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双语推荐：幂律

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针对传统GM(1,1)幂模型不具备幂指数律重合性的问题,分别从灰导数和背景值两个方面改进GM(1,1)幂模型的灰色微分方程,提出了两种具有幂指数律重合性的GM(1,1)幂模型并从理论上加以证明.通过变换将两个具有幂指数律的灰色微分方程转化成完全一致的形式,在此基础上进行参数估计.数值模拟和应用实例表明,具有幂指数律重合性的GM(1,1)幂模型能够有效地提高模型的模拟和预测精度.
As the traditional GM(1,1) model does not have the property of exponential law coincidence, this paper improves the grey differential equation of GM(1,1) model from grey derivative and background value respectively. Two kinds of GM(1,1) power model with power exponential law coincidence are proposed and relevant theoretical proofs are also given. Two grey differential equations with power exponential law coincidence are transformed into exactly the same form, based on which parameters can be effectively estimated. Numerical simulation and application examples show that the simulation and prediction accuracy of GM(1,1) power model is effectively enhanced by using the proposed method.

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对滑坡、崩塌和不稳定斜坡等地质灾害规模参数幂律相依性进行定量研究，拓展了规模参数之间幂律相依性的研究范围。研究结果发现：①地质灾害规模参数的幂律相依性不仅存在于体积与面积之间，而且存在于面积与长、面积与宽等参数之间；②幂指数可以作为间接反映区域地质灾害或者不同类型地质灾害的宏观特征表征谱；③体积与面积关系式的幂指数分布为不稳定斜坡>滑坡>崩塌；面积与长关系式的幂指数分布为崩塌>滑坡>不稳定斜坡。面积与宽关系式的幂指数的分布为滑坡>崩塌>不稳定斜坡。
Landslides are significant natural hazards in many areas of the world.they often resulting in both hu-man and material losses.A number of authors have argued that the power law is the symbol of self-organized critical state.Many empirical observations have shown that landslides caused by various triggers,including earthquakes,rainfall and rapid snowmelt,and are influenced by multiple factors,such as local and regional mor-phological and topography,soil and lithological setting,fractures and bedding planes and moisture content obey power law statistics.In this paper,we first collect information witch include volume,area,length,width,depth in a dababase of landslides,collapses and unstable slope. Based on the geological hazards, such as landslides, col-lapses and unstable slope, the power-law dependence was quantitative researched, explore the power law rela-tionship between the scale parameter for the first time in domestic, and the research scope of scale parameter between po

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为了揭示科研人员网络文献采纳行为及相关变量概率分布的幂律渐近行为,选取了中文社会科学引文索引CSSCI(1998-2009年)情报学和图书馆学期刊发表文献中引证的网络文献作为数据样本,结果表明网络文献采纳行为存在集中现象,且与加菲尔德提出的文献引用集中定律较为一致;同时运用KS统计量和极大似然估计拟合幂律分布xmin值和a指数进行幂律分布检验,并通过非参数Bootstrap方法估计出xmin不确定性,其结果证明网络文献采纳频次服从幂律分布。
This paper is to examine the behaviors of web-based resources citation and Power-law of probability for researchers. Using Web-based resources cited by published papers of Information Science and Library Science extracted from Chinese Social Science Index as data sample, this paper applied Kolmogorov-Smirnov ( KS) and maximum likelihood estimation to calculate xmin andafor Power-law test of cited frequency, and used Bootstrap to estimate uncertainty of xmin . The results demonstrate that there exists the phenomenon of concentration of web-based resources adoption, the laws of adoption are more consistent with Garfield''s Law of Concentration and Power-law distribution.

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以剪切应力符合Ostwald-de Waele关系式的幂律非牛顿流体为研究对象.针对幂律非牛顿流体的表观黏度随剪切速率变化且计算过程有别于牛顿流体的问题,运用基元中心法对非线性粘性系数进行离散.采用有限体积法对幂律非牛顿流体在偏心圆环管中的充分发展层流流动和传热进行数值计算.计算结果表明流体的幂律因子对流动的影响较大,但对传热的影响受到到偏心率的影响.流道偏心会引起圆环通道内速度和温度的周向分布不均匀,且偏心程度越严重,周向分布不均匀性越强烈.
This paper studies power-law non-Newtonian fluid where the shearing stress accords with the Ostwald-de Waele relational formula.It aims to solve the problem of the apparent viscosity changing with the shearing rates and the calculation which is different from Newtonian fluid.Cell-based central method is used for the non-linear viscosity coefficient discretization.It adopts FVM for flow and heat transfer numerical simulation of fully developed laminar in eccentric annular channel.The calculation results show that the power-law factor has a great impact on the fluid flow,but the impact on the heat transfer is influenced by the eccentricity .The eccentric-ity of annular channel can lead to the asymmetrical distribution of circumferential temperature and velocity.

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网络是一个包含了大量个体及个体之间相互作用的系统，近年来在对复杂网络的研究过程中，科学家们发现了众多的幂律分布现象。不仅网页的点击次数存在幂律分布现象，微博也同样存在着幂律分布现象。利用新浪微博的API技术抓取了新浪微博数据，对其进行了详细的数据清理和统计，对统计结果进行分析发现，新浪微博的转发数也同样存在着幂律分布现象。只有为数不多的微博，才能被大量的阅读和转发，进而成为热点微博，而绝大多数微博的阅读次数和转发次数都是非常少的。
Network contains a large number of interaction between the individual and the individual system.In recent years, the scientists find a large number of power-law distribution phenomenon in the research of complex networks. The power-law distribution phenomenon exists not only in the page clicks, but also in the number of micro- blog access. In this paper, we use API technology of Sina micro-blog to capture the recent micro-blog data, make the data cleaning and statistic , by analysing the final statistical results,we find that the phenomenon of power-law distribution also exists in the number of forwards in Sina micro-blog. Only a few micro-blog, can be a hot micro-blog which has a large number of reading and forwarding,in contrast the vast majority of others have very few number of reading and forwarding.

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为了解决数控机床最小维修的可靠性评估问题,提出了基于幂律过程的可靠性评估方法,建立了基于幂律过程的故障数据模型。对故障数据进行趋势检验和更新过程检验,验证了幂律过程应用的前提条件成立。提出CBT与CLT的分步检验方法对评估涉及的多台机床的同质性进行了验证。用极大似然估计法和Fisher信息矩阵法给出了模型参数的点估计与区间估计,并给出了机床可靠性指标的点估计和基于Delta法的区间估计。应用Cramér-von Mises法对模型进行拟合优度检验。实例分析表明:幂律过程能够反映出数控机床的瞬时与累积可靠性特性,提出的CBTCLT分步检验方法能够有效地对多台机床同质性做出判断,得到的结果更符合实际。
An approach of assessing reliability for multiple NC machine tools with minimal repair based on power law process (PLP)was proposed,and a PLP function for failure times was built. Trend test and renewal test were performed on the failure data to assure the application of power law process was valid. CBT (common beta test)and CLT (common lambda test)two-step-test was de-veloped to check the homogeneity of multiple machines in assessing. Point and confidence interval estimators were given by maximum likelihood method and Fish information matrix. Point estimates of reliability indexes were also derived with their confidence bounds of-fered through Delta method. The Cramér-von Mises method was finally adopted to do the goodness-fit-test. Real example analysis dem-onstrates that PLP can give both instantaneous and cumulative reliability properties for NC machine tools,CBT&CLT test is capable to verify the homogeneity of multiple machines adequately,hence the results are more practical.

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云核质量函数(CMF)是分子云中致密云核的一个基本观测性质,被用来研究恒星的初始质量函数(IMF)的成因。CMF可以用积分和微分两种形式来表达。样本较小时,积分形式的CMF拟合出的结果能够清晰地反映出云核的数目;样本较大时,微分形式的CMF可以合并数据明确地表述CMF。一般来说,CMF有幂律和正态对数两种函数形式。在湍流存在的情况下,正态对数函数可以更好地拟合CMF;幂律形式的CMF谱指数在一定范围内波动,其大小与天区和样本有关。Salpeter提出恒星的初始质量函数(IMF)是一个幂律函数,很多研究认为CMF与IMF是相似的。而近期的一些研究工作认为CMF与IMF是不相同的,这主要有三方面的原因:(1)用一个具体的幂律函数去拟合一个任意的积分函数是不可靠的;(2)只有当M Mmax(或者Mmax-→∞)时,积分形式的CMF可以近似地认为是幂律形式的;(3)采用Monte Carlo方法拟合CMF能够增加拟合结果的可信度。
Star formation is a fundamental field in astrophysics, within which the core mass function (CMF) of molecular clouds is a hot topic. Different models of molecular core evolution predicted different CMFs. Comparing CMF with stellar initial mass function (IMF) would help reveal the origin of stellar mass and the conversion rate between cloud cores and stars. In this review, we describe two expressions of CMFs, namely, differential CMF and cumulative CMF. When the sample size is small, cumulative CMF can clearly reflect the number of cloud cores. When the sample size is big, differential CMF is a straightforward representation based on binning the data. We research and read most of the highly cited papers published before 2013 that are related with CMF. Based on these studies, we found that two function forms of CMF, namely, power law CMF and log-normal CMF, are widely used. Fitting a log-normal function to CMF produces a better result for cores under the influence of turbulence. The CMF

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分析研究了Twitter与YouTube两个在线社会网络的结构。用k-shell（k-壳）分解法对网络分解，并对比分析了它们的入（出）度、入（出）k-shell、以及度与k-shell之间的关系，发现它们之间有较大的差异。YouTube的入（出）度、入（出）k-shell分布均服从幂律分布，而Twitter的分布服从漂移幂律分布、指数截断的幂律分布，但它们的度与k-shell关系基本相同，都未表现出较强的相关性。此外，根据度相关系数的定义还提出k-shell相关性的定义及其计算方法，并用来刻画网络k-shell之间的同（异）配性。
This paper presented a large-scale measurement study and analysis of the structure of two online social net-works———Twitter and YouTube.They were decomposed by k-shell decomposition method,then with the analysis and compari-son of their in (out)-degree distributions,in (out)-k-shell distributions and the relationships between the degree and k-shell, it shows that there is some significant difference between the two networks.The in(out)-degree distribution,in (out)-k-shell distribution of YouTube both obey power law distribution,however Twitter’s obey shifted power law distribution and power law with exponential cutoff respectively.But the relationships between their degree and k-shell were similar,both show no strong correlation.Furthermore,according to the definition of degree correlation coefficient,this paper also put forward the definition of k-shell correlation to characterize the assortativity (disassortativity)between k-shells.

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针对连续非线性系统,采用一种基于幂次趋近律的单向辅助面滑模控制方法。首先依据给定的连续非线性系统,设计单向辅助面滑模控制器,并在此基础上,引入了幂次趋近律,设计基于幂次趋近律的单向辅助面滑模控制器,且给出稳定性和有限时间收敛的理论证明。该方法能够确保系统状态在切换面附近的趋近速度,即当且仅当系统状态位于原点处时趋近律为零,较好地削弱了系统抖振。最后,通过实验仿真,验证了该方法的有效性。
The sliding mode control with unidirectional auxiliary surfaces (UAS-SMC) based on the power reaching law was used for a class of nonlinear continuous systems .According to the nonlinear continuous system,a UAS-SMC was designed.On which basis,the power reaching law was introduced,and a UAS-SMC based on power reaching law was developed .Then,theoretical analysis proved that the system states will converge on the switching surfaces in a finite time and it is stable .The simulation results show that the chattering can be effectively reduced,and the method ensures the reaching speed near the switching surfaces .The reaching law is zero if and only if the system states are zero .

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针对BBV等传统加权网络模型生成的网络聚类系数较小、簇度幂律特征偏弱等不足，提出了一个变聚类系数加权网络模型，其中新节点的加入根据节点强度和初始吸引度共同驱动的优先连接机制或三角连接机制与网络中的旧节点建立连接。仿真表明，当初始吸引度和三角连接概率取不同值时，生成网络的度、强度和边权都服从幂律分布，并且聚类系数可调，特别是随着三角连接概率的变大，簇度之间的幂律特征更加明显。最后构建了基于加权网络的级联故障模型，分析了权重因素、聚类系数等对网络级联抗毁性的影响。
Aiming at the shortage of traditional weighted network models such as BBV model that exhibit low clustering coefficient and weak clustering-degree relation,an evolving model for weighted network with tun-able clustering coefficient is proposed.In this model,the newly added node chooses the existing nodes to estab-lish new edges according to preferential attachment scheme or triangle connection scheme,which is driven by node strength and initial attractiveness.Simulation results show that node degree,node strength and edge weight of the produced networks all obey the power-law distributions as initial attractiveness and triangle con-necting probability get different values,and its clustering coefficient is tunable with these two parameters,espe-cially,the relation between the average of clustering coefficient and degree exhibits better power-law relation when the triangle connecting probability gets larger values.Finally,a cascading failure model for weighted net-works is esta

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