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90,700 | There is a closely related argument from algebraic topology, using the Lefschetz fixed-point theorem. Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0, ... the Lefschetz number (total trace on homology) of the identity mapping is 2. By integrating a vector field we get (at least a small part of) a one-parameter ... | Hairy ball theorem | 0.780805 |
90,701 | For each point p, construct the stereographic projection of s(p) with p as the point of tangency. Then v(p) is the displacement vector of this projected point relative to p. According to the hairy ball theorem, there is a p such that v(p) = 0, so that s(p) = p. This argument breaks down only if there exists a point p f... | Hairy ball theorem | 0.780805 |
90,702 | A consequence of the hairy ball theorem is that any continuous function that maps an even-dimensional sphere into itself has either a fixed point or a point that maps onto its own antipodal point. This can be seen by transforming the function into a tangential vector field as follows. Let s be the function mapping the ... | Hairy ball theorem | 0.780805 |
90,703 | {\displaystyle v(x_{1},\dots ,x_{2n})\bullet (x_{1},\dots ,x_{2n})=(x_{2}x_{1}-x_{1}x_{2})+\cdots +(x_{2n}x_{2n-1}-x_{2n-1}x_{2n})=0.} For a 2n-sphere, the ambient Euclidean space is R 2 n + 1 {\displaystyle \mathbb {R} ^{2n+1}} which is odd-dimensional, and so this simple process of pairing coordinates is not possible... | Hairy ball theorem | 0.780805 |
90,704 | SEPR's auxiliary rocket engines were based on the hypergolic fuel chemistry of nitric acid oxidiser and TX2 (tri-ethylamine xylidine) fuel.Unusually, the turbopump for the engine was mechanically driven from outside. A mechanical drive shaft from the accessory drive of the main turbojet provided the 93 brake horsepower... | SEPR 84 | 0.780803 |
90,705 | 50: Earliest records of Hero's engine (aeolipile). It most likely served no practical purpose, and was rather more of a curiosity; nonetheless, it demonstrated an important principle of physics that all modern turbine engines rely on. 1000: The "Trotting Horse Lamp" (Chinese: 走马灯, zŏumădēng) was used by the Chinese at ... | Combustion turbine | 0.780803 |
90,706 | String phenomenology is a branch of theoretical physics that uses tools from mathematics and computer science to study the implications of string theory for particle physics and cosmology. In cosmology, string phenomenology studies, among others, implications of string theory for inflation, dark matter and dark energy.... | String phenomenology | 0.780802 |
90,707 | The dual of the Lie algebra of Diff(S1) can be identified with the space of Hill's operators on S1 d 2 d θ 2 + q ( θ ) , {\displaystyle {d^{2} \over d\theta ^{2}}+q(\theta ),} and the coadjoint action of Diff(S1) invokes the Schwarzian derivative. The inverse of the diffeomorphism f sends the Hill's operator to d 2 d θ... | Schwarzian derivative | 0.780802 |
90,708 | The crossed homomorphisms in turn give rise to the central extension of Diff(S1) and of its Lie algebra Vect(S1), the so-called Virasoro algebra. | Schwarzian derivative | 0.780802 |
90,709 | The 1-cocycles define the three pseudogroups by 𝜙k(f) = 0: this gives the scaling group (k = 0); the affine group (k = 1); and the whole complex Möbius group (k = 2). So these 1-cocycles are the special ordinary differential equations defining the pseudogroup. More significantly they can be used to define correspondin... | Schwarzian derivative | 0.780802 |
90,710 | There the calculation was for the whole Witt algebra acting on densities of order k, whereas here it is just for a subalgebra acting on holomorphic (or polynomial) differentials of order k. Again, assuming that 𝜙 vanishes on rotations of C, there are non-zero 1-cocycles, unique up to scalar multiples. only for differe... | Schwarzian derivative | 0.780802 |
90,711 | Accordingly, it defines a 1-cocycle on holomorphic vector fields on C: φ ( ) = X φ ( Y ) − Y φ ( X ) . {\displaystyle \varphi ()=X\varphi (Y)-Y\varphi (X).} Restricting to the Lie algebra of polynomial vector fields with basis dn = zn+1 d/dz (n ≥ −1), these can be determined using the same methods of Lie algebra cohom... | Schwarzian derivative | 0.780802 |
90,712 | It contains d0 and is invariant under Ad(Sa). Since a {\displaystyle {\mathfrak {a}}} is a Lie subalgebra of the Witt algebra, the only possibility is that it has basis d0 or basis d0, dn for some n ≥ 1. There are corresponding group elements of the form f(z)= z + bzn+1 + .... Composing this with translations yields T–... | Schwarzian derivative | 0.780802 |
90,713 | Again these act on the space of polynomials of degree ≤ k by differentiation—it can be identified with C]/(zk+1)—and the images of d0, ..., dk – 1 give a basis of the Lie algebra of Gk. Note that Ad(Sa) dn= a–n dn. Let a {\displaystyle {\mathfrak {a}}} denote the Lie algebra of A: it is isomorphic to a subalgebra of th... | Schwarzian derivative | 0.780802 |
90,714 | This classification can easily be reduced to a Lie algebraic problem since the formal Lie algebra g {\displaystyle {\mathfrak {g}}} of G consists of formal vector fields F(z) d/dz with F a formal power series. It contains the polynomial vectors fields with basis dn = zn+1 d/dz (n ≥ 0), which is a subalgebra of the Witt... | Schwarzian derivative | 0.780802 |
90,715 | Truncations similarly define homomorphisms of Gk onto Gk − 1; the kernel consists of maps f with f(z) = z + bzk, so is Abelian. Thus the group Gk is solvable, a fact also clear from the fact that it is in triangular form for the basis of monomials. A flat pseudogroup Γ is said to be "defined by differential equations" ... | Schwarzian derivative | 0.780802 |
90,716 | The Schwarzian derivative and the other 1-cocycle defined on Diff(S1) can be extended to biholomorphic between open sets in the complex plane. In this case the local description leads to the theory of analytic pseudogroups, formalizing the theory of infinite-dimensional groups and Lie algebras first studied by Élie Car... | Schwarzian derivative | 0.780802 |
90,717 | The ordinary differential equation is equivalent to the hypergeometric differential equation and f(z) is the Schwarz triangle function, which can be written in terms of hypergeometric functions. For a quadrilateral the accessory parameters depend on one independent variable λ. Writing U(z) = q(z)u(z) for a suitable cho... | Schwarzian derivative | 0.780802 |
90,718 | Chern classes can be used to construct a homomorphism of rings from the topological K-theory of a space to (the completion of) its rational cohomology. For a line bundle L, the Chern character ch is defined by More generally, if V = L 1 ⊕ ⋯ ⊕ L n {\displaystyle V=L_{1}\oplus \cdots \oplus L_{n}} is a direct sum of line... | Total Chern class | 0.780802 |
90,719 | In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of mathematics and physics, such as string theory, Chern–Simons theory, kno... | Total Chern class | 0.780802 |
90,720 | The solution for λ = 0 corresponds to the group 1-cocycle 𝜙0(f) = log f' . The corresponding Lie algebra 1-cocycles for λ = 0, 1, 2 are given up to a scalar multiple by φ λ ( F d d θ ) = d λ + 1 F d θ λ + 1 ( d θ ) λ . {\displaystyle \varphi _{\lambda }\left(F{d \over d\theta }\right)={d^{\lambda +1}F \over d\theta ^{... | Schwarzian derivative | 0.780802 |
90,721 | By continuity this reduces to the computation of crossed homomorphisms 𝜙 of the Witt algebra into Fλ(S1). The normalisations conditions on the group crossed homomorphism imply the following additional conditions for 𝜙: φ ( Ad ( x ) X ) = x ⋅ φ ( X ) , φ ( d / d θ ) = 0 {\displaystyle \varphi (\operatorname {Ad} (x)... | Schwarzian derivative | 0.780802 |
90,722 | {\displaystyle s()=X\cdot s(Y)-Y\cdot s(X).} In the Lie algebra case, the coboundary maps have the form b(X) = X ⋅ m for m in M. In both cases the 1-cohomology is defined as the space of crossed homomorphisms modulo coboundaries. The natural correspondence between group homomorphisms and Lie algebra homomorphisms leads... | Schwarzian derivative | 0.780802 |
90,723 | There is an infinitesimal version of this result giving a 1-cocycle for Vect(S1), the Lie algebra of smooth vector fields, and hence for the Witt algebra, the subalgebra of trigonometric polynomial vector fields. Indeed, when G is a Lie group and the action of G on M is smooth, there is a Lie algebraic version of cross... | Schwarzian derivative | 0.780802 |
90,724 | He tried to ship her belongings to Sweden, but the Reich Ministry of Education insisted they remain in Germany.Meitner was also concerned about her family back in Austria. One of her first actions in Sweden was to apply for a Swedish immigration permit for Gusti and her husband Justinian (Jutz) Frisch. Hahn selected Jo... | Lise Meitner | 0.780801 |
90,725 | They took a train, and then a steamer to von Bahr's home in Kungälv, where she stayed until September. Hahn told everyone at the KWI for Chemistry that Meitner had gone to Vienna to visit her relatives, and a few days later the institute had closed for the summer vacation. On 23 August, she wrote to Bosch requesting re... | Lise Meitner | 0.780801 |
90,726 | The following morning, Meitner arrived early at the KWI for Chemistry, and Hahn briefed her on the plan. To avoid suspicion, she maintained her usual routine, remaining at the institute until 20:00 correcting one of the associate's papers for publication. Hahn and Paul Rosbaud helped her pack two small suitcases, carry... | Lise Meitner | 0.780801 |
90,727 | On 27 June, Meitner received an offer of a one-year position at Manne Siegbahn's new laboratory in Stockholm, then under construction, which would be devoted to nuclear physics, and she decided to accept it. But on 4 July she learned that academics would no longer be granted permission to travel abroad. | Lise Meitner | 0.780801 |
90,728 | Later that year, perhaps fearing that Meitner was in financial difficulties and might return to Vienna, since her father had died in 1910, Planck appointed her his assistant at the Institute for Theoretical Physics in the Friedrich Wilhelm University. As such, she marked his students' papers. It was her first paid posi... | Lise Meitner | 0.780801 |
90,729 | She became the second woman to earn a doctoral degree in physics at the University of Vienna, after Olga Steindler who had received her degree in 1903; the third was Selma Freud, who worked in the same laboratory as Meitner, and received her doctorate later in 1906. Meitner's thesis was published as Wärmeleitung in inh... | Lise Meitner | 0.780801 |
90,730 | Her sister Gisela passed the Matura, and entered medical school in 1900. In 1899, Meitner began taking private lessons with two other young women, cramming the missing eight years of secondary education into just two. Physics was taught by Arthur Szarvasy. | Lise Meitner | 0.780801 |
90,731 | In 2016, the Institute of Physics in the UK established the Meitner Medal for public engagement within physics. In 2017, the Advanced Research Projects Agency-Energy in the United States named a major nuclear energy research program after her. On 6 November 2020, a satellite named after her (ÑuSat 16 or "Lise", COSPAR ... | Lise Meitner | 0.780801 |
90,732 | In 2006 the "Gothenburg Lise Meitner Award" was established by the University of Gothenburg and Chalmers University of Technology in Sweden; it is awarded annually to a scientist who has made a breakthrough in physics. In October 2010, the building at the Free University of Berlin that had once housed the KWI for Chemi... | Lise Meitner | 0.780801 |
90,733 | In 1947, Meitner moved to the Royal Institute of Technology (KTH) in Stockholm, where Gudmund Borelius established a new facility for atomic research. There had been scant nuclear physics research in Sweden, which was blamed on Siegbahn's lack of support for Meitner's work, and now such knowledge seemed vital for Swede... | Lise Meitner | 0.780801 |
90,734 | With the Anschluss, Germany's unification with Austria on 12 March 1938, Meitner lost her Austrian citizenship. Niels Bohr extended an offer to lecture in Copenhagen, and Paul Scherrer invited her to attend a congress in Switzerland, with all expenses paid. Carl Bosch still said that she could remain at the KWI for Che... | Lise Meitner | 0.780801 |
90,735 | Her unit was soon deployed to the Eastern front in Poland, and she also served on the Italian front for a while before being discharged in September 1916. Meitner returned to the KWI for Chemistry and her research in October. In January 1917, she was appointed the head of her own physics section. | Lise Meitner | 0.780801 |
90,736 | Scientists from Germany and around the world came to the KWI for Chemistry to conduct research under her supervision. In 1930, Meitner taught a seminar on "Questions of Atomic Physics and Atomic Chemistry" with Leó Szilárd.Meitner had a Wilson cloud chamber constructed at the KWI for Chemistry, the first one in Berlin,... | Lise Meitner | 0.780801 |
90,737 | These included Arnold Flammersfeld, Kan-Chang Wang and Nikolaus Riehl. In 1926, she became an außerordentlicher Professor (extraordinary professor), the first woman university physics professor in Germany. Her physics section became larger, and she acquired a permanent assistant. | Lise Meitner | 0.780801 |
90,738 | She therefore gave an inaugural lecture on "Problems of Cosmic Physics". From 1923 to 1933, she taught a colloquium or tutorial at Friedrich Wilhelm University each semester, and supervised doctoral students at the KWI for Chemistry. | Lise Meitner | 0.780801 |
90,739 | She was the first woman to receive her habilitation in physics in Prussia, and only the second in Germany after Hedwig Kohn. Since Meitner had already published over 40 papers, she was not required to submit a thesis, but Max von Laue recommended that the requirement for an inaugural lecture not be waived, since he was... | Lise Meitner | 0.780801 |
90,740 | Assistant was the lowest rung on the academic ladder, and Meitner was the first female scientific assistant in Prussia.Proud officials presented Meitner to Kaiser Wilhelm II at the official opening of the KWI for Chemistry on 23 October 1912. The following year she became a Mitglied (associate), the same rank as Hahn (... | Lise Meitner | 0.780801 |
90,741 | In 1912, Hahn and Meitner moved to the newly founded Kaiser Wilhelm Institute (KWI) for Chemistry. Hahn accepted an offer from Fischer to become a junior assistant in charge of its radiochemistry section, the first laboratory of its kind in Germany. The job came with the title of "professor" and a salary of 5,000 marks... | Lise Meitner | 0.780801 |
90,742 | Barium had an atomic mass 40% less than uranium, and no previously known methods of radioactive decay could account for such a large difference in the mass of the nucleus. Nonetheless, she had immediately written back to Hahn to say: "At the moment the assumption of such a thoroughgoing breakup seems very difficult to ... | Lise Meitner | 0.780801 |
90,743 | Alpha particles were emitted with characteristic energy, and she expected that this would be true of beta particles too. Hahn and Meitner carefully measured the absorption of beta particles by aluminium, but the results were puzzling. In 1914, James Chadwick found that electrons emitted from the atomic nucleus formed a... | Lise Meitner | 0.780801 |
90,744 | The Institute of Physics was more accepting, and she became friends with the physicists there, including Otto von Baeyer, James Franck, Gustav Hertz, Robert Pohl, Max Planck, Peter Pringsheim and Wilhelm Westphal.During the first years Meitner worked together with Hahn they co-authored three papers in 1908, and six mor... | Lise Meitner | 0.780801 |
90,745 | Most of the organic chemists at the chemistry institute did not regard Hahn's work—detecting minute traces of isotopes too small to see, weigh or smell through their radioactivity—as real chemistry. One department head remarked that "it is incredible what one gets to be a Privatdozent these days! | Lise Meitner | 0.780801 |
90,746 | It was not possible to conduct research in the wood shop, but Alfred Stock, the head of the inorganic chemistry department, let Hahn use a space in one of his two private laboratories. Like Meitner, Hahn was unpaid, and lived off an allowance from his father, although somewhat larger than hers. He completed his habilit... | Lise Meitner | 0.780801 |
90,747 | In Montreal, Hahn had become accustomed to collaboration with physicists, including at least one woman, Harriet Brooks. The head of the chemistry institute, Emil Fischer, placed a former woodworking shop (Holzwerkstatt) at Hahn's disposal in the basement to use as a laboratory. Hahn equipped it with electroscopes to me... | Lise Meitner | 0.780801 |
90,748 | He also added that Otto Hahn at the chemistry institute was looking for a physicist to collaborate with. A few minutes later she was introduced to Hahn. He had studied radioactive substances under Sir William Ramsay, and in Montreal under Rutherford, and was already credited with the discovery of what were then thought... | Lise Meitner | 0.780801 |
90,749 | Encouraged and backed by her father's financial support, Meitner went to the Friedrich Wilhelm University, where the renowned physicist Max Planck taught. Planck invited her to his home, and allowed her to attend his lectures, which was an unusual gesture by Planck, who was on the record as opposing the admission of wo... | Lise Meitner | 0.780801 |
90,750 | Both he and Meitner had been nominated for both the chemistry and the physics prizes several times even before the discovery of nuclear fission. According to the Nobel Prize archive, she was nominated 19 times for Nobel Prize in Chemistry between 1924 and 1948, and 30 times for Nobel Prize in Physics between 1937 and 1... | Lise Meitner | 0.780801 |
90,751 | In his report on the work of Meitner and Frisch, Hulthén relied on pre-war papers. He did not think that their work was groundbreaking, and argued that the prize for physics was given for experimental rather than theoretical work, which had not been the case for many years.At the time Meitner herself wrote in a letter,... | Lise Meitner | 0.780801 |
90,752 | All three were part of the Siegbahn school of x-ray spectroscopy. The poor relationship between Siegbahn and Meitner was a factor here, as was the bias towards experimental rather than theoretical physics. | Lise Meitner | 0.780801 |
90,753 | In a 1997 article in the American Physical Society journal Physics Today, Sime and her colleagues Elisabeth Crawford and Mark Walker wrote: It appears that Lise Meitner did not share the 1944 prize because the structure of the Nobel committees was ill-suited to assess interdisciplinary work; because the members of the ... | Lise Meitner | 0.780801 |
90,754 | Without these contributions of Meitner, Hahn would not have found that the uranium nucleus can split in half. In 1945 the Nobel Committee for Chemistry in Sweden that selected the Nobel Prize in Chemistry decided to award that prize solely to Hahn: Hahn only found out from a newspaper while interned in Farm Hall Cambri... | Lise Meitner | 0.780801 |
90,755 | Despite the many honours that Meitner received in her lifetime, she did not receive the Nobel Prize while it was awarded to Otto Hahn for the discovery of nuclear fission. She was nominated 49 times for Physics and Chemistry Nobel Prizes but never won. On 15 November 1945, the Royal Swedish Academy of Sciences announce... | Lise Meitner | 0.780801 |
90,756 | Radiochemistry was now no longer confined to certain heavy elements, but extended to the entire periodic table. Chadwick noted that being electrically neutral, neutrons could penetrate the atomic nucleus more easily than protons or alpha particles. Enrico Fermi and his colleagues in Rome picked up on this idea, and beg... | Lise Meitner | 0.780801 |
90,757 | Stern found Frisch a position with Patrick Blackett at Birkbeck College in England, and he later worked at the Niels Bohr Institute in Copenhagen from 1934 to 1939. Fritz Strassman had come to the Kaiser Wilhelm Institute for Chemistry to study under Hahn to improve his employment prospects. He declined a lucrative off... | Lise Meitner | 0.780801 |
90,758 | This had no effect on her salary or work at the KWI for Chemistry. Carl Bosch, the director of IG Farben, a major sponsor of the KWI for Chemistry, assured Meitner that her position there was safe. Although Hahn and Meitner remained in charge, their assistants, Otto Erbacher and Kurt Philipp respectively, who were both... | Lise Meitner | 0.780801 |
90,759 | On 25 January 1946, Meitner arrived in New York, where she was greeted by her sisters Lola and Frida, and by Frisch, who had made the two-day train trip from Los Alamos. Lola's husband Rudolf Allers arranged a visiting professorship for Meitner at the Catholic University of America. Meitner lectured at Princeton Univer... | Lise Meitner | 0.780801 |
90,760 | Several scientists and journalists have called her exclusion "unjust". According to the Nobel Prize archive, she was nominated 19 times for the Nobel Prize in Chemistry between 1924 and 1948, and 30 times for the Nobel Prize in Physics between 1937 and 1967. Despite not having been awarded the Nobel Prize, Meitner was ... | Lise Meitner | 0.780801 |
90,761 | In their report in February issue of Nature in 1939, they gave it the name "fission". This principle led to the development of the first atomic bomb during World War II, and subsequently other nuclear weapons and nuclear reactors. Meitner did not share the 1944 Nobel Prize in Chemistry for nuclear fission, which was aw... | Lise Meitner | 0.780801 |
90,762 | Hahn and Strassmann later in the year showed that isotopes of barium could be formed by bombardment of uranium. In late December, Meitner and Frisch worked out the physics of such a splitting process. | Lise Meitner | 0.780801 |
90,763 | She spent most of her scientific career in Berlin, Germany, where she was a physics professor and a department head at the Kaiser Wilhelm Institute; she was the first woman to become a full professor of physics in Germany. She lost these positions in the 1930s because of the anti-Jewish Nuremberg Laws of Nazi Germany, ... | Lise Meitner | 0.780801 |
90,764 | Lise Meitner ( LEE-zə MYTE-nər, German: ; born Elise Meitner, 7 November 1878 – 27 October 1968) was an Austrian-Swedish physicist who was one of those responsible for the discovery of the element protactinium and nuclear fission. While working on radioactivity at the Kaiser Wilhelm Institute of Chemistry in Berlin, s... | Lise Meitner | 0.780801 |
90,765 | Vindhyan Ecology and Natural History Foundation challenged the declaration of 1 km Eco-Sensitive Zone around Kaimoor Wildlife Sanctuary in the districts of Mirzapur and Sonbhadra in Uttar Pradesh at the National Green Tribunal, New Delhi The petition said the Ministry of Environment, Forest and Climate Change should ha... | Vindhyan Ecology and Natural History Foundation | 0.780799 |
90,766 | Debadityo Sinha, the founder of Vindhyan Ecology and Natural History Foundation was awarded the Sanctuary Wildlife Service Award on 20 December 2019 by Sanctuary Asia, DSP Mutual Fund and IndusInd Bank. | Vindhyan Ecology and Natural History Foundation | 0.780799 |
90,767 | The Vindhyan Ecology and Natural History Foundation (VENHF) is a registered non-profit organisation (2012) with its headquarter in Mirzapur, Uttar Pradesh, India, working for the protection and conservation of the nature, natural resources and rights of the nature dependent communities in the ecologically fragile lands... | Vindhyan Ecology and Natural History Foundation | 0.780799 |
90,768 | In the year 2017, Vindhyan Ecology and Natural History Foundation in association with WWF-India published a sign-based study on Sloth Bears in Mirzapur, which identified five forest ranges as critical wildlife habitats. The study estimated an area of 430 km2 (170 sq mi). of core Sloth bear habitat and a total of 1,110 ... | Vindhyan Ecology and Natural History Foundation | 0.780799 |
90,769 | The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. Its actions model indivisible communications between exactly two participants. The formal language includes primitives for describing parallel composition, choice bet... | Calculus of Communicating Systems | 0.780799 |
90,770 | Communicating sequential processes (CSP), developed by Tony Hoare, is a formal language that arose at a similar time to CCS. The Algebra of Communicating Processes (ACP) was developed by Jan Bergstra and Jan Willem Klop in 1982, and uses an axiomatic approach (in the style of Universal algebra) to reason about a simila... | Calculus of Communicating Systems | 0.780799 |
90,771 | CCS is useful for evaluating the qualitative correctness of properties of a system such as deadlock or livelock.According to Milner, "There is nothing canonical about the choice of the basic combinators, even though they were chosen with great attention to economy. What characterises our calculus is not the exact choic... | Calculus of Communicating Systems | 0.780799 |
90,772 | Moreover, for commutative rings, this bijective correspondence restricts to prime ideals, maximal ideals, and radical ideals (see the Types of ideals section for the definitions of these ideals). (For those who know modules) If M is a left R-module and S ⊂ M {\displaystyle S\subset M} a subset, then the annihilator Ann... | Finitely generated ideal | 0.780798 |
90,773 | The phenomenon of periodicity named after Raoul Bott (see Bott periodicity theorem) can be formulated this way: K ( X × S 2 ) = K ( X ) ⊗ K ( S 2 ) , {\displaystyle K(X\times \mathbb {S} ^{2})=K(X)\otimes K(\mathbb {S} ^{2}),} and K ( S 2 ) = Z / ( H − 1 ) 2 {\displaystyle K(\mathbb {S} ^{2})=\mathbb {Z} /(H-1)^{2}} w... | Topological K-theory | 0.780796 |
90,774 | {\displaystyle {\widetilde {K}}^{-n}(X):={\widetilde {K}}(S^{n}X),\qquad n\geq 0.} Negative indices are chosen so that the coboundary maps increase dimension. It is often useful to have an unreduced version of these groups, simply by defining: K − n ( X ) = K ~ − n ( X + ) . {\displaystyle K^{-n}(X)={\widetilde {K}}^{-... | Topological K-theory | 0.780796 |
90,775 | The Splitting principle of topological K-theory allows one to reduce statements about arbitrary vector bundles to statements about sums of line bundles. The Thom isomorphism theorem in topological K-theory is where T(E) is the Thom space of the vector bundle E over X. This holds whenever E is a spin-bundle. The Atiyah-... | Topological K-theory | 0.780796 |
90,776 | K n {\displaystyle K^{n}} (respectively, K ~ n {\displaystyle {\widetilde {K}}^{n}} ) is a contravariant functor from the homotopy category of (pointed) spaces to the category of commutative rings. Thus, for instance, the K-theory over contractible spaces is always Z . {\displaystyle \mathbb {Z} .} The spectrum of K-th... | Topological K-theory | 0.780796 |
90,777 | The newly formed diatomic molecules initially have a very high vibrational temperature that efficiently transforms the vibrational energy into radiant energy; i.e., radiative heat flux. The whole process takes place in less than a millisecond which makes modelling a challenge. The experimental measurement of radiative ... | Phenolic impregnated carbon ablator | 0.780796 |
90,778 | The five species model is based upon 5 ordinary differential equations and 17 algebraic equations. Because the 5 ordinary differential equations are tightly coupled, the system is numerically "stiff" and difficult to solve. The five species model is only usable for entry from low Earth orbit where entry velocity is app... | Phenolic impregnated carbon ablator | 0.780796 |
90,779 | With a non-equilibrium program, the computation process is time accurate and follows a solution path dictated by chemical and reaction rate formulas. The five species model has 17 chemical formulas (34 when counting reverse formulas). The Lighthill-Freeman model is based upon a single ordinary differential equation and... | Phenolic impregnated carbon ablator | 0.780796 |
90,780 | A non-equilibrium real gas model is the most accurate model of a shock layer's gas physics, but is more difficult to solve than an equilibrium model. The simplest non-equilibrium model is the Lighthill-Freeman model developed in 1958. The Lighthill-Freeman model initially assumes a gas made up of a single diatomic spec... | Phenolic impregnated carbon ablator | 0.780796 |
90,781 | He then hypothesizes that this energy difference causes the wave function to collapse to a single state, with a probability based on its amplitude in the original wave function, a procedure derived from standard quantum mechanics. Penrose's "'one-graviton' level" criterion forms the basis of his prediction, providing a... | Penrose interpretation of Quantum Theory | 0.780794 |
90,782 | Cybercriminals attack video game players to steal their credentials, ID or data, as well as to steal payment card details or cash held in gaming accounts. Part of the motivation for attacking players is that they are seen as both a honeypot (they have something worth stealing), are a relatively vulnerable target (becau... | Video game behavioral effects | 0.780793 |
90,783 | Other common occurrences include online casino scams, phishing, cell phone dialers, malware in illegal downloads, and money laundering. Others have found ways to use a built-in systems for illegal profit, notably the use of skin gambling tied to games like Counter-Strike: Global Offensive drew attention to how in-game ... | Video game behavioral effects | 0.780793 |
90,784 | These systems use the principle of harnessing the power generated from renewable and inexhaustible sources of energy, for example; solar, wind, thermal, biomass, geothermal, and hydropower energy. Solar power is a widely known and used renewable energy source. An increase in technology has allowed solar power to be use... | Ecological Design | 0.780793 |
90,785 | The design of a product unrelated to its sociological, psychological, or ecological surroundings is no longer possible or acceptable in modern society.With respect to these concepts, online platforms dealing in only Ecodesign products are emerging, with the additional sustainable purpose of eliminating all unnecessary ... | Ecological Design | 0.780793 |
90,786 | Related to ecological urbanism, Urban Ecological Design integrates aesthetic, social, and ecological concerns into an urban design framework that seeks to increase ecological functioning, sustainably generate & consume resources, and create resilient built environments & the infrastructure to maintain them. Urban ecolo... | Ecological Design | 0.780793 |
90,787 | Ecological design or ecodesign is an approach to designing products and services that gives special consideration to the environmental impacts of a product over its entire lifecycle. Sim Van der Ryn and Stuart Cowan define it as "any form of design that minimizes environmentally destructive impacts by integrating itsel... | Ecological Design | 0.780793 |
90,788 | More broadly, the conference emphasized that designers must address human issues. These problems included six items: quality of life, efficient use of natural resources, protecting the global commons, managing human settlements, the use of chemicals and the management of human industrial waste, and fostering sustainabl... | Ecological Design | 0.780793 |
90,789 | (The symbol " ∂ {\displaystyle \partial } " is meant to signify that, in the derivative with respect to some variable, all other variables must be considered fixed.) This equation can be derived from the laws of physics that govern the diffusion of heat in solid media. For that reason, it is called the heat equation in... | Progressive wave | 0.780792 |
90,790 | On the other hand, some waves have envelopes which do not move at all such as standing waves (which are fundamental to music) and hydraulic jumps. Some, like the probability waves of quantum mechanics, may be completely static. A physical wave field is almost always confined to some finite region of space, called its d... | Progressive wave | 0.780792 |
90,791 | Waves are often described by a wave equation (standing wave field of two opposite waves) or a one-way wave equation for single wave propagation in a defined direction. Two types of waves are most commonly studied in classical physics. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibri... | Progressive wave | 0.780792 |
90,792 | In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in ... | Progressive wave | 0.780792 |
90,793 | The DelFly project started in 2005 as a Design Synthesis Exercise for a group of Bachelor of Science students at the Faculty of Aerospace Engineering of the TU Delft. The flapping wing design was mentored by Wageningen University, the remote control and micro camera integration by Ruijsink Dynamic Engineering, and the ... | DelFly | 0.780792 |
90,794 | The design of autonomous, light-weight, less than 20 grams flapping wing MAVs poses challenges in various domains, including materials, electronics, control, aerodynamics, computer vision and artificial intelligence. All these domains feed into each other. For example, studies on the design and aerodynamics of the wing... | DelFly | 0.780791 |
90,795 | The Lick–Carnegie Exoplanet Survey (LCES) is a search for exoplanets using the Keck I optical telescope of the W. M. Keck Observatory in Hawaii. The survey is sponsored by NASA and the National Science Foundation. The survey comprises a decade of observations. The survey is led by Steven Vogt, professor of astronomy an... | Lick–Carnegie Exoplanet Survey | 0.780791 |
90,796 | Wolfgang Ernst Pauli (; German: ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Na... | Wolfgang Pauli | 0.78079 |
90,797 | In 1940, Pauli moved to the United States, where he was employed as a professor of theoretical physics at the Institute for Advanced Study. In 1946, after the war, he became a naturalized U.S. citizen and returned to Zurich, where he mostly remained for the rest of his life. In 1949, he was granted Swiss citizenship. | Wolfgang Pauli | 0.78079 |
90,798 | Robert Oppenheimer called it "the only adult introduction to quantum mechanics. "The German annexation of Austria in 1938 made Pauli a German citizen, which became a problem for him in 1939 after World War II broke out. In 1940, he tried in vain to obtain Swiss citizenship, which would have allowed him to remain at the... | Wolfgang Pauli | 0.78079 |
90,799 | In his discussions with Carl Jung, Pauli developed an ontological theory that has been dubbed the "Pauli–Jung Conjecture" and has been seen a kind of dual-aspect theory. The theory holds that there is "a psychophysically neutral reality" and that mental and physical aspects are derivative of this reality. Pauli thought... | Wolfgang Pauli | 0.78079 |
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