應(yīng)用數(shù)學(xué)漫談

1、應(yīng)用數(shù)學(xué)漫談,現(xiàn)代數(shù)學(xué)的發(fā)展模式,數(shù)學(xué),數(shù)學(xué)技術(shù),數(shù)學(xué)產(chǎn)業(yè)化,,,數(shù)學(xué)在自然科學(xué)和社會(huì)科學(xué)中有著不可思議的有效性,核工業(yè)C-T掃描儀人造地球衛(wèi)星等等,典型例子,,這些都是從數(shù)學(xué)技術(shù)走向工業(yè)化的標(biāo)準(zhǔn)例子,Google搜索與Inter網(wǎng)的信息檢索,數(shù)學(xué)建模的經(jīng)典案例,,,約有307,000 項(xiàng)符合南陽(yáng)師范學(xué)院的查詢結(jié)果，以下是第1-20項(xiàng)。(搜索用時(shí) 0.10秒）,How can google make a ranking of 3

2、07,000 pages in 0.10 seconds?,A main task of Internet (Web) Information Retrieval = Design and Analysis of Search Engine (SE) Algorithm,involving plenty of mathematics,,,? HITS,? PageRank,1998 Jon Kleinberg

3、 Cornell University,Sergey Brin and Larry Page Stanford University,,Nevanlinna Prize（2006)Jon Kleinberg,One of Kleinberg’s most important researchach

4、ievements focuses on the internetwork structure of the World Wide Web. Prior to　Kleinberg‘s work, search engines focused only on the content of web pages，not on the link structure.Kleinberg introduced the idea of “au

5、thorities” and “hubs”: An authority is a web page that contains　information on a particular topic, and a hub is a page that contains links to　many authorities.,Page Rank, the ranking system used by the Google search en

6、gine.,Query independent content independent. using only the web graph structure,The example of web graph structure,,Page Rank, the ranking system used by the Google search engine.,,這恰好可以看成一個(gè)網(wǎng)絡(luò)點(diǎn)擊瀏覽過(guò)程,,,PageRank as a Fun

7、ction of the Damping FactorPaolo Boldi Massimo Santini Sebastiano VignaDSI, Università degli Studi di Milano,WWW 2005 paper,3.1 Choosing the damping factor,3 General Behaviour,3.2 Getting close to 1,can we someh

8、ow characterise the properties of ? what makes different from the other (infinitely many, if P is reducible) limit distributions of P?,is the limit distribution of P when the starting distribution is unif