LIR序关系的一些封闭性质

证明了Location Independent Riskier Order随机序关系关于简单随机样本的极小值与可微递增凹变换的封闭性质，并讨论了Dilation序关系的一些矩不等式．     

复广义权与拟连续性

本文引入复广义权的外权的概念，讨论了某些与复广义权相关的函数的拟连续性。     

Simultaneous confidence bands for ratios of survival functions via empirical likelihood

We derive a simultaneous confidence band for the ratio of two survival functions based on independent right-censored data. Earlier authors have studied such bands for the difference of two survival functions, but the ratio provides a more appropriate comparison in some applications, e.g., in comparing two treatments in biomedical settings. Our approach is formulated in terms of empirical likelihood and allows us to avoid the use of simulation techniques that are often needed for Wald-type confidence bands. By the transformation-preserving property we also obtain confidence bands for the difference in the cumulative hazard functions. The approach is illustrated with a real data example.     

Validity of thermodynamic laws and weak cosmic censorship for AdS black holes and black holes in a cavity

By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and the weak cosmic censorship conjecture (WCCC) with two types of boundary conditions: the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in an asymptotically flat space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and near-extremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and the WCCC is satisfied/violated for the extremal/near-extremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.     

Empirical likelihood inference for the accelerated failure time model

Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method.     

Empirical likelihood for the contrast of two hazard functions with right censoring

In this paper, we consider the standard two-sample framework with right censoring. We construct useful confidence intervals for the ratio or difference of two hazard functions using smoothed empirical likelihood (EL) methods. The empirical log-likelihood ratio is derived and its asymptotic distribution is a standard chi-squared distribution. Bootstrap confidence bands are also proposed. Simulation studies show that the proposed EL confidence intervals have outperformed normal approximation methods in terms of coverage probability. It is concluded that the empirical likelihood methods provide better inference results.     

非光滑映射的局部满射定理

本文首先将Ivar Ekeland新近证明的一个反函数定理,推广到非光滑映射的情形.以此结果为基础结合线性算子广义逆的稳定性理论给出B.H.Pourciauhas关于非光滑映射的局部满射定理的一个新的证明,新证明方法较原先作者的方法更简洁.     

On Triangulating Dimension of Rings

For any right essential overring T of a right FI-extending ring R, it is shown that 𝒯 dim(T) ≤ 𝒯dim(R), where 𝒯dim(?) is triangulating dimension of a ring. As a consequence, we show that for a ring R the maximal right ring of quotients, Q(R), is a direct product of finitely many prime rings if and only if Q(R) is semiprime and 𝒯dim(Q(R)) is finite. Some examples which illustrate and delimit the result are provided.     

Asymmetry in the Converse of Schur's Lemma

We show that the converse of Schur's Lemma can hold in the category of right modules, but not the category of left modules, over an appropriate ring. We exhibit classes of rings over which this left-right asymmetry does not occur, and provide new constructions of rings over whose module categories the converse of Schur's Lemma holds. We propose various open problems and avenues for further research concomitant to our work.     

Complexes of Gorenstein Flat Modules and Gorenstein Cotorsion Modules

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ ⁿ is Gorenstein flat in R-Mod for all n ∈ ?. Let 𝒮𝒢 stand for the class of strongly Gorenstein flat complexes. We show that a complex C of left R-modules over a right coherent ring R is in the right orthogonal class of 𝒮𝒢 if and only if C ⁿ is Gorenstein cotorsion in R-Mod for all n ∈ ? and Hom^.(G, C) is exact for any strongly Gorenstein flat complex G. Furthermore, a bounded below complex C over a right coherent ring R is in the right orthogonal class of 𝒮𝒢 if and only if C ⁿ is Gorenstein cotorsion in R-Mod for all n ∈ ?. Finally, strongly Gorenstein flat covers and 𝒮𝒢^⊥-envelopes of complexes are considered. For a right coherent ring R, we show that every bounded below complex has a 𝒮𝒢^⊥-envelope.