On the distribution of Dedekind sums

Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results about the values of Dedekind sums, their density and uniform distribution. Further topics include mean values, large and small (absolute) values, and the behaviour of Dedekind sums near quadratic irrationals. The present paper can be considered as a supplement to the survey article [R. W. Bruggeman, On the distribution of Dedekind sums, Contemp. Math. 166 (1994), 197--210]

Virtual Leadership: Required Competencies for Effective Leaders

There are countless books, articles, and resources available which attempt to identify the competencies and qualities of effective leaders. Traditionally, leaders have been at the center of a community, be it work, church, or social groups. In these communities, face-to-face meetings and close personal interaction have dominated the way leaders interact with their members. However, with the advent of the internet and the host of communication tools that followed, teams today are becoming increasingly dispersed and diverse. Studies are now being done to understand how leadership has or should evolve in order to meet the changing needs and demands of these new and different communities. Some argue that leadership in the virtual environment is simpler as fewer tools are available to virtual leaders. Others may argue that access to fewer tools makes virtual leadership more complex and challenging than traditional leadership. This paper will explore leadership in virtual settings and how it’s changing as more teams move away from traditional team environments. I’ll review the responsibilities and roles of virtual leaders in an effort to better highlight the core competencies needed in today’s virtual settings. I’ll also look at competencies required of global virtual leaders and I’ll address how these competencies can be cultivated to ensure leaders are more effective in leading teams in these new environments