2,512 research outputs found
Phillips' Lemma for L-embedded Banach spaces
In this note the following version of Phillips' lemma is proved. The
L-projection of an L-embedded space - that is of a Banach space which is
complemented in its bidual such that the norm between the two complementary
subspaces is additive - is weak-weakly sequentially continuous.Comment: accepted by Archiv der Mathematik, The original publication will be
available at http://www.springerlink.co
On quantification of weak sequential completeness
We consider several quantities related to weak sequential completeness of a
Banach space and prove some of their properties in general and in -embedded
Banach spaces, improving in particular an inequality of G. Godefroy, N. Kalton
and D. Li. We show some examples witnessing natural limits of our positive
results, in particular, we construct a separable Banach space with the
Schur property that cannot be renormed to have a certain quantitative form of
weak sequential completeness, thus providing a partial answer to a question of
G. Godefroy.Comment: 9 page
Statistical Classification of Cascading Failures in Power Grids
We introduce a new microscopic model of the outages in transmission power
grids. This model accounts for the automatic response of the grid to load
fluctuations that take place on the scale of minutes, when the optimum power
flow adjustments and load shedding controls are unavailable. We describe
extreme events, initiated by load fluctuations, which cause cascading failures
of loads, generators and lines. Our model is quasi-static in the causal,
discrete time and sequential resolution of individual failures. The model, in
its simplest realization based on the Directed Current description of the power
flow problem, is tested on three standard IEEE systems consisting of 30, 39 and
118 buses. Our statistical analysis suggests a straightforward classification
of cascading and islanding phases in terms of the ratios between average number
of removed loads, generators and links. The analysis also demonstrates
sensitivity to variations in line capacities. Future research challenges in
modeling and control of cascading outages over real-world power networks are
discussed.Comment: 8 pages, 8 figure
The dual of a non-reflexive L-embedded Banach space contains isometrically.
See title. (A Banach space is said to be L-embedded if it is complemented in
its bidual such that the norm between the two complementary subspaces is
additive.)Comment: accepted by Bull. Pol. Acad. Sci
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