Montgomery multiplication over rings

Montgomery multiplication of two elements a and b of a finite field F_q is defined as abr^-1 where r is a fixed field element in . In this paper we define Montgomery multiplication of elements a(x) and b(x) in a polynomial ring modulo the ideal generated by a reducible polynomial f(x). We then show that Montgomery multiplication over a field represented by a polynomial ring modulo an irreducible pentanomial can be performed more efficiently in terms of time delay by embedding the field in a quotient of a polynomial ring modulo a reducible trinomial. The trinomial has a degree that is slightly higher than that of the pentanomial, thereby increasing the number of gates in the multiplier by a small amount.     

Overhyped Fad or Missed Opportunity? A History of Academic Libraries and the Social Web

The emergence of social media has radically transformed the way we create and consume information. These changes have in turn given rise to new models of librarianship centered on principles of participation, interaction, and collaboration. Over the last decade, academic libraries have eagerly adopted social media as a means of enhancing services and connecting with a new generation of users. But how exactly has this technology changed libraries? In what ways has the social web transformed library services or our relationships with users? This article attempts to assess the impact of social media on academic libraries in the United States through a review of the literature published since 2005. In particular, it looks at how academic libraries have used social media to improve or develop new services. By comparing published case studies with the theoretical literature, this article seeks to separate theory from practice and determine the extent to which the social web has transformed library practice. The author concludes that, despite several noteworthy examples, the majority of social library applications ultimately fail to live up to the transformative potential promised within the literature and that this failure may have more to do with philosophical rather than technical limitations.     

A vacuum tube amplifier for small direct voltages

A simple means for combining a small direct voltage with an alternating carrier is described. This consists of connecting the direct voltage in series with an alternating voltage of the same order of magnitude. The two are then passed through a copper oxide rectifier which suppresses one part of the cycle. The degree of suppression depends upon the magnitude of the direct voltage. The resulting fluctuating voltage can be amplified to any desired degree in a conventional amplifier.The theory for the simple case of pure resistance is worked out, with an example. The solution of the more general case with inductances is indicated.The practical circuit which has been used for the amplification of thermo-couple currents, and as a galvanometer power multiplier, is shown.     

Will Obama's My Brother's Keeper and Similar Initiatives Have a Positive Impact on Low-Income Students?

Barack Obama's My Brother's Keeper is designed to narrow persistent gaps that boys and young men of color confront often and to help all young people achieve their potential in college and career. An important part of this initiative is comprehensive mentoring that supports students in schools and in communities. Because ethnic-minority students have extremely low graduation rates in high school and college, an essential question is addressed: Can My Brother's Keeper and similar initiatives with a mentoring component be effective in helping minority students to achieve success in elementary and secondary schools and in college?