关于Moser方程

用初等方法证明：当ｎ、ｒ是正整数,丢番图方程ｎ∑／ｋ＝１Ｋ＾ｒ＝（１＋ｎ）＾ｒ只有正整数解ｒ＝１,ｎ＝２。     

二阶变系数线性方程存在一类解的充要条件

给出了二阶变系数线性微分方程ｘ＋Ｐ（ｔ）ｘ＋Ｑ（ｔ）ｘ＝０具有ｘ＝Ｐ１（ｔ）ｅ∫Ｑ１（ｔ）ｄｔ形式特解的充要条件为Ｐ″１（ｔ）＋［Ｐ（ｔ）＋２Ｑ１（ｔ）］Ｐ′１（ｔ）＋［Ｑ′１（ｔ）＋Ｑ２１（ｔ）＋Ｐ（ｔ）Ｑ１（ｔ）＋Ｑ（ｔ）］Ｐ１（ｔ）＝０     

一类非线性退缩抛物型方程解的爆破

考虑退缩抛物型方程ｕｔ ＝ ｕα（ △ｕ ＋ ｆ（ ｕ）） 的初边值问题,在一定条件下得到了解的存在性,且解在有限时刻Ｔ 爆破,给出了Ｔ 的上界     

对Josephson效应I-V特性的理论研究

用RSJ模型的概率分布函数研究了热涨落对Josephson效应的影响 ,得到了热涨落存在时Josephson结的电流 -电压特性 ,其结果与其它方法得到的结果以及实验结果都是一致的     

有限域上的一类方程组

给出了有限域Fq 上一类方程组∑ski =1 akix1d(k)i1 ……xnd(k)in =bk ,k =1,… ,m的解数公式及其求解方法 ,这里di1(k) ,… ,din(k) >0 ,aki∈Fq ,bk∈Fq,k =1,… ,m ,i=1,… ,sk.     

关于一维波动方程的特征线方法

完整地用特征线法将一维非齐次波动方程始值问题解出来     

关于幂数与完全方幂的Ribenboim问题

本文证明了 :存在无限多个幂数 k,可使 k-1是完全方幂     

白环柄菇子实体的培养及其数量性状的研究

白环柄菇是最新驯化栽培成功的一种新型食用菌和观赏菌。选用棉籽壳、草粉、牛粪粉、麸皮为栽培的培养料进行了 2 8个配方试验 ,结果表明 ,适宜白环柄菇子实体生长的原料为以适当比例配合的草粉、牛粪粉和麸皮。同时分析了子实体产量与培养料的含氮量、子实体干重与菌柄长度、菌柄生长长度与时间的动态关系。白环柄菇饲喂小白兔无毒     

Estimating the Nitrous Oxide Emission Rate from the Soil Surface by Means of a Diffusion Model

Soil cover methods are probably the most widely used methods for measuring the nitrous oxide emission rate from the soil surface. The methodology involves estimation of the emission rate from repeated measurements of the nitrous oxide concentration beneath a soil cover. Based on a deterministic model proposed by Hutchinson & Mosier (1981) we propose to use a diffusion process as a stochastic model for the evolution of the nitrous oxide concentrations beneath a soil cover. From this model we derive methods for statistical inference about the emission rate that significantly extend the method proposed by Hutchinson & Mosier (1981). In particular, the derived methods provide solutions to important problems with the method proposed by Hutchinson & Mosier (1981).     

Expected estimating equations to accommodate covariate measurement error

Estimating equations which are not necessarily likelihood-based score equations are becoming increasingly popular for estimating regression model parameters. This paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects, but surrogate or mismeasured covariates are available instead. The method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data. We propose to base estimation on the expectation of the complete data estimating equation conditioned on available data. The regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations. The expected estimating equation (EEE) estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data. A pseudo-EEE estimator, which requires less computation, is also investigated. Asymptotic distribution theory is derived. Small sample simulations are conducted when the error process is an order 1 autoregressive model. Regression calibration is extended to this setting and compared with the EEE approach. We demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity.