据美国新闻媒体报道，美国东部时间10月14日法裔美国数学家Benoit Mandelbrot 85岁（20 November 1924 14 October 2010）在马塞诸塞州剑桥市临终医院因胰腺癌辞世。Mandelbrot是分形之父， 1982年他出版了著名的自然的分形几何著作，标志着分形几何的诞生。他在分形方面的工作成为混沌理论的基础，也是计算机数据压缩和医学图像纹理以及模拟 湍流对飞机机翼造型设计的关键。Benoit Mandelbrot 出生于波兰(父母是犹太人)，孩童时代移居法国，他大部分时间在美国生活和工作，他具有法国和美国双重国籍。 1958-1987年 Mandelbrot 一直在IBM工作，1987-2005在耶鲁大学工作，2005年退休后一直生活在麻州的剑桥市。 Benoit Mandelbrot, a mathematics pioneer and the father of the principle of fractal geometry, has died in the US at the age of 85. The fractal principle uses mathematical fromulas to attempt to understand complexity of natural world In his seminal 1982 work The Fractal Geometry of Nature, Mandelbrot argued that seemingly random patterns could in fact be the same infinitely repeated shape. He once used a cauliflower to describe the mathematical principle, pointing out that the shape of the vegetable was repeated over and over The mathematical principle has been used to measure shapes previously thought unmeasurable, including coastlines and mountains. Mandelbrot also applied the concept to economics, but he was critical of the global financial system, believing it to be too complex to properly function. Fractal geometry can be depicted in intricate and colourful computer designs which have become popular as artworks in their own right. One fractal variation was even named after Mandelbrot. The Mandelbrot Set has had a huge influence on mathematics and culture - examples have even been known to appear as crop formations. Mandelbrot的早年生活 Early years Mandelbrot was born in Warsaw into a Jewish family from Lithuania .He was born into a family with a strong academic traditionhis mother was a medical doctor and he was introduced to mathematics by two uncles, one of whom, Szolem Mandelbrojt , was a Parisian mathematician. However, his father made his living trading clothing. Anticipating the threat posed by Nazi Germany , the family fled from Poland to France in 1936 when he was 11. Mandelbrot attended the Lyce Rolin in Paris until the start of World War II , when his family moved to Tulle . He was helped by Rabbi David Feuerwerker , the Rabbi of Brive-la-Gaillarde , to continue his studies. In 1944 he returned to Paris. He studied at the Lyce du Parc in Lyon and in 1945-47 attended the cole Polytechnique , where he studied under Gaston Julia and Paul Lvy . From 1947 to 1949 he studied at California Institute of Technology , where he earned a master's degree in aeronautics .Returning to France, he obtained a PhD in Mathematical Sciences at the University of Paris in 1952. From 1949 to 1958 Mandelbrot was a staff member at the Centre National de la Recherche Scientifique . During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey , where he was sponsored by John von Neumann . In 1955 he married Aliette Kagan and moved to Geneva, Switzerland , and later to the Universit Lille Nord de France . In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York . He remained at IBM for thirty-two years, becoming an IBM Fellow , and later Fellow Emeritus . 学术生涯 Academic career From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory , economics , and fluid dynamics . He became convinced that two key themes, fat tails and self-similar structure, ran through a multitude of problems encountered in those fields. Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution , but rather Lvy stable distributions having theoretically infinite variance . He found, for example, that cotton prices followed a Lvy stable distribution with parameter equal to 1.7 rather than 2 as in a Gaussian distribution. Stable distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter . Mandelbrot also put his ideas to work in cosmology . He offered in 1974 a new explanation of Olbers' paradox (the dark night sky riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust ), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred. In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (1975; an English translation Fractals: Form, Chance and Dimension was published in 1977). Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution ) of Czech geographer , demographer and statistician Jaromr Kor?k . While on secondment as Visiting Professor of Mathematics at Harvard University in 1979, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane . Building on previous work by Gaston Julia and Pierre Fatou , Mandelbrot used a computer to plot images of the Julia sets of the formula z ² . While investigating how the topology of these Julia sets depended on the complex parameter he studied the Mandelbrot set fractal that is now named after him. (Note that the Mandelbrot set is now usually defined in terms of the formula z ² + c , so Mandelbrot's early plots in terms of the earlier parameter are leftright mirror images of more recent plots in terms of the parameter c .) In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature . This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as program artifacts . Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division. He joined the Department of Mathematics at Yale , and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences. His awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006. The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Knight in the French Legion of Honour . In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory . Mandelbrot was promoted to Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises. 分形Fractals and regular roughness Although Mandelbrot coined the term fractal , some of the mathematical objects he presented in The Fractal Geometry of Nature had been described by other mathematicians. Before Mandelbrot, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to non-smooth objects in the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance , and a (usually) non-integer Hausdorff dimension . He also emphasized the use of fractals as realistic and useful models of many rough phenomena in the real world. Natural fractals include the shapes of mountains , coastlines and river basins ; the structures of plants, blood vessels and lungs ; the clustering of galaxies ; and Brownian motion . Fractals are found in human pursuits, such as music , painting , architecture , and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry : Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. Mandelbrot, in his introduction to The Fractal Geometry of Nature Mandelbrot has been called a visionary and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics. When visiting the Museu de la Cincia de Barcelona in 1988, he told its director that the painting The Face of War had given him the intuition about the transcendence of the fractal geometry when making intelligible the omnipresent similitude in the forms of nature. He also said that, fractally, Gaud was superior to Van der Rohe . Death Mandelbrot died in a hospice in Cambridge, Massachusetts , on 14 October 2010 from pancreatic cancer , at the age of 85. Reacting to news of his death, mathematician Heinz-Otto Peitgen said if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years. Chris Anderson described Mandelbrot as an icon who changed how we see the world. French President Nicolas Sarkozy said Mandelbrot had a powerful, original mind that never shied away from innovating and shattering preconceived notions. Sarkozy also added, His work, developed entirely outside mainstream research, led to modern information theory.
刚收到 Physical Review E （ PRE ） 编辑部发来的一个好消息：由我们组林苑、吴斌两位本科同学和我一起合作的文章《 Determining mean first-passage time on a class of treelike regular fractals 》已在 PRE 上 正式发表，这是我们组以本科生为第一作者发表在 PRE 上的第一篇论文。 这个工作针对一类树状网络，研究了将陷阱置于某一特殊节点的随机游走时间与全局随机游走时间问题。针对这两个问题，我们分别提出了新的计算方法，该方法计算简单、便捷。为了说明所提出方法的计算过程，我们提出了一类确定性 T 形树，并针对这类树状网络，给出我们所提出方法的计算细节，得到了精确的结果。文章还通过多个例子，说明了所给出的新方法具有普适性。 为了获得计算平均首达时间的简捷方法，林苑和吴斌两位同学付出了大量的时间与精力，他们对这两个问题进行了反复讨论、计算与验算，最终攻克了这些难题。这篇文章的工作量非常大，共有 12 个 PRE 版面（全文见附件）。如今文章在 PRE 上正式发表，这是对两位同学辛勤付出的肯定与鼓励。 本科生以第一作者身份在国际著名期刊上发表文章，说明了在适当的引导与培养之下，本科生是可以做出很出色的工作的。希望我们课题组的本科生同学再接再厉，争取今后做出更加优秀的研究成果。 文章发表的PDF版本
标签: 分形
