The Light Lexicographic path Ordering

We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space bounded by a polynomial in the size of the inputs

Recent progress on the manipulation of single atoms in optical tweezers for quantum computing

This paper summarizes our recent progress towards using single rubidium atoms trapped in an optical tweezer to encode quantum information. We demonstrate single qubit rotations on this system and measure the coherence of the qubit. We move the quantum bit over distances of tens of microns and show that the coherence is reserved. We also transfer a qubit atom between two tweezers and show no loss of coherence. Finally, we describe our progress towards conditional entanglement of two atoms by photon emission and two-photon interferences.Comment: Proceedings of the ICOLS07 conferenc

The motion of two masses coupled to a massive spring

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple elastic function can be inferred are discussed and the normal modes and normal frequencies obtained. An approximation procedure to the evaluation of the normel frequencies in the case of uniform elastic function and mass density is also discussed.Comment: Standard Latex file plus three eps figure

Early Observations and Analysis of the Type 1a SN 2014J in M82

We present optical and near infrared (NIR) observations of the nearby Type Ia SN 2014J. Seventeen optical and 23 NIR spectra were obtained from 10 days before (-10d) to 10 days after (+10d) the time of maximum B-band brightness. The relative strengths of absorption features and their patterns of development can be compared at one day intervals throughout most of this period. Carbon is not detected in the optical spectra, but we identify C I lambda 1.0693 in the NIR spectra. Mg II lines with high oscillator strengths have higher initial velocities than other Mg II lines. We show that the velocity differences can be explained by differences in optical depths due to oscillator strengths. The spectra of SN 2014J show that it is a normal SN Ia, but many parameters are near the boundaries between normal and high-velocity subclasses. The velocities for OI, Mg II, Si II, S Ca a, and Fell suggest that SN 2014J has a layered structure with little or no mixing. That result is consistent with the delayed detonation explosion models. We also report photometric observations, obtained from -10d to +29d, in the UBVRIJH and K-s bands. The template fitting package SNooPy is used to interpret the light curves and to derive photometric parameters. Using R-v = 1.46, which is consistent with previous studies, SNooPy finds that A(v) = 1.80 for E(B - V)(host) = 1.23 +/- 0.06 mag. The maximum B-band brightness of -19.19 +/- 0.10 mag was reached on February 1.74 UT +/- 0.13 days and the supernova has a decline parameter, Delta m(15), of 1.12 +/- 0.02 mag

Least Action Principle in Gait

We apply the laws of human gait vertical ground reaction force and discover the existence of the phenomenon of least action principle in gait. Using a capacitive mat transducer system, we obtain the variations of human gait vertical ground reaction force and establish a structure equation for the resultant of such a force. Defining the deviation of vertical force as an action function, we observe from our gait optimization analysis the least action principle at half of the stride time. We develop an evaluation index of mechanical energy consumption based upon the least action principle in gait. We conclude that these observations can be employed to enhance the accountability of gait evaluation.Comment: 4 pages, 5 figure

High-Velocity Line Forming Regions in the Type Ia Supernova 2009ig

We report measurements and analysis of high-velocity (> 20,000 km/s) and photospheric absorption features in a series of spectra of the Type Ia supernova (SN) 2009ig obtained between -14d and +13d with respect to the time of maximum B-band luminosity. We identify lines of Si II, Si III, S II, Ca II and Fe II that produce both high-velocity (HVF) and photospheric-velocity (PVF) absorption features. SN 2009ig is unusual for the large number of lines with detectable HVF in the spectra, but the light-curve parameters correspond to a slightly overluminous but unexceptional SN Ia (M_B = -19.46 mag and Delta_m15 (B) = 0.90 mag). Similarly, the Si II lambda_6355 velocity at the time of B-max is greater than "normal" for a SN Ia, but it is not extreme (v_Si = 13,400 km/s). The -14d and -13d spectra clearly resolve HVF from Si II lambda_6355 as separate absorptions from a detached line forming region. At these very early phases, detached HVF are prevalent in all lines. From -12d to -6d, HVF and PVF are detected simultaneously, and the two line forming regions maintain a constant separation of about 8,000 km/s. After -6d all absorption features are PVF. The observations of SN 2009ig provide a complete picture of the transition from HVF to PVF. Most SN Ia show evidence for HVF from multiple lines in spectra obtained before -10d, and we compare the spectra of SN 2009ig to observations of other SN. We show that each of the unusual line profiles for Si II lambda_6355 found in early-time spectra of SN Ia correlate to a specific phase in a common development sequence from HVF to PVF.Comment: 19 pages, 11figures, 4 tables, submitted to Ap

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory