Isoperimetric inequality from the poisson equation via curvature

In this paper, we establish an isoperimetric inequality in a metric measure space via the Poisson equation. Let (X,d,μ) be a complete, pathwise connected metric space with locally Ahlfors Q‐regular measure, where Q > 1, that supports a local L²‐Poincaré inequality. We show that, for the Poisson equation Δu = g, if the local L^∞‐norm of the gradient Du can be bounded by the Lorentz norm L^Q,1 of g, then we obtain an isoperimetric inequality and a Sobolev inequality in (X,d,μ) with optimal exponents. By assuming a suitable curvature lower bound, we establish such optimal bounds on $\||Du|\|_{L^\infty_{\rm loc}}$ . © 2011 Wiley Periodicals, Inc.     

Slow mappings of finite distortion

We examine mappings of finite distortion from Euclidean spaces into Riemannian manifolds. We use integral type isoperimetric inequalities to obtain Liouville type growth results under mild assumptions on the distortion of the mappings and the geometry of the manifolds.     

Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle

We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.

     

Emission studies of InGaN layers and LEDs grown by plasma-assisted MBE

We prepared InGaN layers on GaN/sapphire substrates using rf-MBE. Photoluminescence (PL) from these layers, grown at different temperatures T_S, shows that there is a strong tendency of GaN to form a separate phase as T_S is increased from 600°C to 650°C. Concomitant with the phase separation, the PL from the InGaN phase broadens, which indicates that indium composition in this phase becomes increasingly non-uniform. Indium compositions measured by Rutherford backscattering (RBS) are consistent with these results. We also observed an increase in PL intensity for InGaN layers grown at higher temperatures. In this paper, we also report on preparing a top-contact InGaN/GaN light emitting diode. The device was operated at 447 nm and had the emission line width of 37 nm with no observable impurity related features. The turn-on voltage was 3.0 V. The output power was 20 μW at 60 mA drive current.     

Growth of strain-compensated GaInNAs/GaAsP quantum wells for 1.3 μm lasers

Strain-compensated GaInNAs/GaAsP quantum well structures and lasers were grown by gas source molecular beam epitaxy using a RF-plasma nitrogen radical beam source. The optimal growth condition for the quantum well structure was determined based on room-temperature photoluminescence measurements. Effects of rapid thermal annealing (RTA) on the optical properties of GaInNAs/GaAsP quantum well structures as well as laser diodes are examined. It was found to significantly increase the photoluminescence from the quantum wells and reduce the threshold current density of the lasers, due to a removal of N induced nonradiative centers from GaInNAs wells.     

Sharp inequalities via truncation

We show that Sobolev-Poincaré and Trudinger inequalities improve to inequalities on Lorentz-type scales provided they are stable under truncations.     

Covariant fuzzy observables and coarse-graining

A fuzzy observable is regarded as a smearing of a sharp observable, and the structure of covariant fuzzy observables is studied. It is shown that the covariant coarse-grainings of sharp observables are exactly the covariant fuzzy observables. A necessary and sufficient condition for a covariant fuzzy observable to be informationally equivalent to the corresponding sharp observable is given.     

Crystal and molecular structures of hexaaquazinc(II)isonicotinate n-oxide and catena-diaquabis-μ-(isonicotinato n-oxide)cadmium(II)

[Zn(H₂O)₆](N-inicO)₂ is an ionic compound made up of hexaaqua metal cations and isonicotinate N-oxide anions. It forms an isomorphic series with the corresponding Mg²⁺, Fe²⁺, Co²⁺ and Ni²⁺ compounds.In [Cd(N-inicO)₂(H₂O)₂]_n complex, coordination takes place through the NO oxygen and one of the (COO) oxygens with ligand forming thus a double bridge between Cd²⁺ ions. The structure is an endless chain stretching diagonally through the unit cell.The coordination polyhedron in both compounds is almost undistorted octahedron.     

Preference programming for robust portfolio modeling and project selection

In decision analysis, difficulties of obtaining complete information about model parameters make it advisable to seek robust solutions that perform reasonably well across the full range of feasible parameter values. In this paper, we develop the Robust Portfolio Modeling (RPM) methodology which extends Preference Programming methods into portfolio problems where a subset of project proposals are funded in view of multiple evaluation criteria. We also develop an algorithm for computing all non-dominated portfolios, subject to incomplete information about criterion weights and project-specific performance levels. Based on these portfolios, we propose a project-level index to convey (i) which projects are robust choices (in the sense that they would be recommended even if further information were to be obtained) and (ii) how continued activities in preference elicitation should be focused. The RPM methodology is illustrated with an application using real data on road pavement projects.