On the density of the odd values of the partition function

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2. Our main result will relate the densities, say $\delta_t$, of the odd values of the $t$-multipartition functions $p_t(n)$, for several integers $t$. In particular, we will show that if $\delta_t>0$ for some $t\in \{5,7,11,13,17,19,23,25\}$, then (assuming it exists) $\delta_1>0$; that is, $p(n)$ itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that $p(n)$ is odd for $\sqrt{x}$ values of $n\le x$. In general, we conjecture that $\delta_t=1/2$ for all $t$ odd, i.e., that similarly to the case of $p(n)$, all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.Comment: Several changes with respect to the 2015 version. 18 pages. To appear in the Annals of Combinatoric

Empirical Studies Applied to Software Process Models

Working Group Report: ICSE'99 Workshop on Empirical Studies of Software Development and Evolutio

Impacts of a Standing Disaster Payment Program on U.S. Crop Insurance

This research investigates the potential effects of the standing disaster assistance program proposed in the Senate version of the 2008 Farm Bill. Results suggest no significant impact on producer crop insurance purchase decisions. Payments under the program should be expected to differ considerably across geographic regions and levels of diversification, with the program providing the greatest benefit to undiversified producers in more risky production regions (e.g., the Southern Plains).

Real-time in-flight engine performance and health monitoring techniques for flight research application

Procedures for real time evaluation of the inflight health and performance of gas turbine engines and related systems were developed to enhance flight test safety and productivity. These techniques include the monitoring of the engine, the engine control system, thrust vectoring control system health, and the detection of engine stalls. Real time performance techniques were developed for the determination and display of inflight thrust and for aeroperformance drag polars. These new methods were successfully shown on various research aircraft at NASA-Dryden. The capability of NASA's Western Aeronautical Test Range and the advanced data acquisition systems were key factors for implementation and real time display of these methods

Impacts of the SURE Standing Disaster Assistance Program on Producer Risk Management and Crop Insurance Programs

This research investigates the potential effects of the row crop provisions of the standing disaster assistance program (SURE) in the 2008 Farm Bill. Results suggest little impact on producer crop insurance purchase decisions, though the program does seem to provide an incentive for mid-level coverage. Payments under the program should be expected to differ considerably across geographic regions and levels of diversification, with the program providing the greatest benefit to undiversified producers in more risky production regions.crop insurance, disaster assistance, Farm Bill, SURE, Agricultural and Food Policy, Farm Management, Risk and Uncertainty, Q12, Q18,

STOCHASTIC EFFICIENCY ANALYSIS USING MULTIPLE UTILITY FUNCTIONS

Evaluating the risk of a particular decision depends on the risk aversion of the decision maker related to the underlying utility function. The objective of this paper is to use stochastic efficiency with respect to a function (SERF) to compare the ranking of risky alternatives using alternative utility functional forms.Research Methods/ Statistical Methods,

Foot and Mouth Epidemic Reduces Cases of Human Cryptosporidiosis in Scotland.

In Scotland, rates of cryptosporidiosis infection in humans peak during the spring, a peak that is coincident with the peak in rates of infection in farm animals (during lambing and calving time). Here we show that, during the outbreak of foot and mouth disease (FMD) in 2001, there was a significant reduction in human cases of cryptosporidiosis infection in southern Scotland, where FMD was present, whereas, in the rest of Scotland, there was a reduction in cases that was not significant. We associate the reduction in human cases of cryptosporidiosis infection with the reduction in the number of young farm animals, together with restrictions on movement of both farm animals and humans, during the outbreak of FMD in 2001. We further show that, during 2002, there was recovery in the rate of cryptosporidiosis infection in humans throughout Scotland, particularly in the FMD-infected area, but that rates of infection remained lower, though not significantly, than pre-2001 levels