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Technique has been developed for determining values of selected subsets of independent variables in mathematical formulations. Required computation time increases with first power of the number of variables. This is in contrast with classical minimization methods for which computational time increases with third power of the number of variables.
A method is presented for computing initial vectors to be used in conjunction with a numerical optimization procedure for minimizing the probability of misclassification. Preliminary numerical results are presented.
Monte Carlo studies using population models intended to represent response surface applications are reported. Simulated experiments were generated by adding pseudo random normally distributed errors to population values to generate observations. Model equations were fitted to the observations and the decision procedure was used to delete terms. Comparison of values predicted by the reduced models with the true population values enabled the identification of deletion strategies that are approximately optimal for minimizing prediction errors.
Matrix effects related to the chemical form of analyzed materials were studied. An arc in argon was used which was buffered with silver chloride. The effect of chemical form was minimal for a variety of metals, oxides, and carbides representing the most refractory compounds and thermally stable metal-containing molecules. Only four of the most refractory materials known showed significant emission depressions due to incomplete volatilization in the arc system. These results are discussed in terms of vapor pressures of the solid materials placed on the anodes and dissociation reactions of the molecules in the gaseous environment.
General classes of nonlinear and linear transformations were investigated for the reduction of the dimensionality of the classification (feature) space so that, for a prescribed dimension m of this space, the increase of the misclassification risk is minimized.
The present article addresses itself to the prime power requirements of a coupling-modulated gas laser transmitter. The latter consists of a gas discharge tube and electrooptic modulator inside a laser resonator. In performing the calculations, the laser discharge length and the modulator voltage are simultaneously varied so that the transmitted power remains constant. In this way, tradeoffs can be made between the prime power supplied individually to the discharge tube and to the modulator driver to obtain a transmitter configuration that minimizes the total prime power consumption. An analytical expression is derived that describes the effects of information bandwidth and transmitter output power on the prime power requirements. Specific numerical results are obtained for a CO2 laser transmitter based on presently available experimental data.
The main interaction of the earth's interior with the lithosphere is as a material source and sink. An absolute reference frame defined by minimizing the translational motion of tectonic plate boundaries differs by 0.6 cm/year from a frame defined by hot spot traces and by 0.4 cm/year from the frame defined by the most plausible model of drag forces on the plates. The rms absolute translational velocities are about 2 cm/year for ocean-ocean plate boundaries and 1.5 cm/year for ocean-continent plate boundaries. The close agreement between the source and sink and the drag-dependent definitions suggests that the lithosphere, as a stress guide, to some extent controls the locations of its sources and sinks.
This paper presents an algorithm for the computation of the minimal indices for linear multivariable systems. The same algorithm can be used to determine the rank of a transfer function. As an application, this algorithm is shown to be useful in the design of non-interacting control systems.
A rigorous optimality criterion is derived and a hybrid weight-reduction algorithm developed for the weight minimization of lifting surfaces with a constraint on flutter speed. The weight-reduction algorithm incorporates a simple recursion formula derived from the optimality criterion. Monotonic weight reduction is accomplished by dynamically adjusting a parameter in the recursion formula so as to achieve a predetermined weight decrease. The algorithm thus combines the simplicity of optimality-criterion methods with the convergence characteristics of mathematical-programming methods. The imposition of the flutter constraint is simplified by forcing to zero the imaginary part of the flutter eigenvalue, with the airspeed fixed. Four examples are discussed. The results suggest that significant improvements in efficiency are possible, in comparison with techniques based purely on mathematical programming.
The paper reviews NASA's efforts on wake vortex turbulence minimization by aerodynamic design or retrofit modifications to large transport aircraft. Theoretical and experimental (ground-based and flight) results are presented which show that the adverse effects of a vortex wake produced by a large aircraft on a small following aircraft can be reduced significantly.
The method of Seebass and George (1972, 1974) for minimizing certain features of the pressure signature and yielding the corresponding F function and equivalent area distribution A in an isothermal atmosphere is modified to provide the same capability for a real atmosphere. The appropriate equations of George and Plotkin (1969) describing horizontal advance, ray tube area, and signature propagation are used.
A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.
The potential flammability hazard when a water/glycol solution contacts defectively insulated silver-clad copper circuitry or electrical components carrying a direct current is described. The chemical reactions and means for detecting them are explained. Methods for detecting and cleaning contaminated areas and the use of inhibitors to arrest chemical reactivity are also explained. Preventive measures to minimize hazards are given. Photomicrographs of the chemical reactions occurring on silver clad wires are also included.
This paper gives a brief review of the currently accepted understanding of sonic boom phenomena and describes the manner in which modified linearized theory and geometric acoustics are used to predict the sonic boom caused by a complex aircraft configuration. Minimization methods that have evolved in recent years are discussed with particular attention given to a method developed by Seebass and George for an isothermal atmosphere which was modified for the real atmosphere by Darden. An additional modification which permits the relaxation of the nose bluntness requirement in the defining aircraft is also discussed. Finally, an overview of current areas of sonic boom research is given.
Learning of discriminant hyperplanes in imperfectly supervised or unsupervised training sample sets with unreliably labeled samples along the fuzzy joint boundaries between sample clusters is discussed, with the discriminant hyperplane designed to be a least-squares fit to the unreliably labeled data points. (Samples along the fuzzy boundary jump back and forth from one cluster to the other in recursive cluster stabilization and are considered unreliably labeled.) Minimization of the distances of these unreliably labeled samples from the hyperplanes does not sacrifice the ability to discriminate between classes represented by reliably labeled subsets of samples. An equivalent unconstrained linear inequality problem is formulated and algorithms for its solution are indicated. Landsat earth sensing data were used in confirming the validity and computational feasibility of the approach, which should be useful in deriving discriminant hyperplanes separating clusters with fuzzy boundaries, given supervised training sample sets with unreliably labeled boundary samples.
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
This paper describes a study of matrix effects related to the chemical form of materials analyzed. The study was made using an arc in argon buffered with silver chloride. The effect of chemical form was minimal for a variety of metals, oxides, and carbides representing the most refractory compounds and thermally stable metal-containing molecules. Among these, only four of the most refractory materials known showed significant emission depressions due to incomplete volatilization in the arc system. These results are discussed in terms of vapor pressure of the solid materials placed on the anodes and dissociation reactions of the molecules in the gaseous environment.
Cases involving antiplane shear deformation, axisymmetric torsion, and plane strain theory, with surfaces of constant stress magnitude optimal in terms of minimizing stress, are investigated. Results for the plane theory refer to exterior doubly connected domains. Stresses generated by torsion of an elastic solid lying within a radially convex region of revolution with plane ends, body force absent, and lateral surface traction-free, are examined. The unknown portion of the boundary of such domains may involve a hole, fillet, or notch.