1,598 research outputs found
Two closed forms for the Bernoulli polynomials
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
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
AbstractLetVbe a finite additive subgroup of a fieldKof characteristicp>0. We consider sums of the formSh(V:α)=âvâV(v+α)hforhâ„0 and αâK. 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)=âvâV(xâv). We defineVâ =fV(K). In the case thatKis finite, the polynomialfVâ can be viewed as a generalised trace TrV:KâVwhich coincides with the usual trace ifVis a subfield ofK
Representations of integers by the form x2 + xy + y2 + z2 + zt + t2
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
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
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
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
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Effects of Acute Bouts of Aerobic Exercise on Adipokines in Individuals with Mid-Spectrum Chronic Kidney Disease
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
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 particlesâ 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 particlesâ 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
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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