Optimal domain of qq-concave operators and vector measure representation of qq-concave Banach lattices

Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years

Selected Readings on Ethnicity, Family and Community

Selected Readings on Ethnicity, Family and Community; compiled by Mary E. Kelly, Central Missouri State University, and Thomas W. Sanchez, University of Nebraska- Lincoln

Intentionally disordered superlattices with high dc conductance

We study disordered quantum-well-based semiconductor superlattices where the disorder is intentional and short-range correlated. Such systems consist of quantum-wells of two different thicknesses randomly distributed along the growth direction, with the additional constraint that wells of one kind always appears in pairs. Imperfections due to interface roughness are considered by allowing the quantum-well thicknesses to fluctuate around their {\em ideal} values. As particular examples, we consider wide-gap (GaAs-Ga$_{1-x}$Al$_{x}$As) and narrow-gap (InAs-GaSb) superlattices. We show the existence of a band of extended states in perfect correlated disordered superlattices, giving rise to a strong enhancement of their finite-temperature dc conductance as compared to usual random ones whenever the Fermi level matches this band. This feature is seen to survive even if interface roughness is taken into account. Our predictions can be used to demonstrate experimentally that structural correlations inhibit the localization effects of disorder, even in the presence of imperfections. This effect might be the basis of new, filter-like or other specific-purpose electronic devices.Comment: REVTeX 3.0, 20 pages, 7 uuencoded compressed PostScript figures as a separate file. Submitted to IEEE J Quantum Elec