汽车行驶的时间问题

就d>2R的情形解决如下组合几何极值问题:某平原地区有一个很大的湖泊.湖泊周围有两个村庄A,B.村庄A到村庄B的直线距离为已知.一辆汽车从A村庄出发以已知匀速速度驶向村B庄.问:若这辆汽车以最短路径行驶到达B村庄至多需要多少时间?     

确界原理的一个修正证明

分析了华东师大版《数学分析》（第四版）教材中关于确界原理证明的不足之处,给出更为细致的修正证明.     

同分布两两NQD列的最大值不等式及其应用

设{xn，n≥1}是同分布的两两NQD列，记Sn=∑i=1Xi^n．本文讨论了max ｜Si｜/i（n≥1）的分布函数的上下界．作为应用，获得了随机变量supn≥｜Sn｜/n型的1阶矩及p（〉1）阶矩分别存在有限的充分必要条件，这是一个与独立同分布场合相一致的结果．     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

On the limit law of a random walk conditioned to reach a high level

We consider a random walk with a negative drift and with a jump distribution which under Cramér’s change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1.     

广义FGM Copula的一个判定定理及应用

研究了形如C_θ(u,v)=uv θu~av~b(1-u~m)~c(1-v~n)~d的一种新型广义FGM copula中参数θ的精确取值范围．所研究的copula含盖了文献中许多特殊类型的FGM copula,具有广泛的代表性．参数θ的计算方法简单易行,改进并完善了文献中相应的结论．     

常平均曲率超曲面的Ricci曲率

研究单位球面S^n 1中具有常平均曲率H的超曲面M^n，得到supRic≥2。并具体给出了当n≥3时。supRic=n-2可能出现的情况。     

Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

一类随机游动上确界的密度的渐近性

Kluppelberg^[1], Asmussen 等^[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等^[3], 程东亚和王岳宝^[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质.