Several functional equations defined on groups arising from stochastic distance measures.

Several functional equations related to stochastic distance measures have been widely studied when defined on the real line. This dissertation generalizes several of those results to functions defined on groups and fields. Specifically, we consider when the domain is an arbitrary group, G, and the range is the field of complex numbers, C. We begin by looking at the linear functional equation f(pr, qs)+f(ps, qr) = 2f(p, q)+2f(r, s) for all p, q, r, s, € G. The general solution f : G x G → C is given along with a few specific examples. Several generalizations of this equation are also considered and used to determine the general solution f, g, h, k : G x G → C of the functional equation f(pr, qs) + g(ps, qr) = h(p, q) + k(r, s) for all p, q, r, s € G. We then consider the non-linear functional equation f(pr, qs) + f(ps, qr) = f(p, q) f(r, s). The solution f : G x G → C is given for all p, q, r, s € G when f is an abelian function. It is followed by the structure of the general solution, f, dependent upon how the function acts on the center of the group. Several generalizations of the equation are also considered. The general structure of the solution f, g, h : G x G → C of the functional equation f(pr, qs) + f(ps, qr) = g(p, q) h(r, s) is given for all p, q, r, s € G, dependent upon how the function h acts on the center of the group. Future plans related to these equations will be given

Washington Pension System Review

The purpose of this study is to analyze the incidence of Total Permanent Disability (TPD)pensions in Washington State's workers' compensation program. Concerns exist at both thelegislature and in the Department of Labor and Industries as there appears to have been a sharp upturn in the number of pensions awarded since late in the 1990s. This report examines the factors that may be causally related to any upsurge in such awards. Our task is to evaluate pension incidence for both the state fund and the self-insured populations, with a view towards identifying causes of the trend in both sectors, although we concentrate more on the state fund Cclaims due to data limitations

A game theoretic model of kleptoparasitism with strategic arrivals and departures of beetles at dung pats

Dung beetles Onthophagus taurus lay their eggs in brood balls within dung pats. The dung that is used must be sufficiently fresh, and so beetles must keep moving from pat to pat to find fresh dung. If another beetle finds a brood ball it will usually eat the egg inside and lay its own egg in the brood ball instead of constructing its own ball. Thus, beetles will often stay near their eggs to guard them. We model a population of beetles where the times of arrival and departure from pats are strategic choices, and investigate optimal strategies depending upon environmental conditions, which can be reduced to two key parameters, the cost of brood ball construction and the ease of finding balls to parasitise. We predict that beetles should follow one of three distinct behaviors; stay in patches for only short periods, arrive late and be purely parasitic, remain in pats for longer periods in order to guard their brood balls. Under different conditions populations can consist of the first of these types only, a combination of the first and second types, or a combination of all three types

Boundary current experiment I & II, RAFOS float data report, 1994-1997

This is the final data report of all RAFOS (acoustically tracked) float data collected during the 1994-1997 Boundary Current Experiment (BOUNCE) study of the Deep Western Boundary Current (DWBC) in the North Atlantic Ocean. The overall objective of the program was to obtain the first comprehensive description of the North Atlantic DWBC's variability over a large path segment from Cape Hatteras to the Grand Banks. The experiment was comprised of CTD, tracer, and RAFOS float observations to achieve both Eulerian and Lagrangian descriptions of the DWBC. The three main objectives of the Lagrangian float study were 1) to determine fluid parcel pathways in the DWBC and identify regions of exchange with the interior, 2) to estimate the mean speed and variabilty of fluid parcels at two different levels in the DWBC, and 3) to study the kinematics and potential vorticity dynamics of fluid parcels in the DWBC at the Gulf Stream cross-over point near Cape Hatteras. Thirty floats were deployed: 15 were designed to be isopycnal floats, and 15 were isobaric floats. The isopycnal floats were ballasted for the 0, = 27.73 density surface (approximately 800 decibars (db)) to seed the Upper Labrador Sea Water. The isobaric floats were ballasted for 3000 db to seed the Nordic Seas overflow water.Funding was provided by the National Science Foundation under Grant OCE-93-01448

Book Review: Good Jobs, Bad Jobs

Arne Kalleberg’s Good Jobs, Bad Jobs is a deft and concentrated dose of gloom. Kalleberg’s central thesis - that the political, social and economic changes of the past 30 years have permanently altered the structure of the American labor system - is simple, but portends profound ramifications. Among these, according to Kalleberg, is that work has become both more polarized and more precarious

Quantifying Roadside Assessment for Highway Safety

Many of Kentucky’s two-lane rural roads pose an above average risk for fixed object crashes. In Kentucky, run-off-road (ROR) collisions with fixed objects account for 18.9% of all crashes and 41.6% of fatal crashes. Accordingly, ROR crashes are a significant public safety hazard that must be addressed through judicious investments in safety improvements. Until recently, transportation engineers and planners have mostly leveraged qualitative metrics to prioritize safety investments, however, qualitative methodologies are problematic because they may rely excessively on subjective opinion and intuition. This study applied methodologies and software from the U.S. Road Assessment Program (usRAP) to develop quantitative, objective roadside safety ratings for rural two-lane roads in the state of Kentucky on which 20 or more crashes occurred from 2010 to 2015. Kentucky Transportation Center researchers generated usRAP star rating scores following standard protocols and, to validate the methodology, compared those scores to the number of ROR collisions over the specified interval. Analysis revealed robust correlations between star rating scores (and star ratings) and crash data, justifying their as an objective measure of roadside safety. Researchers also delivered a comprehensive database containing over 126,000 records to the Kentucky Transportation Cabinet, which can be used to examine roadside severity and potentially inform future highway investments