网络舆情的分数阶精细化建模与应用

[研究目的]在网络舆情从定性研究向定量研究的过渡过程中,精细化的数学建模对于揭示舆情传播规律、舆情趋势预测以及舆情科学管控等问题都具有重要的理论与实际意义。[研究方法]分数阶微积分学框架下,针对网络舆情系统构建可充分融和历史信息影响因素的分数阶微分方程模型,并借助分数阶导数的定义给出数学模型参数拟合方法,进而实现网络舆情系统更为精细的数学建模。[研究结论]以一类实际网络舆情事件为范例,通过分数阶数学模型的建立与基于数据的模型参数拟合,展示了基于分数阶微分方程建模方法的先进性与准确性,进一步降低了网络舆情系统整数阶数学建模方法的保守性。     

三种途径获取至关重要的“弧微分”

第一种途径是自创的,仅按极限的定义并结合使用两点间的距离公式和拉格朗日中值定理就可获得弧微分计算公式;第二种途径是经典的,需要用到定积分定义、变上限函数等等;第三种途径是高职高专教材编写者常用的,它需要先默认弦长与弧长之比的极限为1;为了按顺序编写教材,第一种途径最宜。     

Application of Think Aloud Protocols for Examining and Confirming Sources of Differential Item Functioning Identified by Expert Reviews

This paper demonstrates and discusses the use of think aloud protocols (TAPs) as an approach for examining and confirming sources of differential item functioning (DIF). The TAPs are used to investigate to what extent surface characteristics of the items that are identified by expert reviews as sources of DIF are supported by empirical evidence from examinee thinking processes in the English and French versions of a Canadian national assessment. In this research, the TAPs confirmed sources of DIF identified by expert reviews for 10 out of 20 DIF items. The moderate agreement between TAPs and expert reviews indicates that evidence from expert reviews cannot be considered sufficient in deciding whether DIF items are biased and such judgments need to include evidence from examinee thinking processes.     

具有多个偏差变元的Lienard型P—Laplacian泛函微分方程的周期解

利用重合度理论中的延拓定理和不等式分析技巧，获得了一类具有多个偏差变元的Lienard型P—Laplacian泛函微分方程的周期解存在性的新的充分条件，推广和改进了已有文献的相关结果．     

Laplace Transforms Without Integration

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.     

硅酸盐-盐（硫酸盐）流体不混溶：蒙古南部Mushugai-Khuduk含火成碳酸岩杂岩体矿物中的熔体包裹体研究

Crystalline and melt inclusions were studied in garnet, diopside, potassium feldspar, and sphene from the garnet syenite porphyry of the carbonatite-bearing complex Mushugai-Khuduk, southern Mongolia. Phlogopite, clinopyroxene, albite, potassium feldspar, sphene, wollastonite, magnetite, Ca and Sr sulfates, fluorite, and apatite were identified among the crystalline inclusions. The melt inclusions were homogenized at 1010℃～1080℃ and analyzed on an electron microprobe. Silicate, salt, and combined silicate-salt melt inclusions were found. Silicate melts show considerable variations in SiO2 concentration （56 to 66wt% ）, high Na2O ＋ K20 （up to 17wt% ）, and elevated Zr, F, and Cl contents. In terms of bulk rock chemistry, the silicate melts are alkali syenites. During thermometric experiments, salt melt inclusions quenched into homogeneous glasses of predominantly sulfate compositions containing no more than 1.3wt% SiO2. These melts are enriched in alkalis, Ba, Sr, P, F, and Cl. The investigation of the silicate and salt melt inclusions in minerals of the garnet syenite porphyries indicate that these rocks were formed under influence of the processes of crystallization differentiation and magma separation into immiscible silicate and salt （sulfate）liquids.     

亚纯函数与其微分多项式的值分布

通过研究亚纯函数的Nevanlinna值分布理论问题,并结合亚纯函数的小函数,及其微分单项式和微分多项式,得到一比较有趣的关于亚纯函数的计数函数密指量和微分多项式的不等式,此不等式改进了Fang,Yang及I Lahiri和S.Dewan等学者的结果。     

罗尔中值定理在高等数学竞赛题中的运用

结合江苏省高等数学竞赛题探讨中值问题中等式的证明,从罗尔中值定理的结构分析、求导法则的熟练使用以及辅助函数构造的对比分析三个角度出发,分析了罗尔中值定理在微分中介值问题证明中的运用.     

一类PDE曲面的动态变形设计及应用

研究了一类偏微分方程(PDE)曲面的动态变形方法.将模型的特征线用动力学四阶偏微分方程来描述,特征线发生改变后,通过采用PDE方法来重构出变形后的曲面模型,则曲面的变形即可相应地由特征线的变形得到.该方法只需要对PDE的几个参数进行调整就可以控制曲面的变形,简单易操作.所得的曲面变形效果自然连贯,在艺术曲面造型设计中具...     

双扰动型无穷时滞微分方程适度解的存在性

本文主要研究实Banach空间中一类双扰动的无穷时滞微分方程．通过综合利用Hausdorff非紧性测度理论、线性算子半群理论和不动点理论,我们给出了当相关半群失去紧性时,一个扰动函数满足Lipschitz条件,另一个扰动函数满足与非紧测度有关的条件等较弱的条件下,Banach空间中双扰动的无穷时滞微分方程的适度解存在的充分条件．