Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Electromagnetic Scattering and Statistic Analysis of Clutter from Oil Contaminated Sea Surface

In order to investigate the electromagnetic (EM) scattering characteristics of the three dimensional sea surface contaminated by oil, a rigorous numerical method multilevel fast multipole algorithm (MLFMA) is developed to preciously calculate the electromagnetic backscatter from the two-layered oil contaminated sea surface. Illumination window and resistive window are combined together to depress the edge current induced by artificial truncation of the sea surface. By using this combination, the numerical method can get a high efficiency at a less computation cost. The differences between backscatters from clean sea and oil contaminated sea are investigated with respect to various incident angles and sea states. Also, the distribution of the sea clutter is examined for the oil-spilled cases in this paper

Axiomatic Foundations for the Principle of Entropy Increase

We show that the principle of entropy increase may be exactly founded on a few axioms valid not only for quantum and classical statistics, but also for a wide range of statistical processes.Comment: 8 page

Light Quark Mass Reweighting

We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_\pi=620 MeV) and m_l=0.01 (m_\pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.Comment: 24 pages and 10 figure