is different and the newer methods provide a sharper view of the approach to infinity. Similar approaches were employed by Durbin, Knott...

Topics: DTIC Archive, Stephens,Michael A, STANFORD UNIV CA DEPT OF STATISTICS, *WEIBULL DENSITY FUNCTIONS,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Three different algorithms--the power series, the asymptotic series, and the recurrence relation method--are investigated with special attention to the single (10 to the -14th power) and double precision (10 to the -29th power) of CDC 6000 Series computers. The final accuracy of each method depends partly on the magnitudes of the largest and smallest terms when floating point additions are involved. Another consideration is the number of terms required for each algorithm. Combination of all...

Topics: DTIC Archive, Kooij, T, DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD SHIP...

This report presents two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of a theorem of V. M. Olovyanisnikov on multiply monotone functions. The second applications gives sufficient conditions for the differentiability of asymptotic expansions.

Topics: DTIC Archive, Schoenberg,I J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *ASYMPTOTIC...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Properties of a probability density estimator having the rational form of a ARMA spectrum are investigated. Under various conditions on the underlying density's Fourier coefficients, the ARMA estimator is shown to have asymptotically smaller mean integrated squared error (MISE) than the best window-type Fourier series estimator. The most interesting cases are those in which the Fourier coefficients are regularly varying with index-p,p 1/2. For example, when p=2 the asymptotic MISE of a certain...

Topics: DTIC Archive, Hart,Jeffrey D, TEXAS A AND M UNIV COLLEGE STATION DEPT OF STATISTICS, *ESTIMATES,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

It is very well known Newton's interpolation series with divided differences simplifies considerably in the case that we interpolate in the points of an arithmetic progression. It seems much less known that a similar simplification occurs in the case when the points of interpolation form a geometric progression. We describe here the practically forgotten work of Stirling (1730), Schellbach) (1864), and Runge (1981), and its connection with the elegant and more recent algorithm of Romberg...

Topics: DTIC Archive, Schoenberg,I J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *POLYNOMIALS,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

The usual power series representations for hypergeometric functions in two variables have a limited range of validity. In particular, they are of little use when the magnitude of one of the variables becomes very large. Using a Barnes-type integral representation and the concept of analytic continuation, the region of utility is extended to the desired domain. The poles that occur in the Barnes-type integral are assumed to be simple. Thus, explicit asymptotic expansions are obtained for each of...

Topics: DTIC Archive, Mudaliar, Saba, ROME LAB HANSCOM AFB MA, *ASYMPTOTIC SERIES, *HYPERGEOMETRIC...

see report

Topics: DTIC Archive, Banks, H T, NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC...

The following topics are the principal ones investigated under this grant: (1) Hypothesis testing for Poisson-like processes. (2) Hilbert space methods in time series analysis. (3) Limit distributions of branching processes. (4) Hausdorff dimension in stochastic processes. (5) Sufficient statistics for stochastic processes. (6) Absolute continuity and orthogonality of stochastic processes. (7) Subordination of stochastic processes. (8) Slowly varying functions in probability. (9) Mixture...

Topics: DTIC Archive, Tucker, Howard G, CALIFORNIA UNIV RIVERSIDE, *TIME SERIES ANALYSIS, *PROBABILITY,...

The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix...

Topics: DTIC Archive, Mentz, Raul P, STANFORD UNIV CA DEPT OF STATISTICS, *TIME SERIES ANALYSIS, ASYMPTOTIC...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Tests of the existence of correlation between the movements in two time series, which eliminate at least the primary effects of trends in the series, are presented in this article. A test of the existence of trend in a time series will also be presented here.

Topics: DTIC Archive, Goodman, Leo A, COLUMBIA UNIV NEW YORK, *STATISTICAL TESTS, *TIME SERIES ANALYSIS,...

The function of factor analysis in time series analysis is discussed. The relationships between the models in the two approaches are observed, with distinction being drawn between exogenous and endogenous variables. Various approaches are suggested for analyzing multiple time series by factor analysis.

Topics: DTIC Archive, Aanderson, T W, COLUMBIA UNIV NEW YORK, *SERIES(MATHEMATICS), *FACTOR ANALYSIS,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

Analysis and methods of computation of the function y(x, rho) = (2/pi) integral from 0 to infinity of (exp-2x/(1+rho - squarez - square)) dz/(1+z - squared) are presented. Power series, asymptotic series, and other expansions are developed for six regions of the positive quadrant of the x rho plane. These expansions allow efficient calculation of y(x, rho) to a relative accuracy of 0.01% or better. (Author)

Topics: DTIC Archive, Young,Stephen J, AEROSPACE CORP EL SEGUNDO CALIF CHEMISTRY AND PHYSICS LAB,...

Andrews (1972) introduced a method of plotting high-dimensional data in two dimensions. In his method, Andrews represents each multidimensional point by a Fourier function. The clustering of plots of these functions is equivalaent to the clustering of the multidimensional points. Andrews method is exploited as a graphical tool for exploratory data analysis for the examination of changes over time in the parameters of a time series model. An example using the total Canadian unemployment figures...

Topics: DTIC Archive, Herzberg,Agnes M, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DATA...

One of the basic problems of mathematical physics is that of replacing a nonlinear functional equation by a more tractable (analytically and computationally) linear equation. More generally, one wants to replace a system of nonlinear equations, often derived from a single equation by means of an expansion in a parameter, an ortho gonal expansion with a system of linear functional equations. To treat this closure problem, the authors presented a method based upon the concept of relative...

Topics: DTIC Archive, RAND CORP SANTA MONICA CA, *INVARIANCE, BOUNDARY VALUE PROBLEMS, DIFFERENTIAL...

Social media data tends to cluster in time and space around events, such as sports competitions and local news-worthy phenomena. However, transforming raw, free-form, real time text into meaningful information remains a challenging task. Confounding factors include the massive volume of posted data lack of reliable event information, hidden temporal trends, and the vastly diverse nature of content. In the present work, we examine spatio-temporal topic distributions and self-exciting time series...

Topics: DTIC Archive, CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS, *TIME SERIES ANALYSIS, CLUSTERING,...

Topics: DTIC Archive, Korevaar, J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *TAYLORS SERIES,...

Topics: DTIC Archive, Bellman, Richard, RAND CORP SANTA MONICA CA, *NONLINEAR DIFFERENTIAL EQUATIONS,...

Topics: DTIC Archive, FRIEDMAN, BERNARD, CALIFORNIA UNIV BERKELEY, *GASES, *ALGEBRA, MISCH METAL,...

We are interested in capturing time series generated by small wireless electronic sensors. Battery-operated sensors must avoid heavy use of their wireless radio which is a key cause of energy dissipation. When many sensors transmit, the resources of the recipient of the data are taxed; hence, limiting communication will benefit the recipient as well. In our paper we show how time series generated by sensors can be captured and stored in a database system (archive). Sensors compress time series...

Topics: DTIC Archive, Lazaridis, Iosif, CALIFORNIA UNIV IRVINE, *DETECTORS, *TIME SERIES ANALYSIS,...

In this note we discuss Newton's method in a setting somewhat more restrictive than customary. In this setting, however, we claim to have proved superlinear convergence of the Newton process without assuming twice differentiability or Lipschitz continuity of the first derivative of the operator. A further feature is that the iteration to be discussed is not initially but is eventually the Newton process. With this feature global rather than local convergence is achieved.

Topics: DTIC Archive, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA, *FUNCTIONAL ANALYSIS, *ITERATIONS,...

Climate change is now a global phenomenon with growth, poverty, food security, and stability implications. Because of significant dependence on the agricultural sector for production, employment, and export revenues, Ethiopia is seriously threatened by climate change, which contributes to frequent drought, flooding, and rising average temperatures. To examine the impact of climate change on agricultural production and to quantify the resulting lost output, this study conducts a time series...

Topics: DTIC Archive, TEXAS UNIV AT AUSTIN, *ETHIOPIA, AGRICULTURE, CLIMATE CHANGE, FOOD, RAINFALL,...

The theory of series cyclic queues is generalized to other configurations such as branching series queueing models. An equivalence relation is developed between time average steady state probabilities and the stationary probabilities of the imbedded Markov Chain of a series cyclic queue. A statistical inference model is developed to estimate the mean exponential service rate for a series cyclic queue model.

Topics: DTIC Archive, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *QUEUEING THEORY, PERMUTATIONS,...

A simple technique is shown to evaluate dx over x to the m power (1 + x to the nth power).

Topics: DTIC Archive, Walters, William, ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD, *INTEGRALS,...

Topics: DTIC Archive, MOSER, JURGEN, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *DIFFERENTIAL...

An annotated bibliography is presented which covers 42 papers dealing mostly with second-order differential equations. Investigations of the behavior of special functions in the neighborhood of a transition point are not included.

Topics: DTIC Archive, CALIFORNIA INST OF TECH PASADENA, *SPECIAL FUNCTIONS(MATHEMATICS), ASYMPTOTIC SERIES,...

The long-range goal of this research is to extend the scientific basis for extracting environmental information regarding the nearshore ocean from remote sensing data. In particular, we seek to quantify how both optical and remote sensors image the breaking of waves in shallow water. The objectives of this project are as follows: (1) Assemble a marine radar wave observation system suitable for the nearshore ocean. Deploy assembled system at Duck, NC; 2. Collect a long time series (weeks to...

Topics: DTIC Archive, OREGON STATE UNIV CORVALLIS, *RADAR, INSHORE AREAS, SHALLOW WATER, MATHEMATICAL...

The angular scattering and polarization properties of polydispersed suspensions of nonabsorbing and partially absorbing spheres have been computed using the complete Mie series. The results with three types of size distributions are presented and compared with observations. These show a strong dependence of angular intensity and polarization patterns on the size distribution, the size range, and the dielectric and absorbing properties of the individual particles. A peculiarity of scattering at...

Topics: DTIC Archive, DEIRMENDJIAN, D, RAND CORP SANTA MONICA CA, *AEROSOLS, NUMERICAL INTEGRATION, OPTICS,...

Two areas of matrix theory are discussed: the theory of permanents, and the theory of nonnegative matrices. Paper (1) deals with permanental compounds and their use in recurrence formulas for permanents of (0,1)-circulants and in related asymptotic formulas. Paper (2) is a extensive survey of the progress in the theory of permanents achieved during the quadrennium 1982-1985. Paper (3) deals with the problem of determining the minimum permanent in the set of n x n doubly stochastic matrices...

Topics: DTIC Archive, Minc, Henryk, CALIFORNIA UNIV SANTA BARBARA DEPT OF MATHEMATICS, *MATRIX THEORY,...