A probabilistic approach to value sets of polynomials over finite fields

In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\mathbb{F}_q$. We obtain the exact probability distribution and show that the number of missing values tends to a normal distribution as $q$ goes to infinity. We obtain these results through a study of a random $r$-th order cyclotomic mappings. A variation on the size of the union of some random sets is also considered

Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of particles of generation $n$ in a given region, we give the second and third orders asymptotic expansions of the central limit theorem under rather weak assumptions on the moments of the underlying branching and moving laws. The obtained results and the developed approaches shed light on higher order expansions. In the proofs, the Edgeworth expansion of central limit theorems for sums of independent random variables, truncating arguments and martingale approximation play key roles. In particular, we introduce a new martingale, show its rate of convergence, as well as the rates of convergence of some known martingales, which are of independent interest.Comment: Accepted by Bernoull

Influence of Heavy Quark Recombination on the Nucleon Strangeness Asymmetry

The nucleon strange and anti-strange distribution asymmetry is an important issue in the study of the nucleon structure. In this work, we show that the heavy quark recombination processes from a perturbative QCD picture can give a sizable influence on the measurement of the nucleon strangeness asymmetry from charged-current charm production processes, such as the CCFR and NuTeV dimuon measurements. When the influence of heavy quark recombination is considered, a positive effective $\delta S^-_{\mathrm{HR}}$ should be added to the initially extracted strangeness asymmetry $S^-\equiv\int dx[s(x)-\bar s(x)]x$, supporting the strangeness asymmetry $S^-$ being positive, which is helpful to explain the NuTeV anomaly within the framework of the standard model.Comment: 5 latex pages, 2 figure

Smart Nanofibrous Nonwovens Fabricated by Electorospinning

信州大学博士（学術）学位論文・平成25年3月20日授与（甲第75号）・Gao QiangThesisGao Qiang. Smart Nanofibrous Nonwovens Fabricated by Electorospinning. 信州大学, 2013, 84p, 博士論文doctoral thesi