On the Equivalence of Forward Mode Automatic Differentiation and Symbolic Differentiation

We show that forward mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that symbolic differentiation suffers from "expression swell" whereas automatic differentiation does not. Here, we show that this statement is not true. "Expression swell" refers to the phenomenon of a much larger representation of the derivative as opposed to the representation of the original function

Cloud cover sensor

An apparatus is described which provides a numerical indication of the cloudiness at a particular time of a day. The apparatus includes a frame holding several light sensors such as photovoltaic cells, with a direct sensor mounted to directly face the Sun and indirect sensors mounted to face different portions of the sky not containing the Sun. A light shield shields the direct sensor from most of the sky except a small portion containing the Sun, and also shields each of the indirect sensors from direct sunlight. The relative values of the outputs from the direct and indirect sensors, enables the generation of a numerical indication of the degree of cloudiness at a particular time of day

Multi-mission module Patent

Multi-mission space vehicle module stage desig

Water-absorbing capacitor system for measuring relative humidity

A method and apparatus using a known water-absorbent polymer as a capacitor which is operated at a dc voltage for measuring relative humidity is presented. When formed as a layer between porous electrically-conductive electrodes and operated in an RC oscillator circuit, the oscillator frequency varies inversely with the partial pressure of the moisture to be measured. In a preferred embodiment, the capacitor is formed from Nafion and is operated at a low dc voltage with a resistor as an RC circuit in an RC oscillator. At the low voltage, the leakage current is proper for oscillation over a satisfactory range. The frequency of oscillation varies in an essentially linear fashion with relative humidity which is represented by the moisture being absorbed into the Nafion. The oscillation frequency is detected by a frequency detector

Passive intrusion detection system

An intrusion detection system is described in which crystal oscillators are used to provide a frequency which varies as a function of fluctuations of a particular environmental property of the atmosphere, e.g., humidity, in the protected volume. The system is based on the discovery that the frequency of an oscillator whose crystal is humidity sensitive, varies at a frequency or rate which is within a known frequency band, due to the entry of an intruder into the protected volume. The variable frequency is converted into a voltage which is then filtered by a filtering arrangement which permits only voltage variations at frequencies within the known frequency band to activate an alarm, while inhibiting the alarm activation when the voltage frequency is below or above the known frequency band

von Laue's Theorem and Its Applications

von Laue's theorem, as well as its generalized form, is strictly proved in detail for its sufficient and necessary condition (SNC). This SNC version of Laue's theorem is used to analyze the infinitely extended electrostatic field produced by a charged metal sphere in free space, and the static field confined in a finite region of space. It is shown in general that the total (Abraham = Minkowski) EM momentum and energy for the electrostatic field cannot constitute a Lorentz four-vector. A derivative von Laue's theorem, which provides a criterion for a Lorentz invariant, is also presented.Comment: Published version, with "Materials to help reading" attached. 12 pages, 1 figur

Small digital recording head has parallel bit channels, minimizes cross talk

A small digital recording head consists of closely spaced parallel wires, imbedded in a ferrite block to concentrate the magnetic flux. Parallel-recorded information bits are converted into serial bits on moving magnetic tape and cross talk is suppressed

Fresnel cup reflector directs maximum energy from light source

To minimize shielding and overheating, a composite Fresnel cup reflector design directs the maximum energy from a light source. It consists of a uniformly ellipsoidal end surface and an extension comprising a series of confocal ellipsoidal and concentric spherical surfaces