Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds \Si with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of \Si at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on \Si. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.Comment: 38 page

C-Cl Bond Fission, Hcl Elimination, And Secondary Radical Decomposition In The 193 Nm Photodissociation Of Allyl Chloride

The primary photodissociation dynamics of allyl chloride upon excitation at 193 nm is investigated in a crossed laser-molecular beam scattering apparatus. Tunable vacuum ultraviolet (VUV) photoionization of the products provides a unique ability to learn about the secondary reaction products of the nascent photoproducts formed. The data show evidence for four significant primary reaction channels: a previously unidentified low kinetic energy C-Cl bond fission channel producing unstable allyl radicals, an excited state C-Cl bond fission channel producing Cl atoms with high translational energy, an HCl elimination pathway releasing significant energy to product translation to HCl and its momentum-matched mass 40 partner, and an HCl elimination channel producing low kinetic energy HCl products and predominantly unstable mass 40 products. The measured branching of these primary reaction channels of [all C-Cl] : [fast C-Cl] : [slow C-Cl] : [fast HCl] : [slow HCl] : [all HCl] is 1.00: 0.971: 0.029: 0.291: 0.167: 0.458 (where fast refers to the high recoil kinetic energy channels). The high internal energy allyl radicals formed in the slow C-Cl fission pathway of allyl chloride further dissociate/isomerize, as do the unstable mass 40 products formed in the HCl elimination pathways, and these products are investigated. Photoionization efficiency (PIE) curves of the HCl product suggest that a three-centered elimination mechanism contributes significantly to an observed HCl elimination reaction. (C) 2002 American Institute of Physics

Monotonicity results and bounds for the inverse hyperbolic sine

In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.Comment: 3 page

A Survey of Positioning Systems Using Visible LED Lights

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.As Global Positioning System (GPS) cannot provide satisfying performance in indoor environments, indoor positioning technology, which utilizes indoor wireless signals instead of GPS signals, has grown rapidly in recent years. Meanwhile, visible light communication (VLC) using light devices such as light emitting diodes (LEDs) has been deemed to be a promising candidate in the heterogeneous wireless networks that may collaborate with radio frequencies (RF) wireless networks. In particular, light-fidelity has a great potential for deployment in future indoor environments because of its high throughput and security advantages. This paper provides a comprehensive study of a novel positioning technology based on visible white LED lights, which has attracted much attention from both academia and industry. The essential characteristics and principles of this system are deeply discussed, and relevant positioning algorithms and designs are classified and elaborated. This paper undertakes a thorough investigation into current LED-based indoor positioning systems and compares their performance through many aspects, such as test environment, accuracy, and cost. It presents indoor hybrid positioning systems among VLC and other systems (e.g., inertial sensors and RF systems). We also review and classify outdoor VLC positioning applications for the first time. Finally, this paper surveys major advances as well as open issues, challenges, and future research directions in VLC positioning systems.Peer reviewe

Competition of different coupling schemes in atomic nuclei

Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explore the competition between the normal monopole pair coupling and the spin-aligned coupling schemes. Such a coupling may be useful in elucidating the structure properties of $N=Z$ and neighboring nuclei.Comment: 10 pages, 7 figures, 1 table. Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie