We revisit the widely investigated problem of maximizing the centralized sum-rate capacity in a cognitive radio network. We consider an interference-limited multi-user multi-channel environment, with a transmit sum-power constraint over all channels as well as an aggregate average interference constraint towards multiple primary users. Until very recently only sub-optimal algorithms were propos...

We introduce a notion of asymptotic stability for bijections between sets of partitions and a class of geometric bijections. We then show that a number of classical partition bijections are geometric and that geometric bijections under certain conditions are asymptotically stable.

Designing optimal microstructures for solid oxide fuel cell (SOFC) electrodes is complicated due to the multitude of electro-chemo-physical phenomena taking place simultaneously that directly affect working conditions of a SOFC electrode and its performance. In this study, a new design paradigm is presented to obtain a balance between electrochemical sites in the form of triple phase boundary (...

After the 1916 success of General relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂gij/∂x 5 = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approa...

After the 1916 success of General relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂gij/∂x 5 = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approa...

In this paper we analyze the problem of bifurcation con trol from a geometric perspective Our goal is to provide coordinate free geometric conditions under which con trol can be used to alter the bifurcation properties of a nonlinear control system These insights are expected to be useful in understanding the role that magnitude and rate limits play in bifurcation control as well as giving deep...

In this paper, we present an algorithm to compute the projection of a quasi variety over an algebraic closed field. Based on the algorithm, we give a method to prove geometric theorem mechanically, and the non-degenerate conditions that we get by the method are proved to be the ”weakest”, i.e. the geometric theorem is true if and only if these non-degenerate conditions are satisfied. A method f...

We give necessary and sufficient conditions for two geometric Goppa codes CL(D,G) and CL(D,H) to be the same. As an application we characterize self-dual geometric Goppa codes.