In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other,...

Topics: NASA Technical Reports Server (NTRS), CATASTROPHE THEORY, DYNAMIC STRUCTURAL ANALYSIS, EIGENVALUES,...

Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. While a reliable technique for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE MATERIALS, THERMOGRAPHY, TEMPERATURE EFFECTS, DATA...

Large composite material structures such as aircraft and Reusable Launch Vehicles (RLVS) operate in severe environments comprised of vehicle dynamic loads, aerodynamic loads, engine vibration, foreign object impact, lightning strikes, corrosion, and moisture absorption. These structures are susceptible to damage such as delamination, fiber breaking/pullout, matrix cracking, and hygrothermal strain. To ensure human safety and load-bearing integrity, these structures must be inspected to detect...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE STRUCTURES, SYSTEMS HEALTH MONITORING, COMPOSITE...

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, ALGORITHMS, PROBLEM SOLVING,...

It is often proposed that the redundancy in choosing a force distribution for multiple arms grasping a single object should be handled by minimizing a quadratic performance index. The performance index may be formulated in terms of joint torques or in terms of the Cartesian space force/torque applied to the body by the grippers. The former seeks to minimize power consumption while the latter minimizes body stresses. Because the cost functions are related to each other by a joint angle dependent...

Topics: NASA Technical Reports Server (NTRS), ENERGY CONSUMPTION, MANIPULATORS, REDUNDANCY, ROBOT ARMS,...

Contents: Some Applications of Transversal Theory to Graph Theory; Upper and Lower Bounds for Unrestricted Binary Error Correcting Codes; and Three-Class Association Schemes on a Small Number of Vertices.

Topics: DTIC Archive, Ray-Chaudhuri,D K, OHIO STATE UNIV COLUMBUS DEPT OF MATHEMATICS, *INFORMATION...

Data association is one of the core problems of simultaneous localization and mapping (SLAM), and it requires knowledge about the uncertainties of the estimation problem in the form of marginal covariances. However, it is often difficult to access these quantities without calculating the full and dense covariance matrix, which is prohibitively expensive. We present a dynamic programming algorithm for efficient recovery of the marginal covariances needed for data association. As input we use a...

Topics: DTIC Archive, MASSACHUSETTS INST OF TECH CAMBRIDGE COMPUTER SCIENCE AND ARTIFICIAL INTELLIGENCE...

Computer program was devised to compute free-fall trajectories of satellites, allowing for injection errors and midcourse velocity perturbations. Program consists of trajectory perturbing program and N-body integrating conic program which can also be used as 2-body patch conic program.

Topics: NASA Technical Reports Server (NTRS), CDC 6400 COMPUTER, COMPUTER PROGRAMS, FORTRAN, MANY BODY...

A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER EQUATIONS, DIFFERENTIAL EQUATIONS, FINITE...

An algorithm for describing optimal linear combinations in the feature selection process is considered. Various proofs are presented.

Topics: NASA Technical Reports Server (NTRS), COMBINATIONS (MATHEMATICS), CONVERGENCE, MATRICES...

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow...

Topics: NASA Technical Reports Server (NTRS), ANGLE OF ATTACK, CIRCULAR CONES, FINITE DIFFERENCE THEORY,...

The analysis and use of the Equation Modifying Program (EQMOD) L219, digital computer program which modifies matrices according to specific instructions was described. The program modifies the theoretical equation of motion and load equations generated by the DYLOFLEX programs Equation of Motion L217 (EOM), and Load Equations, L218 (LOADS), respectively.

Topics: NASA Technical Reports Server (NTRS), COMPUTER SYSTEMS PROGRAMS, EQUATIONS OF MOTION, MATRICES...

A new approach to the eigensystem assignment problem is presented. The approach utilizes a null-space formulation of the eigenvalue/eigenvector assignment problem to simultaneously realize arbitrary eigenvalue specifications, approximate desired modal behavior, and achieve low eigensystem sensitivity with respect to plant parameter variations. The methods are applied to the design of regulator and integral plus proportional servo control systems.

Topics: NASA Technical Reports Server (NTRS), ADAPTIVE CONTROL, CONTROL THEORY, EIGENVALUES, EIGENVECTORS,...

Queuing network models of a computer system operating with a single workload type are presented. Program algorithms are adapted for use on the Texas Instruments SR-52 programmable calculator. By slightly altering the algorithm to process the G and H matrices row by row instead of column by column, six devices and an unlimited job/terminal population could be handled on the SR-52. Techniques are also introduced for handling a simple load dependent server and for studying interactive systems with...

Topics: NASA Technical Reports Server (NTRS), CALCULATORS, COMPUTER SYSTEMS PROGRAMS, QUEUEING THEORY,...

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Topics: NASA Technical Reports Server (NTRS), CONJUGATION, MATRICES (MATHEMATICS), ORTHOGONAL FUNCTIONS,...

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact...

Topics: NASA Technical Reports Server (NTRS), DYNAMIC STRUCTURAL ANALYSIS, RANDOM LOADS, STRESS...

The parallel and pipeline organization of fast unitary transform algorithms such as the Fast Fourier Transform are discussed. The efficiency is pointed out of a combined parallel-pipeline processor of a transform such as the Haar transform in which 2 to the n minus 1 power hardware butterflies generate a transform of order 2 to the n power every computation cycle.

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, FAST FOURIER TRANSFORMATIONS, COMPUTER...

A proportion estimation procedure is presented which requires only on set of ground truth data for determining the error matrix. The error matrix is then used to determine an unbiased estimate. The error matrix is shown to be directly related to the probability of misclassifications, and is more diagonally dominant with the increase in the number of passes used.

Topics: NASA Technical Reports Server (NTRS), ESTIMATING, GROUND TRUTH, PROPORTION, ALGORITHMS, ERROR...

An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile....

Topics: NASA Technical Reports Server (NTRS), COMPUTER GRAPHICS, FINITE ELEMENT METHOD, MATRICES...

An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and...

Topics: NASA Technical Reports Server (NTRS), ORBIT PERTURBATION, ORBITAL MECHANICS, ORBITAL POSITION...

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques...

Topics: NASA Technical Reports Server (NTRS), CHARACTER RECOGNITION, CLASSIFICATIONS, MAXIMUM LIKELIHOOD...

Several approaches for the design of reduced-order linear-quadratic-Gaussian type controllers for large space structures were proposed and evaluated using a continuous model of a long free-free beam. Sufficient conditions were derived for the asymptotic stability with this type of controller. A finite-element model of a free-free-free-free square plate was obtained for use in control systems studies. A method was developed for optimal damping enhancement in large space structures.

Topics: NASA Technical Reports Server (NTRS), CONTROLLERS, FEEDBACK CONTROL, FLEXIBLE BODIES, LARGE SPACE...

The Star Tracker, Crew Optical Alignment Sight (COAS), and Inertial Measurement Unit (IMU) from a complex navigation system with a multitude of error sources were combined. A complete list of the system errors is presented. The errors were combined in a rational way to yield an estimate of the IMU alignment accuracy for STS-1. The expected standard deviation in the IMU alignment error for STS-1 type alignments was determined to be 72 arc seconds per axis for star tracker alignments and 188 arc...

Topics: NASA Technical Reports Server (NTRS), ERROR ANALYSIS, INERTIAL PLATFORMS, ORBITAL MECHANICS, SPACE...

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent...

Topics: NASA Technical Reports Server (NTRS), DIFFERENTIAL EQUATIONS, MATRICES (MATHEMATICS), MATRIX...

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A laboratory experiment was conducted to determine the effects of variations in the rate and magnitude of sound level fluctuations on the annoyance caused by aircraft-flyover noise. The effects of tonal content, noise duration, and sound pressure level on annoyance were also studied. An aircraft-noise synthesis system was used to synthesize 32 aircraft-flyover noise stimuli representing the factorial combinations of 2 tone conditions, 2 noise durations, 2 sound pressure levels, 2 level...

Topics: NASTRAN, STRUCTURAL ANALYSIS, SYSTEMS ANALYSIS, UNIVAC 1110 COMPUTER, COST ANALYSIS, DATA...

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Chemical composition of lunar samples from Apollo 11 and 12 flights

Topics: HERMITIAN POLYNOMIAL, ILLUMINATING, IMAGING TECHNIQUES, LUMINOUS INTENSITY, MATRICES (MATHEMATICS),...

A robust version of Principal Component Analysis (PCA) can be constructed via a decomposition of a data matrix into low-rank and sparse components, the former representing a low-dimensional linear model of the data, and the latter representing sparse deviations from the low-dimensional subspace. This decomposition has been shown to be highly effective, but the underlying model is not appropriate when the data are not modeled well by a single low-dimensional subspace. We construct a new...

Topics: DTIC Archive, LOS ALAMOS NATIONAL LAB NM, *BACKGROUND, *DECOMPOSITION, *IMAGE PROCESSING, *REMOVAL,...

A condition for the Gateaux differentiability of the probability of misclassification as a function of a feature selection matrix B, assuming a maximum likelihood classifier and normally distributed populations, is given. It is also shown that if the probability of error has a local minimum at B then it is differentiable at B.

Topics: NASA Technical Reports Server (NTRS), ERROR ANALYSIS, PROBABILITY DISTRIBUTION FUNCTIONS,...

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized...

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, ANISOTROPY, BOUNDARY VALUE PROBLEMS, DYNAMIC...

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, COMPUTATIONAL FLUID DYNAMICS, FACTORIZATION,...

Further improvements made to advance the current Boundary Layer Integral Matrix Procedure - Version J (BLIMPJ) containing previously modeled simplified calculation methods by accounting for condensed phase, thick boundary layer and free stream turbulence effects are discussed. The condensed phase effects were included through species composition effect considered via input to the code and through particle damping effect considered via a turbulence model. The thrust loss calculation procedure...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYERS, COMPUTER PROGRAMS, ENGINE DESIGN, TURBULENCE...

Development of a new composite beam modeling technique to represent the principal load-carrying member in the wing is reported along with the development of a formal design optimization procedure to investigate the effect of composite tailoring on aeroelastic stability and structural characteristics of airplane wings. The developed procedure is used to perform design optimization studies on realistic airplane configurations to investigate the various aeroelastic/structural/dynamic design issues.

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, COMPOSITE STRUCTURES, WINGS, AIRCRAFT...

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via...

Topics: NASA Technical Reports Server (NTRS), DIFFERENTIAL EQUATIONS, LINEAR EQUATIONS, EIGENVECTORS,...

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X...

Topics: NASA Technical Reports Server (NTRS), CONJUGATE GRADIENT METHOD, CURRENT DISTRIBUTION, IMAGE...

Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The mathematics of the technique is...

Topics: NASA Technical Reports Server (NTRS), DYNAMIC STRUCTURAL ANALYSIS, HARMONIC EXCITATION, LEAST...

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An...

Topics: NASA Technical Reports Server (NTRS), ARCHITECTURE (COMPUTERS), FOURIER TRANSFORMATION, PIPELINING...

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic...

Topics: NASA Technical Reports Server (NTRS), FINITE ELEMENT METHOD, MEASURE AND INTEGRATION, SHELLS...

The Mueller matrix and polarization covariance matrix for polarimetric radar systems were studied. The clutter is modelled by a layer of random permittivity, described by a three dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller...

Topics: NASA Technical Reports Server (NTRS), OPTICAL RADAR, POLARIMETRY, REMOTE SENSING, TERRAIN, BORN...

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on...

Topics: NASA Technical Reports Server (NTRS), MOLECULAR SPECTROSCOPY, LINE SPECTRA, RAMAN SPECTRA, REMOTE...

Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbor interaction and two kinds of atoms (mass-ratio r) arranged according to the self-similar binary Fibonacci sequence ABAABABA..., which is obtained by repeated substitution of A yields AB and B yields A. The implications of the self-similarity of this sequence for the associated orthogonal polynomial systems which govern these Fibonacci chains with fixed mass-ratio r are studied.

Topics: NASA Technical Reports Server (NTRS), DIATOMIC MOLECULES, FIBONACCI NUMBERS, IDENTITIES,...

In sparse approximation problems, the goal is to find an approximate representation of a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major algorithms that are used for solving sparse approximation problems in practice. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in...

Topics: DTIC Archive, CALIFORNIA INST OF TECH PASADENA, *APPROXIMATION(MATHEMATICS), *INVERSE PROBLEMS,...

Uncertainty is an unavoidable aspect of engineering systems and will often degrade system performance or perhaps even lead to system failure. As a result, uncertainty must be considered as a part of the design process for all real-world engineering systems. The presence of reducible uncertainty further complicates matters as designers must not only account for the degrading effects of uncertainty but must also determine what levels of uncertainty can be considered as acceptable. For these...

Topics: DTIC Archive, MARYLAND UNIV COLLEGE PARK, *MATHEMATICAL MODELS, *UNCERTAINTY, COEFFICIENTS,...

Efficient reanalysis models, which provide high quality explicit approximations for the structural behavior, are introduced. The presented algorithms are based on a series expansion which is shown to be equivalent to a simple iteration procedure. Only the decomposed stiffness matrix, known from exact analysis of the initial design, is required to obtain the approximate expressions. Two approaches of accelerated convergence are proposed to improve the quality of the approximations: (a) An...

Topics: DTIC Archive, Kirsch, U., Hofman, B., TECHNION - ISRAEL INST OF TECH HAIFA DEPT OF CIVIL...

This paper presents a proof of correctness of an iterative approximate Byzantine consensus (IABC) algorithm for directed graphs. The iterative algorithm allows fault- free nodes to reach approximate consensus despite the presence of up to f Byzantine faults. Necessary conditions on the underlying network graph for the existence of a correct IABC algorithm were shown in our recent work [15, 16]. [15] also analyzed a specific IABC algorithm and showed that it performs correctly in any network...

Topics: DTIC Archive, ILLINOIS UNIV AT URBANA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING, *CONVERGENCE,...

The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final...

Topics: DTIC Archive, MARYLAND UNIV COLLEGE PARK DEPT OF COMPUTER SCIENCE, *LEAST SQUARES METHOD, *LINEAR...

In this paper we introduce CARRQR, a communication avoiding rank revealing QR factorization with tournament pivoting. We show that CARRQR reveals the numerical rank of a matrix in an analogous way to QR factorization with column pivoting (QRCP). Although the upper bound of a quantity involved in the characterization of a rank revealing factorization is worse for CARRQR than for QRCP, our numerical experiments on a set of challenging matrices show that this upper bound is very pessimistic, and...

Topics: DTIC Archive, CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE,...

This paper provides a methodology for the systematic derivation of subdivision schemes that model solutions to inhomogeneous order linear differential equations. In previous work, we showed that subdivision can be used to capture very efficiently the solutions of homogeneous order, linear differential equations. The resulting subdivision masks are stationary and can be precomputed, allowing for very simple and fast application of these schemes. In this paper, we show that this method can be...

Topics: DTIC Archive, Warren, Joe, Weimer, Henrik, RICE UNIV HOUSTON TX DEPT OF COMPUTER SCIENCE, *LINEAR...

This thesis considers the use of acoustic communications in reducing position uncertainty for collaborating autonomous underwater vehicles. The foundation of the work relies on statistical techniques for accurate navigation without access to GPS, known as Simultaneous Localization and Mapping (SLAM). Multiple AUVs permit increased coverage, system redundancy and reduced mission times. Collaboration through acoustic communications can minimize navigational uncertainty by permitting the group to...

Topics: DTIC Archive, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *ACOUSTIC COMMUNICATIONS, *SELF OPERATION,...

Sequential, adaptive, and gradient diffusion filters are implemented into spatial multiscale three-dimensional variational data assimilation (3DVAR) as alternative schemes to model background error covariance matrix for the commonly used correction scale method, recursive filter method, and sequential 3DVAR. The gradient diffusion filter (GDF) is verified by a two-dimensional sea surface temperature (SST) assimilation experiment. Compared to the existing DF, the new GDF scheme shows a superior...

Topics: DTIC Archive, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OCEANOGRAPHY, *CLIMATE, *OCEAN SURFACE,...

In this thesis we focus on the problem of entanglement in an important class of states, called X-states, that we will introduce. Our study led us to an algebraic formula for the value of multipartite entanglement for X-states. We will take advantage of this formula to further explore the connection of entanglement and mixedness in multipartite systems and study the dynamics of entanglement in open systems. We introduce the entanglement, its definition, and the properties of good measures of...

Topics: DTIC Archive, ROCHESTER UNIV NY, *MATRICES(MATHEMATICS), ALGEBRA, DYNAMICS, FORMULATIONS, FOULING,...