On the determination of the view function to the images of a surface in a nonplanar specular reflector.
View function to images of surface in nonplanar specular reflector determined by general mathematical expressions
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Results for “generalized functions”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Theory of a general class of dissipative processes
General theory of dissipative periodic processes for systems defined by partial, functional, or neutral differential equations
Hale, J. K.↗
On the minimax feedback control of uncertain dynamic systems.
In this paper the problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
Bertsekas, D. P.↗
Effects of voluntary eye movement and convergence on the binocular appreciation of depth.
Scaling techniques were employed to establish the relation between perceived distance ratio and physical distance ratio. Measurements were made both with and without free eye movement and under two states of convergence. The results were confirmed using a matching technique. With free eye movement, the perceived ratio is a monotonic increasing function of the physical ratio. Without eye movement, the perceived ratio generally increases, then decreases, as the physical ratio increases. For a given physical ratio, perceived distance ratio is less in the absence of voluntary eye movements. Convergence produces depth micropsia when eye movements are permitted, but not in their absence.
Foley, J. M.↗
A class of all digital phase locked loops - Modelling and analysis.
An all digital phase locked loop which tracks the phase of the incoming signal once per carrier cycle is proposed. The different elements and their functions, and the phase lock operation are explained in detail. The general digital loop operation is governed by a non-linear difference equation from which a suitable model is developed. The lock range for the general model is derived. The performance of the digital loop for phase step, and frequency step inputs for different levels of quantization without loop filter, are studied. The analytical results are checked by simulating the actual system on the digital computer.
Reddy, C. P.↗
Momentum constraints as integrability conditions for the Hamiltonian constraint in general relativity.
It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.
Moncrief, V.↗
A class of all digital phase locked loops - Modeling and analysis
An all digital phase locked loop which tracks the phase of the incoming signal once per carrier cycle is proposed. The different elements and their functions, and the phase lock operation are explained in detail. The general digital loop operation is governed by a nonlinear difference equation from which a suitable model is developed. The lock range for the general model is derived. The performance of the digital loop for phase step and frequency step inputs for different levels of quantization without loop filter are studied. The analytical results are checked by simulating the actual system on the digital computer.
Reddy, C. P.↗
The viscous lubrication of rolling and sliding rigid cylinders
The viscous lubrication of rolling and sliding cylinders is studied both independently and with the aid of much of the previous work done by other investigators. Building upon the specialized results of others, a problem formulation is obtained which encompasses the general viscous fluid as well as the linear viscous fluid. A uniform solution technique is derived which is adequate for the general problem formulation. Results obtained for three special classes of viscosity functions are presented.
Carlson, S. F.↗
Random coding strategies for minimum entropy
This paper proves that there exists a fixed random coding strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the 'zero-infinity' case.
Posner, E. C.↗
Nutritional studies
Detailed metabolic studies were conducted of the Apollo 16 and Apollo 17 flight crews, and the results are presented in tabular form. Intake and absorption data are also included. Apollo nutrient intakes were found to be characteristically hypocaloric. Estimates of body composition changes from metabolic balance data, from preflight and postflight weights and volumes, and from total body water and potassium provide no evidence for diminished caloric requirements during a flight. As observed during the Gemini Program and during periods of bed rest, measurements of bone density and metabolic balance confirm a tendency toward loss of skeletal tissue in weightlessness. No evidence exists that any inflight metabolic anomaly, including hypokalemia, was induced by marginal or deficient nutrient intakes. In general, the Apollo crewmen were well nourished and exhibited normal gastroenterological functions, although appetite was somewhat diminished and the organoleptic response to food was somewhat modified during flight.
Paul C. Rambaut↗
Optimization of multi-constrained structures based on optimality criteria
A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.
Rizzi, P.↗
Diamagnetic studies on as-processed carbon fibers
The Faraday method has been used to measure the diamagnetic susceptibilities of small bundles of aligned carbon fibers of different types at room temperature. It was found that the tensor trace susceptibility of the fibers varies systematically over the range 0.8-20 (in units of -10 to the -6th emu/g) as a function of precursor type and processing history. The susceptibility increases, in general, with increasing nominal treatment temperature and hot stretching, and with increasing tensile elastic modulus. The anisotropy ratio of fibers increases approximately linearly with tensile elastic modulus for all fibers from about 1 for a modulus of about 70 GN/sq m to about 22 for a modulus of 700 GN/sq m in air, and is quantitatively consistent with the layer-plane orientation textures determined by X-ray diffraction when appropriate values of the crystallite principal susceptibilities are used.
Scott, C. B.↗
MINIS: Multipurpose Interactive NASA Information System
The Multipurpose Interactive NASA Information Systems (MINIS) was developed in response to the need for a data management system capable of operation on several different minicomputer systems. The desired system had to be capable of performing the functions of a LANDSAT photo descriptive data retrieval system while remaining general in terms of other acceptable user definable data bases. The system also had to be capable of performing data base updates and providing user-formatted output reports. The resultant MINI System provides all of these capabilities and several other features to complement the data management system. The MINI System is currently implemented on two minicomputer systems and is in the process of being installed on another minicomputer system. The MINIS is operational on four different data bases.
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C-MOS bulk metal design handbook
The LSI standard cell array technique was used in the fabrication of more than 20 CMOS custom arrays. This technique consists of a series of computer programs and design automation techniques referred to as the Computer Aided Design And Test (CADAT) system that automatically translate a partitioned logic diagram into a set of instructions for driving an automatic plotter which generates precision mask artwork for complex LSI arrays of CMOS standard cells. The standard cell concept for producing LSI arrays begins with the design, layout, and validation of a group of custom circuits called standard cells. Once validated, these cells are given identification or pattern numbers and are permanently stored. To use one of these cells in a logic design, the user calls for the desired cell by pattern number. The Place, Route in Two Dimension (PR2D) computer program is then used to automatically generate the metalization and/or tunnels to interconnect the standard cells into the required function. Data sheets that describe the function, artwork, and performance of each of the standard cells, the general procedure for implementation of logic in CMOS standard cells, and additional detailed design information are presented.
Edge, T. M.↗
Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium
In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.
Wu, S. T.↗
Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity
The Fymat analytic inversion method for retrieving a particle-area distribution function from anomalous diffraction multispectral extinction data and total area is generalized to the case of a variable complex refractive index m(lambda) near unity depending on spectral wavelength lambda. Inversion tests are presented for a water-haze aerosol model. An upper-phase shift limit of 5 pi/2 retrieved an accurate peak area distribution profile. Analytical corrections using both the total number and area improved the inversion.
Smith, C. B.↗
AK-cut crystal resonators
Calculations have predicted the existence of crystallographically doubly rotated quartz orientations with turnover temperatures which are considerably less sensitive to angular misorientation then comparable AT- or BT-cuts. These crystals are arbitrarily designated as the AK-cut. Experimental data is given for seven orientations, phi-angle variations between 30-46 deg and theta-angle variations between 21-28 deg measured on 3.3-3.4 MHz fundamental mode resonators vibrating in the thickness shear c-mode. The experimental turnover temperatures of these resonators are between 80 C and 150 C, in general agreement with calculated values. The normalized frequency change as a function of temperature has been fitted with a cubic equation.
Kahan, A.↗
Reflected solar radiances from broken cloud scenes and the interpretation of scanner measurements
If an adequate model of the reflection characteristics of a given scene is available, the reflected solar irradiance from the scene may be determined from radiance measurements made by satellite-borne scanning radiometers. A theoretical analysis of the reflection functions of broken cloud scenes is presented, using Monte Carlo simulations of the radiative transfer in various three-dimensional geometries. It is shown that the reflection functions of horizontally extensive (stratiform) and horizontally limited (cumuliform) clouds are generally quite different. The differences are greatest for nadir and limb views, but tend to vanish for reflected radiances with a zenith angle of 60 deg. Applications to satellite observations suggest potential errors of a factor of 2 in the inferred irradiance are likely due to scene misidentification when the radiances are interpreted indiscriminantly. Selection of preferred satellite viewing directions, however, can significantly reduce this error.
Davies, R.↗