Visibly irreducible polynomials over finite fields

H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the other. We classify polynomials over finite fields that admit an irreducibility proof with this structure.Comment: 11 pages. To appear in the American Mathematical Monthl

Strategic HR: Outsource Yourself?

[Excerpt] Human Resources has undergone a major transformation over the past three decades. Instead of solely pursuing a functional approach of delivering services, HR professionals now seek to develop and support the critical firm capabilities that drive business strategy. This shift indicates an important change in the way HR contributes to the achievement of an organization’s objectives. And yet responsibility for the older, functional aspects of HR still resides within the field, intertwining two components with considerable differences

Why Deporting Immigrants for “Crimes Involving Moral Turpitude” is Now Unconstitutional

In the best of times, immigrants should only be deported according to the rule of law and not by the whim of executive branch officials. Now, it is imperative. Yet the statute authorizing removal of immigrants for “crimes involving moral turpitude” invites officials to base their prosecutorial choices on political or personal views. As a result, defense attorneys advising their clients on the immigration consequences of pleas have no basis for prediction. Although the Supreme Court long ago rejected the argument that the “moral turpitude” clause was void for vagueness, one of the Court’s most recent decisions now makes that conclusion unsupportable. The notion that due process permits officials to banish legal permanent residents based on “moral turpitude,” which never comported with common sense, is now legally incorrect

Comparative Study of Photosynthesis Rates between Native Red Maple and Invasive Norway Maple in the Eastern Deciduous Forest

Invasive species, such as the Norway Maple, are often able to outcompete native species, such as the Red Maple by performing more efficiently in the environment compared to the native species. In this study, we examined if the Norway maple was able to outcompete the Red Maple in the Eastern Deciduous Forest because the Norway Maple had a higher rate of photosynthesis. The study found that the Norway Maple leaves had a slightly higher rate of carbon dioxide consumption than Red Maple leaves and that the Red Maple leaves had a higher rate of oxygen production compared to the Norway Maples. Since these differences were not statistically significant, the data suggested that the differences in the rate of photosynthesis between the two tree species is most likely very small. This suggests that the rate of photosynthesis is most likely not the advantage Norway Maples have over Red Maples that allows this invader to better compete for space in a forest