15,158 research outputs found
On character sums over flat numbers
Let be an integer, be any non-principal character mod
, and In this paper the authors prove some estimates
for character sums of the form
where
\mathscr{F}(H)=\left\{n\in\mathbb{Z}|(n,q)=1,1\leqslant n,\bar{n}\leqslant q,
|n-\bar{n}|\leqslant H\}, is defined by Comment: 9 pages, with a complete proof of Theorem 3, Section 5. Accepted by
J. Number Theor
Modelling the number counts of early-type galaxies by pure luminosity evolution
In this paper, we explore the plausible luminosity evolution of early-type
galaxies in different cosmological models by constructing a set of pure
luminosity evolution (PLE) models via the choices of the star formation rate
(SFR) parameters and formation redshift of galaxies, with the
observational constraints derived from the Hubble Space Telescope (HST)
morphological number counts for elliptical and S0 galaxies of the Medium Deep
Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of
early-type galaxies can be explained by the pure luminosity evolution models,
without invoking exotic scenarios such as merging or introducing an additional
population. But the evolution should be nearly passive, with a high
assumed. The conclusion is valid in all of the three cosmological models we
adopted in this paper. We also present the redshift distributions for three
bins of observed magnitudes in F814w pass-band, to show at which redshift are
the objects that dominate the counts at a given magnitude. The predictions of
the redshift distribution of are also presented for comparison
with future data.Comment: Plain tex, 15pages, 9 eps figures, plus an extra figure fig2c.eps,
with the tex-macro mn.tex. MNRAS, accepte
The tensor renormalization group study of the general spin-S Blume-Capel model
We focus on the special situation of of the general spin-S Blume-Capel
model on the square lattice. Under the infinitesimal external magnetic field,
the phase transition behaviors due to the thermal fluctuations are discussed by
the newly developed tensor renormalization group method. For the case of the
integer spin-S, the system will undergo first-order phase transitions with
the successive symmetry breaking with the magnetization . For the
half-integer spin-S, there are similar first order phase transition
with stepwise structure, in addition, there is a continuous
phase transition due to the spin-flip symmetry breaking. In the low
temperature regions, all first-order phase transitions are accompanied by the
successive disappearance of the optional spin-component pairs(),
furthermore, the critical temperature for the nth first-order phase transition
is the same, independent of the value of the spin-S. In the absence of the
magnetic field, the visualization parameter characterizing the intrinsic
degeneracy of the different phases clearly demonstrates the phase transition
process.Comment: 6 pages, 7 figure
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