Nested recursions with ceiling function solutions

Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling functions that appear as solutions to R(n). The pattern that emerges from this empirical investigation leads us to the following general result: every ceiling function of the form ceiling{n/q}$ is the solution of infinitely many such recursions. Further, the empirical evidence suggests that the converse conjecture is true: if ceiling{rn/q} is the solution generated by any recursion R(n) of the form above, then r=1. We also use our ceiling function methodology to derive the first known connection between the recursion R(n) and a natural generalization of Conway's recursion.Comment: Published in Journal of Difference Equations and Applications, 2010. 11 pages, 1 tabl

A solenoidal electron spectrometer for a precision measurement of the neutron β\beta-asymmetry with ultracold neutrons

We describe an electron spectrometer designed for a precision measurement of the neutron $\beta$-asymmetry with spin-polarized ultracold neutrons. The spectrometer consists of a 1.0-Tesla solenoidal field with two identical multiwire proportional chamber and plastic scintillator electron detector packages situated within 0.6-Tesla field-expansion regions. Select results from performance studies of the spectrometer with calibration sources are reported.Comment: 30 pages, 19 figures, 1 table, submitted to NIM

Mitochondrial Genetic Differentiation of Spirlin (Actinopterigii: Cyprinidae) in the South Caspian Sea basin of Iran

Background Knowledge about Alburnoides remains lacking relative to many other species, resulting in a lack of a systematic position and taxonomic diagnosis. Basic biological information for Alburnoides has been constructed, and it is necessary to understand further and obtain more information about this species. Its phylogenetic relationships are still debated and no molecular data have been used to study this taxon in Iran. A holistic approach for genetic methods was adopted to analyze possible spirlin population differences at selected centers in the south Caspian Sea basin of Iran. Methods The phylogenetic relationships were determined based on 774 base pairs of the mitochondrial cytochrome b gene of 32 specimens of spirlin from nine locations in the south Caspian Sea drainage basin of Iran. The nucleotide sequences were subjected to phylogenetic analysis using the neighbor-joining, maximum parsimony, maximum likelihood, and Bayesian methods. Results The mitochondrial gene tree largely supports the existence of three major clades. The western populations (clade I) may be considered as Alburnoides eichwaldii , whereas the Talar river populations (clade II) are represented as Alburnoides sp. 1 and the eastern populations (clade III) may be distinct taxa of Alburnoides sp.2. Conclusion This molecular evidence supports the hypothesis that A. bipunctatus does not exist in the south Caspian Sea basin of Iran, and that the western and eastern populations are distinct taxa

Transverse Momentum in Semi-Inclusive Polarized Deep Inelastic Scattering and the Spin-Flavor Structure of the Proton

The non-valence spin-flavor structure of the nucleon extracted from semi-inclusive measurements of polarized deep inelastic scattering depends strongly on the transverse momentum of the detected hadrons which are used to determine the individual polarized sea distributions. This physics may explain the recent HERMES observation of a positively polarized strange sea through semi-inclusive scattering, in contrast to the negative strange sea polarization deduced from inclusive polarized deep inelastic scattering.Comment: 4 pages, revtex style, 2 figure

Associated Higgs production with top quarks at the Large Hadron Collider: NLO QCD corrections

We present in detail the calculation of the O(alpha_s^3) inclusive total cross section for the process pp -> t-tbar-h, in the Standard Model, at the CERN Large Hadron Collider with center-of-mass energy sqrt(s_H)=14 TeV. The calculation is based on the complete set of virtual and real O(alpha_s) corrections to the parton level processes q-qbar -> t-tbar-h and gg -> t-tbar-h, as well as the tree level processes (q,qbar)g -> t-tbar-h-(q,qbar). The virtual corrections involve the computation of pentagon diagrams with several internal and external massive particles, first encountered in this process. The real corrections are computed using both the single and the two cutoff phase space slicing method. The next-to-leading order QCD corrections significantly reduce the renormalization and factorization scale dependence of the Born cross section and moderately increase the Born cross section for values of the renormalization and factorization scales above m_t.Comment: 70 pages, 12 figures, RevTeX4: one word changed in the abstract, one sentence reworded in the introduction. To appear in Phys. Rev.

Strongly focused light beams interacting with single atoms in free space

We construct 3-D solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.Comment: 9 pages, 9 figure

Cryogenic magnetic coil and superconducting magnetic shield for neutron electric dipole moment searches

A magnetic coil operated at cryogenic temperatures is used to produce spatial, relative field gradients below 6 ppm/cm, stable for several hours. The apparatus is a prototype of the magnetic components for a neutron electric dipole moment (nEDM) search, which will take place at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory using ultra-cold neutrons (UCN). That search requires a uniform magnetic field to mitigate systematic effects and obtain long polarization lifetimes for neutron spin precession measurements. This paper details upgrades to a previously described apparatus [1], particularly the introduction of super-conducting magnetic shielding and the associated cryogenic apparatus. The magnetic gradients observed are sufficiently low for the nEDM search at SNS

Argon behaviour in an inverted Barrovian sequence, Sikkim Himalaya: the consequences of temperature and timescale on ⁴⁰Ar/³⁹Ar mica geochronology

40Ar/39Ar dating of metamorphic rocks sometimes yields complicated datasets which are difficult to interpret in terms of timescales of the metamorphic cycle. Single-grain fusion and step-heating data were obtained for rocks sampled through a major thrust-sense shear zone (the Main Central Thrust) and the associated inverted metamorphic zone in the Sikkim region of the eastern Himalaya. This transect provides a natural laboratory to explore factors influencing apparent 40Ar/39Ar ages in similar lithologies at a variety of metamorphic pressure and temperature (P–T) conditions. The 40Ar/39Ar dataset records progressively younger apparent age populations and a decrease in within-sample dispersion with increasing temperature through the sequence. The white mica populations span ~ 2–9 Ma within each sample in the structurally lower levels (garnet grade) but only ~ 0–3 Ma at structurally higher levels (kyanite-sillimanite grade). Mean white mica single-grain fusion population ages vary from 16.2 ± 3.9 Ma (2σ) to 13.2 ± 1.3 Ma (2σ) from lowest to highest levels. White mica step-heating data from the same samples yields plateau ages from 14.27 ± 0.13 Ma to 12.96 ± 0.05 Ma. Biotite yield older apparent age populations with mean single-grain fusion dates varying from 74.7 ± 11.8 Ma (2σ) at the lowest structural levels to 18.6 ± 4.7 Ma (2σ) at the highest structural levels; the step-heating plateaux are commonly disturbed. Temperatures > 600 °C at pressures of 0.4–0.8 GPa sustained over > 5 Ma, appear to be required for white mica and biotite ages to be consistent with diffusive, open-system cooling. At lower temperatures, and/or over shorter metamorphic timescales, more 40Ar is retained than results from simple diffusion models suggest. Diffusion modelling of Ar in white mica from the highest structural levels suggests that the high-temperature rocks cooled at a rate of ~ 50–80 °C Ma− 1, consistent with rapid thrusting, extrusion and exhumation along the Main Central Thrust during the mid-Miocene

The HERMES Dual-Radiator Ring Imaging Cerenkov Detector

The construction and use of a dual radiator Ring Imaging Cerenkov(RICH) detector is described. This instrument was developed for the HERMES experiment at DESY which emphasizes measurements of semi-inclusive deep-inelastic scattering. It provides particle identification for pions, kaons, and protons in the momentum range from 2 to 15 GeV, which is essential to these studies. The instrument uses two radiators, C4F10, a heavy fluorocarbon gas, and a wall of silica aerogel tiles. The use of aerogel in a RICH detector has only recently become possible with the development of clear, large homogeneous and hydrophobic aerogel. A lightweight mirror was constructed using a newly perfected technique to make resin-coated carbon-fiber surfaces of optical quality. The photon detector consists of 1934 photomultiplier tubes for each detector half, held in a soft steel matrix to provide shielding against the residual field of the main spectrometer magnet.Comment: 25 pages, 23 figure

A-dependence of nuclear transparency in quasielastic A(e,e'p) at high Q^2

The A-dependence of the quasielastic A(e,e'p) reaction has been studied at SLAC with H-2, C, Fe, and Au nuclei at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV/c)^2. We extract the nuclear transparency T(A,Q^2), a measure of the average probability that the struck proton escapes from the nucleus A without interaction. Several calculations predict a significant increase in T with momentum transfer, a phenomenon known as Color Transparency. No significant rise within errors is seen for any of the nuclei studied.Comment: 5 pages incl. 2 figures, Caltech preprint OAP-73