For two normed algebras $A$ and $B$ with the character space   $bigtriangleup(B)neq emptyset$  and a left $B-$module $X,$  a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$  as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...

We examine a model for a bandpass Σ∆ modulator introduced by Feely and co-workers. This is shown to have the dynamics of a piecewise isometry of a union of convex polygons on the plane by an appropriate transformation of the linearised parts into normal form. Using these we show that the periodically coded regions form a packing of the phase space by circles and we link this system to a number ...

The strength of a homogeneous polynomial (or form) is the smallest length an additive decomposition expressing it whose summands are reducible forms. Using functors, we show that set forms with bounded not always Zariski-closed. More specifically, if ground field algebraically closed, prove quartics ≤3 Zariski-closed for large number variables.

Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by ...

We consider set valued mappings de ned on a topological space with convex closed images in IRn The measurability of a multifunction is characterized by the existence of a Castaing representation for it a countable set of measurable selections that pointwise ll up the graph of the multifunction Our aim is to construct a Castaing representation which inherits the regularity properties of the mult...