Concentric differential gearing arrangement

Two input members and two concentric rotatable output members are interconnected by a planetary gear arrangement. The first input drives directly the first output. The second input engages a carrier having the planetary gears affixed thereto. Rotation of the carriage causes rotation of the central sun gear of the planetary gear system. The sun gear is journaled to the carriage and is drivingly connected to the second output through a direction reversing set of bevel gears. The first input drive member includes a ring gear drivingly connected to the planetary gears for driving the second output member in the same direction and by the same amount as the first output member. Motion of the first input results in equal motion of the two outputs while input motion of the second input results in movement of the second output relative to the first output. This device is useful where non-interacting two-axis control of remote gimbaled systems is required

Formaldehyde Silhouettes Against the Cosmic Microwave Background: A Mass-Limited, Distance-Independent, Extinction-Free Tracer of Star Formation Across the Epoch of Galaxy Evolution

We examine the absorption of cosmic microwave background (CMB) photons by formaldehyde (H2CO) over cosmic time. The K-doublet rotational transitions of H2CO become "refrigerated" - their excitation temperatures are driven below the CMB temperature - via collisional pumping by molecular hydrogen (H2). "Anti-inverted" H2CO line ratios thus provide an accurate measurement of the H2 density in molecular clouds. Using a radiative transfer model, we demonstrate that H2CO centimeter wavelength line excitation and detectability are nearly independent of redshift or gas kinetic temperature. Since the H2CO K-doublet lines absorb CMB light, and since the CMB lies behind every galaxy and provides an exceptionally uniform extended illumination source, H2CO is a distance-independent, extinction-free molecular gas mass-limited tracer of dense gas in galaxies. A Formaldehyde Deep Field could map the history of cosmic star formation in a uniquely unbiased fashion and may be possible with large bandwidth wide-field radio interferometers whereby the silhouettes of star-forming galaxies would be detected across the epoch of galaxy evolution. We also examine the possibility that H2CO lines may provide a standardizable galaxy ruler for cosmology similar to the Sunyaev-Zel'dovich effect in galaxy clusters but applicable to much higher redshifts and larger samples. Finally, we explore how anti-inverted meterwave H2CO lines in galaxies during the peak of cosmic star formation may contaminate HI 21 cm tomography of the Epoch of Reionization.Comment: Accepted by ApJ Letters. 5 pages, 5 figure

Mechanical planetary compensating drive system

Drive enables two concentric output shafts to be controlled independently or rotated as a unit. Possible uses are pointing and tracking devices, rotary camera shutters with variable light control, gimbal systems with yaw and pitch movement, spectrometer mirror scanning devices, etc

SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio

Cascade synthesis of finite-state machines

One can construct any finite-state machine as a cascade interconnection of machines whose inputs either permute the states or reset them all to one state. Each permutation group needed in the construction is a homomorphic image of a group generated by the action of a set of input sequences on a state subset of the original machine. Proofs of these facts will be given and their application to the Krohn-Rhodes theory described