The celebrated odd-even exchange algorithm by Batcher provides the quantity average number of exchanges, which was a mystery a few years ago and is still tricky today. We provide an approach that is purely based on generating functions to provide an explicit expression. The asymptotic analysis was done several years ago but never published in a journal and is thus provided here. It is a combina...

In this paper, some generalized integral inequalities which originate from an open problem posed in [F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math., 1(2) (2000), Art. 19] are established.

Responsibility and accountability of CEOs has been a major ethical concern over the past 10 years. Major ethical dilemmas at Enron, Worldcom, AIG, as well as other well-known organizations have been at least partially blamed on CEO malfeasance. Interviews with Ken Lay, CEO of Enron, after his 2006 fraud convictions provides an opportunity to document his perceived role in the demise of Enron. P...

In mitosis, the spindle checkpoint detects a single unattached kinetochore, inhibits the anaphase-promoting complex or cyclosome (APC/C), and prevents premature sister chromatid separation. The checkpoint kinase Bub1 contributes to checkpoint sensitivity through phosphorylating the APC/C activator, Cdc20, and inhibiting APC/C catalytically. We report here the crystal structure of the kinase dom...

Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n ≥ n0 is divisible by r and whose minimum degree is at least (1−1/χcr(K − r ))n contains a perfect K− r -packing, i.e. a collection of disjoint copies of K− r which covers all vertices of G. Here χcr(K − r ) = r(r−2) r−1 is...

Prof. Ken Chay Department of Economics Fall Semester, 2005 ECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2 Question 1: a. Below are the scatter plots of hourly wages and log-wages on the y-axes and education on the x-axis, respectively. In both figures, there appears to be evidence of heteroskedasticity in the variance of the outcome with respect to education. Notice how the dispersion of ...