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94,700 | F. Q. Gouvêa's 1994 article "A Marvelous Proof", which reviews some of the required topics, won a Lester R. Ford award from the Mathematical Association of America. Faltings' 5-page technical bulletin on the matter is a quick and technical review of the proof for the non-specialist. For those in search of a commerciall... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,701 | Wiles's paper is over 100 pages long and often uses the specialised symbols and notations of group theory, algebraic geometry, commutative algebra, and Galois theory. The mathematicians who helped to lay the groundwork for Wiles often created new specialised concepts and technical jargon. Among the introductory present... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,702 | The proof falls roughly in two parts. In the first part, Wiles proves a general result about "lifts", known as the "modularity lifting theorem". This first part allows him to prove results about elliptic curves by converting them to problems about Galois representations of elliptic curves. He then uses this result to p... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,703 | Wiles proved the modularity theorem for semistable elliptic curves, from which Fermat’s last theorem follows using proof by contradiction. In this proof method, one assumes the opposite of what is to be proved, and shows if that were true, it would create a contradiction. The contradiction shows that the assumption (th... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,704 | Wiles's goal was to verify that the map R → T {\displaystyle R\rightarrow \mathbf {T} } is an isomorphism and ultimately that R = T {\displaystyle R=\mathbf {T} } . In treating deformations, Wiles defined four cases, with the flat deformation case requiring more effort to prove and treated in a separate article in the ... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,705 | This is sometimes referred to as the "numerical criterion". Given this result, Fermat's Last Theorem is reduced to the statement that two groups have the same order. Much of the text of the proof leads into topics and theorems related to ring theory and commutation theory. | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,706 | Wiles initially presented his proof in 1993. It was finally accepted as correct, and published, in 1995, following the correction of a subtle error in one part of his original paper. His work was extended to a full proof of the modularity theorem over the following six years by others, who built on Wiles's work. | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,707 | His article was published in 1990. In doing so, Ribet finally proved the link between the two theorems by confirming, as Frey had suggested, that a proof of the Taniyama–Shimura–Weil conjecture for the kinds of elliptic curves Frey had identified, together with Ribet's theorem, would also prove Fermat's Last Theorem. I... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,708 | However his partial proof came close to confirming the link between Fermat and Taniyama. In the summer of 1986, Ken Ribet succeeded in proving the epsilon conjecture, now known as Ribet's theorem. | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,709 | To complete this link, it was necessary to show that Frey's intuition was correct: that a Frey curve, if it existed, could not be modular. In 1985, Jean-Pierre Serre provided a partial proof that a Frey curve could not be modular. Serre did not provide a complete proof of his proposal; the missing part (which Serre had... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,710 | The main conjectures Chapter 3 517 Estimates for the Selmer group Chapter 4 525 1. The ordinary CM case 533 2. Calculation of η Chapter 5 541 Application to elliptic curves Appendix 545 Gorenstein rings and local complete intersectionsGerd Faltings subsequently provided some simplifications to the 1995 proof, primarily... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,711 | It is easy to demonstrate that these representations come from some elliptic curve but the converse is the difficult part to prove. Instead of trying to go directly from the elliptic curve to the modular form, one can first pass to the ( m o d ℓ n ) {\displaystyle (\mathrm {mod} \,\ell ^{n})} representation for some ℓ ... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,712 | This would finally prove Fermat's Last Theorem.However, despite the progress made by Serre and Ribet, this approach to Fermat was widely considered unusable as well, since almost all mathematicians saw the Taniyama–Shimura–Weil conjecture itself as completely inaccessible to proof with current knowledge. : 203–205, 223... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,713 | Following the developments related to the Frey curve, and its link to both Fermat and Taniyama, a proof of Fermat's Last Theorem would follow from a proof of the Taniyama–Shimura–Weil conjecture—or at least a proof of the conjecture for the kinds of elliptic curves that included Frey's equation (known as semistable ell... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,714 | Fermat's Last Theorem, formulated in 1637, states that no three positive integers a, b, and c can satisfy the equation a n + b n = c n {\displaystyle a^{n}+b^{n}=c^{n}} if n is an integer greater than two (n > 2). Over time, this simple assertion became one of the most famous unproved claims in mathematics. Between its... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,715 | Fermat claimed to "... have discovered a truly marvelous proof of this, which this margin is too narrow to contain". Wiles's proof is very complex, and incorporates the work of so many other specialists that it was suggested in 1994 that only a small number of people were capable of fully understanding at that time all... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,716 | The two papers were vetted and finally published as the entirety of the May 1995 issue of the Annals of Mathematics. The new proof was widely analysed, and became accepted as likely correct in its major components. These papers established the modularity theorem for semistable elliptic curves, the last step in proving ... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,717 | It was the most important moment of my working life. Nothing I ever do again will mean as much. On 6 October Wiles asked three colleagues (including Faltings) to review his new proof, and on 24 October 1994 Wiles submitted two manuscripts, "Modular elliptic curves and Fermat's Last Theorem" and "Ring theoretic properti... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,718 | The error would not have rendered his work worthless—each part of Wiles's work was highly significant and innovative by itself, as were the many developments and techniques he had created in the course of his work, and only one part was affected. : 289, 296–297 Without this part proved, however, there was no actual pro... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,719 | During 21–23 June 1993, Wiles announced and presented his proof of the Taniyama–Shimura conjecture for semistable elliptic curves, and hence of Fermat's Last Theorem, over the course of three lectures delivered at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England. There was a relatively large a... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,720 | This became known as the Taniyama–Shimura conjecture. In the West, this conjecture became well known through a 1967 paper by André Weil, who gave conceptual evidence for it; thus, it is sometimes called the Taniyama–Shimura–Weil conjecture. By around 1980, much evidence had been accumulated to form conjectures about el... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,721 | Separately from anything related to Fermat's Last Theorem, in the 1950s and 1960s Japanese mathematician Goro Shimura, drawing on ideas posed by Yutaka Taniyama, conjectured that a connection might exist between elliptic curves and modular forms. These were mathematical objects with no known connection between them. Ta... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,722 | Frey showed that there were good reasons to believe that any set of numbers (a, b, c, n) capable of disproving Fermat's Last Theorem could also probably be used to disprove the Taniyama–Shimura–Weil conjecture. Therefore, if the Taniyama–Shimura–Weil conjecture were true, no set of numbers capable of disproving Fermat ... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,723 | Such an elliptic curve would enjoy very special properties due to the appearance of high powers of integers in its equation and the fact that an + bn = cn would be an nth power as well. In 1982–1985, Gerhard Frey called attention to the unusual properties of this same curve, now called a Frey curve. He showed that it w... | Wiles's proof of Fermat's Last Theorem | 0.779037 |
94,724 | The United States Naval Research Laboratory used steel rods wrapped into a helix, but this was useful only for low frequencies under 1 MHz. Raytheon used a magnesium alloy originally developed for making bells.The first practical de-cluttering system based on the concept was developed by J. Presper Eckert at the Univer... | Mercury delay line | 0.779035 |
94,725 | Understanding the stereochemistry of α-diazo ketones is essential in elucidating the mechanism of the Wolff rearrangement. α-diazocarbonyl compounds are generally locally planar, with large rotational barriers (55–65 kJ/mol) due to C-C olefin character between the carbonyl and α-carbon, illustrated in the rightmost res... | Wolff rearrangement | 0.779035 |
94,726 | The reaction is occasionally called the Wolff-Schröter rearrangement. The Wolff rearrangement was not commonly used until 20 years after it was discovered, as facile diazo ketone synthesis was unknown until the 1930s. The reaction has proven useful in synthetic organic chemistry and many reviews have been published. | Wolff rearrangement | 0.779035 |
94,727 | The Wolff rearrangement is a reaction in organic chemistry in which an α-diazocarbonyl compound is converted into a ketene by loss of dinitrogen with accompanying 1,2-rearrangement. The Wolff rearrangement yields a ketene as an intermediate product, which can undergo nucleophilic attack with weakly acidic nucleophiles ... | Wolff rearrangement | 0.779035 |
94,728 | Opricovic had developed the basic ideas of VIKOR in his Ph.D. dissertation in 1979, and an application was published in 1980. The name VIKOR appeared in 1990 from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje, that means: Multicriteria Optimization and Compromise Solution, with pronunciation: vikor. | VIKOR method | 0.779033 |
94,729 | Pósa's theorem, in graph theory, is a sufficient condition for the existence of a Hamiltonian cycle based on the degrees of the vertices in an undirected graph. It implies two other degree-based sufficient conditions, Dirac's theorem on Hamiltonian cycles and Ore's theorem. Unlike those conditions, it can be applied to... | Pósa's theorem | 0.779029 |
94,730 | As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L(E, s) of E at s = 1 implies that the p-adic Selmer group of E is infinite. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich c... | Iwasawa main conjecture | 0.779028 |
94,731 | In mathematics, the main conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by Mazur and Wiles (1984). The Herbrand–Ribet theorem and the Gra... | Iwasawa main conjecture | 0.779028 |
94,732 | The main conjecture of Iwasawa theory was formulated as an assertion that two methods of defining p-adic L-functions (by module theory, by interpolation) should coincide, as far as that was well-defined. This was proved by Mazur & Wiles (1984) for Q, and for all totally real number fields by Wiles (1990). These proofs ... | Iwasawa main conjecture | 0.779028 |
94,733 | In some approaches the floorplan may be a partition of the whole chip area into axis aligned rectangles to be occupied by IC blocks. This partition is subject to various constraints and requirements of optimization: block area, aspect ratios, estimated total measure of interconnects, etc. Finding good floorplans has be... | Floorplan (microelectronics) | 0.779028 |
94,734 | On the December 2006 analyst day, Executive vice president Marty Seyer announced a new mobile core codenamed Griffin launched in 2008 with inherited power optimizations technologies from the K10 microarchitecture, but based on a K8 design. | AMD 10h | 0.779024 |
94,735 | The National Materials Advisory Board (NMAB) of the National Academy of Engineering (NAE) committee proposed the following definition for the term ICME cyberinfrastructure: "The Internet-based collaborative materials science and engineering research and development environments that support advanced data acquisition, d... | ICME cyberinfrastructure | 0.779021 |
94,736 | Integrated computational materials engineering (ICME) involves the integration of experimental results, design models, simulations, and other computational data related to a variety of materials used in multiscale engineering and design. Central to the achievement of ICME goals has been the creation of a cyberinfrastru... | ICME cyberinfrastructure | 0.779021 |
94,737 | A conditional knockout mouse line, called Slc16a2tm1a(KOMP)Wtsi was generated as part of the International Knockout Mouse Consortium program—a high-throughput mutagenesis project to generate and distribute animal models of disease to interested scientists.Male and female animals underwent a standardized phenotypic scre... | Monocarboxylate transporter 8 | 0.779018 |
94,738 | Two orbits that have been used for such purposes include halo and Lissajous orbits.One important Lagrange point is Earth-Sun L1, and three heliophysics missions have been orbiting L1 since approximately 2000. Station-keeping propellant use can be quite low, facilitating missions that can potentially last decades should... | Orbital station keeping | 0.779017 |
94,739 | The "application" of the operator on a differentiable wave function is as follows: In a basis of Hilbert space consisting of momentum eigenstates expressed in the momentum representation, the action of the operator is simply multiplication by p, i.e. it is a multiplication operator, just as the position operator is a m... | Momentum operator | 0.779016 |
94,740 | In quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is: where ħ is Planck's reduced constant, i the imaginar... | Momentum operator | 0.779016 |
94,741 | The principle of sampling was developed during the 1930s in Bell Laboratories by Nyquist, after whom the sampling theorem is named. The first sampling oscilloscope was, however, developed in the late 1950s at the Atomic Energy Research Establishment at Harwell in England by G.B.B. Chaplin, A.R. | PC-based oscilloscope | 0.779014 |
94,742 | A screen image can also be saved to internal or removable storage, or sent to a built-in or externally connected printer, without the need for an oscilloscope camera. The oscilloscope's own signal analysis software can extract many useful time-domain features (e.g., rise time, pulse width, amplitude), frequency spectra... | PC-based oscilloscope | 0.779014 |
94,743 | Multiple studies in various disciplines and countries found that teachers systematically give higher grades to girls and women. This bias is present at every level of education, in elementary school (United States), middle school (France, Norway, United Kingdom, United States) and high school (Czech Republic). Grading ... | Discrimination in education | 0.779014 |
94,744 | Information gathered with LLDP can be stored in the device management information base (MIB) and queried with the Simple Network Management Protocol (SNMP) as specified in RFC 2922. The topology of an LLDP-enabled network can be discovered by crawling the hosts and querying this database. Information that may be retrie... | Link Layer Discovery Protocol | 0.779012 |
94,745 | The observatory originally contained the Rayna Telescope, an 18 inches (460 mm) newtonian reflector on a fork mount, this was dedicated to long standing member Ray Jackson and his wife Ina. The telescope was built by Peter Drew of the Amateur Astronomy Centre, Todmorden. It was based around an 18-inch f/4.5 parabolic m... | Hoober Observatory | 0.779012 |
94,746 | The Hoober Observatory is owned and operated by Mexborough & Swinton Astronomical Society, a society and charity based in Swinton, South Yorkshire. Founded on 21 May 1978 as "The Night Sky Astronomy Club" it amalgamated with "The Mexborough Astronomy Club" in late 1978 and became the "Mexborough & Swinton Astronomical ... | Hoober Observatory | 0.779012 |
94,747 | {\displaystyle f^{!}} , the Grothendieck residue symbol, the dualizing sheaf in the Cohen–Macaulay case. In order to get a statement in more classical language, but still wider than Serre duality, Hartshorne (Algebraic Geometry) uses the Ext functor of sheaves; this is a kind of stepping stone to the derived category. | Coherent duality | 0.779011 |
94,748 | = R f ∗ {\displaystyle Rf_{! }=Rf_{\ast }} is a right adjoint to the inverse image functor f ∗ {\displaystyle f^{\ast }} . The existence theorem for the twisted inverse image is the name given to the proof of the existence for what would be the counit for the comonad of the sought-for adjunction, namely a natural trans... | Coherent duality | 0.779011 |
94,749 | . Higher direct images are a sheafified form of sheaf cohomology in this case with proper (compact) support; they are bundled up into a single functor by means of the derived category formulation of homological algebra (introduced with this case in mind). If f {\displaystyle f} is proper, then R f ! | Coherent duality | 0.779011 |
94,750 | If such a rigid dualizing complex exists, then it is unique in a strong sense.Assuming A {\displaystyle A} is a localization of a finite type k {\displaystyle k} -algebra, existence of a rigid dualizing complex over A {\displaystyle A} relative to k {\displaystyle k} was first proved by Yekutieli and Zhang assuming k {... | Coherent duality | 0.779011 |
94,751 | This notion was first defined by Van den Bergh in a noncommutative context. The construction is based on a variant of derived Hochschild cohomology (Shukla cohomology): Let k {\displaystyle k} be a commutative ring, and let A {\displaystyle A} be a commutative k − {\displaystyle k-} algebra. There is a functor R H o m ... | Coherent duality | 0.779011 |
94,752 | The resulting theory is now sometimes called Serre–Grothendieck–Verdier duality, and is a basic tool in algebraic geometry. A treatment of this theory, Residues and Duality (1966) by Robin Hartshorne, became a reference. | Coherent duality | 0.779011 |
94,753 | In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory. The historical roots of the theory lie in the idea of the adjoint ... | Coherent duality | 0.779011 |
94,754 | Continuity of set-valued functions is commonly defined in terms of lower- and upper-hemicontinuity popularized by Berge. In this sense, a set-valued function is continuous if and only if the function f S: X → 2 Y {\displaystyle f_{S}:X\to 2^{Y}} defined by f ( x ) = S ( x ) {\displaystyle f(x)=S(x)} is continuous with ... | Kuratowski convergence | 0.77901 |
94,755 | In fractal geometry, the generalized Hurst exponent has been denoted by H or Hq in honor of both Harold Edwin Hurst and Ludwig Otto Hölder (1859–1937) by Benoît Mandelbrot (1924–2010). H is directly related to fractal dimension, D, and is a measure of a data series' "mild" or "wild" randomness.The Hurst exponent is ref... | Hurst exponent | 0.779008 |
94,756 | As Artificial Intelligence and ground-sensing technologies like LIDAR began to improve in the 2000s, major automotive manufacturers such as Ford, Nissan and General Motors began developing self-driving prototypes. Google began developing a self-driving vehicle prototype, named Waymo in 2009 while Tesla Motors rolled ou... | Technologies in Minority Report | 0.779007 |
94,757 | As the geometry of the brush is also distorted from circular by the accelerator bar, the contact angle of the bristle tips with the surface is also nearer to perpendicular than the tangential contact of the circular rotary brush. This encourages a cleaning action and reduces the burnishing action that can be a problem ... | Bristle blasting | 0.779006 |
94,758 | A commutative C*-algebra is σ-unital if and only if its spectrum is σ-compact. In general, a C*-algebra A is σ-unital if and only if A contains a strictly positive element, i.e. there exists h in A+ such that the hereditary C*-subalgebra generated by h is A. One sometimes considers approximate identities consisting of ... | Approximation of the identity | 0.779004 |
94,759 | For example, for compact operators acting on a Hilbert space, the net consisting of finite rank projections would be another approximate identity. If an approximate identity is a sequence, we call it a sequential approximate identity and a C*-algebra with a sequential approximate identity is called σ-unital. Every sepa... | Approximation of the identity | 0.779004 |
94,760 | For C*-algebras, a right (or left) approximate identity consisting of self-adjoint elements is the same as an approximate identity. The net of all positive elements in A of norm ≤ 1 with its natural order is an approximate identity for any C*-algebra. This is called the canonical approximate identity of a C*-algebra. A... | Approximation of the identity | 0.779004 |
94,761 | In mathematics, particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element. | Approximation of the identity | 0.779004 |
94,762 | In ring theory, an approximate identity is defined in a similar way, except that the ring is given the discrete topology so that a = aeλ for some λ. A module over a ring with approximate identity is called non-degenerate if for every m in the module there is some λ with m = meλ. | Approximation of the identity | 0.779004 |
94,763 | Community fingerprinting is a set of molecular biology techniques that can be used to quickly profile the diversity of a microbial community. Rather than directly identifying or counting individual cells in an environmental sample, these techniques show how many variants of a gene are present. In general, it is assumed... | Community fingerprinting | 0.779002 |
94,764 | Ranjard et al. discuss several examples of types of studies in which RISA can be used. They cite several studies that have used this technique to fingerprint bacterial communities following such disturbances as antibiotic treatment, mercury stress and deforestation. They also demonstrated the successful use of ARISA fo... | Community fingerprinting | 0.779002 |
94,765 | Gamma ray and X-ray sources may be treated as a point source if sufficiently small. Radiological contamination and nuclear sources are often point sources. This has significance in health physics and radiation protection. Examples: Radio antennas are often smaller than one wavelength, even though they are many metres a... | Point light source | 0.779002 |
94,766 | Depth measurement: Depth gauge (using pressure as a proxy) Dive computer (using pressure as a proxy) Measuring tape (direct linear measurement) Pneumofathometer (using pressure as a proxy)Length measurement in other directions: Measuring tape Surveyor's chain Calibrated distance line Towed GPS receiver on float (by sph... | Underwater survey | 0.779002 |
94,767 | This meaning is often used in scientific contexts, and also in civil engineering and mineral extraction. Another meaning, often used in a civil, structural, or marine engineering context, is the inspection of a structure or vessel to compare actual condition with the specified nominal condition, usually with the purpos... | Underwater survey | 0.779002 |
94,768 | They consist typically of a tight grid of high resolution (high frequency) reflection seismology profiles to look for possible gas hazards in the shallow section beneath the seabed and detailed bathymetric data to look for possible obstacles on the seafloor (e.g. shipwrecks, existing pipelines) using multibeam echosoun... | Underwater survey | 0.779002 |
94,769 | To operate, the frame is lowered until the rope slacks off, then lifted and the boat moved to the next position. Underwater videography, the branch of electronic underwater photography concerned with capturing underwater moving images, and live video feeds, which allow a remote operator to see the underwater environmen... | Underwater survey | 0.779001 |
94,770 | A geological survey is the systematic investigation of the geology beneath a given piece of ground for the purpose of creating a geological map or model. Underwater geological surveying employs techniques from the underwater equivalent of a traditional walk-over survey, studying outcrops and landforms, to intrusive met... | Underwater survey | 0.779001 |
94,771 | In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (the z-domain or z-plane) representation.It can be considered as a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). This simi... | Z-transform | 0.779001 |
94,772 | He was appointed the UK's first Regius Professor of Computer Science in 2014. From 2010 to 2015, he was the UK Government's first Chief Scientific Advisor for National Security.In 2016, he moved to Imperial College to be the Vice-Provost (Research and Enterprise), as well as a Professor of Artificial Intelligence. In 2... | Nick Jennings (computer scientist) | 0.778996 |
94,773 | In undertaking this research, he has attracted grant income of £33M, published more than 700 articles (with over 400 co-authors) and graduated over 50 PhD students (including two winners and one runner-up of the British Computer Society (BCS)/CPHC Distinguished Dissertation Award.) He has over 90,000 citations in Googl... | Nick Jennings (computer scientist) | 0.778996 |
94,774 | His research is on developing AI systems for large-scale, open and dynamic environments. In particular, he focuses on endowing individual autonomous agents with the ability to act and interact in flexible ways and with building systems that contain both humans and software agents. He has been involved with deployments ... | Nick Jennings (computer scientist) | 0.778996 |
94,775 | 2003 (2003): Fellow European Association for Artificial Intelligence 2003 (2003): Fellow British Computer Society (FBCS) 2004 (2004): Fellow Institution of Engineering and Technology (FIET) 2005 (2005): Fellow of the Royal Academy of Engineering (FREng) 2006 (2006): Fellow Society for the Study of Artificial Intelligen... | Nick Jennings (computer scientist) | 0.778996 |
94,776 | Nicholas Robert Jennings is a British computer scientist and the current Vice-Chancellor and President of Loughborough University. He was previously the Vice-Provost for Research and Enterprise at Imperial College London, the UK's first Regius Professor of Computer Science, and the inaugural Chief Scientific Adviser to... | Nick Jennings (computer scientist) | 0.778996 |
94,777 | Jennings was born in London. He grew up on the Isle of Portland in Dorset and attended Weymouth Grammar School. He studied for an undergraduate degree in computer science at the University of Exeter and his PhD was from the Department of Electronic Engineering at Queen Mary, University of London. | Nick Jennings (computer scientist) | 0.778996 |
94,778 | Jennings was appointed Companion of the Order of the Bath (CB) in the 2016 New Year Honours for services to computer science and national security science. 1999 (1999): IJCAI Computers and Thought Award 2000 (2000): IEE Achievement Medal for contributions to agent-based computing 2003 (2003): ACM Autonomous Agents Rese... | Nick Jennings (computer scientist) | 0.778996 |
94,779 | Knowing this chord and the foreground object's size, a more precise orbit for the object can be determined. This usage of the term "chord" is similar to the geometric concept (see: Chord (geometry)). The difference being that in the geometric sense a chord refers to a line segment whose ends lie on a circle, whereas in... | Chord (astronomy) | 0.778993 |
94,780 | In the field of astronomy the term chord typically refers to a line crossing an object which is formed during an occultation event. By taking accurate measurements of the start and end times of the event, in conjunction with the known location of the observer and the object's orbit, the length of the chord can be deter... | Chord (astronomy) | 0.778993 |
94,781 | A second method of achieving very high temporal accuracy is to actually use a long exposure and allow the target star to drift across the CCD during the exposure. This method, known as the trailed image method, produces a streak along the photograph whose thickness corresponds to the brightness of the target star with ... | Chord (astronomy) | 0.778993 |
94,782 | Propranolol does not help with the mental symptoms of anxiety including the emotional feeling of nervousness since the drug does not alter the neurochemistry of the brain unlike typical medications prescribed for other forms of anxiety such as anti-depressants.There are also ways to treat performance anxiety without th... | Performance anxiety | 0.778992 |
94,783 | An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime. While this notion makes sense for any Lorentzian manifold, it is most oft... | Asymptotically flat spacetime | 0.778991 |
94,784 | But another well known generalization of the Schwarzschild vacuum, the Taub–NUT space, is not asymptotically flat. An even simpler generalization, the de Sitter-Schwarzschild metric solution, which models a spherically symmetric massive object immersed in a de Sitter universe, is an example of an asymptotically simple ... | Asymptotically flat spacetime | 0.778991 |
94,785 | In mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an isometry, the symmetr... | Weakly symmetric space | 0.778991 |
94,786 | Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. In 1976... | Pursuit–evasion | 0.778987 |
94,787 | Formally, a topological space X is called compact if every open cover of X has a finite subcover. That is, X is compact if for every collection C of open subsets of X such that X = ⋃ S ∈ C S , {\displaystyle X=\bigcup _{S\in C}S\ ,} there is a finite subcollection F ⊆ C such that X = ⋃ S ∈ F S . {\displaystyle X=\bigcu... | Compact topological space | 0.778985 |
94,788 | Let X be a topological space and C(X) the ring of real continuous functions on X. For each p ∈ X, the evaluation map ev p: C ( X ) → R {\displaystyle \operatorname {ev} _{p}\colon C(X)\to \mathbb {R} } given by evp(f) = f(p) is a ring homomorphism. The kernel of evp is a maximal ideal, since the residue field C(X)/ker ... | Compact topological space | 0.778985 |
94,789 | Supramolecular chemistry was investigated, using donor and acceptor molecules that assemble upon spin casting and heating. Most supramolecular assemblies employ small molecules. Donor and acceptor domains in a tubular structure appear ideal for organic solar cells.Diblock polymers containing fullerene yield stable orga... | Organic Photovoltaic | 0.778984 |
94,790 | Since the very beginning of human outer space activities in 1944, and possibly before that, life has been present with microscopic life as space contaminate and after 1960 as space research subjects. Prior to crewed spaceflight non-human animals had been subjects of space research, specifically bioastronautics and astr... | Space habitation | 0.778983 |
94,791 | A key-recovery attack is an adversary's attempt to recover the cryptographic key of an encryption scheme. Normally this means that the attacker has a pair, or more than one pair, of plaintext message and the corresponding ciphertext. : 52 Historically, cryptanalysis of block ciphers has focused on key-recovery, but sec... | Key-recovery attack | 0.778981 |
94,792 | In cryptography, the key-recovery advantage (KR advantage) of a particular algorithm is a measure of how effective an algorithm can mount a key-recovery attack. Consequently, the maximum key-recovery advantage attainable by any algorithm with a fixed amount of computational resources is a measure of how difficult it is... | Key-recovery attack | 0.778981 |
94,793 | It is under the authority of the Ministry of Ecology, Sustainable Development, Transport and Housing.The BEA was created in 1946. It operates under, amongst other texts, the French civil aviation and transports codes.Following international rules, French authorities are responsible for investigating all aircraft accide... | Bureau of Enquiry and Analysis for Civil Aviation Safety | 0.77898 |
94,794 | A metal screen reflects radio waves as well as a solid metal sheet as long as the holes in the screen are smaller than about one-tenth of a wavelength, so screens are often used to reduce weight and wind loads on the antenna. They usually consist of a grill of parallel wires or rods, oriented parallel to the axis of th... | Reflective array antenna | 0.778979 |
94,795 | The Data Distribution Service (DDS) for real-time systems is an Object Management Group (OMG) machine-to-machine (sometimes called middleware or connectivity framework) standard that aims to enable dependable, high-performance, interoperable, real-time, scalable data exchanges using a publish–subscribe pattern. DDS add... | Data Distribution Service | 0.778979 |
94,796 | Euclid was employed in the widest variety of engineering domains, from general mechanical and automotive engineering to the complex robotics and aerospace industries. 1993: a development platform called CAS.CADE (Computer Aided Software for Computer Aided Design and Engineering) created by Matra Datavision was released... | OPEN CASCADE | 0.778979 |
94,797 | Sirius supports a variety of applications with a set of features, including: Building and editing chemical structures using a library of fragments Protein structure and sequence alignment Command line interpreter and scripting support fully compatible with extant RasMol scripts Full support for molecular dynamics traje... | Sirius visualization software | 0.778979 |
94,798 | Sirius is a molecular modelling and analysis system developed at San Diego Supercomputer Center. Sirius is designed to support advanced user requirements that go beyond simple display of small molecules and proteins. Sirius supports high quality interactive 3D graphics, structure building, displaying protein or DNA pri... | Sirius visualization software | 0.778979 |
94,799 | Mercury(II) acetate is a crystalline solid consisting of isolated Hg(OAc)2 molecules with Hg-O distances of 2.07 Å. Three long, weak intermolecular Hg···O bonds of about 2.75 Å are also present, resulting in a slightly distorted square pyramidal coordination geometry at Hg. | Mercuric acetate | 0.778976 |
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