A negative mass theorem for surfaces of positive genus

We define the "sum of squares of the wavelengths" of a Riemannian surface (M,g) to be the regularized trace of the inverse of the Laplacian. We normalize by scaling and adding a constant, to obtain a "mass", which is scale invariant and vanishes at the round sphere. This is an anlaog for closed surfaces of the ADM mass from general relativity. We show that if M has positive genus then on each conformal class, the mass attains a negative minimum. For the minimizing metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a Moser-Trudinger-Onofri type inequality.Comment: 8 page

A note on entropic uncertainty relations of position and momentum

We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one.Comment: 2 pages, 2 figures, 2 references adde

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Closure properties of solutions to heat inequalities

We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by $u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2}$ also satisfies a heat inequality of a similar type provided $\tfrac{1}{p_1} + \tfrac{1}{p_2} = 1 + \tfrac{1}{p}$. On iterating, this result leads to an analogous statement concerning $n$-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp $n$-fold Young convolution inequality and its reverse form.Comment: 12 page

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl

Hydrogen storage in engineered carbon nanospaces

doi: 10.1088/0957-4484/20/20/204026It is shown how appropriately engineered nanoporous carbons provide materials for reversible hydrogen storage, based on physisorption, with exceptional storage capacities (~80 g H2/kg carbon, ~50 g H2/liter carbon, at 50 bar and 77 K). Nanopores generate high storage capacities (a) by having high surface area to volume ratios, and (b) by hosting deep potential wells through overlapping substrate potentials from opposite pore walls, giving rise to a binding energy nearly twice the binding energy in wide pores. Experimental case studies are presented with surface areas as high as 3100 m2 g−1, in which 40% of all surface sites reside in pores of width ~0.7 nm and binding energy ~9 kJ mol−1, and 60% of sites in pores of width>1.0 nm and binding energy ~5 kJ mol−1. The findings, including the prevalence of just two distinct binding energies, are in excellent agreement with results from molecular dynamics simulations. It is also shown, from statistical mechanical models, that one can experimentally distinguish between the situation in which molecules do (mobile adsorption) and do not (localized adsorption) move parallel to the surface, how such lateral dynamics affects the hydrogen storage capacity, and how the two situations are controlled by the vibrational frequencies of adsorbed hydrogen molecules parallel and perpendicular to the surface: in the samples presented, adsorption is mobile at 293 K, and localized at 77 K. These findings make a strong case for it being possible to significantly increase hydrogen storage capacities in nanoporous carbons by suitable engineering of the nanopore space.This material is based upon work supported in part by the Department of Energy under Award No. DE-FG02-07ER46411. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DEAC02-06CH11357. CW and RC gratefully acknowledge the University of Missouri Bioinformatics Consortium for the use of their computational facilities. The authors would like to thank M Frederick Hawthorne, Francisco Rodr´ıguez-Reinoso, Louis Schlapbach, Andreas Z¨uttel, Bogdan Kuchta, Lucyna Firlej, Michael Roth, and Michael Gordon for valuable contributions. Finally, the authors would like to acknowledge helpful contributions by Hiden Isochema Ltd,Warrington, UK

Differences in Performance Decline Between Sex Under Simulated Military Operational Stress Differences In Performance Decline Between Sex Under Simulated Military Operational Stress

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Extracellular Vesicle Concentration but Not Size Differs Between Men and Women During Military Operational Stress

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