Let Q be an infinite set of positive integers, τ 〉 1 be a real number and let Wτ（Q）={x∈R：｜x-p/q｜〈^-τ for infinitely many （p,q）∈ Z×Q}.For any given positive integer m, set Q（m）={n∈N：（n,m）=1}. ...Let Q be an infinite set of positive integers, τ 〉 1 be a real number and let Wτ（Q）={x∈R：｜x-p/q｜〈^-τ for infinitely many （p,q）∈ Z×Q}.For any given positive integer m, set Q（m）={n∈N：（n,m）=1}. If m is divisible by at least two prime factors, Adiceam [1] showed that Wτ（N） ／ Wτ（Q（m）） contains uncountably many Liouville numbers, and asked if it contains any non-Liouville numbers？ In this note, we give an affirmative answer to Adiceam＇s question.展开更多
In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are o...In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.展开更多
Abstract In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical di...The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).展开更多
基金Supported by National Natural Science Foundation of China(11661025)Science Research Foundation of Guangxi Education department(YB2014117)Guangxi Programme for Promoting Young Teachers's Ability(2017KY0191)
文摘Let Q be an infinite set of positive integers, τ 〉 1 be a real number and let Wτ（Q）={x∈R：｜x-p/q｜〈^-τ for infinitely many （p,q）∈ Z×Q}.For any given positive integer m, set Q（m）={n∈N：（n,m）=1}. If m is divisible by at least two prime factors, Adiceam [1] showed that Wτ（N） ／ Wτ（Q（m）） contains uncountably many Liouville numbers, and asked if it contains any non-Liouville numbers？ In this note, we give an affirmative answer to Adiceam＇s question.
基金the National Natural Science Foundation of China (Grant No. 10071072) by NSC 88-2118-M029-001 of Taiwan of China.
文摘In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.
基金Supported by the National Natural Science Foundation of China (No.10071072).
文摘Abstract In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
文摘The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).
