1,598 research outputs found

    Two closed forms for the Bernoulli polynomials

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    In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 page

    Simple formulas for lattice paths avoiding certain periodic staircase boundaries

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    There is a strikingly simple classical formula for the number of lattice paths avoiding the line x = ky when k is a positive integer. We show that the natural generalization of this simple formula continues to hold when the line x = ky is replaced by certain periodic staircase boundaries--but only under special conditions. The simple formula fails in general, and it remains an open question to what extent our results can be further generalized.Comment: Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs adde

    Power Sums over Finite Subspaces of a Field

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    AbstractLetVbe a finite additive subgroup of a fieldKof characteristicp>0. We consider sums of the formSh(V:α)=∑v∈V(v+α)hforh≄0 and α∈K. In particular, we give necessary and sufficient conditions for the vanishing ofSh(V; α), in terms of the digit sum in the base-pexpansion ofh, in the case thatVhas indexpinK. The proof involves the polynomialfV(x)=∏v∈V(x−v). We defineV†=fV(K). In the case thatKis finite, the polynomialfV†can be viewed as a generalised trace TrV:K→Vwhich coincides with the usual trace ifVis a subfield ofK

    Representations of integers by the form x2 + xy + y2 + z2 + zt + t2

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    Electronic version of an article published in International Journal of Number Theory Volume 04, Issue 05, October 2008, pp. 709-714. DOI: 10.1142/S1793042108001638. Copyright © 2008 World Scientific Publishing Company: http://www.worldscientific.com/worldscinet/ijntWe give an elementary proof of the number of representations of an integer by the quaternary quadratic form x2 + xy + y2 + z2 + zt + t2

    Creativity and the computer nerd: an exploration of attitudes

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    This study arises from our concern that many of our best art and design students are failing to make the most of the opportunities provided by IT because of their fear or dislike of computers. This not only deprives them of useful skills, but, even more importantly, deprives many IT based developments of their input. In this paper we investigate the relationship between attitudes to creativity and to computers among students. We quickly discard an approach based on theories of personality types as philosophically and educationally problematic. An approach based on the self-concept of artists and designers, in relation to their own creativity and to their feelings about computers, offers more hope of progress. This means that we do not try to define the attributes of "creative people". Rather, we ask what creativity means to students of art and design and relate these responses to their attitudes to computers. Self-concept depends on how the subjects see themselves within society and culture, and is liable to change as culture changes. One major instrument of cultural change at the present time is the growth of IT itself. We then describe a first attempt at using a psychological method - Kelly's Repertory Grids - to investigate the self-concept of artists and designers. It is hoped to continue with this approach in further studies over the next few years

    An HST/ACS View of the Inhomogeneous Outer Halo of M31

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    We present a high precision photometric view of the stellar populations in the outer halo of M31, using data taken with the Hubble Space Telescope Advanced Camera for Surveys (HST/ACS). We analyse the field populations adjacent to 11 luminous globular clusters which sample the galactocentric radial range 18 < R < 100 kpc and reach a photometric depth of ~2.5 magnitudes below the horizontal branch (m_F814W ~27 mag). The colour-magnitude diagrams (CMDs) are well populated out to ~60 kpc and exhibit relatively metal-rich red giant branches, with the densest fields also showing evidence for prominent red clumps. We use the Dartmouth isochrones to construct metallicity distribution functions (MDFs) which confirm the presence of dominant populations with = -0.6 to -1.0 dex and considerable metallicity dispersions of 0.2 to 0.3 dex (assuming a 10 Gyr population and scaled-Solar abundances). The average metallicity over the range 30 - 60 kpc is [Fe/H] = -0.8 +/- 0.14 dex, with no evidence for a significant radial gradient. Metal-poor stars ([Fe/H] <= -1.3) typically account for < 10-20 % of the population in each field, irrespective of radius. Assuming our fields are unbiased probes of the dominant stellar populations in these parts, we find that the M31 outer halo remains considerably more metal-rich than that of the Milky Way out to at least 60 kpc.Comment: Accepted for publication in MNRAS. 10 pages, 6 figure

    Mapping the Galactic Halo with blue horizontal branch stars from the 2dF quasar redshift survey

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    We use 666 blue horizontal branch (BHB) stars from the 2Qz redshift survey to map the Galactic halo in four dimensions (position, distance and velocity). We find that the halo extends to at least 100 kpc in Galactocentric distance, and obeys a single power-law density profile of index ~-2.5 in two different directions separated by 150 degrees on the sky. This suggests that the halo is spherical. Our map shows no large kinematically coherent structures (streams, clouds or plumes) and appears homogeneous. However, we find that at least 20% of the stars in the halo reside in substructures and that these substructures are dynamically young. The velocity dispersion profile of the halo appears to increase towards large radii while the stellar velocity distribution is non Gaussian beyond 60 kpc. We argue that the outer halo consists of a multitude of low luminosity overlapping tidal streams from recently accreted objects.Comment: Accepted for publication in the Astrophysical Journal Requires emulateapj to proces

    Effects of Acute Bouts of Aerobic Exercise on Adipokines in Individuals with Mid-Spectrum Chronic Kidney Disease

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    Adipokines have been known to influence various health-related complications such as chronic kidney disease (CKD) and cardiovascular diseases. Fluctuations in adipokines are commonly seen from changes in body composition, however, some evidence shows acute changes may be seen from exercise. Individuals with CKD are commonly characterized by a decline in renal filtration and systemic inflammation. It may be possible that an acute bout of aerobic exercise may improve pro- and anti-inflammatory adipokine concentrations typically seen in individuals with moderate stages of CKD. PURPOSE: To determine the acute effects of aerobic exercise on adipokine concentrations in individuals with moderate stages of CKD. METHODS: Fourteen participants (8 females and 6 males, age = 58.7 ± 9.3 yrs., and %BF = 36.0 ± 9.6) were classified as having moderate stages of CKD (stages G3 and G4). Participants completed 30 min of steady-state moderate intensity exercise (SSE) at 65% VO2 reserve and high-intensity interval training (HIIE) at a 90% VO2 reserve separated by 2 min of slow walking (20% VO2 reserve) in a randomized, crossover design fashion. Venous blood samples were obtained at baseline, 1 h, and 24 h post-exercise. Data were analyzed using a repeated measures ANOVA (p \u3c 0.05) and a paired t-test. If any significant main or interaction effects were found, a post-hoc test was performed. RESULTS: There were no significant differences in adiponectin and leptin levels within treatments. However, significant differences were seen between baseline and 24 h omentin concentrations when performing HIIE (F(2,26) = 5.001, p = .015). Omentin rose significantly 24 h after an acute bout of HIIE (214.69 ± 83.28 to 252.04 ± 91.22, p = .034). A paired t-test showed no significant differences between SSE and HIIE for adiponectin and leptin. Although, there was a significant difference between 24 h omentin concentrations for SSE and HIIE (t = -2.327, p \u3c .037). Omentin concentrations were significantly higher when performing HIIE (252.04 ± 91.22) as opposed to SSE (218.70 ± 82.00, p \u3c .001). CONCLUSION: Omentin plays an anti-inflammatory role in chronic diseases. Thus, individuals experiencing systemic inflammation from moderate stages of CKD may see benefits after performing an acute bout of HIIE due to the up-regulated release of omentin 24 h post-exercise

    CO2/pH-responsive particles with built-in fluorescence read-out

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    yesA novel fluorescent monomer was synthesized to probe the state of CO2-responsive cross-linked polymeric particles. The fluorescent emission of this aminobromomaleimide-bearing monomer, being sensitive to protic environments, can provide information on the core hydrophilicity of the particles and therefore indicates the swollen state and size of the particles. The particles’ core, synthesized from DEAEMA (N,N-diethylaminoethyl methacrylate), is responsive to CO2 through protonation of the tertiary amines of DEAEMA. The response is reversible and the fluorescence emission can be recovered by simply bubbling nitrogen into the particle solution. Alternate purges of CO2 and N2 into the particles’ solution allow several ON/OFF fluorescence emission cycles and simultaneous particle swelling/shrinking cycles.British Petroleum Company (BP), Engineering and Physical Sciences Research Council (EPSRC

    A Keck/DEIMOS spectroscopic survey of the faint M31 satellites And IX, And XI, And XII, and And XIII

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    We present the first spectroscopic analysis of the faint M31 satellite galaxies, AndXI and AndXIII, and a reanalysis of existing spectroscopic data for two further faint companions, And IX and AndXII. By combining data obtained using the DEIMOS spectrograph mounted on the Keck II telescope with deep photometry from the Suprime-Cam instrument on Subaru, we have calculated global properties for the dwarfs, such as systemic velocities, metallicites and half-light radii.We find each dwarf to be very metal poor ([Fe/H] -2 both photometrically and spectroscopically, from their stacked spectrum), and as such, they continue to follow the luminosity-metallicity relationship established with brighter dwarfs. We are unable to resolve a dispersion for And XI due to small sample size and low S/N, but we set a one sigma upper limit of sigma-v <5 km/s. For And IX, And XII and And XIII we resolve velocity dispersions of v=4.5 (+3.4,-3.2), 2.6(+5.1,-2.6) and 9.7(+8.9,-4.5) km/s, and derive masses within the half light radii of 6.2(+5.3,-5.1)x10^6 Msun, 2.4 (+6.5,-2.4)x10^6 Msun and 1.1(+1.4,-0.7)x10^7 Msun respectively. We discuss each satellite in the context of the Mateo relations for dwarf spheroidal galaxies, and the Universal halo profiles established for Milky Way dwarfs (Walker et al. 2009). For both galaxies, this sees them fall below the Universal halo profiles of Walker et al. (2009). When combined with the findings of McConnachie & Irwin (2006a), which reveal that the M31 satellites are twice as extended (in terms of both half-light and tidal radii) as their Milky Way counterparts, these results suggest that the satellite population of the Andromeda system could inhabit halos that are significantly different from those of the Milky Way in terms of their central densities (abridged).Comment: 26 pages, 18 figures, MNRAS submitte
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