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The application of linear programming tech- niques to rational approximation problems, ii
Linear programming algorithms for approximation of many variable function over finite point set
The rolling power of two wing-aileron configu- rations as affected by flexibility
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Rational mechanics of deformation and flow
Large deformations and viscous flow in isomorphic and isotropic materials
Scientific rational for Apollo lunar /orbital/ electromagnetic sounder experiment Final technical report
Scientific rationale for Apollo 19 lunar orbital electromagnetic sounder experiment
Measured electron conversion rations for the 1064-keV gamma ray of bismuth-207
Electron conversion ratios for 1064 keV gamma ray of bismuth 207
A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations
Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.
Recursive formulas for the partial fraction expansion of a rational function with multiple poles.
The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.
Partial-fraction expansion and inverse Laplace transform of a rational function with real coefficients
This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.
Results concerning the complete controllability and observability of systems in series using the coprime decomposition of a rational matrix
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An experimental and theoretical study of low-aspect ration swept and oblique wings at Mach numbers between 0.6 and 1.4
Experimental forces and moments for two wing-body combinations having (a) a swept wing and (b) an oblique wing are compared. At all Mach numbers, the oblique wing (at its optimum sweep angle) had higher maximum lift-to-drag ratios than the fixed, swept wing. At high angles of attack, the direction of the pitching or rolling tendencies of the oblique wing was a function of the spanwise distribution of wing bend or washout for the two bends being investigated. At low angles of attack, linear theory gave satisfactory predictions of the subsonic lift-curve slope, the aerodynamic-center travel with Mach number, and the maximum lift-to-drag ratio.
Necessary and sufficient conditions for the complete controllability and observability of systems in series using the coprime factorization of a rational matrix
The series connection of two linear time-invariant systems that have minimal state space system descriptions is considered. From these descriptions, strict-system-equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of the subsystems as a ratio of two right or left coprime polynomial matrices. They give rise to a simple polynomial matrix system description of the tandem connection. Theorem 1 states that for the complete controllability and observability of the state space system description of the series connection, it is necessary and sufficient that certain 'denominator' and 'numerator' groups are coprime. Consequences for feedback systems are drawn in Corollary 1. The role of pole-zero cancellations is explained by Lemma 3 and Corollaires 2 and 3.
Rational approximation to e to the -x power with negative poles
MACSYMA was applied to the generation of an expansion in terms of Laguerre polynomials to obtain approximations to e to the -x power on 0, infinity. These approximations are compared with those developed by Saff, Schonhage, and Varga.
On the rational design of compressible flow ejectors
A fluid mechanics review of chemical laser ejectors is presented. The characteristics of ejectors with single and multiple driver nozzles are discussed. Methods to compute an optimized performance map in which secondary Mach number and performance are computed versus mass ratio, to compute the flow distortion at each optimized condition, and to determine the thrust area for the design point to match diffuser impedence are examined.
An examination of spectral band rationing to reduce the topographic effect on remotely sensed data
There are no author-identified significant results in this report.
Hamiltonian indices and rational spectral densities
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Comparisons of rational engineering correlations of thermophoretically-augmented particle mass transfer with STAN5-predictions for developing boundary layers
Modification of the code STAN5 to properly include thermophoretic mass transport, and examination of selected test cases developing boundary layers which include variable properties, viscous dissipation, transition to turbulence and transpiration cooling. Under conditions representative of current and projected GT operation, local application of St(M)/St(M),o correlations evidently provides accurate and economical engineering design predictions, especially for suspended particles characterized by Schmidt numbers outside of the heavy vapor range.
Performance of a high-work low aspect ration turbine tested with a realistic inlet radial temperature profile
Experimental results are presented for a 0.767 scale model of the first stage of a two-stage turbine designed for a high by-pass ratio engine. The turbine was tested with both uniform inlet conditions and with an inlet radial temperature profile simulating engine conditions. The inlet temperature profile was essentially mixed-out in the rotor. There was also substantial underturning of the exit flow at the mean diameter. Both of these effects were attributed to strong secondary flows in the rotor blading. There were no significant differences in the stage performance with either inlet condition when differences in tip clearance were considered. Performance was very close to design intent in both cases.