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Poincaré Conjecture
In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured by Henri Poincaré in 1904, the theorem concerns spaces that locally look like ordinary three-dimensional space but which are finite in extent. Poincaré hypothesized that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. Attempts to resolve the conjecture drove much progress in the field of geometric topology during the 20th century. The eventual proof built upon Richard S. Hamilton's program of using the Ricci flow to solve the problem. By developing a number of new techniques and results in the theory of Ricci flow, Grigori Perelman was able to modify and complete Hamilton's program. In papers posted to the arXiv reposi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topological spaces. One suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Unit Ball
Unit may refer to: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, historical units of measurement used in England up to 1824 ** Unit of length Science and technology Physical sciences * Natural unit, a physical unit of measurement * Geological unit or rock unit, a volume of identifiable rock or ice * Astronomical unit, a unit of length roughly between the Earth and the Sun Chemistry and medicine * Equivalent (chemistry), a unit of measurement used in chemistry and biology * Unit, a vessel or section of a chemical plant * Blood unit, a measurement in blood transfusion * Enzyme unit, a measurement of active enzyme in a sample * International unit, a unit of measurement for nutrients and drugs Mathematics * Unit number, the number 1 * Unit, identity element * Unit (ring theory), an element that is i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Breakthrough Of The Year
The Breakthrough of the Year is an annual award for the most significant development in scientific research made by the American Association for the Advancement of Science, AAAS journal ''Science (journal), Science,'' an academic journal covering all branches of science. Originating in 1989 as the ''Molecule of the Year'', and inspired by ''Time (magazine), Time'' Time Magazine Person of the Year, Person of the Year, it was renamed the Breakthrough of the Year in 1996. Molecule of the Year * 1989 Polymerase chain reaction, PCR and DNA polymerase * 1990 the manufacture of synthetic diamonds * 1991 buckminsterfullerene * 1992 nitric oxide * 1993 p53 * 1994 DNA repair enzyme Breakthrough of the Year * 1996: Understanding HIV * 1997: Dolly (sheep), Dolly the sheep, the first mammal to be Clone (genetics), cloned from adult cells * 1998: Accelerating expansion of the universe, Accelerating universe * 1999: Prospective stem-cell therapy, stem-cell therapies * 2000: Full genome sequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Science (journal)
''Science'' is the peer review, peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' cover the full range of List of academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
