2,079 research outputs found
Dimension of gradient measures
We prove that if pure derivatives with respect to all coordinates of a
function on are signed measures, then their lower Hausdorff
dimension is at least . The derivatives with respect to different
coordinates may be of different order.Comment: 8 page
Atomic-state diagnostics and optimization in cold-atom experiments
We report on the creation, observation and optimization of superposition
states of cold atoms. In our experiments, rubidium atoms are prepared in a
magneto-optical trap and later, after switching off the trapping fields,
Faraday rotation of a weak probe beam is used to characterize atomic states
prepared by application of appropriate light pulses and external magnetic
fields. We discuss the signatures of polarization and alignment of atomic spin
states and identify main factors responsible for deterioration of the atomic
number and their coherence and present means for their optimization, like
relaxation in the dark with the strobe probing. These results may be used for
controlled preparation of cold atom samples and in situ magnetometry of static
and transient fieldsComment: 15 pages and 9 figures (including supplementary information
Surfactant mixtures at the oil–water interface
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Colloid and Interface Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF COLLOID AND INTERFACE SCIENCE, VOL 398, (2013) DOI 10.1016/j.jcis.2013.01.06
Unboundedness of adjacency matrices of locally finite graphs
Given a locally finite simple graph so that its degree is not bounded, every
self-adjoint realization of the adjacency matrix is unbounded from above. In
this note we give an optimal condition to ensure it is also unbounded from
below. We also consider the case of weighted graphs. We discuss the question of
self-adjoint extensions and prove an optimal criterium.Comment: Typos corrected. Examples added. Cute drawings. Simplification of the
main condition. Case of the weight tending to zero more discussed
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