Voiculescu's free probability theory { which was introduced in an operator algebraic context, but has since then developed into an exciting theory with a lot of links to other elds { has an interesting combinatorial facet: it can be described by the combinatorial concept of multiplicative functions on the lattice of non-crossing partitions. In this survey I want to explain this connection { wit...

In a recent work, T.S. Evans has claimed that the multiplicative anomaly associated with the zeta-function regularization of functional determinants is regularization dependent. We show that, if one makes use of consistent definitions, this is not the case and clarify some points in Evans’ argument. PACS numbers: 05.30.-d,05.30.Jp,11.10.Wx,11.15.Ex Recently, T.S. Evans [1] has investigated the ...

We give a new construction of the algebraic K-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output. This requires us to define multiplicative structure on the category of small permutative categories. The framework we use is the concept of multicategory, a ...

There are several notions of largeness that make sense in any semigroup, and others such as the various kinds of density that make sense in sufficiently well-behaved semigroups including (N,+) and (N, ·). It was recently shown that sets in N which are multiplicatively large must contain arbitrarily large geoarithmetic progressions, that is, sets of the form { rj(a+ id) : i, j ∈ {0, 1, . . . , k...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) g...

The study of parameter estimation under additive and multiplicative noise terms constitutes an interesting signal processing research topic with important consequences in the development of high-performance digital communication receivers. In this sense, the paper addresses the analysis of non-assisted digital synchronizers based on up to fourthorder moments and it shows how this alternative ou...

The present study investigates the performance of population codes when the fluctuations in neural activity have mutual correlation with strength being proportional to the neuronal firing rate (multiplicative noise). The neural field is used to calculate the Fisher information, which is decomposed in two parts, one due to the tuning function and spatial correlation, and the other due to the mul...

One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro...

We study the multiplicative Schwarz method for the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind and for the h-version for a hypersingular integral equation of the rst kind. We prove that the rate of convergence of the multiplicative Schwarz operator is strictly less than 1 for the h-version for both two level and multilev...