We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs.

Abstract. A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Möbius graphs. The contribution of each graph is an invariant of the topological type of the surface on which the graph is drawn. As an example, we calculate the inte...

It is shown that toroidal surfaces that extremize a properly weighted surface integral of the squared normal component of a solenoidal three-vector field capture the local invariant dynamics, in that a field line that is anywhere tangential to the surface must be confined to the surface everywhere. In addition to an elementary three-vector calculus derivation, which relies on a curvilinear toro...

We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs.

provided it was defined, was a number equal to the area under the graph of f over [a, b]. You also likely learned that the definite integral was defined as a limit of Riemann sums. The Riemann sums you most likely used involved partitioning [a, b] into n uniform subintervals of length (b− a)/n and evaluating f at either the right-hand endpoint, the left-hand endpoint, or the midpoint of each su...

We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Pathby-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale. Th...

In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we pro...

In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that G is a parity graph, if and only if the cartesian product G K2 is a perfect graph. Furthermore, as a consequence we get a result for the polyhedron corresponding to an integer linear program formulat...

A seminal result of Reed, Robertson, Seymour, and Thomas says that a directed graph has either k vertex-disjoint directed circuits or a set of at most f(k) vertices meeting all directed circuits. This paper aims at generalizing their result to packing directed circuits through prescribed vertices. Even, Naor, Schieber, and Sudan showed a fractional version of packing such circuits. In this pape...

This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason’s Direct Rule....