Groupoids with quasigroup and Latin square properties

Connections of some groupoid identities with the quasigroup and Latin square properties are investigated using combinatorial methods.     

Amarts: A class of asymptotic martingales B. Continuous parameter

A continuous-parameter ascending amart is a stochastic process (X_t)_{t +} such that E[X_τn] converges for every ascending sequence (τ_n) of optional times taking finitely many values. A descending amart is a process (X_t)_{t +} such that E[X_τn] converges for every descending sequence (τ_n), and an amart is a process which is both an ascending amart and a descending amart. Amarts include martingales and quasimartingales. The theory of continuous-parameter amarts parallels the theory of continuous-parameter martingales. For example, an amart has a modification every trajectory of which has right and left limits (in the ascending case, if it satisfies a mild boundedness condition). If an amart is right continuous in probability, then it has a modification every trajectory of which is right continuous. The Riesz and Doob-Meyer decomposition theorems are proved by applying the corresponding discrete-parameter decompositions. The Doob-Meyer decomposition theorem applies to general processes and generalizes the known Doob decompositions for continuous-parameter quasimartingales, submartingales, and supermartingales. A hyperamart is a process (X_t) such that E[X_τn] converges for any monotone sequence (τ_n) of bounded optional times, possibly not having finitely many values. Stronger limit theorems are available for hyperamarts. For example: A hyperamart (which satisfies mild regularity and boundedness conditions) is indistinguishable from a process all of whose trajectories have right and left limits.     

删失场合下回归函数估计的强相合性

本文给出随机删失场合下非参数回归函数的一类核估计，得到核估计的强相合性，并证得对数律。     

Essay: Cosmic Censorship: The Role of Quantum Gravity

The cosmic censorship hypothesis introduced by Penrose thirty years ago is still one of the most important open questions in classical general relativity. In this essay we put forward the idea that cosmic censorhip is intrinsically a quantum gravity phenomena. To that end, we construct a gedanken experiment in which cosmic censorship is violated within the purely classical framework of general relativity. We prove, however, that quantum effects restore the validity of the conjecture. This suggests that classical general relativity is inconsistent and that cosmic censorship might be enforced only by a quantum theory of gravity.     

Continuity in G

For a discrete group G, we consider βG, the Stone– ech compactification of G, as a right topological semigroup, and G^*=βGG as a subsemigroup of βG. We study the mappings λ_p^* :G^*→G^*and μ^* :G^*→G^*, the restrictions to G^* of the mappings λ_p :βG→βG and μ :βG→βG, defined by the rules λ_p(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λ_p^* or μ^* at some point of G^* implies the existence of a P-point in ω^*.     

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.     

环的（几乎）优越扩张

设环S是环R的优越扩张．本文证明了如一环是右IF-环；则另一环亦是，同时还得出了一个S是SF-环是正则的充要条件．     

非光滑多目标规划的最优性

本文给出了一种新的右上导数定义,利用这一右上导数定义了几类广义凸性条件,进而讨论了非光滑多目标规划的最优性．包括Ｆｒｉｔｚ－Ｊｏｈｎ条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ条件．     

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。