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Benoit B. Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of #Fractals and the "theory of roughness", roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having Multiple citizenship , dual French nat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumflex
The circumflex () is a diacritic in the Latin and Greek scripts that is also used in the written forms of many languages and in various romanization and transcription schemes. It received its English name from la, circumflexus "bent around"a translation of the el, περισπωμένη (). The circumflex in the Latin script is chevron-shaped (), while the Greek circumflex may be displayed either like a tilde () or like an inverted breve (). For the most commonly encountered uses of the accent in the Latin alphabet, precomposed characters are available. In English, the circumflex, like other diacritics, is sometimes retained on loanwords that used it in the original language (for example, ''crème brûlée''). In mathematics and statistics, the circumflex diacritic is sometimes used to denote a function and is called a ''hat operator''. A free-standing version of the circumflex symbol, , has become known as ''caret'' and has acquired special uses, particularly in computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murad Taqqu
Murad Taqqu (Arabic: مراد تقّو) is an Iraqi probabilist and statistician specializing in time series and stochastic processes. His research areas have included long-range dependence, self-similar processes, and heavy tails. He is a Professor of Mathematics at Boston University and received his Ph.D. from Columbia University. He has published over 250 papers, many of which are considered seminal work. He has co-authored or co-edited 9 books. Education and career Taqqu was born in Baghdad, Iraq, and grew up in Switzerland. As an undergraduate, he studied Physics and Mathematics at the École Polytechnique Fédérale de Lausanne. He pursued his PhD at Columbia University, during which time he studied with Benoit Mandelbrot. Between 1972 and 1974 Taqqu lectured at Hebrew University in Jerusalem and worked as a post-doctoral fellow at the Weizmann Institute in Rehovot, Israel. From 1974 to 1985, he was a faculty member at the School of Operations Research and Industrial Engine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of nationality, race, colour, religion, sex or political views."'' History The prize is awarded in Israel by the Wolf Foundation, founded by Ricardo Wolf, a German-born inventor and former Cuban ambassador to Israel. It is awarded in six fields: Agriculture, Chemistry, Mathematics, Medicine, Physics, and an Arts prize that rotates between architecture, music, painting, and sculpture. Each prize consists of a diploma and US$100,000. The awards ceremony typically takes place at a session in the Knesset. The prize is described by the Foundation as being "awarded annually", but is not in fact awarded every year: between 2000 and 2010, only six prizes were awarded in most fields, and only four in Physics. The Wolf Prizes in Physics and Chemistry ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japan Prize
is awarded to people from all parts of the world whose "original and outstanding achievements in science and technology are recognized as having advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind." The Prize is presented by the Japan Prize Foundation. Since its inception in 1985, the Foundation has awarded 81 people from 13 countries. The Japan Prize consists of a certificate, a commemorative medal and a cash award of ¥50 million. No discrimination is made as to nationality, occupation, race, or gender. Only living persons may be named. Every November, the Japan Prize Foundation selects two fields for the award according to current trends in science and technology. The nomination and selection process takes about one year. The laureates, one from each field, are announced in January. The prestigious prize presentation ceremony is held in the presence of the Emperor and the Empress of Japan. According to his book ''Dancing Naked in the M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Légion D'honneur
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon Bonaparte, it has been retained (with occasional slight alterations) by all later French governments and regimes. The order's motto is ' ("Honour and Fatherland"); its seat is the Palais de la Légion d'Honneur next to the Musée d'Orsay, on the left bank of the Seine in Paris. The order is divided into five degrees of increasing distinction: ' (Knight), ' (Officer), ' (Commander), ' (Grand Officer) and ' (Grand Cross). History Consulate During the French Revolution, all of the French orders of chivalry were abolished and replaced with Weapons of Honour. It was the wish of Napoleon Bonaparte, the First Consul, to create a reward to commend civilians and soldiers. From this wish was instituted a , a body of men that was not an order of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pacific Northwest National Laboratory
Pacific Northwest National Laboratory (PNNL) is one of the United States Department of Energy national laboratories, managed by the Department of Energy's (DOE) Office of Science. The main campus of the laboratory is in Richland, Washington. Originally named the Pacific Northwest Laboratory, PNL was established in 1965 when research and development at the Hanford Site was separated from other Hanford operations. In 1995, the laboratory was renamed the Pacific Northwest National Laboratory also known as PNNL. Facilities PNNL houses several scientific user facilities and research facilities. Scientific user facilities The Environmental Molecular Sciences Laboratory (EMSL) is a U.S. Department of Energy national scientific user facility. EMSL provides researchers around the world with integrated capabilities in oxide and mineral interface chemistry, high-performance computing and computational chemistry software, mass spectrometry, high-field magnetic resonance, and subsurface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world. It is a member of the Ivy League. Chartered by the Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research. Yale is organized into fourteen constituent schools: the original undergraduate col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nassim Nicholas Taleb
Nassim Nicholas Taleb (; alternatively ''Nessim ''or'' Nissim''; born 12 September 1960) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist whose work concerns problems of randomness, probability, and uncertainty. ''The Sunday Times'' called his 2007 book '' The Black Swan'' one of the 12 most influential books since World War II. Taleb is the author of the ''Incerto'', a five-volume philosophical essay on uncertainty published between 2001 and 2018 (of which the best-known books are ''The Black Swan'' and ''Antifragile''). He has been a professor at several universities, serving as a Distinguished Professor of Risk Engineering at the New York University Tandon School of Engineering since September 2008. He has been co-editor-in-chief of the academic journal ''Risk and Decision Analysis'' since September 2014. He has also been a practitioner of mathematical finance, a hedge fund manager, and a derivatives trader, and i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szolem Mandelbrojt
Szolem Mandelbrojt (10 January 1899 – 23 September 1983) was a Polish-French mathematician who specialized in mathematical analysis. He was a professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics. Biography Szolem Mandelbrojt was born on 10 January 1899 in Warsaw, Poland into a Jewish family of Lithuanian descent. He was initially educated in Warsaw, then in 1919 he moved to Kharkov, Ukraine (then USSR) and spent a year as a student of the Russian mathematician Sergei Bernstein. A year later, he emigrated to France and settled in Paris. In subsequent years, he attended the seminars of Jacques Hadamard, Henri Lebesgue, Émile Picard, and others. In 1923, he received a doctorate from Paris-Sorbonne University on the analytic continuation of the Taylor series. Hadamard was his Ph.D. advisor. In 1924 Mandelbrojt was awarded a Rockefeller Fellowship in the United States. In May 1926 he married Gladys Manuell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zipf–Mandelbrot Law
In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it. The probability mass function is given by: :f(k;N,q,s)=\frac where H_ is given by: :H_=\sum_^N \frac which may be thought of as a generalization of a harmonic number. In the formula, k is the rank of the data, and q and s are parameters of the distribution. In the limit as N approaches infinity, this becomes the Hurwitz zeta function \zeta(s,q). For finite N and q=0 the Zipf–Mandelbrot law becomes Zipf's law. For infinite N and q=0 it becomes a Zeta distribution. Applications The distribution of words ranked by their frequency in a random text corpus is approximated by a power-law distribution, known as Zipf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
