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

Multi-mission module Patent

Multi-mission space vehicle module stage desig

Reactor for simulation and acceleration of solar ultraviolet damage

An environmental test chamber providing acceleration of UV radiation and precise temperature control (+ or -)1 C was designed, constructed and tested. This chamber allows acceleration of solar ultraviolet up to 30 suns while maintaining temperature of the absorbing surface at 30 C - 60 C. This test chamber utilizes a filtered medium pressure mercury arc as the source of radiation, and a combination of selenium radiometer and silicon radiometer to monitor solar ultraviolet (295-340 nm) and total radiant power output, respectively. Details of design and construction and operational procedures are presented along with typical test data

Driving lamps by induction

An electrodeless lamp circuit with a coil surrounding a krypton lamp is driven by an RF input source. A coil surrounding a mercury lamp is tapped across the connection of the input central to the krypton-lamp coil. Each coil is connected in parallel with separate capacitors which form resonant circuits at the input frequency

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

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

Quartz crystal microbalance use in biological studies

Design, development, and applications of quartz crystal microbalance are discussed. Two types of crystals are used. One serves as reference and other senses changes in mass. Specific application to study of bacterial spores is described