Spherical Gravitational Collapse: Tangential Pressure and Related Equations of State

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of the Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.     

Asymptotics for a censored generalized linear model with unknown link function

For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.      

Quasistationary collapse to the extreme Kerr black hole

It is shown that the extreme Kerr black hole, i.e. the one with the maximal angular momentum for a given mass, is the only candidate for a black hole limit of rotating fluid bodies in equilibrium.     

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．     

REMARKS ON h-TRANSFORM AND DRIFT

51.h-TransformsInthispaperwearegoingtogiveaformulacharacterizingRevuzmeasuresunderhtrallsform.AssumethatXisarightMarkovprocesswithstatespace(E,B)whichismel,rizable,constructedonthecanonicalspacefiofrightcontinuouspaths,and(Pt)and(Ua)arethesemigroupandresolventofXrespectively.LethbeanexcessivefunctionandletEh:={0相似文献   

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。     

A nonsymmetric matrix with integer eigenvalues

A nonsymmetric N?×?N matrix with elements as certain simple functions of N distinct real or complex numbers r ₁, r ₂, …, r_N is presented. The matrix is special due to its eigenvalues???the consecutive integers 0,1,2, …, N?1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.     

区间值不确定推理真值传播的计算方法

通过用方差定义左右修正量,将点值不确定推理真值传播计算方法推广到区间值情形,提出了一种区间值不确定推理真值传播计算方法.本文所提出的方法表达式简单,易于理解与计算.     

A basis for the right quantum algebra and the “1=q” principle

We construct a basis for the right quantum algebra introduced by Garoufalidis, Lê and Zeilberger and give a method making it possible to go from an algebra subject to commutation relations (without the variable q) to the right quantum algebra by means of an appropriate weight-function. As a consequence, a strong quantum MacMahon Master Theorem is derived. Besides, the algebra of biwords is systematically in use.