10,370 research outputs found
A Complete Monotonicity of the Gamma Function
The function 1/x ln Ī(x+1)āln x+1 is strictly completely monotonic
on (0,ā)
Logarithmically Completely Monotonic Ratios of Mean Values and an Application
In the article, some strictly Logarithmically completely monotonic
ratios of mean values are presented
Monotonicity and Inequalities for Ratio of the Generalized Logarithmic Means
Let c > b > a > 0 be real numbers. Then the function f(r) =
Lr(a,b)/Lr(a,c) is strictly decreasing on (āā,ā), where Lr(a, b) denotes the generalized (extended) logarithmic mean of two positive numbers a and b
Constraints on the Brans-Dicke gravity theory with the Planck data
Based on the new cosmic CMB temperature data from the Planck satellite, the 9
year polarization data from the WMAP, the BAO distance ratio data from the SDSS
and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt
a parametrization \zeta=\ln(1+1/\omega}), where the general relativity (GR)
limit corresponds to . We find no evidence of deviation from general
relativity. At 95% probability, , correspondingly,
the region is excluded. If we restrict ourselves to
the (i.e. ) case, then the 95% probability interval is
. We can also translate this
result to a constraint on the variation of gravitational constant, and find the
variation rate today as yr ( error bar), the integrated change since the epoch of
recombination is ( error
bar). These limits on the variation of gravitational constant are comparable
with the precision of solar system experiments.Comment: 7 pages, 5 figures, 2 table
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