1,936 research outputs found
Monotonicity and logarithmic convexity relating to the volume of the unit ball
Let stand for the volume of the unit ball in for
. In the present paper, we prove that the sequence
is logarithmically convex and that the sequence
is strictly
decreasing for . In addition, some monotonic and concave properties of
several functions relating to are extended and generalized.Comment: 12 page
Generalized Convexity and Inequalities
Let R+ = (0,infinity) and let M be the family of all mean values of two
numbers in R+ (some examples are the arithmetic, geometric, and harmonic
means). Given m1, m2 in M, we say that a function f : R+ to R+ is
(m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The
usual convexity is the special case when both mean values are arithmetic means.
We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient
conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The
criteria involve the Maclaurin coefficients. Our results yield a class of new
inequalities for several special functions such as the Gaussian hypergeometric
function and a generalized Bessel function.Comment: 17 page
Modular Equations and Distortion Functions
Modular equations occur in number theory, but it is less known that such
equations also occur in the study of deformation properties of quasiconformal
mappings. The authors study two important plane quasiconformal distortion
functions, obtaining monotonicity and convexity properties, and finding sharp
bounds for them. Applications are provided that relate to the quasiconformal
Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds
for singular values of complete elliptic integrals.Comment: 23 page
The Baryon asymmetry in the Standard Model with a low cut-off
We study the generation of the baryon asymmetry in a variant of the standard
model, where the Higgs field is stabilized by a dimension-six interaction.
Analyzing the one-loop potential, we find a strong first order electroweak
phase transition for Higgs masses up to at least 170 GeV. Dimension-six
operators induce also new sources of CP violation. We compute the baryon
asymmetry in the WKB approximation. Novel source terms in the transport
equations enhance the generated baryon asymmetry. For a wide range of
parameters the model predicts a baryon asymmetry close to the observed value.Comment: 22 pages, latex, 6 figure
Fermi edge singularities in X-ray spectra of strongly correlated fermions
We discuss the problem of the X-ray absorption in a system of interacting
fermions and, in particular, those features in the X-ray spectra that can be
used to discriminate between conventional Fermi-liquids and novel "strange
metals". Focusing on the case of purely forward scattering off the core-hole
potential, we account for the relevant interactions in the conduction band by
means of the bosonization technique. We find that the X-ray Fermi edge
singularities can still be present, although modified, even if the density of
states vanishes at the Fermi energy, and that, in general, the relationship
between the two appears to be quite subtle.Comment: Latex, 16 pages, Princeton preprin
Auxiliary particle theory of threshold singularities in photoemission and X-ray absorption spectra: Test of a conserving T-matrix approximation
We calculate the exponents of the threshold singularities in the
photoemission spectrum of a deep core hole and its X-ray absorption spectrum in
the framework of a systematic many-body theory of slave bosons and
pseudofermions (for the empty and occupied core level). In this representation,
photoemission and X-ray absorption can be understood on the same footing; no
distinction between orthogonality catastrophe and excitonic effects is
necessary. We apply the conserving slave particle T-matrix approximation
(CTMA), recently developed to describe both Fermi and non-Fermi liquid behavior
systems with strong local correlations, to the X-ray problem as a test case.
The numerical results for both photoemission and X-ray absorption are found to
be in agreement with the exact infrared powerlaw behavior in the weak as well
as in the strong coupling regions. We point out a close relation of the CTMA
with the parquet equation approach of Nozi{\`e}res et al.Comment: 10 pages, 9 figures, published versio
Critical slowing down in the geometrically frustrated pyrochlore antiferromagnet Gd_2Ti_2O_7
Longitudinal-field muon spin relaxation experiments have been carried out in
the paramagnetic state of single-crystal Gd_2Ti_2O_7 just above the phase
transition at T_m = 1.0 K. At high applied fields the exponential relaxation
time T_1 is proportional to field, whereas T_1 saturates below a crossover
field B_c that is ~2.5 T at 1.5 K and decreases as T_m is approached. At low
fields the relaxation rate increases markedly as the freezing temperature is
approached, as expected for critical slowing down of the spin fluctuations, but
the increase is suppressed by applied field. This behavior is consistent with
the very long autocorrelation function cutoff time implied by the low value of
B_c.Comment: 4 pages, 2 figures, submitted to 10th International Conference on
Muon Spin Rotation, Relaxation, and Resonance, Oxford, UK, August 200
Isolating JavaScript with Filters, Rewriting, and Wrappers
Abstract. We study methods that allow web sites to safely combine JavaScript from untrusted sources. If implemented properly, filters can prevent dangerous code from loading into the execution environment, while rewriting allows greater expressiveness by inserting run-time checks. Wrapping properties of the execution environment can prevent misuse without requiring changes to imported JavaScript. Using a formal semantics for the ECMA 262-3 standard language, we prove security properties of a subset of JavaScript, comparable in expressiveness to Facebook FBJS, obtained by combining three isolation mechanisms. The isolation guarantees of the three mechanisms are interdependent, with rewriting and wrapper functions relying on the absence of JavaScript constructs eliminated by language filters.
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