On the existence of orthonormal geodesic bases for Lie algebras

We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product

Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime

We discuss the relation between string quantization based on the Schild path integral and the Nambu-Goto path integral. The equivalence between the two approaches at the classical level is extended to the quantum level by a saddle--point evaluation of the corresponding path integrals. A possible relationship between M-Theory and the quantum mechanics of string loops is pointed out. Then, within the framework of ``loop quantum mechanics'', we confront the difficult question as to what exactly gives rise to the structure of spacetime. We argue that the large scale properties of the string condensate are responsible for the effective Riemannian geometry of classical spacetime. On the other hand, near the Planck scale the condensate ``evaporates'', and what is left behind is a ``vacuum'' characterized by an effective fractal geometry.Comment: 19pag. ReVTeX, 1fig. Invited paper to appear in the special issue of {\it Chaos, Solitons and Fractals} on ``Super strings, M,F,S,...Theory'' (M.S. El Naschie and C.Castro, ed

Hyperpaths in network based on transit schedules

The concept of a hyperpath was introduced for handling passenger strategies in route choice behavior for public transit, especially in a frequency-based transit service environment. This model for handling route choice behavior has been widely used for planning transit services, and hyperpaths are now applied in areas beyond public transit. A hyperpath representing more specific passenger behaviors on a network based on transit schedules is proposed. A link-based time-expanded (LBTE) network for transit schedules is introduced; in the network each link represents a scheduled vehicle trip (or trip segment) with departure time and travel time (or arrival time) between two consecutive stops. The proposed LBTE network reduces the effort to build a network based on transit schedules because the network is expanded with scheduled links. A link-based representation of a hypergraph with existing hyperpath model properties that is directly integrated with the LBTE network is also proposed. Transit passenger behavior was incorporated for transfers in the link-based hyperpath. The efficiency of the proposed hyperpath model was demonstrated. The proposed models were applied on a test network and a real transit network represented by the general specification of Google's transit feed

Technologies de l’information, productivité et croissance des entreprises : résultats basés sur de nouvelles microdonnées internationales

La relation entre les technologies de l’information (TI), la productivité et la croissance économique a été établie au niveau agrégé. Cependant, les mécanismes par lesquels l’effet se manifeste au niveau de l’entreprise restent à préciser. Les organismes statistiques ont élaboré des indicateurs de l’aptitude des entreprises à utiliser les technologies de l’information (p. ex. l’infrastructure des technologies de l’information, la diffusion de technologies particulières) et certains indicateurs de l’utilisation réelle (p. ex. buts et fréquence d’utilisation). L’étape suivante consiste à produire des estimations de l’impact de l’utilisation des technologies de l’information. Une étude menée récemment par l’OCDE visait à résoudre cette question en utilisant des données agrégées pour les pays membres de l’OCDE, ainsi que des microdonnées pour l’Allemagne et les États‑Unis. Une deuxième phase de l’étude de l’OCDE consistera en une série de projets, regroupant deux ou trois pays, réalisée au moyen de nouvelles microdonnées obtenues récemment pour une douzaine de pays environ. Le présent article décrit l’un de ces projets, destiné à évaluer l’effet des technologies de l’information au Danemark, au Japon et aux États‑Unis. Chacun de ces pays a recueilli récemment de nouvelles données sur l’utilisation des technologies de l’information au niveau de l’entreprise et procédé à l’analyse préliminaire de celles-ci. En outre, chaque pays se distingue des autres par sa structure de marché et sa structure institutionnelle. La prochaine phase du projet consistera à élaborer des estimations de l’effet de l’utilisation des technologies de l’information fondées sur ces nouvelles microdonnées, ainsi qu’à émettre et à tester des hypothèses qui tiennent compte des différences entre les structures de marché et les structures institutionnelles de ces pays.A positive relationship between information technology (IT), productivity, and growth has been established at the aggregate level. What remain unclear are the mechanisms through which the effect operates at the level of specific businesses. Statistical agencies have developed indicators of businesses’ readiness to use IT (e.g. the IT infrastructure, diffusion of specific technologies), and some indicators on actual usage (e.g., purposes, frequency of use). The next phase is using those data to develop estimates of the impact of IT use. A recent study addressed this question using aggregate data for Organization for Economic Cooperation and Development (OECD) countries, and micro data (data for specific businesses) for Germany and the U.S. A second phase of that study envisions a series of two- and three-country studies making use of newly available micro data for roughly a dozen countries. This paper outlines one such study, a three-country project addressing the impact of IT use in Denmark, Japan, and the U.S. Each country recently collected new data at the level of specific businesses on the use of IT by businesses, and has conducted preliminary analyses of its own data. Each country also has different underlying market and institutional structures. The findings presented here are preliminary. They show that network information technology has a significant impact on labour productivity growth in United States. The next phase of this project will develop estimates of the impact of IT use based on these new micro data, developing and testing hypotheses that acknowledge differences among the countries in market and institutional structures

The influence of mixed solvents volatility on charge state distribution of peptides during positive electrospray ionization mass spectrometry

Understanding the mechanisms that control and concentrate the observed electrospray ionisation (ESI) response from peptides is important. Controlling these mechanisms can improve signal-to-noise ratio in the mass spectrum, and enhances the generation of intact ions, and thus, improves the detection of peptides when analysing mixtures. The effects of different mixtures of aqueous: organic solvents (25, 50, 75%; v/v): formic acid solution (at pH 3.26) compositions on the ESI response and chargestate distribution (CSD) during mass spectrometry (MS) were determined in a group of biologically active peptides (molecular wt range 1.3 - 3.3 kDa). The ESI response is dependent on type of organic solvent in the mobile phase mixture and therefore, solvent choice affects optimal ion intensities. As expected, intact peptide ions gave a more intense ESI signal in polar protic solvent mixtures than in the low polarity solvent. However, for four out of the five analysed peptides, neither the ESI response nor the CSD were affected by the volatility of the solvent mixture. Therefore, in solvent mixtures, as the composition changes during the evaporation processes, the pKb of the amino acid composition is a better predictor of multiple charging of the peptides

Nanofocusing in SOI-based hybrid plasmonic metal slot waveguides

Abstract: Through a process of efficient dielectric to metallic waveguide mode conversion, we calculate a >400-fold field intensity enhancement in a silicon photonics compatible nanofocusing device. A metallic slot waveguide sits on top of the silicon slab waveguide with nanofocusing being achieved by tapering the slot width gradually. We evaluate the conversion between the numerous photonic modes of the planar silicon waveguide slab and the most confined plasmonic mode of a 20 x 50 nm2 slot in the metallic film. With an efficiency of ~80%, this system enables remarkably effective nanofocusing, although the small amount of inter-mode coupling shows that this structure is not quite adiabatic. In order to couple photonic and plasmonic modes efficiently, in-plane focusing is required, simulated here by curved input grating couplers. The nanofocusing device shows how to efficiently bridge the photonic micro-regime and the plasmonic nano-regime whilst maintaining compatibility with the silicon photonics platform