A note on log-convexity of q-Catalan numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted

Protective telescoping shield for solar concentrator

An apparatus is described for use with a solar concentrator such as a parabolic dish which concentrates sunlight onto a small opening of a solar receiver, for protecting the receiver in the event of a system failure that could cause concentrated sunlight to damage the receiver. The protective apparatus includes a structure which can be moved to a stowed position where it does not block sunlight, to a deployed position. In this position, the structure forms a tube which substantially completely surrounds an axis connecting the receiver opening to the center of the concentrator at locations between the receiver and the concentrator

Measurement of SIFT operating system overhead

The overhead of the software implemented fault tolerance (SIFT) operating system was measured. Several versions of the operating system evolved. Each version represents different strategies employed to improve the measured performance. Three of these versions are analyzed. The internal data structures of the operating systems are discussed. The overhead of the SIFT operating system was found to be of two types: vote overhead and executive task overhead. Both types of overhead were found to be significant in all versions of the system. Improvements substantially reduced this overhead; even with these improvements, the operating system consumed well over 50% of the available processing time

SURE reliability analysis: Program and mathematics

The SURE program is a new reliability analysis tool for ultrareliable computer system architectures. The computational methods on which the program is based provide an efficient means for computing accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. Once a semi-Markov model is described using a simple input language, the SURE program automatically computes the upper and lower bounds on the probability of system failure. A parameter of the model can be specified as a variable over a range of values directing the SURE program to perform a sensitivity analysis automatically. This feature, along with the speed of the program, makes it especially useful as a design tool

The fault-tree compiler

The Fault Tree Compiler Program is a new reliability tool used to predict the top event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, and M OF N gates. The high level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precise (within the limits of double precision floating point arithmetic) to the five digits in the answer. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Corporation VAX with the VMS operation system

The Fault Tree Compiler (FTC): Program and mathematics

The Fault Tree Compiler Program is a new reliability tool used to predict the top-event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, AND m OF n gates. The high-level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precisely (within the limits of double precision floating point arithmetic) within a user specified number of digits accuracy. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Equipment Corporation (DEC) VAX computer with the VMS operation system

Pathways to Economic Mobility: Key Indicators

Outlines how indicators of social, human, and financial capital affect an individual's chances of moving up or down the economic ladder. Analyzes data on family structure, community, education, race/ethnicity, health, home ownership, and other factors

Particle-size characteristics of the vertical dust profiles of two contrasting dust events in the Channel Country of western Queensland, Australia

Spatial and temporal variations in vegetation and soil surface conditions of rangelands add a level of complexity to wind erosion processes which is often difficult to model or measure. Butler and colleagues have developed a methodology which combines computer simulation and experimental measurement to analyse how spatial and temporal changes in dust source area emission rates and atmospheric conditions affect vertical dust concentration profiles during wind erosion events in the Queensland Channel Country. This methodology has not, however, taken into account how variations in dust source area particle-size can affect vertical dust concentration profiles. The present paper examines how the particle-size characteristics of dust source soils affect both vertical dust concentration profiles and the vertical distribution of particle-sizes in two contrasting wind erosion events in the Queensland Channel Country. Comparisons are made between computer simulations of these events and the results of field measurements (of vertical dust concentration profiles) and laboratory measurements (of dust particle-size). Computer simulations of the particle-size emissions from the different dust source areas during the two events produce vertical distributions of dust particle-sizes which are similar to the measured dust particle-sizes for these events. These results indicate that erodibility-induced spatial and temporal variations in particle-size emissions of dust source areas have important influences upon: dust fluxes, vertical dust concentration profiles and the vertical distribution of dust particle-sizes within these profile

The Relation Between the Photoelectric and the Photographic Effect in Silver Bromide

Toy, Edgerton, and Vick have recently shown that the photoelectric effect in silver bromide is due to ultraviolet light of wavelength less than λ 2800A. Since the photographic effect extends to λ 5000A they concluded that there is no relation between the photoelectric and the photographic effects in silver bromide. Before this article appeared, the writer had obtained approximately the same result with silver bromide formed by fuming the surface of a silver plate. Our data was obtained by the use of more sensitive apparatus than that employed by the above named investigators. In order to prevent deterioration of the silver bromide the plate was kept in complete darkness until the time of exposure by which measurements were made