An environmentally benign synthesis of isoxazolines and isoxazoles mediated by potassium chloride in water

An effective and environmentally benign procedure for the synthesis of isoxazolines and isoxazoles has been developed by a cycloaddition of nitrile oxides with alkenes or alkynes in water. In this approach, potassium chloride is first oxidized into chlorine in water by the environmentally friendly oxidant Oxone®, then aldoximes are oxidized into nitrile oxides by the in situ generated hypochlorous acid, finally a 1,3-dipolar cycloaddition between nitrile oxides and alkenes or alkynes occurs to provide the corresponding isoxazolines and isoxazoles in good yields.     

Strong limit theorems for oscillation moduli of PL-process and cumulative hazard process under truncation and censorship with applications

In this paper we obtain exact rates of uniform convergence for oscillation moduli and Lipschitz-1/2 moduli of PL-process and cumulative hazard process when the data are subject to left truncation and right censorship. Based on these results, the exact rates of uniform convergence for various types of density and hazard function estimators are derived. Research supported by the Postdoctoral Programme Foundation and the National Natural Science Foundation of China     

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

1991MRSubjectClassification62G05,62E201IntroductionandtheMainResultsInthisarticlewestudysllrvivaldatawhicharesubjecttobothlefttrull(:ationandrightcensoring(LTRC).Morespecifically,let(X,T,Y)denoterandomvariableswhereXisthevariableofinterest,calledthelifetimevariable,withunknowndistributionfullctioll(d.f.)F;Tistherandomlefttruncatiolltiliiewitharbitraryd.f.G,andYistherandorl.1rightcensoringtirliewitharbitraryd.f.H.ItisassumedthatX,T,Yarerxlutuallyindependent.Intheran相似文献   

Congruences modulo powers of 3 for 3- and 9-colored generalized Frobenius partitions

Let $c{?}_k\left(n\right)$ be the number of $k$-colored generalized Frobenius partitions of $n$. We establish some infinite families of congruences for $c{?}_3\left(n\right)$ and $c{?}_9\left(n\right)$ modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for $k\ge 3$ and $n\ge 0$, we prove that

$c{?}_3\left(3^{2k}n+\frac{7?3^{2k}+1}{8}\right)\equiv 0(mod{3}^{4k+5}).$

We give two different proofs to the congruences satisfied by $c{?}_9\left(n\right)$. One of the proofs uses a relation between $c{?}_9\left(n\right)$ and $c{?}_3\left(n\right)$ due to Kolitsch, for which we provide a new proof in this paper.     

随机删失数据下核密度估计的Berry-Esseen界

本文在随机删失数据下研究了概率密度函数的核估计,获得了此核估计的一个Berry－Esseen界.     

A class of weighted estimating equations for additive hazard models with covariates missing at random

Missing covariate data arise frequently in biomedical studies. In this article, we propose a class of weighted estimating equations for the additive hazard regression model when some of the covariates are missing at random. Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations. Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modeling schemes. The resulting estimators have closed forms and are shown to be consistent and asymptotically normal. Simulation studies indicate that the proposed estimators perform well for practical settings. An application to a mouse leukemia study is illustrated.

     

Congruences for cubic partition pairs modulo powers of 3

Let b(n) be the number of cubic partition pairs of n. We establish three congruences for b(n) modulo arbitrary powers of 3. Meanwhile, we prove some conjectures proposed by the first author.     

Ramanujan-type $$1/\pi $$ -series from bimodular forms

The Ramanujan Journal - We develop an approach to establish $$1/\pi $$ -series from bimodular forms. Utilizing this approach, we obtain new families of 2-variable $$1/\pi $$ -series associated to...     

Effective α-Tosyloxylation of Ketones Using 1,1,1-Trifluoro-2-iodoethane as Catalyst

With 1,1,1-trifluoro-2-iodoethane as catalyst, a novel and efficient procedure has been developed for preparation of α-tosyloxyketones from ketones. In this protocol, 1,1,1-trifluoro-2-iodoethane is first oxidized by m-chloroperbenzoic acid to a hypervalent iodine intermediate. The in situ–generated active iodine species then reacts with ketones to afford the corresponding α-tosyloxyketones in good yields.     

左截断右删失下乘积限过程的振动模的强极限定理

本文在左截断右删失模型下获得了乘积限过程和累积失效率过程的振动模和Ｌｉｐｓｃｈｉｔｚ－１２模的强一致收敛的精确速度．作为定理的应用，推导了各种核密度估计和失效率估计的强一致收敛的精确速度．