Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Revised IR spectrum, radiative efficiency and global warming potential of nitrogen trifluoride

Nitrogen trifluoride (NF3) is an industrial gas used in the semiconductor industry as a plasma etchant and chamber cleaning gas. NF3 is an alternative to other potent greenhouse gases and its usage has increased markedly over the last decade. In recognition of its increased relevance and to aid planning of future usage we report an updated radiative efficiency and global warming potentials for NF3. Laboratory measurements give an integrated absorption cross section of 7.04 x 10(-17) cm(2) molecule(-1) cm(-1) over the spectral region 200 2000 cm(-1). The radiative efficiency is calculated to be 0.21 Wm(-2) ppbv(-1) and the 100 year GWP, relative to carbon dioxide, is 17200. These values are approximately 60% higher than previously published estimates, primarily reflecting the higher infrared absorption cross-sections reported here.

Century-of-Information Research (CIR): a strategy for research and innovation in the century of information

More data will be produced in the next five years than in the entire history of human kind, a digital deluge that marks the beginning of the Century of Information. Through a year-long consultation with UK researchers, a coherent strategy has been developed, which will nurture Century-of-Information Research (CIR); it crystallises the ideas developed by the e-Science Directors' Forum Strategy Working Group. This paper is an abridged version of their latest report which can be found at: http://wikis.nesc.ac.uk/escienvoy/Century_of_Information_Research_Strategy which also records the consultation process and the affiliations of the authors. This document is derived from a paper presented at the Oxford e-Research Conference 2008 and takes into account suggestions made in the ensuing panel discussion. The goals of the CIR Strategy are to facilitate the growth of UK research and innovation that is data and computationally intensive and to develop a new culture of 'digital-systems judgement' that will equip research communities, businesses, government and society as a whole, with the skills essential to compete and prosper in the Century of Information. The CIR Strategy identifies a national requirement for a balanced programme of coordination, research, infrastructure, translational investment and education to empower UK researchers, industry, government and society. The Strategy is designed to deliver an environment which meets the needs of UK researchers so that they can respond agilely to challenges, can create knowledge and skills, and can lead new kinds of research. It is a call to action for those engaged in research, those providing data and computational facilities, those governing research and those shaping education policies. The ultimate aim is to help researchers strengthen the international competitiveness of the UK research base and increase its contribution to the economy. The objectives of the Strategy are to better enable UK researchers across all disciplines to contribute world-leading fundamental research; to accelerate the translation of research into practice; and to develop improved capabilities, facilities and context for research and innovation. It envisages a culture that is better able to grasp the opportunities provided by the growing wealth of digital information. Computing has, of course, already become a fundamental tool in all research disciplines. The UK e-Science programme (2001-06)—since emulated internationally—pioneered the invention and use of new research methods, and a new wave of innovations in digital-information technologies which have enabled them. The Strategy argues that the UK must now harness and leverage its own, plus the now global, investment in digital-information technology in order to spread the benefits as widely as possible in research, education, industry and government. Implementing the Strategy would deliver the computational infrastructure and its benefits as envisaged in the Science & Innovation Investment Framework 2004-2014 (July 2004), and in the reports developing those proposals. To achieve this, the Strategy proposes the following actions: support the continuous innovation of digital-information research methods; provide easily used, pervasive and sustained e-Infrastructure for all research; enlarge the productive research community which exploits the new methods efficiently; generate capacity, propagate knowledge and develop skills via new curricula; and develop coordination mechanisms to improve the opportunities for interdisciplinary research and to make digital-infrastructure provision more cost effective. To gain the best value for money strategic coordination is required across a broad spectrum of stakeholders. A coherent strategy is essential in order to establish and sustain the UK as an international leader of well-curated national data assets and computational infrastructure, which is expertly used to shape policy, support decisions, empower researchers and to roll out the results to the wider benefit of society. The value of data as a foundation for wellbeing and a sustainable society must be appreciated; national resources must be more wisely directed to the collection, curation, discovery, widening access, analysis and exploitation of these data. Every researcher must be able to draw on skills, tools and computational resources to develop insights, test hypotheses and translate inventions into productive use, or to extract knowledge in support of governmental decision making. This foundation plus the skills developed will launch significant advances in research, in business, in professional practice and in government with many consequent benefits for UK citizens. The Strategy presented here addresses these complex and interlocking requirements.

Coriolis perturbations in the infrared spectrum of ethylene

Rotational structure has been resolved and analyzed in two of the infrared‐active perpendicular bands of C2H4 vapor: the Type b fundamental band, ν10, at 826 cm—1, and the Type c fundamental band, ν7, at 949 cm—1. Many of the individual PP and RR branch lines have been observed. The analysis has been confined to values of the quantum number K≥3, for which energy levels ethylene shows no detectable deviations from a symmetric‐top rotational structure. The analysis reveals a Coriolis interaction between ν7 and ν10, and between ν4 and ν10, and values of the Coriolis constants ζ7,10z and ζ4,10y are obtained; these are related to normal coordinate calculations for the appropriate symmetry species, and force constants are derived to fit the observed zeta constants. The band center of ν10 has been revised from the original figure of 810 cm—1 to the new value, 826 cm—1, and the inactive frequency ν4 is estimated to lie at 1023±3 cm—1, in good agreement with the previous estimate of 1027 cm—1. The change in the value of ν10 leads to a suggested change in the value of the Raman‐active fundamental ν6 from 1236 to 1222 cm—1. New combination bands have been observed at 2174 cm—1, assigned as ν3+ν10; and at 2252 cm—1, assigned as ν4+ν6; also rotational structure has been resolved and analyzed in the ν6+ν10 band at 2048 cm—1. The new data obtained for the C2H4 molecule are summarized in Table XII, with all of the other data presently available on the vibrational and rotational constants.

A refined quartic forcefield for acetylene: accurate calculation of the vibrational spectrum

It is now possible to calculate the nine-dimensional rovibrational wavefunctions of sequentially bonded four-atom molecules variationally without dynamical approximation. In the case of HCCH, the simplest such molecule, many hundreds of rovibrational (J = 0, 1, 2) levels can be converged to better than 1.5 cm −1. Variational calculations of this kind are used here systematically to refine the well-known quartic valence-coordinate forcefleld of Strey and Mills [J.Mol. Spectrosc.59, 103-115 (1976)] against experimental term values up to three C-H stretch quanta for the principal and two deuterated isotopomers, yielding a new surface that reproduces the energies of all the known Σ, Π, and Δ states of these species up to the energy of two C-H stretch quanta with an rms error of 3 cm−1 . The refined forcefield is used to study the resonances associated with the accidental degeneracies (ν2 + ν4 + ν5, ν3) and (ν2 + 2ν5, ν1) in the principal isotopomer, leading to a clarification of the assignment of she experimentally detected states in the 2ν3 and 3ν3, polyads, and to the finding that vibrational Coriolis (kinetic energy) terms, rather than quartic anharmonicities in the potential, are the primary cause of the resonant interactions. Using a new cubic ab initio electric dipole field to calculate IR absorption coefficients, 24 undetected Σ and Π states of 1H12C12C1H and 5 undetected Σ states of D12C12CD are identified as candidates for experimental study, and their calculated energies and assignments are given.