Symplectic Microgeometry II: Generating functions

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur

Project Title: Nuclear Astrophysics Data from Radioactive Beam Facilities

The scientific aims of this project have been the evaluation and dissemination of key nuclear reactions in nuclear astrophysics, with a focus on ones to be studied at new radioactive beam facilities worldwide. These aims were maintained during the entire funding period from 2003 - 2006. In the following, a summary of the reactions evaluated during this period is provided. Year 1 (2003-04): {sup 21}Na(p,{gamma}){sup 22}Mg and {sup 18}Ne({alpha},p){sup 21}Na - The importance of the {sup 21}Na(p,{gamma}){sup 22}Mg and the {sup 18}Ne({alpha},p){sup 21}Na reactions in models of exploding stars has been well documented: the first is connected to the production of the radioisotope {sup 22}Na in nova nucleosynthesis, while the second is a key bridge between the Hot-CNO cycles and the rp-process in X-ray bursts. By the end of Summer 2004, our group had updated these reaction rates to include all published data up to September 2004, and cast the reaction rates into standard analytical and tabular formats with the assistance of Oak Ridge National Laboratory's computational infrastructure for reaction rates. Since September 2004, ongoing experiments on these two reactions have been completed, with our group's participation in both: {sup 21}Na(p,{gamma}){sup 22}Mg at the TRIUMF-ISAC laboratory (DRAGON collaboration), and 18Ne({alpha},p){sup 21}Na at Argonne National Laboratory (collaboration with Ernst Rehm, Argonne). The data from the former was subsequently published and included in our evaluation. Publication from the latter still awaits independent confirmation of the experimental results. Year 2 (2004-05): The 25Al(p,{gamma}){sup 26}Si and {sup 13}N(p,{gamma})14O reactions - For Year 2, we worked on evaluations of the {sup 25}Al(p,{gamma}){sup 26}Si and {sup 13}N(p,{gamma}){sup 14}O reactions, in accordance with our proposed deliverables and following similar standard procedures to those used in Year 1. The {sup 25}Al(p,{gamma}){sup 26}Si reaction is a key uncertainty in the understanding the origin of galactic {sup 26}Al, a target radioisotope for gamma ray astronomy; the {sup 13}N(p,{gamma}){sup 14}O reaction in turn is the trigger reaction for the transition into the Hot-CNO cycles in novae and X-ray bursts. A graduate student of mine, who has been supported part-time by this grant, completed the evaluation of the {sup 25}Al(p,{gamma}){sup 26}Si reaction as part of his plans to measure this reaction at TRIUMF for his Ph.D. thesis project. I also hired a part-time undergraduate student for the 2004-05 academic year to assist with the evaluations, including that of the {sup 13}N(p,{gamma}){sup 14}O reaction. Year 3 (2005-06): The {sup 40}Ca({alpha},{gamma}){sup 44}Ti and {sup 26}Al(p,{gamma}){sup 27}Si reactions - This year's progress was closely coupled to new results coming from our collaboration on the DRAGON spectrometer team at TRIUMF. The {sup 40}Ca({alpha},{gamma}){sup 44}Ti and {sup 26}Al(p,{gamma}){sup 27}Si reactions were both measured, and significant modifications to their respective reaction rates were required. Both are required input toward predicting the respective amounts of Titanium-44 and Aluminum-26 produced in our galaxy, in supernovae, massive stars, and nova explosions. The {sup 26}Al(p,{gamma}){sup 27}Si reaction rate was successfully completed. The {sup 40}Ca({alpha},{gamma}){sup 44}Ti reaction in particular served as the Ph.D. thesis for Christian Ouellet, and therefore the evaluation of this rate fell naturally within his thesis project. Christian successfully defended his thesis in 2007 and is now working for me on the McMaster DOE-funded Nuclear Data Project. In light of the recent data from his thesis, Christian is now putting the final touches on this evaluation, and will disseminate it through the Oak Ridge National Laboratory reaction rate database

Unparticle physics in top pair signals at the LHC and ILC

We study the effects of unparticle physics in the pair productions of top quarks at the LHC and ILC. By considering vector, tensor and scalar unparticle operators, as appropriate, we compute the total cross sections for pair production processes depending on scale dimension d_{\U}. We find that the existence of unparticles would lead to measurable enhancements on the SM predictions at the LHC. In the case of ILC this may become two orders of magnitude larger than that of SM, for smaller values of d_\U, a very striking signal for unparticles.Comment: 19 pages, 9 figures, analysis for ILC has been adde

An Optimal Acceptance Policy for an Urn Scheme

An urn contains m balls of value -1 and p balls of value +1. At each turn a ball is drawn randomly, without replacement, and the player decides before the draw whether or not to accept the ball, i.e., the bet where the payoff is the value of the ball. The process continues until all m+p balls are drawn. Let V(m,p) denote the value of this acceptance (m,p) urn problem under an optimal acceptance policy. In this paper, we first derive an exact closed form for V(m,p) and then study its properties and asymptotic behavior. We also compare this acceptance (m,p) urn problem with the original (m,p) urn problem which was introduced by Shepp [Ann. Math. Statist., 40 (1969), pp. 993--1010]. Finally, we briefly discuss some applications of this acceptance (m,p) urn problem and introduce a Bayesian approach to this optimal stopping problem. Some numerical illustrations are also provided

Ecosystem carbon 7 dioxide fluxes after disturbance in forests of North America

Disturbances are important for renewal of North American forests. Here we summarize more than 180 site years of eddy covariance measurements of carbon dioxide flux made at forest chronosequences in North America. The disturbances included stand-replacing fire (Alaska, Arizona, Manitoba, and Saskatchewan) and harvest (British Columbia, Florida, New Brunswick, Oregon, Quebec, Saskatchewan, and Wisconsin) events, insect infestations (gypsy moth, forest tent caterpillar, and mountain pine beetle), Hurricane Wilma, and silvicultural thinning (Arizona, California, and New Brunswick). Net ecosystem production (NEP) showed a carbon loss from all ecosystems following a stand-replacing disturbance, becoming a carbon sink by 20 years for all ecosystems and by 10 years for most. Maximum carbon losses following disturbance (g C m−2y−1) ranged from 1270 in Florida to 200 in boreal ecosystems. Similarly, for forests less than 100 years old, maximum uptake (g C m−2y−1) was 1180 in Florida mangroves and 210 in boreal ecosystems. More temperate forests had intermediate fluxes. Boreal ecosystems were relatively time invariant after 20 years, whereas western ecosystems tended to increase in carbon gain over time. This was driven mostly by gross photosynthetic production (GPP) because total ecosystem respiration (ER) and heterotrophic respiration were relatively invariant with age. GPP/ER was as low as 0.2 immediately following stand-replacing disturbance reaching a constant value of 1.2 after 20 years. NEP following insect defoliations and silvicultural thinning showed lesser changes than stand-replacing events, with decreases in the year of disturbance followed by rapid recovery. NEP decreased in a mangrove ecosystem following Hurricane Wilma because of a decrease in GPP and an increase in ER

Bandit Problems With Infinitely Many Arms

We consider a bandit problem consisting of a sequence of n choices from an infinite number of Bernoulli arms, with n → ∞. The objective is to minimize the long-run failure rate. The Bernoulli parameters are independent observations from a distribution F. We first assume F to be the uniform distribution on (0, 1) and consider various extensions. In the uniform case we show that the best lower bound for the expected failure proportion is between √2/√n and 2/√n and we exhibit classes of strategies that achieve the latter

Triphenylarsonium-functionalised gold nanoparticles: potential nanocarriers for intracellular therapeutics.

This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.Two new triphenylarsonium alkylthiolate precursors, a thiosulfate zwitterion and a thioacetate salt, have been structurally characterised and their cytotoxicity evaluated against PC3 cells. The arsonium compounds have been used to prepare gold nanoparticles decorated with triphenylarsonium groups.Sheffield Hallam University and Indian Institute of Science (NL)