47,343 research outputs found
Very smooth points of spaces of operators
In this paper we study very smooth points of Banach spaces with special
emphasis on spaces of operators. We show that when the space of compact
operators is an -ideal in the space of bounded operators, a very smooth
operator attains its norm at a unique vector (up to a constant
multiple) and is a very smooth point of the range space. We show that if
for every equivalent norm on a Banach space, the dual unit ball has a very
smooth point then the space has the Radon--Nikod\'{y}m property. We give an
example of a smooth Banach space without any very smooth points.Comment: 12 pages, no figures, no table
Quenching of fluorescence of aromatic molecules by graphene due to electron transfer
Investigations on the fluorescence quenching of graphene have been carried
out with two organic donor molecules, pyrene butanaoic acid succinimidyl ester
(PyBS, I) and oligo(p-phenylenevinylene) methyl ester (OPV-ester, II).
Absorption and photoluminescence spectra of I and II recorded in mixture with
increasing the concentrations of graphene showed no change in the former, but
remarkable quenching of fluorescence. The property of graphene to quench
fluorescence of these aromatic molecules is shown to be associated with
photo-induced electron transfer, on the basis of fluorescence decay and
time-resolved transient absorption spectroscopic measurements.Comment: 18 pages, 6 figure
Applications of fuzzy theories to multi-objective system optimization
Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis
The Minimum Rank Problem: a counterexample
We provide a counterexample to a recent conjecture that the minimum rank of
every sign pattern matrix can be realized by a rational matrix. We use one of
the equivalences of the conjecture and some results from projective geometry.
As a consequence of the counterexample, we show that there is a graph for which
the minimum rank over the reals is strictly smaller than the minimum rank over
the rationals. We also make some comments on the minimum rank of sign pattern
matrices over different subfields of .Comment: 4 pages, 1 figur
Charge order suppression and antiferromagnetic to ferromagnetic switch over in Pr_0.5Ca_0.5MnO_3 nanowires
We have prepared crystalline nanowires (diameter ~ 50 nm, length ~ a few
microns) of the charge ordering manganite Pr_0.5Ca_0.5Mn_O3 using a low
reaction temperature hydrothermal method and characterized them using X-ray
diffraction, transmission electron microscopy, SQUID magnetometry and electron
magnetic resonance measurements. While the bulk sample shows a charge ordering
transition at 245 K and an antiferromagnetic transition at 175 K, SQUID
magnetometry and electron magnetic resonance experiments reveal that in the
nanowires phase, a ferromagnetic transition occurs at ~ 105 K. Further, the
antiferromagnetic transition disappears and the charge ordering transition is
suppressed. This result is particularly significant since the charge order in
Pr_0.5Ca_0.5MnO_3 is known to be very robust, magnetic fields as high as 27 T
being needed to melt it.Comment: 12 pages including 4 figures. submitted to Applied Physics Letter
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