The Generalized k-Resultant Modulus Set Problem in Finite Fields

The Generalized Graetz Problem in Finite Domains

We consider the generalized Graetz problem associated with stationary convection-diffusion inside a domain having any regular three dimensional translationally invariant section and finite or semi-infinite extent. Our framework encompasses any previous “extended” and “conjugated” Graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized twodimensional...

On the K-theory of Finite Fields

In this talk we introduce higher algebraicK-groups via Quillen’s plus construction.We then give a brief tour of algebraicK-theory and its relation to stable homotopy theory and number theory — in particular noting that aK-theory computation of the integers is equivalent to the Kummer–Vandiver conjecture. We next state Quillen’s computations of the K-theory of Fq and Fq. The remainder of the tal...

The Generalized Max-Controlled Set Problem

In this work we deal with sandwich graphs G = (V,E) and present the notion of vertices f -controlled by a subset M ⊆ V . We introduce the generalized maxcontrolled set problem (gmcsp), where gaps and positive weights are associated to each vertex of V . In this case, the objective is find a sandwich graph G in order to maximize the sum of the weights associated to all vertices f -controlled by ...

The Minimum Rank Problem over Finite Fields

Let Gk(F ) = {G | mr(F,G) ≤ k}, the set of simple graphs with minimum rank at most k. The problem of finding mr(F,G) and describing Gk(F ) has recently attracted considerable attention, particularly for the case in which F = R (see [Nyl96, CdV98, JD99, Hsi01, JS02, CHLW03, vdH03, BFH04, BvdHL04, HLR04, AHK05, BD05, BFH05a, BFH05b, BvdHL05, DK06, BF07]). The minimum rank problem over R is a sub-...

Algebraic K-theory of Finite Fields