We propose a simple physical model that predicts the optical properties of a class of microstructured waveguides consisting of high-index inclusions that surround a low-index core. On the basis of this model, it is found that a large regime exists where transmission minima are determined by the geometry of the individual high-index inclusions. The locations of these minima are found to be large...

We compute indices of the inclusions of type III1/2 factors arising from endomorphisms of the Cuntz algebra O2 associated to the ranktwo permutation matrices. MSC 2000: 46L37, 46L05

The mechanisms of cold and pressure denaturation of proteins are a matter of debate, but it is commonly accepted that water plays a fundamental role in the process. It has been proposed that the denaturation process is related to an increase of hydrogen bonds among hydration water molecules. Other theories suggest that the causes of denaturation are the density fluctuations of surface water, or...

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In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index of the locally trivial inclusions of irrational rotation algebras.

respectively, where F : [0,T]×D→ (Rn) is amultivaluedmap,D = {ψ : [−r,0]→Rn; ψ is continuous everywhere except for a finite number of points t̃ at which ψ(t̃−) and ψ(t̃+) exist with ψ(t̃−)= ψ(t̃)}, φ ∈D, p : [0,T]→R+ is continuous, η ∈Rn, (Rn) is the family of all nonempty subsets of Rn, 0 < r < ∞, 0 = t0 < t1 < ··· < tm < tm+1 = T , Ik, Jk : Rn → Rnk = 1, . . . ,m are continuous functions. y(t− k )...

A direct and elementary proof of an estimate of Littlewood is given together with an application concerning the sharpness and strictness of some inclusions in mixed norm spaces of analytic functions.

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chieey using Ky Fan's xed point principle. The main result of the paper improves Theorem 1 in 16] as well as Theorem 2.2 of 3]. Some meaningful concrete cases are also presented and discussed. KEY WORDS: operator inclusions in Banach spaces, Ky Fan's xed poi...