论文标题
影响信息及以后的影响
Impact in informetrics and beyond
论文作者
论文摘要
影响的概念是信息术中最重要的概念之一。它在这里进行了数学研究。我们首先修复了一个主题，我们希望找到一个有影响力的对象，例如作者或期刊及其生产，例如发表引用的出版物。然后说这些物体具有一定程度的影响。我们在三个级别上工作。在第一级上，我们需要对这些对象的度量，以其等级频率函数为代表，描述每个源的项目数（以项目数量的减少顺序排名）：一个影响度量。这些措施集中在最有生产力的来源的生产上。 H索引是一个例子。在第二篇论文中，我们研究了基于代表这些对象的源范围频率函数的这些左侧的影响度量的形式定义。第二层的影响调查使用的是影响捆绑包（或滑轮），如论文III所示。作为例证，我们提到函数z的h索引定义为x，z（x）= x，即，z图与线y = x的图表的横坐标。 H-束的定义是相同的，但是现在Y = X线被越来越多的线所取代：y = $θ$ .x，$θ$> 0。因此，我们有一系列的影响度量，可以更强大地衡量对象z的影响。影响Z的影响件在论文III中是表征的。第三级的影响研究涉及洛伦兹曲线的非归一化形式。在论文IV和V中，我们研究了全球影响度量，作为尊重代表对象的等级频率函数之间非归一化的洛伦兹的措施。我们说，如果在非归一化的洛伦兹阶的意义上，如果y比y小于z，则对象z具有更大的影响。这是影响治疗的最高水平：概念本身的数学定义。
The concept of impact is one of the most important concepts in informetrics. It is here studied mathematically. We first fix a topic for which we want to find influential objects such as authors or journals, and their production, such as publications generating citations. These objects are then said to have a certain degree of impact. We work on three levels. On the first level, we need a measure for these objects, represented by their rank-frequency function, describing the number of items per source (ranked in decreasing order of the number of items): an impact measure. These measures focus on the production of the most productive sources. The h-index is one example. In paper II we study a formal definition of impact measures based on these left-hand sides of the source-item rank-frequency functions representing these objects. The second level of impact investigation is using impact bundles (or sheaves) as in paper III. As an illustration, we mention that the h-index of a function Z is defined as x for which Z(x) = x, i.e., the abscissa of the intersection of the graph of Z with the line y = x. The h-bundle is defined in the same way but now the line y = x is replaced by an increasing line through the origin: y = $θ$.x, $θ$ > 0. So, we have a bundle of impact measures which is more powerful to measure the impact of an object Z. Impact bundles are characterized in paper III. A third level of impact investigations involves the non-normalized form of the Lorenz curve. In papers IV and V we study global impact measures as measures that respect the non-normalized Lorenz order between the rank-frequency functions representing objects Z. We say that object Z has more impact than object Y if Y is smaller than Z in the sense of the non-normalized Lorenz order. This is the highest level of impact treatment: a mathematical definition of the concept itself.
