Distinguishing partitions of complete multipartite graphs

A \textit{distinguishing partition} of a group $X$ with automorphism group ${aut}(X)$ is a partition of $X$ that is fixed by no nontrivial element of ${aut}(X)$. In the event that $X$ is a complete multipartite graph with its automorphism group, the existence of a distinguishing partition is equivalent to the existence of an asymmetric hypergraph with prescribed edge sizes. An asymptotic result is proven on the existence of a distinguishing partition when $X$ is a complete multipartite graph with $m_1$ parts of size $n_1$ and $m_2$ parts of size $n_2$ for small $n_1$, $m_2$ and large $m_1$, $n_2$. A key tool in making the estimate is counting the number of trees of particular classes

Bounding Betti numbers of bipartite graph ideals

We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs

Edge growth in graph squares

We resolve a conjecture of Hegarty regarding the number of edges in the square of a regular graph. If $G$ is a connected $d$-regular graph with $n$ vertices, the graph square of $G$ is not complete, and $G$ is not a member of two narrow families of graphs, then the square of $G$ has at least $(2-o_d(1))n$ more edges than $G$

Effects Of Instructor Continuity On A Large-Scale Pilot Training Program

In a large-scale pilot training program, like those run by the United States Air Force, Navy or many civilian colleges, quality of instruction is a very important question. These programs will have large numbers of instructors and students, but the effect of flying a student with a large number of different instructors is unknown. This paper will use continuous performance and failure data to see if there is a relationship between flying with too many instructors and failing or scoring poorly on a checkride. Multiple regression, difference in differencing, and probit analysis will be used to explore this question

Double-cropping sorghum for biomass production

The production of biomass using double-cropping systems may have the advantage of producing more feedstock for refineries by extending the growing season, while also providing many environmental benefits, such as the reduction of erosion. Past research indicates that there may be a genotypic effect for the suitability of a crop for use within these systems. There has been little research conducted to explicitly examine this effect in sorghum, despite the crop\u27s diverse genetic background. The objective of this study was to evaluate the biomass production of twelve sorghum genotypes grown as a sole crop and within a double-cropping system with triticale. It was shown that both triticale and sorghum are acceptable as potential feedstocks for ethanol conversion. Because of adverse weather conditions, the chemical composition of both crops varied over all study environments and was the result of the differences in maturity at the time of harvest. Although genotypes within the single-cropping system produced higher biomass system yields than the double-cropping systems, the difference was not significant for several genotypes. These sorghums were characterized as being earlier maturing varieties and had nearly maximized dry matter production at the earlier harvest of the double-cropping system. Thus, the additional biomass that the crop would have accrued was capable of being supplemented by the growth of the triticale. However, the theoretical ethanol yields were significantly higher within the single-cropping system for these cultivars. This indicates that although it could offset any loss in dry matter production, the triticale crop was of lower quality for conversion to ethanol compared to the sorghum biomass. The double-cropping systems were more costly to produce than the single-cropped sorghums; however, there are favorable environmental benefits associated with the double-cropped sorghum that may warrant the additional costs