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

A Partition Theorem for a Randomly Selected Large Population

We state and prove a proposition on partitioning of a randomly selected large population into stationary and non-stationary populations by using a property of stationary population identity. Applicability of this theorem for practical purposes is summarized at the end.Comment: 7 pages, a new result in population dynamic

On the mechanics of cropping single thin-walled metallic tubes

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Complementarity of perturbations driving insulator-to-metal transition in a charge ordered manganite

Modulation of charge carrier dynamics and hence electrical conductivity of solids by photoexcitation has been a rich field of research with numerous applications. Similarly, electric and magnetic field assisted enhancement of conductivity are of fundamental importance and technological use. Hole doped manganites of the type (A$_{1-x}$B$_{x})$MnO$_{3}$, where A and B are rare and alkaline earth metals respectively have the distinction of showing all three effects. Here we establish the complementarity of the electric, magnetic and photon fields in driving an insulator-metal transition in epitaxial thin films of La$_{0.175}$Pr$_{0.45}$Ca$_{0.375}$MnO$_{3}$ whose electrical ground state is insulating. Both pulsed and CW lasers cause a giant photon flux dependent enhancement of conductivity. It is further observed that electric and magnetic fields trigger the persistent enhancement of conductivity whose magnitude can be accentuated by application of these fields in parallel.Comment: 17 pages 6 figure

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