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101.
102.
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 LQ,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. 相似文献
103.
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. 相似文献
104.
Sergey Korotov Michal Krí zek Pekka Neittaanmä ki. 《Mathematics of Computation》2001,70(233):107-119
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.
105.
Pekka Laukkanen Sami Lehkonen Petteri Uusimaa Markus Pessa Anni Seppl Tommy Ahlgren Eero Rauhala 《Journal of Crystal Growth》2001,230(3-4):503-506
We prepared InGaN layers on GaN/sapphire substrates using rf-MBE. Photoluminescence (PL) from these layers, grown at different temperatures TS, shows that there is a strong tendency of GaN to form a separate phase as TS 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. 相似文献
106.
Wei Li Jani Turpeinen Petri Melanen Pekka Savolainen Petteri Uusimaa Markus Pessa 《Journal of Crystal Growth》2001,230(3-4):533-536
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. 相似文献
107.
108.
P.J. Lahti 《Reports on Mathematical Physics》1985,21(2):267-280
The role of the projection postulate in quantum theory is discussed. This postulate can be considered as a theorem according to which each property of a physical system admits a pure ideal first-kind measurement, or as an axiom formalizing such a measurement theoretical assumption, or as a precondition for an operational semantics of a scientific language. Moreover, this postulate appears as a presupposition of the fundamental quantum principles. 相似文献
109.
Pekka Koskela 《Journal of Mathematical Analysis and Applications》2003,278(2):324-334
We show that Sobolev-Poincaré and Trudinger inequalities improve to inequalities on Lorentz-type scales provided they are stable under truncations. 相似文献
110.
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. 相似文献