Properties of G-martingales with finite variation and the application to G-Sobolev spaces

As is known, if $B={\left(B_t\right)}_{t\in [0,T]}$ is a $G$-Brownian motion, a process of form ${\int }_0^t{\eta }_{s}d{〈B〉}_s?{\int }_0^{t}2G\left({\eta }_s\right)ds$, $\eta \in M_G^1(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale cannot be form of ${\int }_0^t{\eta }_{s}ds$ or ${\int }_0^t{\gamma }_{s}d{〈B〉}_s$, $\eta ,\gamma \in M_G^1(0,T)$, which implies that the decomposition for generalized $G$-Itô processes is unique: For arbitrary $\zeta \in H_G^1(0,T)$, $\eta \in M_G^1(0,T)$ and non-increasing $G$-martingales $K,L$, if ${\int }_0^t{\zeta }_{s}d{B}_s+{\int }_0^t{\eta }_{s}ds+K_t=L_t,t\in [0,T],$then we have $\eta \equiv 0$, $\zeta \equiv 0$ and$K_t=L_t$. As an application, we give a characterization to the $G$-Sobolev spaces introduced in Peng and Song (2015).     

汉字识别的加工模型

通过文献分析,概述了认知心理学关于汉字识别过程及其加工机制研究的几种主要的加工模型,即经成分识别模型、多层次交互激活模型、连接主义模型、合体汉字字形识别模型和汉字识别的多层次格式塔双向加工模型.     

基于景气指数的我国工业经济周期性波动特征及本轮波动特点研究

通过多方面收集与我国工业部门经济运行相关的月度经济指标,利用时差相关分析等方法从中筛选出我国工业经济运行的先行、一致和滞后指标,并利用国际上先进的合成指数方法构建了我国工业部门的景气指数,根据其波动态势具体分析了我国工业经济的周期性波动特征,并结合主要经济指标的变动对我国工业部门的本轮景气波动特点进行了具体分析。结果表明2000年以来我国工业经济共经历了三次完整地景气循环,现正处于第四次循环的下降期。其中第一轮循环属于典型的长扩张型周期,并且呈现明显的非对称性周期特征,第二轮循环属于典型的震荡型周期,且收缩幅度和扩张幅度明显缩小,受金融危机影响第三轮景气循环的谷底较深,但随后我国工业景气呈现强劲上升态势,目前工业景气指数处于下降期.     

Covering partially directed graphs with directed paths

We consider graphs which contain both directed and undirected edges (partially directed graphs). We show that the problem of covering the edges of such graphs with a minimum number of edge-disjoint directed paths respecting the orientations of the directed edges is polynomially solvable. We exhibit a good characterization for this problem in the form of a min-max theorem. We introduce a more general problem including weights on possible orientations of the undirected edges. We show that this more general weighted formulation is equivalent to the weighted bipartite b-factor problem. This implies the existence of a strongly polynomial algorithm for this weighted generalization of Euler's problem to partially directed graphs (compare this with the negative results for the mixed Chinese postman problem). We also provide a compact linear programming formulation for the weighted generalization that we propose.     

Modeling of mixed liquor inorganic suspended solids and membrane flux at different ratio of SRT to HRT in a submerged membrane bioreactor

In order to investigate the influence of mixed liquor inorganic suspended solids (MLISS) on membrane flux at different ratio of sludge retention time (SRT) to hydraulic retention time (HRT) in a submerged membrane bioreactor (SMBR), a pilot scale test was conducted for 452 days using traditional Chinese medicine (TCM) wastewater as influent. SRT/HRT was controlled at 150, 480 and 750, respectively. The experimental results showed that the average values of MLISS were 1271.9, 1664.5 and 6898.8 mg/L at different SRT/HRT, respectively; MLISS were accumulated from 265.5 g/h to 4912.93 g/h, which indicated that SMBR could not steadily operate for a long period without sludge withdrawal. Sludge oxygen utilized rate (SOUR) decreased from 5.115 to 1.292 mgO₂/(gVSS h) and volume oxygen utilized rate (VOUR) increased from 10.84 to 18.13 mgO₂/(L h). Model of membrane flux and MLISS were developed under different temperature and operational pressure by regressions, which were then satisfactorily employed to predict the trend of membrane flux during the experiment.     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

基于Bootstrap-DEA的工业能源效率分析

传统DEA方法存在小样本估计有偏、无法进行统计检验等缺点.而Bootstrap-DEA方法能够通过数值模拟技术产生大量的模拟样本,通过对新生成的样本进行估计来修正DEA效率估计偏差,进而计算出效率值的置信区间.作者利用Bootstrap-DEA方法首次对我国36个工业行业1995-2008年的能源利用效率进行分析.研究结果表明,我国工业行业的能源效率呈现出U字型变动趋势,行业间的能源效率差异不断减小.     

气候对安徽中药材产业经济影响分析——基于经济气候模型

通过考虑气候和经济社会因素,将气候因素与函数综合考虑并进行分析,构建“经济气候”模型,分析并得出气候因素对安徽省中药材产业影响程度,利用所构建BP神经网络模型,分析数据,对气象因素对中药材产业的影响结果进行预测。通过分析安徽省气候变化的特点与方向,确定气候因素对中药材产业的影响程度,为中药材产业发展提供一定的数据分析支撑,为有针对性的管理中药材产业提供方法与数据基础,同时对降低严重气象灾害对中药材生产带来的负面作用具有一定的理论与实践意义。     

Routing problems: A bibliography

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.     

On the existence of common fixed points for a pair of lipschitzian mappings in banach spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆａＢａｎａｃｈｓｐａｃｅＸ .ＴｈｅｎａｍａｐｐｉｎｇＴ :Ｋ→ＫｉｓｓａｉｄｔｏｂｅａＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇｉｆ,ｆｏｒｅａｃｈｉｎｔｅｇｅｒｎ≥ 1 ,ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｓｔａｎｔｋｎ >0ｓｕｃｈｔｈａｔ‖Ｔｎｘ-Ｔｎｙ‖ ≤ｋｎ‖ｘ-ｙ‖　ｆｏｒａｌｌｘ ,ｙ∈Ｋ .ＡＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇＴｉｓｓａｉｄｔｏｂｅｕｎｉｆｏｒｍｌｙｋ＿Ｌｉｐｓｃｈｉｔｚｉａｎｉｆｋｎ =ｋｆｏｒａｌｌｎ ≥ 1 ;ｎｏ…