Fine scales of decay of operator semigroups

Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay of operator semigroups and yields a number of new ones. Its core is a new operator-theoretical method of deriving rates of decay combining ingredients from functional calculus, and complex, real and harmonic analysis. It also leads to several results of independent interest.Comment: Version 2 includes numerous minor corrections, and is the authors' final version. The pape will be published in the Journal of the European Mathematical Society in April 201

The determination of the global average OH concentration using a deuteroethane tracer

It is proposed to measure the decreasing global concentration of an OH reactive isotopic tracer, G sub 2 D sub 6, after its introduction into the troposphere in a manner to facilitate uniform global mixing. Analyses at the level of 2 x 10 to the -19th power fraction, corresponding to one kg uniformly distributed globally, should be possible by a combination of cryogenic absorption techniques to separate ethane from air and high sensitivity isotopic analysis of ethane by mass spectrometry. Aliquots of C sub 2 D sub 6 totaling one kg would be introduced to numerous southern and northern latitudes over a 10 day period in order to achieve a uniform global concentration within 3 to 6 months by the normal atmospheric circulation. Then samples of air of 1000 l (STP) would be collected periodically at a tropical and temperate zone location in each hemisphere and spiked with a known amount of another isotopic species of ethane, C-13 sub 2 H sub 6, at the level of 10 to the -11th power mole fraction. After separation of the ethanes from air, the absolute concentration of C sub 2 D sub 6 would be analyzed using the Argonne 100-inch radius mass spectrometer

New secondary batteries utilizing electronically conductive polymer cathodes

The objectives are to optimize the transport rates in electronically conductive polypyrrole films by controlling the morphology of the film and to assess the utility of these films as cathodes in a lithium/polypyrrole secondary battery. During this research period, a better understanding was gained of the fundamental electrochemical switching processes within the polypyrrole film. Three publications were submitted based on the work completed

Weak measurement and control of entanglement generation

In this paper we show how weak joint measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace (DFS). Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of differences between purification and generating entanglement

Drainage and irrigation of a thirty-six square mile tract of land in Louisiana

Because of the fact that I was unable to secure all of the necessary data concerning the topography of the section in question I made several assumptions. However, these assumptions were not made at random, as the land lies on the coast and is subject to the same conditions as does the southern portion of Jefferson County, Texas, of which I have accurate knowledge and which lies directly across Sabine Pass --Introduction, page iv