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Properties of a transformation method, which was developed for solving fluid dynamic problems on general two dimensional regions, are discussed. These include construction error of the transformation and applications to mesh generation. An error and stability analysis for the numerical solution of a model parabolic problem is also presented.
An algorithm for computing a Fourier-like transform over GF(2 to the (second power) to the n power), where n = 1,2,3,4,5, was developed to encode and decode and Reed-Solomon (RS) codes of length 2 to the (second power) to the n power. Such as RS detector is considerably faster than a decoder that uses the conventional fast transform over GF(2 to the (second power) to the n power).
A method is proposed to streamline the transform decoding algorithm for Reed-Solomon (RS) codes of length equal to 2 raised to the power 2n. It is shown that a high-radix fast Fourier transform (FFT) type algorithm with generator equal to 3 on GF(F sub n), where F sub n is a Fermat prime, can be used to decode RS codes of this length. For a 256-symbol RS code, a radix 4 and radix 16 FFT over GF(F sub 3) require, respectively, 30 and 70% fewer modulo F sub n multiplications than the usual radix 2 FFT.
It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.
The author has identified the following significant results. The effects of earth's atmosphere were accounted for, and a simple algorithm, based upon a radiative transfer model, was developed to determine the radiance at earth's surface free of atmospheric effects. Acutal multispectral remote sensor data for Lake Erie and associated optical thickness data were used to demonstrate the effectiveness of the atmospheric transformation algorithm. The basic transformation was general in nature and could be applied to the large scale processing of multispectral aircraft or satellite remote sensor data.
Methods for automatically constructing concrete executable programs from an abstract prototype program by applying transformations based on theorems of matrix algebra and on algebraic properties of programming languages are described. These methods provide a user with highly efficient programs tailored to his environment while maintaining the advantages of high reliability and low cost associated with routines from the best mathematical software libraries. Also, the transformations which produce such programs represent a formal codification of rules for writing linear algebra programs.
A direct current transformer in which the primary consists of an elongated strip of superconductive material, across the ends of which is direct current potential is described. Parallel and closely spaced to the primary is positioned a transformer secondary consisting of a thin strip of magnetoresistive material.
A cable fault locator is described for sensing faults such as short circuits in power cables. The apparatus includes a plurality of current transformers strategically located along a cable. Trigger circuits are connected to each of the current transformers for placing a resistor in series with a resistive element responsive to an abnormally high current flowing through that portion of the cable. By measuring the voltage drop across the resistive element, the location of the fault can be determined.
The principle features and special testing of a high voltage high power transformer designed and developed for space application are described. The transformer is operated in a series resonant inverter supplying beam power to a 30 cm mercury ion thruster. Electrical requirements include operation of 2.3 kW continuous power output, primary currents to 35 amps rms, and frequencies up to 20 kHz. High efficiency was obtained through detailed considerations of the tradeoffs available in core materials, wire selection, coil configurations and thermal control. A number of novel heat removal techniques are discussed which control the winding temperature using only the available conductive cooling.
A system is presented for automatically controlling transformer coupled alternating current electric lines. The secondary winding of each transformer is provided with a center tap. A switching circuit is connected to the center taps of a pair of secondary windings and includes a switch controller. An impedance is connected between the center taps of the opposite pair of secondary windings. The switching circuit has continuity when the AC lines are continuous and discontinuity with any disconnect of the AC lines. Normally open switching means are provided in at least one AC line. The switch controller automatically opens the switching means when the AC lines become separated.
A data compression technique for multitemporal Landsat imagery which extracts phenological growth pattern information for agricultural crops is described. The principal component greenness transformation was applied to multitemporal agricultural Landsat data for information retrieval. The transformation was favorable for applications in agricultural Landsat data analysis because of its physical interpretability and its relation to the phenological growth of crops. It was also found that the first and second greenness eigenvector components define a temporal small-grain trajectory and nonsmall-grain trajectory, respectively.
The paper describes the principal features and special testing of a high-frequency high-power low-specific-weight (0.57 kg/kW) 2.3-kW electronic power transformer developed for space applications. The transformer is operated in a series resonant inverter supplying beam power to a 30-cm mercury ion thruster. High efficiency (above 98.5%) is obtained through careful detailed design. A number of unique heat removal techniques are discussed which control the winding temperature using only the available conductive cooling.
It is shown that the Winograd transform can be combined with a complex integer transform over the Galois field GF(q-squared) to yield a new algorithm for computing the discrete cyclic convolution of complex number points. By this means a fast method for accurately computing the cyclic convolution of a sequence of complex numbers for long convolution lengths can be obtained. This new hybrid algorithm requires fewer multiplications than previous algorithms.
A simpler technique than those introduced by Lenard and Bernstein (1958), and Dougherty (1964) is employed to obtain the perturbed species density from a specified kinetic equation for a plasma in a given uniform magnetic field. The technique is a generalization of the velocity-Fourier transform method employed by Karpman (1967) for B sub 0 identical to zero, and relies on the fact that in transform space the model collision operator, used to obtain the kinetic equation for waves in a magnetized plasma, contains only first derivatives. The technique is illustrated by evaluating the perturbed density of an arbitrary species.
Transformer transmits power and digital data across rotating interface. Array has many parallel data channels, each with potential l megabaud data rate. Ferrite-cored transformers are spaced along rotor; airgap between them reduces crosstalk.
Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.
Heats of transformation of eutectic alloys were measured for many binary and ternary systems by differential scanning calorimetry and thermal analysis. Only the relatively cheap and plentiful elements Mg, Al, Si, P, Ca, Cu, Zn were considered. A method for measuring volume change during transformation was developed using x-ray absorption in a confined sample. Thermal expansion coefficients of both solid and liquid states of aluminum and of its eutectics with copper and with silicon also were determined. Preliminary evaluation of containment materials lead to the selection of silicon carbide as the initial material for study. Possible applications of alloy PCMs for heat storage in conventional and solar central power stations, small solar receivers and industrial furnace operations are under consideration.
The feasibility of using metal alloys as thermal energy storage media was investigated. The elements selected as candidate media were limited to aluminum, copper, magnesium, silicon, zinc, calcium, and phosphorus on the basis of low cost and latent heat of transformation. Several new eutectic alloys and ternary intermetallic phases were determined. A new method employing X-ray absorption techniques was developed to determine the coefficients of thermal expansion of both the solid and liquid phases and the volume change during phase transformation. The method and apparatus are discussed and the experimental results are presented for aluminum and two aluminum-eutectic alloys. Candidate materials were evaluated to determine suitable materials for containment of the metal alloys. Graphite was used to contain the alloys during the volume change measurements. Silicon carbide was identified as a promising containment material and surface-coated iron alloys were also evaluated. System considerations that are pertinent if alloy eutectics are used as thermal energy storage media are discussed. Potential applications to solar receivers and industrial furnaces are illustrated schematically.