Temporal bibliographic networks

We present two ways (instantaneous and cumulative) to transform bibliographic networks, using the works’ publication year, into corresponding temporal networks based on temporal quantities. We also show how to use the addition of temporal quantities to define interesting temporal properties of nodes, links and their groups thus providing an insight into evolution of bibliographic networks. Using the multiplication of temporal networks we obtain different derived temporal networks providing us with new views on studied networks. The proposed approach is illustrated with examples from the collection of bibliographic networks on peer review.     

图的Fractional边控制与Fractional边全控制

设G=(V,E)是一个图,一个函数f:E→[0,1]如果对所有的边e∈E(G),都有∑e∈N(e’)f(e)≥1成立,则称f为图G的一个Fractional边全控制函数,简记为F边全控制函数,此处N(e’)表示G中与边e’相关联的边集。图G的F边全控制数定义为γ’tf(G)=min{∑e∈E(G)f(e)f是G的一个F边全控制函数}.本文得到了一般图的F边全控制数的若干界限,还确定了一些特殊图的F边全控制数。     

关于分数阶导数定义的商榷

导数的概念最早是由莱布尼茨引入的,记作dn y dx n 。当函数导数次数不是整数而是分数时,即为分数阶导数dαy dxα蓸0<α<1蔀。本文利用数学归纳法推导出分数阶导数的两种公式,即所谓的分数阶导数Riemann-liouville(R-L)“定义”、和Caputo“定义”。但他们都是从分数阶导数dαy dxα蓸0<α<1蔀出发推导得到,并且互为等价,所以只是表达形式不同,含义相同。以此类推,或许存在其他的所谓的“定义”也是从dαy dxα蓸0<α<1蔀出发获得,因而他们也只是分数阶导数不同的计算公式,而非定义。因此,分数阶导数的定义应是dαy dxα蓸0<α<1蔀,而所谓的Riemann-liouville(R-L)“定义”、和Caputo“定义”只能称作是分数阶导数的两种不同的计算公式。这是本文商榷的问题。     

分数阶微分方程初值问题解的存在性

利用Leray-Schauder度理论,证明了Caputo和Remann-Liouville分数阶微分方程初值问题解的存在性。     

分数跳－扩散模型的标准回望期权定价

文章以看涨期权为例探讨了分数跳－扩散模型的标准回望期权定价问题,其中 H∈（12,1）,并给出了定价公式。     

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.     

Two direct Tustin discretization methods for fractional-order differentiator/integrator

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given.     

Measuring scientific contributions with modified fractional counting

We develop and propose a new counting method at the aggregate level for contributions to scientific publications called modified fractional counting (MFC). We show that, compared to traditional complete-normalized fractional counting, it eliminates the extreme differences in contributions over time that otherwise occur between scientists that mainly publish alone or in small groups and those that publish with large groups of co-authors. As an extra benefit we find that scientists in different areas of research turn out to have comparable average contributions to scientific articles. We test the method on scientists at Norway’s largest universities and find that, at an aggregate level, it indeed supports comparability across different co-authorship practices as well as between areas of research. MFC is thereby useful whenever the research output from institutions with different research profiles are compared, as e.g., in the Leiden Ranking. Finally, as MFC is actually a family of indicators, depending on a sensitivity parameter, it can be adapted to the circumstances.     

分数阶微分方程初值问题解的存在性

利用Leray-Schauder度理论,证明了Caputo和Remann-Liouville分数阶微分方程初值问题解的存在性。     

非局部分数阶椭圆型方程在主特征值附近解的多重性

利用山路引理、Ekeland 变分原理及鞍点定理,得到了一类非局部分数阶椭圆型方程在主特征值附近解的多重性。