ON RESOLVABLE INCOMPLETE BLOCK DESIGNS1

A method of constructing resolvable incomplete block designs for v(=ks, 2 ≤ k ≤ s - 1) treatments in blocks of size k using mutually orthogonal Latin squares is proposed. It has been seen in particular that when the number of replications is s — 1 (or s), which is feasible if s is a prime or a prime power, the method gives PBIB (3) (or semi-regular GD) designs. The analysis of such designs has also been discussed.     

THE SLIPPERY SLOPE OF CONCESSION

We show that with common knowledge and a common rate of time preference, the potential loser can always avoid wasteful conflict through a time-consistent series of small concessions. We examine how the failure of each of these assumptions may explain why conflicts arise. We also debate which actions may be helpful in such unfortunate circumstances.     

The Dynamics of Disaster Recovery: Resilience and Entropy in Hurricane Response Systems 2005–2008

The challenge for policy makers and disaster managers is to achieve a balance between two dynamics — resilience and entropy — in order to develop sustainable risk reduction. Achieving an appropriate balance between resilience and entropy in any given community requires a systematic exploration of both dynamics. The recent hurricanes that struck Louisiana, Hurricane Katrina on August 29, 2005 and Hurricane Gustav, on September 1, 2008, offer an unusual opportunity to assess the degree to which both dynamics operated following Hurricane Katrina.     

The Joint Effects of Offender Race/Ethnicity and Sex on Sentence Length Decisions in Federal Courts

The current study examined the main and interactive effects of offender race/ethnicity and sex on sentence length decisions for drug offenders convicted in three federal courts located in Iowa, Minnesota, and Nebraska. The additive model showed that females received shorter prison sentences than similarly situated male offenders, but there were no differences between white offenders and minority offenders. However, when the data were partitioned by sex, black males were found to receive lengthier prison terms than white males. There were no differences between white males and Hispanic males, and white females were treated no differently than either black or Hispanic females. Moreover, when the data were partitioned by race/ethnicity, white females were treated no differently than white males. However, black females received shorter sentences than black males and Hispanic females received shorter sentences than Hispanic males. Further analyses showed that black and Hispanic males also received longer sentences than white females and that black males received longer sentences than all other offenders (with the exception of Hispanic male offenders). These findings mesh with those gleaned from other sentencing studies, although they are at odds with theoretical notions that leniency at the sentencing stage is reserved only for white women.     

On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

Distributions of the lifetimes of system components operating under an unknown common environment

SUMMARY Families of joint distributions for describing the lifetimes of a system of components that operate under an unknown environment, when the environment follows a Weibull distribution, are derived. The reliability function for this system is calculated and several properties of the aforementioned joint distributions are investigated.