基于R的概率统计直观教学展示

为了提高学生对概率论与数理统计课程基本概念和定理的理解,加强知识的实际运用能力,本文利用R软件进行直观教学展示.一方面,能够使抽象的概念、定理生动和直观,展示课程魅力,有助于激发学习兴趣.另一方面利用R进行统计模拟,加强课程在不同学科、专业的实际应用,强化应用能力.     

西南地区林业产业结构分析

通过马尔科夫预测法建立了林业产业最小偏离模型,基于1998-2013年西南地区林业三次产业产值数据,求得西南地区林业产业结构的马尔科夫状态转移概率矩阵并验证其准确性,预测出2014-2023年西南地区林业三次产业产值比重.以2020年的预测值为参照标准,计算出1998-2013年西南地区林业产业结构的有序度为0.68-0.97,表明近十几年来西南地区林业产业结构调整的方向是正确的,但仍需进一步进行调整,最后提出西南地区林业产业结构优化升级对策.     

B值随机元阵列加权和的收敛性与大数定律

令｛Ｘｎｉ，１≤ｉ≤ｋｎ↑∞，ｎ≥１｝为Ｂ值随机元阵列，｛ａｎｉ，１≤ｉ≤ｋｎ，ｎ≥１｝为实数阵列．讨论加权和Ｓｎ＝ｋｎｉ＝１ａｎｉＸｎｉ，ｎ≥１的收敛性．在条件ｓｕｐｎ，ｉＰ（Ｘｎｉ＞ｘ）＝０（ｘ－ｒ）下给出了一些收敛性结果（１≤ｒ＜ｐ≤２），同时用这种收敛性刻划了Ｂａｎａｃｈ空间的ｐ型性质     

集合交集元素和的保密计算

安全多方计算作为密码学的重要分支,长期以来主要致力于解决两方或多方参与者隐私数据的联合计算.集合交集元素和的隐私计算作为安全多方计算中的科学计算问题,在保密计算广告转化率中具有重要作用.我们利用保密替换和加密选择求集合的交集,结合Lifted ElGamal加密算法,研究了不同限制下（数据范围较小和数据范围较大）集合交集元素和多方保密计算.本文方案解决两方计算时,Bob只需从Alice发送的数据中选择数据,避免了复杂的模指数运算,且双方不需多次交互,降低了计算成本和通信次数.多方参与计算时,根据加密选择和保密替换的性质,得到集合交集的密文,然后在密文上计算得到集合交集元素的和.通过理论分析和实验证明,本文协议是高效的.最后利用模拟范例证明本文协议是安全的.     

一种基于谱相关性的概率松弛匹配算法

为了可靠实现点模式匹配,提出了一种基于谱相关性的概率松弛匹配算法。先根据待匹配点集的形状上下文计算初始匹配概率,然后由待匹配点集构造亲近矩阵并进行奇异值分解,将得到的谱的相关性作为初始支持度。最后利用概率松弛迭代方法实现两个点集之间的匹配。实验结果表明该算法匹配精度较高。     

Explanation of Theoretical Mechanism of Isomerization of L-Alanine Conformation for Experimental Results

B3LYP/6-31＋＋G＊＊ method was applied to investigate the mechanism of alanine isomerization.12 minima and 22 transition states were obtained after optimization and several paths of isomerization were found.It is found that intramolecular single-bond rotation and proton transfer might lead to isomerization.The energy barrier of C–N bond rotation was lower than 2.52 kcal·mol 1,while the energy barrier ranges of the rotation of C–C and C–O were separately 0.43~ 7.01 and 4.69~12.19 kcal·mol 1,and the minimum energy barrier of proton transfer was 30.76 kcal·mol 1.The most probable isomerization path and mechanism for the two most stable conformations was discussed to find that the highest energy barrier to be crossed in this path was 11.87 kcal·mol 1.In order to understand the microscopic nature why only 4 conformations were detected in the experiment,thermodynamic properties of all conformations at the experimental temperature of 391 K was calculated.It is found that conformations XII,XI,X and IX can only unidirectionally convert into conformations rapidly with low energy and vanish immediately.The other conformations were distributed according to Maxwell-Boltzman＇s law,and the distribution probabilities of conformations I,II,III,IV,V,VI,VII and VIII were respectively 27.2%,26.5%,25.8%,6.4%,5.2%,4.8%,2.5% and 1.6%.Conformations I,II and III with bigger probability and stronger absorption peak were easy to detect in the experiment.Conformation IV had a relatively smaller probability（6.4%） and weak absorption peak which,however,could also be identified.The other conformations had too small probability to identify in the spectrum.     

浅析几类双输入排队系统模型

从矩阵几何解的角度出发,分析了七种类型的Geom/Geom/(Geom/Geom)/H 双输入排队系统.对这几个模型进行了描述,使用拟生灭过程探讨了各类模型的矩阵结构,并给出了其状态转移概率矩阵.     

上概率下的Chebyshev大数定律

讨论了非可加概率ω(·)和非可加期望E[·]的某些性质,并由上期望下随机变量的独立性概念,给出了上概率下的Chebyshev大数定律,它是经典概率论中Chebyshev大数定律在非可加概率下的推广.