ON NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CARATHÉODORY SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS

Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example.     

大学生婚前性行为Simmons模型下分层三阶段抽样调查

调查安徽某独立学院在校大学生婚前性行为发生的比例,为保护大学生的个人隐私,设置敏感问题Simmons模型对"你是否发生过婚前性行为?"问题进行调查,采用随机应答技术,结合全概率公式及方差的性质,应用Cochran W.G抽样理论,给出各层各阶段大学生婚前性行为发生比例的估计值及方差,该调查方法及其统计公式科学、有效。调查结果显示大学生婚前性行为发生比例高。     

On the L2n 1– Extension Properties

We have proved that for all compact linear operator u from R into an L_p ([0,1], ν) (0 < p < 1) extends to L ₁ ([0,1], ν), where R denotes the closed linear subspace in L ₁ ([0,1], ν) of the Rademacher functions {r_n }_{n ? N}. In this paper, we study this type of extension for E_n ? L_2n ¹ where E_n is the n–dimensional subspace which appears in Kasin's theorem such that L_2n ¹ = E_n ⊕ E ^⊥ _n and the L_2n ¹ , L_2n ² norms are universally equivalent on both E_n , E ^⊥ _n. We show that, the precedent extension fails for the pair (E_n , L_2n ¹ ) and we generalize this to any E in an L ₁(Ω, A, P) by giving some conditions on E.