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88,000 | In the United States, the director of the Cybersecurity and Infrastructure Security Agency (CISA), Jen Easterly, described the exploit as "one of the most serious I've seen in my entire career, if not the most serious", explaining that hundreds of millions of devices were affected and advising vendors to prioritize sof... | Log4Shell | 0.781832 |
88,001 | This was confirmed both in the original issue thread and by external security researchers.Technology magazine Wired wrote that despite the previous "hype" surrounding multiple vulnerabilities, "the Log4j vulnerability ... lives up to the hype for a host of reasons". The magazine explains that the pervasiveness of Log4j... | Log4Shell | 0.781832 |
88,002 | Amazon, Google and Microsoft cloud data was affected by Log4Shell. Microsoft asked Windows and Azure customers to remain vigilant after observing state-sponsored and cyber-criminal attackers probing systems for the Log4j 'Log4Shell' flaw through December 2021.The human resource management and workforce management compa... | Log4Shell | 0.781832 |
88,003 | The exploit was simple to execute and is estimated to have had the potential to affect hundreds of millions of devices.The vulnerability takes advantage of Log4j's allowing requests to arbitrary LDAP and JNDI servers, allowing attackers to execute arbitrary Java code on a server or other computer, or leak sensitive inf... | Log4Shell | 0.781832 |
88,004 | The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. The conjectures, formulated by Kiiti Morita in 1976, asked If X × Y {\displaystyle X\times Y} is normal for every normal space Y, is X a discrete space? If X × Y {\displaystyle X\times Y} is normal for ev... | Morita conjectures | 0.78183 |
88,005 | A Biographical Dictionary of Civil Engineers in Great Britain and Ireland discusses the lives of the people who were concerned with building harbours and lighthouses, undertook fen drainage and improved river navigations, built canals, roads, bridges and early railways, and provided water supply facilities. Volume One,... | A Biographical Dictionary of Civil Engineers | 0.781829 |
88,006 | The Tenerife Experiment was a Cosmic Microwave Background (CMB) experiment built by Jodrell Bank (then known as the Nuffield Radio Astronomy Laboratories) of the University of Manchester in collaboration with the Instituto de Astrofisica de Canarias (IAC). It was the first CMB experiment to be installed and run at the ... | Tenerife Experiment | 0.781827 |
88,007 | Over the last decade with the aid of science and technology, we are more familiar with the human brain and its function than ever before. Development in neuroimaging techniques has greatly enhanced the scope and outcome of neurorehabilitation. Now, scientists are using technology with neurorehabilitation to provide cut... | Motor rehabilitation | 0.781826 |
88,008 | 1992: Manchester, NH 1993–1994: Nashua, NH 1995–2002: Orlando, FL, at Epcot Center, Walt Disney World 2003: Houston, at Reliant Park (now known as NRG Park) 2004–2010: Atlanta, at Georgia Dome 2011–2017: St. Louis, at Dome at America's Center, America's Center, Renaissance St. Louis Grand Hotel (2015-2017), Union Stati... | FIRST Championship | 0.781826 |
88,009 | The winning alliance on the Einstein Field is declared the FIRST Champion. The FIRST Robotics Competition Championship was initially divided into 4 divisions: Newton Galileo Archimedes CurieIn 2015, the 4 divisions were further divided into 8 divisions (not including the final Einstein Field) and expanding naming to sh... | FIRST Championship | 0.781826 |
88,010 | The FIRST Robotics Competition Championship is the final and largest event of the season. The winners of each regional competition as well as the top teams from each district advance to the FIRST Championship. They are placed into one of the 8 divisions to compete. The winning alliance from each division (a set of 4 te... | FIRST Championship | 0.781826 |
88,011 | The new Innovation Faire featuring displays and demonstrations from FIRST Sponsors, Partners and Suppliers took place at the Renaissance St. Louis Grand Hotel, The FIRST Tech Challenge World Championship and the Junior FIRST Lego League World Festival took place at Union Station (St. Louis), and the FIRST LEGO League W... | FIRST Championship | 0.781826 |
88,012 | The winning teams from each of these tournaments join the global competition at the FIRST Championship. The FIRST Championship was formally held in conjunction with the FIRST Robotics Conference, which covers a wide variety of topics in science, technology, engineering, and robotics fields.The 2011 championship was als... | FIRST Championship | 0.781826 |
88,013 | The FIRST Tech Challenge is a mid-level competition program for middle school and high school aged students with a more accessible and affordable robotics kit. FIRST LEGO League is a competition program for elementary and middle school students using LEGO Mindstorms robotics kits. Teams for each program compete in tour... | FIRST Championship | 0.781826 |
88,014 | In 2018 and 2019, the Championship was held in Houston and Detroit, Michigan at the TCF Center and Ford Field. The event comprises four competitions; the FIRST Robotics Competition Championship, the FIRST Tech Challenge World Championship, the FIRST Lego League World Festival, and the FIRST Lego League Junior World Exp... | FIRST Championship | 0.781826 |
88,015 | The FIRST Championship is a four-day robotics championship held annually in April at which FIRST student robotics teams compete. For several years, the event was held at the Georgia Dome in Atlanta, Georgia, but moved to the Edward Jones Dome in St. Louis, Missouri in 2011, where it remained through 2017. In 2017, the ... | FIRST Championship | 0.781826 |
88,016 | Perchloric acid is mainly produced as a precursor to ammonium perchlorate, which is used in rocket fuel. The growth in rocketry has led to increased production of perchloric acid. Several million kilograms are produced annually. Perchloric acid is one of the most proven materials for etching of liquid crystal displays ... | HClO4 | 0.781825 |
88,017 | Chemistry of Penicillin. pp. 310–366. | Barbara Low (biochemist) | 0.781824 |
88,018 | She relocated to Columbia University in 1956 as an associate professor, and was promoted to a full professorship in 1966. Low continued at Columbia until her retirement in 1990 as professor emerita of biochemistry and molecular biophysics. She still did routine academic rounds as a "Special Lecturer" at the university,... | Barbara Low (biochemist) | 0.781824 |
88,019 | Low obtained Master's and doctoral degrees in chemistry from Oxford University in 1946 and 1948 respectively, before moving on to a research associate position at the California Institute of Technology (Caltech). To do so, she obtained a United States passport through emigration and later full citizenship in 1956.While... | Barbara Low (biochemist) | 0.781824 |
88,020 | These areas remain TDK's focus today.Since acquiring numerous companies and sharpening its product line focus in recent years, TDK has begun building a portfolio of varying sensors, actuators and power electronic components through these brands. These include multi-axis MEMS motion tracking devices and MEMS microphones... | TDK | 0.781824 |
88,021 | In vector calculus, a topic in pure and applied mathematics, a poloidal–toroidal decomposition is a restricted form of the Helmholtz decomposition. It is often used in the spherical coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids. | Toroidal–poloidal decomposition | 0.781824 |
88,022 | It is known by the Darmon–Granville theorem, which uses Faltings's theorem, that for any fixed choice of positive integers m, n and k satisfying (2), only finitely many coprime triples (a, b, c) solving (1) exist. : p. 64 However, the full Fermat–Catalan conjecture is stronger as it allows for the exponents m, n and k ... | Fermat-Catalan conjecture | 0.781824 |
88,023 | In neuroscience, homeostatic plasticity refers to the capacity of neurons to regulate their own excitability relative to network activity. The term homeostatic plasticity derives from two opposing concepts: 'homeostatic' (a product of the Greek words for 'same' and 'state' or 'condition') and plasticity (or 'change'), ... | Homeostatic plasticity | 0.781823 |
88,024 | According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. Many Bell tests have been performed, using entangled particles, and they have shown results incompatible with the constrain... | Quantum laws | 0.781823 |
88,025 | Quantum entanglement enables the counter-intuitive properties of quantum pseudo-telepathy, and can be a valuable resource in communication protocols, such as quantum key distribution and superdense coding. Contrary to popular misconception, entanglement does not allow sending signals faster than light, as demonstrated ... | Quantum laws | 0.781823 |
88,026 | In classical mechanics this particle would be trapped. Quantum tunnelling has several important consequences, enabling radioactive decay, nuclear fusion in stars, and applications such as scanning tunnelling microscopy and the tunnel diode.When quantum systems interact, the result can be the creation of quantum entangl... | Quantum laws | 0.781823 |
88,027 | Other atomic-scale entities, such as electrons, are found to exhibit the same behavior when fired towards a double slit. This behavior is known as wave–particle duality. Another counter-intuitive phenomenon predicted by quantum mechanics is quantum tunnelling: a particle that goes up against a potential barrier can cro... | Quantum laws | 0.781823 |
88,028 | Another consequence of the mathematical rules of quantum mechanics is the phenomenon of quantum interference, which is often illustrated with the double-slit experiment. In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the lig... | Quantum laws | 0.781823 |
88,029 | The Schrödinger equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another. One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between different measurable quantities. The mo... | Quantum laws | 0.781823 |
88,030 | Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.A fundamental feature of the theory is that it usually cannot predict with certainty what will happen, but only give probabilities. Mathematically, a probability is found by taking the square of the absolute value... | Quantum laws | 0.781823 |
88,031 | Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles. It has been demonstrated to hold for complex molecules with thousands of atoms, but its application to human beings raises philosophical pr... | Quantum laws | 0.781823 |
88,032 | 3DS is one of the file formats used by the Autodesk 3ds Max 3D modeling, animation and rendering software. It was the native file format of the old Autodesk 3D Studio DOS (releases 1 to 4), which was popular until its successor (3D Studio MAX 1.0) replaced it in April 1996. Having been around since 1990 (when the first... | .3ds | 0.781819 |
88,033 | and Ph.D. programs in Solar Engineering. School of Liberal Studies (Established, 2009) offers UG honors degree programs in Humanities, Management, Science, and Commerce viz. Business Administration, Economics, English Literature, International Relations, Public Policy & Administration, Psychology, Mass Communication, C... | Pandit Deendayal Energy University | 0.781818 |
88,034 | A radio frequency (RF) resonant cavity thruster is a device that is claimed to be a spacecraft thruster. In 2016, the Advanced Propulsion Physics Laboratory at NASA reported observing a small apparent thrust from one such test, a result not since replicated. One of the designs is called EMDrive. In December 2002, Satel... | Interstellar space travel | 0.781817 |
88,035 | Near-lightspeed nano spacecraft might be possible within the near future built on existing microchip technology with a newly developed nanoscale thruster. Researchers at the University of Michigan are developing thrusters that use nanoparticles as propellant. Their technology is called "nanoparticle field extraction th... | Interstellar space travel | 0.781817 |
88,036 | Even with a hypothetically perfectly efficient propulsion system, the kinetic energy corresponding to those speeds is enormous by today's standards of energy development. Moreover, collisions by spacecraft with cosmic dust and gas at such speeds would be very dangerous for both passengers and the spacecraft itself.A nu... | Interstellar space travel | 0.781817 |
88,037 | Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast difference in the scale of the involved distances. Whereas the distance between a... | Interstellar space travel | 0.781817 |
88,038 | In Euclidean geometry, the Droz-Farny line theorem is a property of two perpendicular lines through the orthocenter of an arbitrary triangle. Let T {\displaystyle T} be a triangle with vertices A {\displaystyle A} , B {\displaystyle B} , and C {\displaystyle C} , and let H {\displaystyle H} be its orthocenter (the comm... | Droz-Farny line theorem | 0.781816 |
88,039 | A generalization of the Droz-Farny line theorem was proved in 1930 by René Goormaghtigh.As above, let T {\displaystyle T} be a triangle with vertices A {\displaystyle A} , B {\displaystyle B} , and C {\displaystyle C} . Let P {\displaystyle P} be any point distinct from A {\displaystyle A} , B {\displaystyle B} , and C... | Droz-Farny line theorem | 0.781816 |
88,040 | The theorem was further generalized by Dao Thanh Oai. The generalization as follows: First generalization: Let ABC be a triangle, P be a point on the plane, let three parallel segments AA', BB', CC' such that its midpoints and P are collinear. Then PA', PB', PC' meet BC, CA, AB respectively at three collinear points. S... | Droz-Farny line theorem | 0.781816 |
88,041 | In 1998, the Toronto Renewable Energy Co-operative (TREC) was incorporated. The next year in 1999, the TREC received a grant to study three potential sites for an urban wind turbine project in Toronto. On June 30, 1999, the TREC formed an ad hoc partnership with Toronto Hydro to build wind turbines in Toronto. In Febru... | ExPlace Wind Turbine | 0.781816 |
88,042 | The ExPlace Wind Turbine is a 91-metre (299 ft) tall wind turbine located on the grounds of the Exhibition Place co-owned by the WindShare for-profit co-operative and Toronto Hydro. It is the first wind turbine installed in a major North American urban city centre, and the first community-owned wind power project in On... | ExPlace Wind Turbine | 0.781816 |
88,043 | Perceptual robotics is an interdisciplinary science linking Robotics and Neuroscience. It investigates biologically motivated robot control strategies, concentrating on perceptual rather than cognitive processes and thereby sides with J. J. Gibson's view against the Poverty of the stimulus theory. As a working definiti... | Perceptual Robotics | 0.781816 |
88,044 | In mathematics, the Beurling–Lax theorem is a theorem due to Beurling (1949) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space H 2 ( D , C ) {\displaystyle H^{2}(\mathbb {D} ,\mathbb {C} )} . It states that each such space is of the form θ H 2 ( D , C ) , {\displaystyle \theta H^{2}(\m... | Beurling–Lax theorem | 0.781815 |
88,045 | Distance matrix completion, in which case there is a positive definiteness constraint. Natural language processing, in which case the approximation is nonnegative. Computer algebra, in which case the approximation is Sylvester structured. | Low-rank approximation | 0.781814 |
88,046 | Linear system identification, in which case the approximating matrix is Hankel structured. Machine learning, in which case the approximating matrix is nonlinearly structured. Recommender systems, in which cases the data matrix has missing values and the approximation is categorical. | Low-rank approximation | 0.781814 |
88,047 | In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling a... | Low-rank approximation | 0.781814 |
88,048 | In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set.For example, in the case d = 2, any set of four po... | Radon's theorem | 0.781814 |
88,049 | Concepts related to Radon's theorem have also been considered for convex geometries, families of finite sets with the properties that the intersection of any two sets in the family remains in the family, and that the empty set and the union of all the sets belongs to the family. In this more general context, the convex... | Radon's theorem | 0.781814 |
88,050 | Carathéodory's theorem states that any point in the convex hull of some set of points is also within the convex hull of a subset of at most d + 1 of the points; that is, that the given point is part of a Radon partition in which it is a singleton. One proof of Carathéodory's theorem uses a technique of examining soluti... | Radon's theorem | 0.781814 |
88,051 | The Radon point of any four points in the plane is their geometric median, the point that minimizes the sum of distances to the other points.Radon's theorem forms a key step of a standard proof of Helly's theorem on intersections of convex sets; this proof was the motivation for Radon's original discovery of Radon's th... | Radon's theorem | 0.781814 |
88,052 | Tverberg's theorem. A generalization for partition into r sets was given by Helge Tverberg (1966) and is now known as Tverberg's theorem. It states that for any set of ( d + 1 ) ( r − 1 ) + 1 {\displaystyle (d+1)(r-1)+1\ } points in Euclidean d-space, there is a partition into r subsets whose convex hulls intersect in ... | Radon's theorem | 0.781814 |
88,053 | Geometric median. The Radon point of three points in a one-dimensional space is just their median. The geometric median of a set of points is the point minimizing the sum of distances to the points in the set; it generalizes the one-dimensional median and has been studied both from the point of view of facility locatio... | Radon's theorem | 0.781814 |
88,054 | Every Kähler manifold is also a symplectic manifold. Well into the 1970s, symplectic experts were unsure whether any compact non-Kähler symplectic manifolds existed, but since then many examples have been constructed (the first was due to William Thurston); in particular, Robert Gompf has shown that every finitely pres... | Symplectic structure | 0.781813 |
88,055 | Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain... | Symplectic structure | 0.781813 |
88,056 | The program uses a wizard based interface which asks the user questions about the project and its data. After a test is run, the user receives a detailed report that interprets the results. If installed with SigmaPlot, SigmaStat integrated with SigmaPlot and SigmaPlot gained advanced statistical analysis capabilities f... | SigmaStat | 0.781813 |
88,057 | In optical physics, laser detuning is the tuning of a laser to a frequency that is slightly off from a quantum system's resonant frequency. When used as a noun, the laser detuning is the difference between the resonance frequency of the system and the laser's optical frequency (or wavelength). Lasers tuned to a frequen... | Laser detuning | 0.781813 |
88,058 | In generalized functions theory, discretization arises as a particular case of the Convolution Theorem on tempered distributions F { f ∗ III } = F { f } ⋅ III {\displaystyle {\mathcal {F}}\{f*\operatorname {III} \}={\mathcal {F}}\{f\}\cdot \operatorname {III} } F { α ⋅ III } = F { α } ∗ III {\displaystyle {\mathcal {F}... | Discretization | 0.781813 |
88,059 | In statistics and machine learning, discretization refers to the process of converting continuous features or variables to discretized or nominal features. This can be useful when creating probability mass functions. | Discretization | 0.781813 |
88,060 | Political ecology, which expands ecological concerns to respond to the inclusion of cultural and political activity within an analysis of ecosystems that are significantly but not always entirely socially constructed. Environmental history which arose from the rich accumulation of material documenting relationships bet... | Socio-ecological system | 0.781812 |
88,061 | Through to the final decades of the twentieth century, the point of contact between social sciences and natural sciences was very limited in dealing with social-ecological systems. Just as mainstream ecology had tried to exclude humans from the study of ecology, many social science disciplines had ignored the environme... | Socio-ecological system | 0.781812 |
88,062 | Elinor Ostrom and her many co-researchers developed a comprehensive "Social-Ecological Systems (SES) framework", which includes much of the theory of common-pool resources and collective self-governance. It draws heavily on systems ecology and complexity theory. The studies of SES include some central societal concerns... | Socio-ecological system | 0.781812 |
88,063 | Although panarchy theory originates in ecology, it has found widespread applications in other disciplines. For example, in management, Wieland (2021) describes a panarchy that represents the planetary, political-economic, and supply chain levels. Hereby, the panarchical understanding of the supply chain leads to a soci... | Socio-ecological system | 0.781812 |
88,064 | Caltech physics professor David Goodstein has stated that ... you would have to build 10,000 of the largest power plants that are feasible by engineering standards in order to replace the 10 terawatts of fossil fuel we're burning today ... that's a staggering amount and if you did that, the known reserves of uranium wo... | Sustainability measurement | 0.78181 |
88,065 | At the political right, Fred Ikle has warned about "conservatives addicted to the Utopia of Perpetual Growth". Brief oil interruptions in 1973 and 1979 markedly slowed – but did not stop – the growth of world GDP.Between 1950 and 1984, as the Green Revolution transformed agriculture around the globe, world grain produc... | Sustainability measurement | 0.78181 |
88,066 | Once a benchmark is established it is possible to assess trends and measure progress. Baseline global data on a range of sustainability parameters is available in the list of global sustainability statistics.IndicesA sustainability index is an aggregate sustainability indicator that combines multiple sources of data. T... | Sustainability measurement | 0.78181 |
88,067 | Chimpanzees are the closest living species to humans. Chimpanzees are closer to humans, in genetic and evolutionary terms, than they are to gorillas or other apes. The fact that a chimpanzee will not acquire speech, even when raised in a human home with all the environmental input of a normal human child, is one of the... | Human communication | 0.78181 |
88,068 | The currently accepted taxonomy is based solemnly on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI) Phylum Elusimicrobiota Geissinger et al. 2021 Class "Elusimicrobiia" Oren, Parte & Garrity 2016 ex Cavalier-Smith 2020 Order "Obscuribacterial... | Elusimicrobiota | 0.781808 |
88,069 | Rutgers University Nuclear Physics Home Page Publications - High Energy Nuclear Physics (HENP) https://web.archive.org/web/20101212105542/http://www.er.doe.gov/np/ == References == | Heavy-Ion collisions | 0.781808 |
88,070 | A conservation management system (CMS) is a procedure for maintaining a species or habitat in a particular state. It is a means whereby humankind secures wildlife in a favourable condition for contemplation, education or research, in perpetuity. It is an important topic in cultural ecology, where conservation managemen... | Conservation management system | 0.781805 |
88,071 | Open Systems & Information Dynamics (OSID) is a journal published by World Scientific. It covers interdisciplinary research in mathematics, physics, engineering and life sciences based upon the fields of information processing, storage and transmission, in both quantum and classical settings, with a theoretical focus. ... | Open Systems & Information Dynamics | 0.781805 |
88,072 | The first synthetic dye, mauve, was discovered serendipitously by William Henry Perkin in 1856. The discovery of mauveine started a surge in synthetic dyes and in organic chemistry in general. Other aniline dyes followed, such as fuchsine, safranine, and induline. | Organic dye | 0.781803 |
88,073 | The International Association for Cereal Science and Technology (ICC) was founded in 1955 and was originally called the International Association for Cereal Chemistry. It was set up to develop international standard testing procedures for cereals and flour. It has currently more than fifty member countries and headquar... | International Association for Cereal Science and Technology | 0.781801 |
88,074 | NTCDI is redox-active, forming stable radical anions near -1.10 V vs. Fc/Fc+. Its ability to accept electrons reflects the presence of an extended conjugated ring system and the electron withdrawing groups (carbonyl centers). NDI is used in supramolecular chemistry owing to its tendency to form charge-transfer complexe... | Naphthalenetetracarboxylic diimide | 0.781801 |
88,075 | The proof of the Abel–Ruffini theorem predates Galois theory. However, Galois theory allows a better understanding of the subject, and modern proofs are generally based on it, while the original proofs of the Abel–Ruffini theorem are still presented for historical purposes.The proofs based on Galois theory comprise fou... | Abel–Ruffini theorem | 0.7818 |
88,076 | It follows that the Galois group Gal ( H / K ) {\displaystyle \operatorname {Gal} (H/K)} is the symmetric group S n . {\displaystyle {\mathcal {S}}_{n}.} The fundamental theorem of symmetric polynomials implies that the b i {\displaystyle b_{i}} are algebraic independent, and thus that the map that sends each a i {\d... | Abel–Ruffini theorem | 0.7818 |
88,077 | The general or generic polynomial equation of degree n is the equation x n + a 1 x n − 1 + ⋯ + a n − 1 x + a n = 0 , {\displaystyle x^{n}+a_{1}x^{n-1}+\cdots +a_{n-1}x+a_{n}=0,} where a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} are distinct indeterminates. This is an equation defined over the field F = Q ( a 1 , ... | Abel–Ruffini theorem | 0.7818 |
88,078 | Thus, the Abel–Ruffini theorem results from the existence of polynomials with a symmetric Galois group; this will be shown in the next section. On the other hand, for n ≤ 4, the symmetric group and all its subgroups are solvable. This explains the existence of the quadratic, cubic, and quartic formulas, since a major r... | Abel–Ruffini theorem | 0.7818 |
88,079 | A simplification of Abel's proof was published by Pierre Wantzel in 1845. When Wantzel published it, he was already aware of the contributions by Galois and he mentions that, whereas Abel's proof is valid only for general polynomials, Galois' approach can be used to provide a concrete polynomial of degree 5 whose roots... | Abel–Ruffini theorem | 0.7818 |
88,080 | (Abel adopted a very terse style to save paper and money: the proof was printed at his own expense.) A more elaborated version of the proof would be published in 1826.Proving that the general quintic (and higher) equations were unsolvable by radicals did not completely settle the matter, because the Abel–Ruffini theore... | Abel–Ruffini theorem | 0.7818 |
88,081 | But then the numbers 10 ± 5 i {\displaystyle 10\pm 5i} cannot belong to Q ( r 1 , r 2 , r 3 ) {\displaystyle \mathbf {Q} (r_{1},r_{2},r_{3})} . While Cauchy either did not notice Ruffini's assumption or felt that it was a minor one, most historians believe that the proof was not complete until Abel proved the theorem o... | Abel–Ruffini theorem | 0.7818 |
88,082 | However, in general, Ruffini's proof was not considered convincing. Abel wrote: "The first and, if I am not mistaken, the only one who, before me, has sought to prove the impossibility of the algebraic solution of general equations is the mathematician Ruffini. But his memoir is so complicated that it is very difficult... | Abel–Ruffini theorem | 0.7818 |
88,083 | Actually, Gauss published nothing else on this subject. The theorem was first nearly proved by Paolo Ruffini in 1799. He sent his proof to several mathematicians to get it acknowledged, amongst them Lagrange (who did not reply) and Augustin-Louis Cauchy, who sent him a letter saying: "Your memoir on the general solutio... | Abel–Ruffini theorem | 0.7818 |
88,084 | Around 1770, Joseph Louis Lagrange began the groundwork that unified the many different methods that had been used up to that point to solve equations, relating them to the theory of groups of permutations, in the form of Lagrange resolvents. This innovative work by Lagrange was a precursor to Galois theory, and its fa... | Abel–Ruffini theorem | 0.7818 |
88,085 | An algebraic solution of the initial polynomial equation exists if and only if there exists such a sequence of fields such that F k {\displaystyle F_{k}} contains a solution. For having normal extensions, which are fundamental for the theory, one must refine the sequence of fields as follows. If F i − 1 {\displaystyle ... | Abel–Ruffini theorem | 0.7818 |
88,086 | This field is changed only for the steps involving the computation of an nth root. So, an algebraic solution produces a sequence F 0 ⊆ F 1 ⊆ ⋯ ⊆ F k {\displaystyle F_{0}\subseteq F_{1}\subseteq \cdots \subseteq F_{k}} of fields, and elements x i ∈ F i {\displaystyle x_{i}\in F_{i}} such that F i = F i − 1 ( x i ) {\dis... | Abel–Ruffini theorem | 0.7818 |
88,087 | An algebraic solution of a polynomial equation is an expression involving the four basic arithmetic operations (addition, subtraction, multiplication, and division), and root extractions. Such an expression may be viewed as the description of a computation that starts from the coefficients of the equation to be solved ... | Abel–Ruffini theorem | 0.7818 |
88,088 | The Abel–Ruffini theorem proves that this is impossible. However, this impossibility does not imply that a specific equation of any degree cannot be solved in radicals. On the contrary, there are equations of any degree that can be solved in radicals. | Abel–Ruffini theorem | 0.7818 |
88,089 | In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.... | Abel–Ruffini theorem | 0.7818 |
88,090 | The Galois correspondence establishes a one to one correspondence between the subextensions of a normal field extension F / E {\displaystyle F/E} and the subgroups of the Galois group of the extension. This correspondence maps a field K such E ⊆ K ⊆ F {\displaystyle E\subseteq K\subseteq F} to the Galois group Gal ( ... | Abel–Ruffini theorem | 0.7818 |
88,091 | This is the case of the equation x n − 1 = 0 {\displaystyle x^{n}-1=0} for any n, and the equations defined by cyclotomic polynomials, all of whose solutions can be expressed in radicals. Abel's proof of the theorem does not explicitly contain the assertion that there are specific equations that cannot be solved by rad... | Abel–Ruffini theorem | 0.7818 |
88,092 | This is the fundamental theorem of algebra, which does not provide any tool for computing exactly the solutions, although Newton's method allows approximating the solutions to any desired accuracy. From the 16th century to beginning of the 19th century, the main problem of algebra was to search for a formula for the so... | Abel–Ruffini theorem | 0.7818 |
88,093 | Decision-makers are those who apply changes and determine the direction of development in a company. In this case, they would make important decisions according to the trends and information highlighted by the data produced either in their own companies internally or statistics of the target market they want their corp... | Data culture | 0.781799 |
88,094 | Data culture is the principle established in the process of social practice in both public and Private sectors which requires all staffs and decision-makers to focus on the information conveyed by the existing data, and make decisions and changes according to these results instead of leading the development of the comp... | Data culture | 0.781799 |
88,095 | Participants are both producers of data and people who can contribute to the data culture by making influential changes. In the building process of data culture in a particular entity, employees at different levels are all supposed to obtain the ability of illustrating their works with relative statistics. This include... | Data culture | 0.781799 |
88,096 | These programs were to take the form of "star hunts" or "star counts", providing people with a fun and direct way to acquire heightened awareness about light pollution through firsthand observations of the night sky. Together, the three programs were to cover the entire International Year of Astronomy 2009, namely GLOB... | International Year of Astronomy | 0.781799 |
88,097 | Dark Skies Awareness was a worldwide astronomy event that ran from 2 to 5 April 2009. The IAU collaborated with the U.S. National Optical Astronomy Observatory (NOAO), representatives of the International Dark-Sky Association (IDA), the Starlight Initiative, and other national and international partners in dark-sky and... | International Year of Astronomy | 0.781799 |
88,098 | The International Year of Astronomy 2009 was supported by eleven Cornerstone projects. These are global programs of activities centered on specific themes and are some of the projects that helped to achieve IYA2009's main goals; whether it is the support and promotion of women in astronomy, the preservation of dark-sky... | International Year of Astronomy | 0.781799 |
88,099 | This initiative was an opportunity for the citizens of Earth to gain a deeper insight into astronomy's role in enriching all human cultures. Moreover, served as a platform for informing the public about the latest astronomical discoveries while emphasizing the essential role of astronomy in science education. IYA2009 w... | International Year of Astronomy | 0.781799 |
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