Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel

Interaction Mechanism Insights on the Solvation of Fullerene B(80)with Choline-based Ionic Liquids

Beyond carbon allotropes, other nanostructures such as fullerene B80 are attracting a growing interest due to their potential applications. The use of new materials based on fullerene B80 is still in a premature stage; however many of these applications would require the use of B80 in solution. This paper reports an unprecedented density functional theory (DFT) analysis on the interaction mechanism between B80 and two choline-based ionic liquids as a first insight for the fullerene B80 solvation by ionic liquids. The analysis of properties such as binding energies, charge distributions or intermolecular interactions shed light on the main features, which should govern interaction between ionic liquids and fullerene B80. In addition, the optimization of systems composed by six ionic pairs around a fullerene B80 has supplied some information about the first solvation shell at the molecular level. As a summary, this paper provides the first insights in the rational design of ionic liquids with suitable properties for the solvation of B80.Gregorio García acknowledges the funding by Junta de Castilla y León (Spain), cofunded by European Social Fund, for a postdoctoral contract. This work was funded by Ministerio de Economía y Competitividad (Spain, project CTQ2013-40476-R) and Junta de Castilla y León (Spain, project BU324U14). We also acknowledge The Foundation of Supercomputing Center of Castile and León (FCSCL, Spain), Computing and Advanced Technologies Foundation of Extremadura (CénitS, LUSITANIA Supercomputer, Spain) and Consortium of Scientific and Academic Services of Cataluña (CSUC, Spain) for providing supercomputing facilities. This work was also made possible by NPRP grant # 6-330-2-140 from the Qatar National Research Fund (a member of Qatar Foundation). We also thank Dr. J. T. Muya and A. Ceulemans (University of Richmond) for providing us the optimized structures of pristine B80. The statements made herein are solely the responsibility of the authors

The Identification and Verification of Hazardous Convective Cells Over Oceans Using Visible and Infrared Satellite Observations

Three algorithms based on geostationary visible and infrared (IR) observations are used to identify convective cells that do (or may) present a hazard to aviation over the oceans. The performance of these algorithms in detecting potentially hazardous cells is determined through verification with Tropical Rainfall Measuring Mission (TRMM) satellite observations of lightning and radar reflectivity, which provide internal information about the convective cells. The probability of detection of hazardous cells using the satellite algorithms can exceed 90% when lightning is used as a criterion for hazard, but the false-alarm ratio with all three algorithms is consistently large (40%), thereby exaggerating the presence of hazardous conditions. This shortcoming results in part from the algorithms’ dependence upon visible and IR observations, and can be traced to the widespread prevalence of deep cumulonimbi with weak updrafts but without lightning over tropical oceans, whose origin is attributed to significant entrainment during ascent

Emerging Approaches to DNA Data Storage: Challenges and Prospects

With the total amount of worldwide data skyrocketing, the global data storage demand is predicted to grow to 1.75 × 1014GB by 2025. Traditional storage methods have difficulties keeping pace given that current storage media have a maximum density of 103GB/mm3. As such, data production will far exceed the capacity of currently available storage methods. The costs of maintaining and transferring data, as well as the limited lifespans and significant data losses associated with current technologies also demand advanced solutions for information storage. Nature offers a powerful alternative through the storage of information that defines living organisms in unique orders of four bases (A, T, C, G) located in molecules called deoxyribonucleic acid (DNA). DNA molecules as information carriers have many advantages over traditional storage media. Their high storage density, potentially low maintenance cost, ease of synthesis, and chemical modification make them an ideal alternative for information storage. To this end, rapid progress has been made over the past decade by exploiting user-defined DNA materials to encode information. In this review, we discuss the most recent advances of DNA-based data storage with a major focus on the challenges that remain in this promising field, including the current intrinsic low speed in data writing and reading and the high cost per byte stored. Alternatively, data storage relying on DNA nanostructures (as opposed to DNA sequence) as well as on other combinations of nanomaterials and biomolecules are proposed with promising technological and economic advantages. In summarizing the advances that have been made and underlining the challenges that remain, we provide a roadmap for the ongoing research in this rapidly growing field, which will enable the development of technological solutions to the global demand for superior storage methodologies

Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant to Part-per-Million Precision

We report a measurement of the positive muon lifetime to a precision of 1.0 parts per million (ppm); it is the most precise particle lifetime ever measured. The experiment used a time-structured, low-energy muon beam and a segmented plastic scintillator array to record more than 2 x 10^{12} decays. Two different stopping target configurations were employed in independent data-taking periods. The combined results give tau_{mu^+}(MuLan) = 2196980.3(2.2) ps, more than 15 times as precise as any previous experiment. The muon lifetime gives the most precise value for the Fermi constant: G_F(MuLan) = 1.1663788 (7) x 10^-5 GeV^-2 (0.6 ppm). It is also used to extract the mu^-p singlet capture rate, which determines the proton's weak induced pseudoscalar coupling g_P.Comment: Accepted for publication in Phys. Rev. Let

THE GENUS HYPOGLOSSUM KÜTZING (DELESSERIACEAE, RHODOPHYTA) IN THE TROPICAL WESTERN ATLANTIC, INCLUDING H. ANOMALUM SP. NOV. 1

Observations are made on the occurrence and distribution of the red algal genus Hypoglossum KÜtzing (Delesseriaceae, Ceramiales) in the tropical western Atlantic. In addition to the type of the genus, H. hypoglossoides (Stackh.) Coll. & Herv., three other species are reported: H. anomalum sp. nov., H. involvens (Harv.) J. Ag., and H. tenuifolium (Harv.) J. Ag. A key is presented to distinguish these four species. The newly described species, H. anomalum, is like other species in the genus in that its branches arise endogenously from the primary axial row but it is unique in that the branches emerge from the parent blade at some point between the midline and the margin of the blade. The new species is reported from Puerto Rico and Florida.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65648/1/j.1529-8817.1986.tb04162.x.pd

Improved Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant

The mean life of the positive muon has been measured to a precision of 11 ppm using a low-energy, pulsed muon beam stopped in a ferromagnetic target, which was surrounded by a scintillator detector array. The result, tau_mu = 2.197013(24) us, is in excellent agreement with the previous world average. The new world average tau_mu = 2.197019(21) us determines the Fermi constant G_F = 1.166371(6) x 10^-5 GeV^-2 (5 ppm). Additionally, the precision measurement of the positive muon lifetime is needed to determine the nucleon pseudoscalar coupling g_P.Comment: As published version (PRL, July 2007