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 $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains its norm at a unique vector $x$ (up to a constant multiple) and $T(x)$ 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 $\mathbb R$.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