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92,000 | Also, Awad and Lage: obtained a modified form of the Bejan number, originally proposed by Bhattacharjee and Grosshandler for momentum processes, by replacing the dynamic viscosity appearing in the original proposition with the equivalent product of the fluid density and the momentum diffusivity of the fluid. This modif... | Bejan number | 0.78031 |
92,001 | The British Computer Society (BCS), branded BCS, The Chartered Institute for IT, since 2009, is a professional body and a learned society that represents those working in information technology (IT), software engineering and computer science, both in the United Kingdom and internationally. Founded in 1957, BCS has play... | BCS Professional Certification | 0.780309 |
92,002 | From a physicalist perspective, even abstract concepts such as mathematics, morality, consciousness, intentionality, and meaning are considered physical entities, although they may consist of a large ontological object and a causally complex structure.According to a 2009 survey, physicalism is the majority view among p... | Reductive physicalism | 0.780309 |
92,003 | The terms "physicalism" and "materialism" are often used interchangeably, but can be distinguished based on their philosophical implications. Physicalism encompasses matter, but also energy, physical laws, space, time, structure, physical processes, information, state, and forces, among other things, as described by ph... | Reductive physicalism | 0.780309 |
92,004 | One of the book reviews is that of Dr. Nelson V. Nemerow, a Civil Engineering professor at Syracuse University in New York state, published in 1968 in the American Chemical Society's journal Environmental Science and Technology. == References == | Aqueous Wastes from Petroleum and Petrochemical Plants | 0.780306 |
92,005 | The proof of Lüroth's theorem can be derived easily from the theory of rational curves, using the geometric genus. This method is non-elementary, but several short proofs using only the basics of field theory have long been known. Many of these simple proofs use Gauss's lemma on primitive polynomials as a main step. ==... | Lüroth's theorem | 0.780306 |
92,006 | In mathematics, Lüroth's theorem asserts that every field that lies between two other fields K and K(X) must be generated as an extension of K by a single element of K(X). This result is named after Jacob Lüroth, who proved it in 1876. | Lüroth's theorem | 0.780306 |
92,007 | Reverso has been active since 1998, with the aim of providing online translation and linguistic tools to corporate and mass markets.In 2013 it released Reverso Context, a bilingual dictionary tool based on big data and machine learning algorithms.In 2016 Reverso acquired Fleex, a service for learning English via subtit... | Reverso (language tools) | 0.780305 |
92,008 | For example, the multiplication theorem for the gamma function follows from the Chowla–Selberg formula, which follows from the theory of complex multiplication. The infinite sums are much more common, and follow from characteristic zero relations on the hypergeometric series. | Gauss multiplication theorem | 0.780305 |
92,009 | The multiplication theorem takes two common forms. In the first case, a finite number of terms are added or multiplied to give the relation. In the second case, an infinite number of terms are added or multiplied. The finite form typically occurs only for the gamma and related functions, for which the identity follows ... | Gauss multiplication theorem | 0.780305 |
92,010 | Let f ( n ) {\displaystyle f(n)} be totally multiplicative; that is, f ( m n ) = f ( m ) f ( n ) {\displaystyle f(mn)=f(m)f(n)} for any integers m, n. Define its Fourier series as g ( x ) = ∑ n = 1 ∞ f ( n ) exp ( 2 π i n x ) {\displaystyle g(x)=\sum _{n=1}^{\infty }f(n)\exp(2\pi inx)} Assuming that the sum converges... | Gauss multiplication theorem | 0.780305 |
92,011 | The transfer operator L k {\displaystyle {\mathcal {L}}_{k}} corresponding to the shift operator on the Bernoulli scheme is given by ( x ) = 1 k ∑ n = 0 k − 1 f ( x + n k ) {\displaystyle (x)={\frac {1}{k}}\sum _{n=0}^{k-1}f\left({\frac {x+n}{k}}\right)} Perhaps not surprisingly, the eigenvectors of this operator are ... | Gauss multiplication theorem | 0.780305 |
92,012 | Interactive Voice Systems Virtual Assistants Voice Identification Emotion Recognition Call Center Automation Robotics | Speech signal processing | 0.780305 |
92,013 | The following tabulates the various appearances of the multiplication theorem for finite characteristic; the characteristic zero relations are given further down. In all cases, n and k are non-negative integers. For the special case of n = 2, the theorem is commonly referred to as the duplication formula. | Gauss multiplication theorem | 0.780305 |
92,014 | In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley (1907–1933) and Norbert Wiener (1894–1964). The original theorems did not use the language of distributions, and... | Paley–Wiener theorem | 0.780304 |
92,015 | Riccardo Giacconi shared the 2002 Nobel Prize in Physics for his study of X-ray astronomy, including the study of emissions from the Sun onboard Skylab, contributing to the birth of X-ray astronomy. | Skylab | 0.780303 |
92,016 | NASA History Series Publications (many of which are on-line) SP-4011 Skylab, a Chronology (1977) 1 SP-401 Skylab, Classroom in Space (1977) SP-399 Skylab EREP Investigations Summary (1978) SP-402 A New Sun: Solar Results from Skylab (1979) SP-404 Skylab's Skylab's Astronomy and Space Sciences (1979) Skylab: Four Rooms ... | Skylab | 0.780303 |
92,017 | The Journal of Experimental Marine Biology and Ecology is a peer-reviewed bimonthly journal which publishes work on the biochemistry, physiology, behaviour, and genetics of marine plants and animals in relation to their ecology. According to the Journal Citation Reports, the journal has a 2015 impact factor of 1.796. =... | Journal of Experimental Marine Biology and Ecology | 0.780303 |
92,018 | Ecological evolutionary developmental biology integrates research from developmental biology and ecology to examine their relationship with evolutionary theory. Researchers study concepts and mechanisms such as developmental plasticity, epigenetic inheritance, genetic assimilation, niche construction and symbiosis. | Morphological evolution | 0.780303 |
92,019 | For example, the fruit fly's compound eye is made of hundreds of small lensed structures (ommatidia); the human eye has a blind spot where the optic nerve enters the eye, and the nerve fibres run over the surface of the retina, so light has to pass through a layer of nerve fibres before reaching the detector cells in t... | Morphological evolution | 0.780303 |
92,020 | Due to the chiral nature of lactic acid, several distinct forms of polylactide exist: poly-L-lactide (PLLA) is the product resulting from polymerization of L,L-lactide (also known as L-lactide). Progress in biotechnology has resulted in the development of commercial production of the D enantiomer form.Polymerization of... | Poly(lactic acid) | 0.780302 |
92,021 | Its widespread application has been hindered by numerous physical and processing shortcomings. PLA is the most widely used plastic filament material in FDM 3D printing, due to its low melting point, high strength, low thermal expansion, and good layer adhesion, although it possesses poor heat resistance unless annealed... | Poly(lactic acid) | 0.780302 |
92,022 | The far end (the non console or splitter end) of a cable segment should be terminated. RDM requires two significant topology changes compared to DMX. | RDM (lighting) | 0.780301 |
92,023 | Neuronal oscillations are important components of neuroscience research. During the last two decades, hippocampal oscillations have been a major focus in the research of neuronal oscillations. Among different oscillations present in the brain, SWRs are the first and only population activity that start in the developing... | Sharp waves and ripples | 0.780301 |
92,024 | MXNet supports Python, R, Scala, Clojure, Julia, Perl, MATLAB and JavaScript for front-end development, and C++ for back-end optimization. | Apache MXNet | 0.7803 |
92,025 | MXNet is supported by public cloud providers including Amazon Web Services (AWS) and Microsoft Azure. Amazon has chosen MXNet as its deep learning framework of choice at AWS. Currently, MXNet is supported by Intel, Baidu, Microsoft, Wolfram Research, and research institutions such as Carnegie Mellon, MIT, the Universit... | Apache MXNet | 0.7803 |
92,026 | Apache MXNet is an open-source deep learning software framework used to train and deploy deep neural networks. It is scalable, allowing for fast model training, and supports a flexible programming model and multiple programming languages (including C++, Python, Java, Julia, MATLAB, JavaScript, Go, R, Scala, Perl, and W... | Apache MXNet | 0.7803 |
92,027 | Apache MXNet is a scalable deep learning framework that supports deep learning models, such as: convolutional neural networks (CNNs) and long short-term memory networks (LSTMs). | Apache MXNet | 0.7803 |
92,028 | In molecular biology, the FAD dependent oxidoreductase family of proteins is a family of FAD dependent oxidoreductases. Members of this family include Glycerol-3-phosphate dehydrogenase EC 1.1.99.5, Sarcosine oxidase beta subunit EC 1.5.3.1, D-amino-acid dehydrogenase EC 1.4.99.1, D-aspartate oxidase EC 1.4.3.1. D-amin... | FAD dependent oxidoreductase family | 0.780299 |
92,029 | The s-cobordism theorem states for a closed connected oriented manifold M of dimension n > 4 that an h-cobordism W between M and another manifold N is trivial over M if and only if the Whitehead torsion of the inclusion M ↪ W {\displaystyle M\hookrightarrow W} vanishes. Moreover, for any element in the Whitehead group ... | Whitehead torsion | 0.780299 |
92,030 | It is also the key algebraic result used in the surgery theory classification of piecewise linear manifolds of dimension at least 5 which are homotopy equivalent to a torus; this is the essential ingredient of the 1969 Kirby–Siebenmann structure theory of topological manifolds of dimension at least 5.The Whitehead grou... | Whitehead torsion | 0.780299 |
92,031 | The restriction to manifolds of dimension greater than four are due to the application of the Whitney trick for removing double points. In generalizing the h-cobordism theorem, which is a statement about simply connected manifolds, to non-simply connected manifolds, one must distinguish simple homotopy equivalences and... | Whitehead torsion | 0.780299 |
92,032 | In geometric topology, a field within mathematics, the obstruction to a homotopy equivalence f: X → Y {\displaystyle f\colon X\to Y} of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion τ ( f ) {\displaystyle \tau (f)} which is an element in the Whitehead group Wh ( π 1 ( Y ) ) {\displa... | Whitehead torsion | 0.780299 |
92,033 | Unlike most mathematicians, she did not make abstractions by generalizing from known examples; rather, she worked directly with the abstractions. In his obituary of Noether, her student van der Waerden recalled that The maxim by which Emmy Noether was guided throughout her work might be formulated as follows: "Any rela... | Emmy Noether | 0.780296 |
92,034 | Any set of things that obeys all the rules for one (or two) operation(s) is, by definition, a group (or ring), and obeys all theorems about groups (or rings). Integer numbers, and the operations of addition and multiplication, are just one example. For example, the elements might be computer data words, where the first... | Emmy Noether | 0.780296 |
92,035 | An important special case of this is an algebra. (The word algebra means both a subject within mathematics as well as an object studied in the subject of algebra.) An algebra consists of a choice of two rings and an operation which takes an element from each ring and returns an element of the second ring. | Emmy Noether | 0.780296 |
92,036 | Noether used these sorts of symmetries in her work on invariants in physics. A powerful way of studying rings is through their modules. A module consists of a choice of ring, another set, usually distinct from the underlying set of the ring and called the underlying set of the module, an operation on pairs of elements ... | Emmy Noether | 0.780296 |
92,037 | Two of the most basic objects in abstract algebra are groups and rings. A group consists of a set of elements and a single operation which combines a first and a second element and returns a third. The operation must satisfy certain constraints for it to determine a group: It must be closed (when applied to any pair of... | Emmy Noether | 0.780296 |
92,038 | An important example is the fundamental theorem of arithmetic, which says that every positive integer can be factored uniquely into prime numbers. Unique factorizations do not always exist in other rings, but Noether found a unique factorization theorem, now called the Lasker–Noether theorem, for the ideals of many rin... | Emmy Noether | 0.780296 |
92,039 | Noether was recorded as having given at least five semester-long courses at Göttingen: Winter 1924/1925: Gruppentheorie und hyperkomplexe Zahlen Winter 1927/1928: Hyperkomplexe Grössen und Darstellungstheorie Summer 1928: Nichtkommutative Algebra Summer 1929: Nichtkommutative Arithmetik Winter 1929/30: Algebra der ... | Emmy Noether | 0.780296 |
92,040 | Two female students once approached her during a break in a two-hour class to express their concern, but they were unable to break through the energetic mathematical discussion she was having with other students.According to van der Waerden's obituary of Emmy Noether, she did not follow a lesson plan for her lectures, ... | Emmy Noether | 0.780296 |
92,041 | She was paid more generously later in her life, but saved half of her salary to bequeath to her nephew, Gottfried E. Noether.Biographers suggest that she was mostly unconcerned about appearance and manners, focusing on her studies. A distinguished algebraist Olga Taussky-Todd described a luncheon during which Noether, ... | Emmy Noether | 0.780296 |
92,042 | In Göttingen, Noether supervised more than a dozen doctoral students; her first was Grete Hermann, who defended her dissertation in February 1925. She later spoke reverently of her "dissertation-mother". Noether also supervised Max Deuring, who distinguished himself as an undergraduate and went on to contribute to the ... | Emmy Noether | 0.780296 |
92,043 | She solved it immediately, but the riddle has been lost.In September of the same year, Noether delivered a plenary address (großer Vortrag) on "Hyper-complex systems in their relations to commutative algebra and to number theory" at the International Congress of Mathematicians in Zürich. The congress was attended by 80... | Emmy Noether | 0.780296 |
92,044 | In 1932 Emmy Noether and Emil Artin received the Ackermann–Teubner Memorial Award for their contributions to mathematics. The prize included a monetary reward of 500 ℛ︁ℳ︁ and was seen as a long-overdue official recognition of her considerable work in the field. Nevertheless, her colleagues expressed frustration at the ... | Emmy Noether | 0.780296 |
92,045 | In 1923–1924, Noether applied her ideal theory to elimination theory in a formulation that she attributed to her student, Kurt Hentzelt. She showed that fundamental theorems about the factorization of polynomials could be carried over directly. Traditionally, elimination theory is concerned with eliminating one or more... | Emmy Noether | 0.780296 |
92,046 | According to Hermann Weyl, Fischer was an important influence on Noether, in particular by introducing her to the work of David Hilbert. From 1913 to 1916 Noether published several papers extending and applying Hilbert's methods to mathematical objects such as fields of rational functions and the invariants of finite g... | Emmy Noether | 0.780296 |
92,047 | She was taught to cook and clean, as were most girls of the time, and she took piano lessons. She pursued none of these activities with passion, although she loved to dance.She had three younger brothers: the eldest, Alfred, was born in 1883, was awarded a doctorate in chemistry from Erlangen in 1909, but died nine yea... | Emmy Noether | 0.780296 |
92,048 | Noether's suggestion that topology be studied algebraically was adopted immediately by Hopf, Alexandrov, and others, and it became a frequent topic of discussion among the mathematicians of Göttingen. Noether observed that her idea of a Betti group makes the Euler–Poincaré formula simpler to understand, and Hopf's own ... | Emmy Noether | 0.780296 |
92,049 | According to the account of Alexandrov, Noether attended lectures given by Heinz Hopf and by him in the summers of 1926 and 1927, where "she continually made observations which were often deep and subtle" and he continues that, When ... she first became acquainted with a systematic construction of combinatorial topolog... | Emmy Noether | 0.780296 |
92,050 | As noted by Pavel Alexandrov and Hermann Weyl in their obituaries, Noether's contributions to topology illustrate her generosity with ideas and how her insights could transform entire fields of mathematics. In topology, mathematicians study the properties of objects that remain invariant even under deformation, propert... | Emmy Noether | 0.780296 |
92,051 | Another source of support at the college was the Bryn Mawr president, Marion Edwards Park, who enthusiastically invited mathematicians in the area to "see Dr. Noether in action!" Noether and a small team of students worked quickly through van der Waerden's 1930 book Moderne Algebra I and parts of Erich Hecke's Theorie ... | Emmy Noether | 0.780296 |
92,052 | She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor. In the third epoch (1927–1935), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to... | Emmy Noether | 0.780296 |
92,053 | Her work on differential invariants in the calculus of variations, Noether's theorem, has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics". In the second epoch (1920–1926), she began work that "changed the face of algebra". In her classic 1921 paper... | Emmy Noether | 0.780296 |
92,054 | The following year, Germany's Nazi government dismissed Jews from university positions, and Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania where she taught, among others, doctoral and post-graduate women including Marie Johanna Weiss, Ruth Stauffer, Grace Shover Quinn and ... | Emmy Noether | 0.780296 |
92,055 | Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the "Noether boys". In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the lea... | Emmy Noether | 0.780296 |
92,056 | In physics, Noether's theorem explains the connection between symmetry and conservation laws.Noether was born to a Jewish family in the Franconian town of Erlangen; her father was the mathematician Max Noether. She originally planned to teach French and English after passing the required examinations, but instead studi... | Emmy Noether | 0.780296 |
92,057 | Amalie Emmy Noether (US: , UK: ; German: ; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorems, which are fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean ... | Emmy Noether | 0.780296 |
92,058 | He began referring to her as der Noether, using the masculine German article as a term of endearment to show his respect. She tried to arrange for him to obtain a position at Göttingen as a regular professor, but was able only to help him secure a scholarship from the Rockefeller Foundation. They met regularly and enjo... | Emmy Noether | 0.780296 |
92,059 | In 1931 he published Moderne Algebra, a central text in the field; its second volume borrowed heavily from Noether's work. Although Noether did not seek recognition, he included as a note in the seventh edition "based in part on lectures by E. Artin and E. Noether".Van der Waerden's visit was part of a convergence of m... | Emmy Noether | 0.780296 |
92,060 | The following year she published a paper called Idealtheorie in Ringbereichen, analyzing ascending chain conditions with regard to (mathematical) ideals. Noted algebraist Irving Kaplansky called this work "revolutionary"; the publication gave rise to the term "Noetherian ring" and the naming of several other mathematic... | Emmy Noether | 0.780296 |
92,061 | Although Noether's theorem had a significant effect upon classical and quantum mechanics, among mathematicians she is best remembered for her contributions to abstract algebra. In his introduction to Noether's Collected Papers, Nathan Jacobson wrote thatThe development of abstract algebra, which is one of the most dist... | Emmy Noether | 0.780296 |
92,062 | (1935), "Nachruf auf Emmy Noether" , Mathematische Annalen (in German), 111: 469–74, doi:10.1007/BF01472233, S2CID 179178055, archived from the original on 3 September 2014. Reprinted in Dick 1981 ——— (1985), A History of Algebra: from al-Khwārizmī to Emmy Noether, Berlin: Springer-Verlag, ISBN 978-0-387-13610-3 Weyl, ... | Emmy Noether | 0.780296 |
92,063 | OCLC 223099225. Tent, M.B.W. (2008), Emmy Noether: The Mother of Modern Algebra, CRC Press van der Waerden, B.L. | Emmy Noether | 0.780296 |
92,064 | (eds. ), Women of Mathematics, New York: Greenwood Press, ISBN 978-0-313-24849-8 Noether, Max (1914), "Paul Gordan", Mathematische Annalen, 75 (1): 1–41, doi:10.1007/BF01564521, S2CID 179178051, archived from the original on 4 September 2014 Radford, Deborah (1 April 2016). On Emmy Noether and Her Algebraic Works (Mast... | Emmy Noether | 0.780296 |
92,065 | (2006), Helmut Hasse und Emmy Noether – Die Korrespondenz 1925–1935 (PDF), DE: Göttingen University, doi:10.17875/gup2006-49, ISBN 978-3-938616-35-2 Hilbert, David (December 1890). "Ueber die Theorie der algebraischen Formen". Mathematische Annalen (in German). | Emmy Noether | 0.780296 |
92,066 | ), Emmy Noether: A Tribute to Her Life and Work, New York: Marcel Dekker, pp. 131–43, ISBN 978-0-8247-1550-2 Gordan, Paul (1870), "Die simultanen Systeme binärer Formen", Mathematische Annalen (in German), 2 (2): 227–80, doi:10.1007/BF01444021, S2CID 119558943, archived from the original on 3 September 2014 Haboush, W.... | Emmy Noether | 0.780296 |
92,067 | Byers, Nina (2006), "Emmy Noether", in Byers, Nina; Williams, Gary (eds. ), Out of the Shadows: Contributions of 20th Century Women to Physics, Cambridge: Cambridge University Press, ISBN 978-0-521-82197-1 Dick, Auguste (1981), Emmy Noether: 1882–1935, translated by Blocher, H.I., Boston: Birkhäuser, doi:10.1007/978-1-... | Emmy Noether | 0.780296 |
92,068 | Israel: Bar-Ilan University. arXiv:physics/9807044. Bibcode:1998physics...7044B. | Emmy Noether | 0.780296 |
92,069 | For many years, determining the truth or falsehood of this bound for this particular case was an open problem, called "Noether's gap". It was finally solved independently by Fleischmann in 2000 and Fogarty in 2001, who both showed that the bound remains true.In her 1926 paper, Noether extended Hilbert's theorem to repr... | Emmy Noether | 0.780296 |
92,070 | Ges. Wiss (in German), DE: 28–35, archived from the original on 8 March 2013 ——— (1926b), "Ableitung der Elementarteilertheorie aus der Gruppentheorie" , Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), DE, 34 (Abt. 2): 104, archived from the original on 8 March 2013 ——— (1927), "Abstrakter Aufbau der ... | Emmy Noether | 0.780296 |
92,071 | 918 (3): 235–57. arXiv:physics/0503066. Bibcode:1971TTSP....1..186N. | Emmy Noether | 0.780296 |
92,072 | In these epochs, she was not merely applying ideas and methods of earlier mathematicians; rather, she was crafting new systems of mathematical definitions that would be used by future mathematicians. In particular, she developed a completely new theory of ideals in rings, generalizing earlier work of Richard Dedekind. ... | Emmy Noether | 0.780296 |
92,073 | After moving to Göttingen in 1915, she produced her work for physics, the two Noether's theorems. In the second epoch (1920–1926), Noether devoted herself to developing the theory of mathematical rings.In the third epoch (1927–1935), Noether focused on noncommutative algebra, linear transformations, and commutative num... | Emmy Noether | 0.780296 |
92,074 | Noether's work in abstract algebra and topology was influential in mathematics, while in physics, Noether's theorem has consequences for theoretical physics and dynamical systems. She showed an acute propensity for abstract thought, which allowed her to approach problems of mathematics in fresh and original ways. Her f... | Emmy Noether | 0.780296 |
92,075 | Noether's work continues to be relevant for the development of theoretical physics and mathematics and she is consistently ranked as one of the greatest mathematicians of the twentieth century. In his obituary, fellow algebraist BL van der Waerden says that her mathematical originality was "absolute beyond comparison",... | Emmy Noether | 0.780296 |
92,076 | In 1943, French mathematician Claude Chevalley coined the term, Noetherian ring, to describe this property. A major result in Noether's 1921 paper is the Lasker–Noether theorem, which extends Lasker's theorem on the primary decomposition of ideals of polynomial rings to all Noetherian rings. The Lasker–Noether theorem ... | Emmy Noether | 0.780296 |
92,077 | Noether's paper, Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921), is the foundation of general commutative ring theory, and gives one of the first general definitions of a commutative ring. Before her paper, most results in commutative algebra were restricted to special examples of commutative ri... | Emmy Noether | 0.780296 |
92,078 | Noether's theorem has become a fundamental tool of modern theoretical physics, both because of the insight it gives into conservation laws, and also, as a practical calculation tool. Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it fa... | Emmy Noether | 0.780296 |
92,079 | The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place a... | Emmy Noether | 0.780296 |
92,080 | The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff. For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the angular mom... | Emmy Noether | 0.780296 |
92,081 | Noether was brought to Göttingen in 1915 by David Hilbert and Felix Klein, who wanted her expertise in invariant theory to help them in understanding general relativity, a geometrical theory of gravitation developed mainly by Albert Einstein. Hilbert had observed that the conservation of energy seemed to be violated in... | Emmy Noether | 0.780296 |
92,082 | A subsequent paper by Noether showed, as a special case of a more general theorem, that all maximal subfields of a division algebra D are splitting fields. This paper also contains the Skolem–Noether theorem which states that any two embeddings of an extension of a field k into a finite-dimensional central simple algeb... | Emmy Noether | 0.780296 |
92,083 | Noether also was responsible for a number of other advances in the field of algebra. With Emil Artin, Richard Brauer, and Helmut Hasse, she founded the theory of central simple algebras. A paper by Noether, Helmut Hasse, and Richard Brauer pertains to division algebras, which are algebraic systems in which division is ... | Emmy Noether | 0.780296 |
92,084 | Much work on hypercomplex numbers and group representations was carried out in the nineteenth and early twentieth centuries, but remained disparate. Noether united these results and gave the first general representation theory of groups and algebras.Briefly, Noether subsumed the structure theory of associative algebras... | Emmy Noether | 0.780296 |
92,085 | Invariant theory was an active area of research in the later nineteenth century, prompted in part by Felix Klein's Erlangen program, according to which different types of geometry should be characterized by their invariants under transformations, e.g., the cross-ratio of projective geometry. An example of an invariant ... | Emmy Noether | 0.780296 |
92,086 | Much of Noether's work in the first epoch of her career was associated with invariant theory, principally algebraic invariant theory. Invariant theory is concerned with expressions that remain constant (invariant) under a group of transformations. As an everyday example, if a rigid yardstick is rotated, the coordinates... | Emmy Noether | 0.780296 |
92,087 | In the winter of 1928–1929 Noether accepted an invitation to Moscow State University, where she continued working with P.S. Alexandrov. In addition to carrying on with her research, she taught classes in abstract algebra and algebraic geometry. She worked with the topologists Lev Pontryagin and Nikolai Chebotaryov, who... | Emmy Noether | 0.780296 |
92,088 | Her oral examination was held in late May, and she successfully delivered her habilitation lecture in June 1919. Three years later she received a letter from Otto Boelitz, the Prussian Minister for Science, Art, and Public Education, in which he conferred on her the title of nicht beamteter ausserordentlicher Professor... | Emmy Noether | 0.780296 |
92,089 | American physicists Leon M. Lederman and Christopher T. Hill argue in their book Symmetry and the Beautiful Universe that Noether's theorem is "certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem". When World ... | Emmy Noether | 0.780296 |
92,090 | Soon after arriving at Göttingen, however, she demonstrated her capabilities by proving the theorem now known as Noether's theorem, which shows that a conservation law is associated with any differentiable symmetry of a physical system. The paper was presented by a colleague, F. Klein, on 26 July 1918 to a meeting of t... | Emmy Noether | 0.780296 |
92,091 | In the century from 1832 to Noether's death in 1935, the field of mathematics – specifically algebra – underwent a profound revolution, whose reverberations are still being felt. Mathematicians of previous centuries had worked on practical methods for solving specific types of equations, e.g., cubic, quartic, and quint... | Emmy Noether | 0.780296 |
92,092 | Theorems of abstract algebra are powerful because they are general; they govern many systems. It might be imagined that little could be concluded about objects defined with so few properties, but precisely therein lay Noether's gift to discover the maximum that could be concluded from a given set of properties, or conv... | Emmy Noether | 0.780296 |
92,093 | Since the Galois group does not change the ground field, it leaves the coefficients of the polynomial unchanged, so it must leave the set of all roots unchanged. Each root can move to another root, however, so transformation determines a permutation of the n roots among themselves. The significance of the Galois group ... | Emmy Noether | 0.780296 |
92,094 | These conclusions often are crucial steps in a proof. Many types of objects in abstract algebra can satisfy chain conditions, and usually if they satisfy an ascending chain condition, they are called Noetherian in her honor. By definition, a Noetherian ring satisfies an ascending chain condition on its left and right i... | Emmy Noether | 0.780296 |
92,095 | The resulting solution for an infinite line source is: χ = ∫ 0 ∞ q π ( u c d x 2 ) ( c o s α ) ( exp y 2 2 c 2 x 2 ) d x {\displaystyle \chi \ =\int _{0}^{\infty }{\frac {q}{\pi \left(ucdx^{2}\right)\left(cos\alpha \ \right)}}\left(\exp {\frac {y^{2}}{2c^{2}x^{2}}}\right)dx} where: x is the distance from the observer... | Roadway air dispersion model | 0.780296 |
92,096 | While the ESL mathematical model was completed for a line source by 1970, model refinement resulted in a “strip source”, emulating the horizontal extent of the roadway surface. This theory would be the precursor of area source dispersion models. But their focus was roadway simulation, so they proceeded with the develop... | Roadway air dispersion model | 0.780296 |
92,097 | Typically these might be stated as concentrations of carbon monoxide, total reactive hydrocarbons, oxides of nitrogen, particulate or benzene. The air quality scientist can run the model successively to study techniques of reducing adverse air pollutant concentrations (for example, by redesigning roadway geometry, alte... | Roadway air dispersion model | 0.780296 |
92,098 | The basic concept of the roadway air dispersion model is to calculate air pollutant levels in the vicinity of a highway or arterial roadway by considering them as line sources. The model takes into account source characteristics such as traffic volume, vehicle speeds, truck mix, and fleet emission controls; in addition... | Roadway air dispersion model | 0.780296 |
92,099 | Let π {\displaystyle \pi } be an irreducible, admissible unitary representation of G A {\displaystyle G_{\mathbb {A} }} . By the tensor product theorem, π {\displaystyle \pi } is of the form π = ⨂ p ≤ ∞ π p {\textstyle \pi =\bigotimes _{p\leq \infty }\pi _{p}} (see cuspidal representations of the adele group) Let S {\d... | Maass cusp form | 0.78029 |
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