Depolarization remote sensing by orthogonality breaking

A new concept devoted to sensing the depolarization strength of materials from a single measurement is proposed and successfully validated on a variety of samples. It relies on the measurement of the orthogonality breaking between two orthogonal states of polarization after interaction with the material to be characterized. The two fields orthogonality being preserved after propagation in birefringent media, this concept is shown to be perfectly suited to depolarization remote sensing through fibers, opening the way to real time depolarization endoscopy.Comment: 5 pages, 4 figure

S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem

Character amenability of Banach algebras

We introduce the notion of character amenable Banach algebras. We prove that character amenability for either of the group algebra L(1)(G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G. Character amenability of the measure algebra M(G) is shown to be equivalent to G being a discrete amenable group. We also study functorial properties of character amenability. For a commutative character amenable Banach algebra A, we prove all cohomological groups with coefficients in finite-dimensional Banach A-bimodules, vanish. As a corollary we conclude that all finite-dimensional extensions of commutative character amenable Banach algebras split strongly