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81,100 | Breaking ODEs into largest irreducible components, reduces the process of solving the original equation to solving irreducible equations of lowest possible order. This procedure is algorithmic, so that the best possible answer for solving a reducible equation is guaranteed. A detailed discussion may be found in.Loewy's... | Loewy decomposition | 0.784724 |
81,101 | In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy.Solving differential equations is one of the most important subfields in mathematics. Of particular int... | Loewy decomposition | 0.784724 |
81,102 | For partial derivatives of a single function their definition is analogous to the monomial orderings in commutative algebra. The S-pairs in commutative algebra correspond to the integrability conditions. | Loewy decomposition | 0.784724 |
81,103 | Therefore, M. Janet introduced a normal form for systems of linear PDEs (see Janet basis). They are the differential analog to Gröbner bases of commutative algebra (which were originally introduced by Bruno Buchberger); therefore they are also sometimes called differential Gröbner basis. | Loewy decomposition | 0.784724 |
81,104 | The ring D {\displaystyle {\mathcal {D}}} is non-commutative, ∂ x a = a ∂ x + ∂ a ∂ x {\textstyle \partial _{x}a=a\partial _{x}+{\frac {\partial a}{\partial x}}} and similarly for the other variables; a {\displaystyle a} is from the base field. For an operator L = ∑ i + j ≤ n r i , j ( x , y ) ∂ x i ∂ y j {\textstyle L... | Loewy decomposition | 0.784724 |
81,105 | In order to generalize Loewy's result to linear PDEs it is necessary to apply the more general setting of differential algebra. Therefore, a few basic concepts that are required for this purpose are given next. A field F {\displaystyle {\mathcal {F}}} is called a differential field if it is equipped with a derivation o... | Loewy decomposition | 0.784724 |
81,106 | (Note: In the general pseudoRiemannian case, orthonormality means: ∀ i , j ∈ { 1 , … , n } , ⟨ e i , e j ⟩ ∈ { δ i j , − δ i j } {\displaystyle \forall i,j\in \{1,\ldots ,n\},\,\langle e_{i},e_{j}\rangle \in \{\delta _{ij},-\delta _{ij}\}} .) The Hodge star operator is a linear operator on the exterior algebra of V, ma... | Hodge dual | 0.784721 |
81,107 | Generalizing this to an n-dimensional vector space, the Hodge star is a one-to-one mapping of k-vectors to (n – k)-vectors; the dimensions of these spaces are the binomial coefficients ( n k ) = ( n n − k ) {\displaystyle {\tbinom {n}{k}}={\tbinom {n}{n-k}}} . The naturalness of the star operator means it can play a ro... | Hodge dual | 0.784721 |
81,108 | In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by ... | Hodge dual | 0.784721 |
81,109 | IAPSO’s prime goal is "promoting the study of scientific problems relating to the oceans and the interactions taking places at the sea floor, coastal, and atmospheric boundaries insofar as such research is conducted by the use of mathematics, physics, and chemistry." This goal is addressed through four objectives: Orga... | International Association for the Physical Sciences of the Oceans | 0.784721 |
81,110 | International Association for the Physical Sciences of the Oceans (IAPSO) is one of eight associations of the International Union of Geodesy and Geophysics (IUGG), constituted within the International Science Council (ISC). It was founded in 1919 as an oceanographic section of the IUGG and renamed an association in 193... | International Association for the Physical Sciences of the Oceans | 0.784721 |
81,111 | These agencies often cooperate for better mission coverage. In particular, DSN has a cross-support agreement with ESA that allows mutual use of both networks for more effectiveness and reduced risk. In addition, radio astronomy facilities, such as Parkes Observatory or the Green Bank Telescope, are sometimes used to su... | Deep Space Network | 0.78472 |
81,112 | The network is a NASA facility and is managed and operated for NASA by JPL, which is part of the California Institute of Technology (Caltech). The Interplanetary Network Directorate (IND) manages the program within JPL and is charged with the development and operation of it. The IND is considered to be JPL's focal poin... | Deep Space Network | 0.78472 |
81,113 | The NASA Deep Space Network (DSN) is a worldwide network of American spacecraft communication ground segment facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary spacecraft missions. It also performs radio and radar astronomy observations f... | Deep Space Network | 0.78472 |
81,114 | The DSN forms one portion of the radio sciences experiment included on most deep space missions, where radio links between spacecraft and Earth are used to investigate planetary science, space physics and fundamental physics. The experiments include radio occultations, gravity field determination and celestial mechanic... | Deep Space Network | 0.78472 |
81,115 | Arraying of antennas within the three DSN locations is also used. For example, a 70-meter (230 ft) dish antenna can be arrayed with a 34-meter dish. For especially vital missions, like Voyager 2, non-DSN facilities normally used for radio astronomy can be added to the array. | Deep Space Network | 0.78472 |
81,116 | Long Lived In-situ Solar System Explorer (LLISSE) is a possible NASA payload on the Russian Venera-D mission to Venus. LLISSE uses new materials and heat-resistant electronics that would enable independent operation for about 90 Earth days. This endurance may allow it to obtain periodic measurements of weather data to ... | Long Lived In-situ Solar System Explorer | 0.784719 |
81,117 | One of the first recorded uses of virtual reality in architecture was in the late 1990s when the University of North Carolina virtually modelled Sitterman Hall, home of its computer science department. Designers wore a headset and used a hand controller to simulate moving around a virtual space. With an Autodesk Revit ... | Applications of virtual reality | 0.784717 |
81,118 | Subsidence is sometimes regarded as a form of mass wasting. A distinction is then made between mass wasting by subsidence, which involves little horizontal movement, and mass wasting by slope movement. Rapid mass wasting events, such as landslides, can be deadly and destructive. More gradual mass wasting, such as soil ... | Mass wasting | 0.784717 |
81,119 | Immersive virtual reality is used in the High school classroom as a tool to help students learn and be immersed in their subject matter. Immersive virtual reality has been used to teach students interactive history lessons and STEM subjects such as physics. In some cases, virtual reality laboratories have been set in u... | Applications of virtual reality | 0.784717 |
81,120 | In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the ... | Semiparametric regression | 0.784716 |
81,121 | Electromagnetic (e.g. radio or light) waves are conceptually pure single frequency phenomena while pulses may be mathematically thought of as composed of a number of pure frequencies that sum and nullify in interactions that create a pulse train of the specific amplitudes, PRRs, base frequencies, phase characteristics,... | Pulse Repetition Frequency | 0.784715 |
81,122 | PRF is crucial to perform measurements for certain physics phenomenon. For example, a tachometer may use a strobe light with an adjustable PRF to measure rotational velocity. The PRF for the strobe light is adjusted upward from a low value until the rotating object appears to stand still. The PRF of the tachometer woul... | Pulse Repetition Frequency | 0.784715 |
81,123 | In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, they play important roles in various optics branches such as beam optics and... | Zernike polynomial | 0.784714 |
81,124 | Some bacteria break down the rocks of the sea floor, influencing seawater chemistry. Oil spills, and runoff containing human sewage and chemical pollutants have a marked effect on microbial life in the vicinity, as well as harbouring pathogens and toxins affecting all forms of marine life. | Sea water | 0.784713 |
81,125 | These statistics may be improved when applied to women newly diagnosed, bearing in mind that these outcomes may be partly based on the state of treatment five years ago when the women studied were first diagnosed.With treatment, 80–90% of women with stage I cancer and 60–75% of those with stage II cancer are alive 5 ye... | Cervical cancer | 0.784712 |
81,126 | High-resolution digital elevation maps generated by airborne and stationary lidar have led to significant advances in geomorphology (the branch of geoscience concerned with the origin and evolution of the Earth surface topography). The lidar abilities to detect subtle topographic features such as river terraces and riv... | Laser imaging | 0.784707 |
81,127 | The ESA wind mission ADM-Aeolus will be equipped with a Doppler lidar system in order to provide global measurements of vertical wind profiles. A doppler lidar system was used in the 2008 Summer Olympics to measure wind fields during the yacht competition.Doppler lidar systems are also now beginning to be successfully ... | Laser imaging | 0.784707 |
81,128 | Discussion on the brain's criticality have been done since 1950, with the paper on the imitation game for a Turing test. In 1995, Herz and Hopfield noted that self-organized criticality (SOC) models for earthquakes were mathematically equivalent to networks of integrate-and-fire neurons, and speculated that perhaps SOC... | Critical brain hypothesis | 0.784707 |
81,129 | In neuroscience, the critical brain hypothesis states that certain biological neuronal networks work near phase transitions. Experimental recordings from large groups of neurons have shown bursts of activity, so-called neuronal avalanches, with sizes that follow a power law distribution. These results, and subsequent r... | Critical brain hypothesis | 0.784707 |
81,130 | In the mathematical field of graph theory, the Barnette–Bosák–Lederberg graph is a cubic (that is, 3-regular) polyhedral graph with no Hamiltonian cycle, the smallest such graph possible. It was discovered in the mid-1960s by Joshua Lederberg, David Barnette, and Juraj Bosák, after whom it is named. It has 38 vertices ... | Barnette–Bosák–Lederberg graph | 0.784706 |
81,131 | The proof of the Solovay–Kitaev theorem proceeds by recursively constructing a gate sequence giving increasingly good approximations to U ∈ SU ( 2 ) {\displaystyle U\in \operatorname {SU} (2)} . Suppose we have an approximation U n − 1 ∈ SU ( 2 ) {\displaystyle U_{n-1}\in \operatorname {SU} (2)} such that ‖ U − U n... | Solovay–Kitaev theorem | 0.784703 |
81,132 | In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2), then that set can be used to approximate any desired quantum gate with a relatively short sequence of gates. This theorem is considered one of the most signifi... | Solovay–Kitaev theorem | 0.784703 |
81,133 | Statistics show that the current probability of any message being spam is 80%, at the very least: Pr ( S ) = 0.8 ; Pr ( H ) = 0.2 {\displaystyle \Pr(S)=0.8;\Pr(H)=0.2} However, most bayesian spam detection software makes the assumption that there is no a priori reason for any incoming message to be spam rather than ham... | Bayesian spam filter | 0.784702 |
81,134 | Each word in the email contributes to the email's spam probability, or only the most interesting words. This contribution is called the posterior probability and is computed using Bayes' theorem. Then, the email's spam probability is computed over all words in the email, and if the total exceeds a certain threshold (sa... | Bayesian spam filter | 0.784702 |
81,135 | A simple solution is to simply avoid taking such unreliable words into account as well. Applying again Bayes' theorem, and assuming the classification between spam and ham of the emails containing a given word ("replica") is a random variable with beta distribution, some programs decide to use a corrected probability: ... | Bayesian spam filter | 0.784702 |
81,136 | A composition algebra with a null vector is a split algebra.In a composition algebra (A, +, ×, *), the quadratic form is q(x) = x x*. When x is a null vector then there is no multiplicative inverse for x, and since x ≠ 0, A is not a division algebra. In the Cayley-Dickson construction, the split algebras arise in the s... | Null cone | 0.7847 |
81,137 | In concrete applications, there is usually a reference distribution μ {\displaystyle \mu } on Ω {\displaystyle \Omega } (for example, when Ω = R n {\displaystyle \Omega =\mathbb {R} ^{n}} , the reference distribution is the Lebesgue measure), such that P , Q ≪ μ {\displaystyle P,Q\ll \mu } , then we can use Radon-Nikod... | F-divergence | 0.784698 |
81,138 | Applying this theorem to KL-divergence yields the Donsker–Varadhan representation. Attempting to apply this theorem to the general α {\displaystyle \alpha } -divergence with α ∈ ( − ∞ , 0 ) ∪ ( 0 , 1 ) {\displaystyle \alpha \in (-\infty ,0)\cup (0,1)} does not yield a closed-form solution. | F-divergence | 0.784698 |
81,139 | In probability theory and statistics, a zero-order process is a stochastic process in which each observation is independent of all previous observations. For example, a zero-order process in marketing would be one in which the brands purchased next do not depend on the brands purchased before, implying a fixed probabil... | Zero-order process (statistics) | 0.784698 |
81,140 | The measured half-life of this process, which is several orders of magnitude larger than the age of the Universe, demonstrates the capabilities of xenon-based detectors to search for rare events and showcases the broad physics reach of even larger next-generation experiments. This measurement represents a first step in... | XENON | 0.784698 |
81,141 | The experiment detects scintillation and ionization signals produced when external particles interact in the liquid xenon volume, to search for an excess of nuclear recoil events against known backgrounds. The detection of such a signal would provide the first direct experimental evidence for dark matter candidate part... | XENON | 0.784698 |
81,142 | The Schlenk line (also vacuum gas manifold) is a commonly used chemistry apparatus developed by Wilhelm Schlenk. It consists of a dual manifold with several ports. One manifold is connected to a source of purified inert gas, while the other is connected to a vacuum pump. The inert-gas line is vented through an oil bubb... | Vacuum gas manifold | 0.784698 |
81,143 | Albertus Magnus produced the Speculum Astronomiae (The Mirror of Astronomy) (de refutatione librorum astronomiae, incipit Occasione quorundam librorum apud quos non est radix sciencie) sometime after 1260 to defend astrology as a Christian form of knowledge (Zambelli, 1992; Hendrix, 2007). Though Albert's authorship of... | Speculum Astronomiae | 0.784694 |
81,144 | L. Bianchi, Censure et liberté intellectuelle à l' Université de Paris (XIII-XIV siècles). Paris: J. Vrin, 1999. Scott Hendrix, How Albert the Great’s Speculum astronomiae Was interpreted and Used by Four Centuries of Readers: A Study in Late Medieval Medicine, Astronomy and Astrology. Lewiston: The Edwin Mellen Press,... | Speculum Astronomiae | 0.784694 |
81,145 | Electromagnetic metamaterials show promise to fill the Terahertz gap (0.1 – 10 THz). The terahertz gap is caused by two general shortfalls. First, almost no naturally occurring materials are available for applications which would utilize terahertz frequency sources. Second is the inability to translate the successes wi... | Terahertz metamaterial | 0.784694 |
81,146 | Moreover, there is a fundamental lack of natural materials that strongly interact with light's magnetic field. Metamaterials, a synthetic composite structure, overcomes this limitation. In addition, the choice of interactions can be invented and re-invented during fabrication, within the laws of physics. Hence, the cap... | Terahertz metamaterial | 0.784694 |
81,147 | Designs of folded-waveguide traveling-wave tubes are at frequencies of 670, 850, and 1030 GHz. In order to ameliorate the power limitations due to small dimensions and high attenuation, novel planar circuit designs are also being investigated.In-house work at the NASA Glenn Research Center has investigated the use of m... | Terahertz metamaterial | 0.784694 |
81,148 | Let H {\displaystyle H} be a Hilbert space and let B ( H ) {\displaystyle B(H)} be the algebra of linear operators from H {\displaystyle H} to H {\displaystyle H} . By the polar decomposition theorem, there exists a unique partial isometry U {\displaystyle U} such that T = U | T | {\displaystyle T=U|T|} and ker ( U )... | Aluthge transform | 0.784694 |
81,149 | The approach is akin to the use of metaphor in language; metaphors are used to help explain concepts that are new or unfamiliar, and to bridge between a problem we understand and a problem we don't. Design paradigms then can be seen as higher order metaphors; as the often three-dimensional distillation of a working rel... | Design paradigm | 0.784694 |
81,150 | The term is credited to Jomini, and the term and its etymology criticized by Georges de Chambray in 1832, writing: Logistique: Ce mot me paraît être tout-à-fait nouveau, car je ne l'avais encore vu nulle part dans la littérature militaire. … il paraît le faire dériver du mot logis, étymologie singulière … Logistic: Thi... | Logistics Management | 0.784693 |
81,151 | Although there is some overlap in functionality, warehouse management systems (WMS) can differ significantly from warehouse control systems (WCS). Simply put, a WMS plans a weekly activity forecast based on such factors as statistics and trends, whereas a WCS acts like a floor supervisor, working in real-time to get th... | Logistics Management | 0.784693 |
81,152 | A number of tactical decisions regarding picking must be made: Routing path: standard alternatives include transversal routing, return routing, midpoint routing, and largest gap return routing Replenishment method: standard alternatives include equal space supply for each product class and equal time supply for each pr... | Logistics Management | 0.784693 |
81,153 | The Planck unit system uses the following defining constants: c, ħ, G, kB,where c is the speed of light, ħ is the reduced Planck constant, G is the gravitational constant, and kB is the Boltzmann constant. Planck units form a system of natural units that is not defined in terms of properties of any prototype, physical ... | Natural unit | 0.784692 |
81,154 | Owing to its ability to realise high purity results, orbital welding found its place in the production of clean-room components for the semiconductor industry. Its application has now expanded to the construction of pipework and equipment for diverse industries like food processing, pharmaceuticals, chemical engineerin... | Orbital welding | 0.784689 |
81,155 | A number of rodents live at high altitude, including deer mice, guinea pigs, and rats. Several mechanisms help them survive these harsh conditions, including altered genetics of the hemoglobin gene in guinea pigs and deer mice. Deer mice use a high percentage of fats as metabolic fuel to retain carbohydrates for small ... | High-altitude adaptation | 0.784687 |
81,156 | The bridge won the Institution of Structural Engineers' Supreme Award for Structural Excellence 2009, the premier structural engineering award in the UK. It also won in its own category of Pedestrian Bridges. The other awards the bridge has won include the British Constructional Steelwork Association's Structural Steel... | Infinity Bridge | 0.784687 |
81,157 | The bridge was constructed in 18 months between June 2007 and December 2008 by site constructor Balfour Beatty Regional Civil Engineering and steel fabricator Cleveland Bridge & Engineering Company with White Young Green managing the whole project. At the start of construction, a temporary jetty was built on the south ... | Infinity Bridge | 0.784687 |
81,158 | Initial investigations for the footbridge were done by the White Young Green Group, who with English Partnerships produced a brief for an international architectural design competition, organised with RIBA Competitions and launched in April 2003. The brief was for a "prestigious" and "iconic" "landmark" footbridge at N... | Infinity Bridge | 0.784687 |
81,159 | In the mathematical field of differential geometry a Liouville surface is a type of surface which in local coordinates may be written as a graph in R3 z = f ( x , y ) {\displaystyle z=f(x,y)} such that the first fundamental form is of the form d s 2 = ( f 1 ( x ) + f 2 ( y ) ) ( d x 2 + d y 2 ) . {\displaystyle ds^{2}=... | Liouville surface | 0.784686 |
81,160 | Mindspark operated a range of consumer mobile applications, desktop utilities, and browser applications. Mindspark's mobile division produced popular applications, including Weather Live and Pimp Your Screen. The company's desktop utilities division offered optimization services.The company offered browser-based consum... | Mindspark Interactive Network | 0.784685 |
81,161 | On May 20, 2010, Mindspark bought a majority stake in diet tracking site DailyBurn, which was responsible for Mindspark's fitness products. On October 6, 2010, Mindspark announced its Mindspark Worlds division would begin developing applications focused on social gaming.In 2011, Mindspark Interactive Network, Inc acqui... | Mindspark Interactive Network | 0.784685 |
81,162 | This surgery is done by a surgeon specializing in gynecology and is performed in a hospital. Anesthesia varies according to the needs of each woman. | Cystocele | 0.784685 |
81,163 | The incidence of cystocele is around 9 per 100 women-years. The highest incidence of symptoms occurs between ages of 70 and 79 years. Based on population growth statistics, the number of women with prolapse will increase by a minimum of 46% by the year 2050 in the US. Surgery to correct prolapse after hysterectomy is 3... | Cystocele | 0.784685 |
81,164 | Cystocele and a prolapsed urethra often occur together and is called a cystourethrocele. Cystocele can negatively affect quality of life.Causes include childbirth, constipation, chronic cough, heavy lifting, hysterectomy, genetics, and being overweight. The underlying mechanism involves weakening of muscles and connect... | Cystocele | 0.784685 |
81,165 | Differential Geometry and Physics:Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics (Nankai Tracts in Mathematics) eds. Mo-Lin Ge and Weiping Zhang (World Scientific Publishing Company (December 30, 2006)) ISBN 981-270-377-2 | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,166 | Conference on Differential Geometric Methods in Theoretical PhysicsInternational Centre for Theoretical Physics, Trieste, 30 June-3 July 1981 by G. Denardo; H. D. Doebner; International Centre for Theoretical Physics. Type: Book Language: English Publisher: Singapore: World Scientific, ©1983. ISBN 9971-950-58-8 ISBN 97... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,167 | Proceedings of the XXIIth International Conference on Differential Geometric Methods in Theoretical PhysicsIxtapa-Zihuatanejo, México, September 20–24, 1993 by J. Keller; Zbigniew Oziewicz Type: Book Language: English Publisher: México, D.F. : Universidad Nacional Autónoma de México, ©1994. ISBN 968-36-4137-7 ISBN 978-... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,168 | Proceedings of the XVII International Conference on Differential Geometric Methods in Theoretical PhysicsChester, England 15–19 August 1988 by Allan I. Solomon Type: Book Language: English Publisher: Singapore ; Teaneck, N.J. : World Scientific, ©1989. ISBN 9971-5-0836-2 ISBN 978-9971-5-0836-4 OCLC: 123106675 | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,169 | International Conference on Differential Geometrical Methods in Theoretical PhysicsProceedings of the NATO Advanced Research Workshop and the 16th International Conference on Differential Geometrical Methods in Theoretical Physics edited by K. Bleuler, M. Werner (16th: 1987: Como, Italy) (Dordrecht; Boston :Kluwer Acad... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,170 | International Conference on Differential Geometric Methods in Theoretical PhysicsProceedings of the Xxth International Conference on Differential Geometric Methods in Theoretical Physics, June 3–7, 1991, New York City, USA eds. Sultan Catto, Alvany Rocha (World Scientific Pub. Co., Inc., 1992) ISBN 981-02-0993-2 | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,171 | International Conference on Differential Geometric Methods in Theoretical PhysicsProceedings of the XXI International Conference on Differential Geometric Methods in Theoretical Physics: Tianjin, China, 5–9 June 1992 (21st: 1992: Tianjin, China) editors, Chen Ning Yang, Mo-Lin Ge, X.W. Zhou Related name: Hsing-wei Chou... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,172 | International Conference on Differential Geometric Methods in Theoretical PhysicsProceedings of the XV International Conference on Differential Geometric Methods in Theoretical Physics edited by H.D. Doebner, J.D. Hennig (15th: 1986: Clausthal-Zellerfeld, Germany) (Singapore: World Scientific, 1987) ISBN 9971-5-0328-X | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,173 | International Conference on Differential Geometric Methods in Theoretical PhysicsProceedings of the XIII International Conference on Differential Geometric Methods in Theoretical Physics Heinz Dietrich Doebner, Tchavdar D. Palev (13th: 1984: Shumen, Bulgaria) (Singapore: World Scientific, 1986) ISBN 9971-5-0070-1 ISBN... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,174 | International Conference on Differential Geometric Methods in Theoretical PhysicsDifferential Geometric Methods in Theoretical Physics Proceedings of the 19th International Conference held in Rapallo, Italy, 19–24 June 1990 (19th: 1990: Rapallo, Italy) eds. Claudio Bartocci, Ugo Bruzzo, Roberto Cianci (Berlin; New York... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,175 | International Conference on Differential Geometric Methods in Theoretical Physics: Physics and GeometryDifferential Geometric Methods in Theoretical Physics: Physics and Geometry Proceedings of the NATO Advanced Research Workshop and the 18th International Conference on Differential Geometric Methods in Theoretical Phy... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,176 | International Conference on Differential Geometric Methods in Theoretical Physics are congresses held every few years on the subject of Differential geometric methods in Theoretical physics. Lectures, seminars, and discussions are held in different universities throughout the world, every few years, and a book compilat... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,177 | International Conference on Differential Geometric Methods in Mathematical PhysicsProceedings of the 14th International Conference on Differential Geometric Methods in Theoretical Physics held in Salamanca, Spain, June 24–29, 1985 edited by Pedro Luis García Pérez and A. Pérez-Rendón (14th: 1985: Salamanca, Spain) (Ber... | International Conference on Differential Geometric Methods in Theoretical Physics | 0.784684 |
81,178 | The computer is an exaflop computer, but was not submitted to the TOP500 list; the first exaflop machine submitted to the TOP500 list was Frontier. Analysts suspected that the reason the NSCQ did not submit what would otherwise have been the world's first exascale supercomputer was to avoid inflaming political sentimen... | TOP500 | 0.784684 |
81,179 | In the early 1990s, a new definition of supercomputer was needed to produce meaningful statistics. After experimenting with metrics based on processor count in 1992, the idea arose at the University of Mannheim to use a detailed listing of installed systems as the basis. In early 1993, Jack Dongarra was persuaded to jo... | TOP500 | 0.784684 |
81,180 | It does satisfy a weaker condition: the ascending chain condition on principal ideals. A ring of polynomials in infinitely-many variables is an example of a non-Noetherian unique factorization domain. A valuation ring is not Noetherian unless it is a principal ideal domain. It gives an example of a ring that arises nat... | Noetherian rings | 0.784684 |
81,181 | (In the special case when S is commutative, this is known as Eakin's theorem.) However, this is not true if R is not commutative: the ring R of the previous paragraph is a subring of the left Noetherian ring S = Hom(Q2, Q2), and S is finitely generated as a left R-module, but R is not left Noetherian. A unique factoriz... | Noetherian rings | 0.784684 |
81,182 | The ring of polynomials in finitely-many variables over the integers or a field is Noetherian.Rings that are not Noetherian tend to be (in some sense) very large. Here are some examples of non-Noetherian rings: The ring of polynomials in infinitely-many variables, X1, X2, X3, etc. The sequence of ideals (X1), (X1, X2),... | Noetherian rings | 0.784684 |
81,183 | The coordinate ring of an affine variety is a Noetherian ring, as a consequence of the Hilbert basis theorem. The enveloping algebra U of a finite-dimensional Lie algebra g {\displaystyle {\mathfrak {g}}} is a both left and right Noetherian ring; this follows from the fact that the associated graded ring of U is a quot... | Noetherian rings | 0.784684 |
81,184 | A ring is Noetherian if it is both left- and right-Noetherian. Noetherian rings are fundamental in both commutative and noncommutative ring theory since many rings that are encountered in mathematics are Noetherian (in particular the ring of integers, polynomial rings, and rings of algebraic integers in number fields),... | Noetherian rings | 0.784684 |
81,185 | Given a ring, there is a close connection between the behaviors of injective modules over the ring and whether the ring is a Noetherian ring or not. Namely, given a ring R, the following are equivalent: R is a left Noetherian ring. (Bass) Each direct sum of injective left R-modules is injective. Each injective left R-m... | Noetherian rings | 0.784684 |
81,186 | There are rings that are left-Noetherian and not right-Noetherian, and vice versa. There are other, equivalent, definitions for a ring R to be left-Noetherian: Every left ideal I in R is finitely generated, i.e. there exist elements a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} in I such that I = R a 1 + ⋯ + R a n ... | Noetherian rings | 0.784684 |
81,187 | Many important theorems in ring theory (especially the theory of commutative rings) rely on the assumptions that the rings are Noetherian. | Noetherian rings | 0.784684 |
81,188 | The annulus theorem is trivial in dimensions 0 and 1. It was proved in dimension 2 by Radó (1924), in dimension 3 by Moise (1952), in dimension 4 by Quinn (1982), and in dimensions at least 5 by Kirby (1969). | Annulus theorem | 0.784684 |
81,189 | Robion Kirby's torus trick is a proof method employing an immersion of a punctured torus T n − D n {\displaystyle \mathbb {T} ^{n}-\mathbb {D} ^{n}} into R n {\displaystyle \mathbb {R} ^{n}} , where then smooth structures can be pulled back along the immersion and be lifted to covers. The torus trick is used in Kirby's... | Annulus theorem | 0.784684 |
81,190 | In mathematics, the annulus theorem (formerly called the annulus conjecture) states roughly that the region between two well-behaved spheres is an annulus. It is closely related to the stable homeomorphism conjecture (now proved) which states that every orientation-preserving homeomorphism of Euclidean space is stable. | Annulus theorem | 0.784684 |
81,191 | If S and T are topological spheres in Euclidean space, with S contained in T, then it is not true in general that the region between them is an annulus, because of the existence of wild spheres in dimension at least 3. So the annulus theorem has to be stated to exclude these examples, by adding some condition to ensure... | Annulus theorem | 0.784684 |
81,192 | In the mathematical field of graph theory, a hypergraph H is called a hypertree if it admits a host graph T such that T is a tree. In other words, H is a hypertree if there exists a tree T such that every hyperedge of H is the set of vertices of a connected subtree of T. Hypertrees have also been called arboreal hyperg... | Hypertree | 0.784683 |
81,193 | There are 4 main telescopes on site: a 3.5-meter (138-inch), 2.2 m (87 in), and a 1.23 m (48 in) telescope, and an 80 cm (31 in) Schmidt reflector. The 3.5-meter is the largest telescope on European soil with an equatorial mount. There is also a 1.52 m (60 in) telescope that is owned and operated by the Spanish Nationa... | Calar Alto Observatory | 0.784679 |
81,194 | The site was proposed in 1970, and was officially opened in July 1975 with the commissioning of its 1.23-meter (48 in) telescope. The site developed thanks to German and Spanish cooperation in astronomy. Eventually, four more telescopes were commissioned. | Calar Alto Observatory | 0.784679 |
81,195 | The Calar Alto Observatory (Centro Astronómico Hispano en Andalucía or "Spanish Astronomical Centre in Andalusia") is an astronomical observatory located in Almería province in Spain on Calar Alto, a 2,168-meter-high (7,113 ft) mountain in the Sierra de Los Filabres range.Until 2018, Calar Alto was owned and operated j... | Calar Alto Observatory | 0.784679 |
81,196 | Since every non-empty set in Σ 0 {\displaystyle \Sigma _{0}} is infinite, then, for every non-empty set A ∈ Σ 0 {\displaystyle A\in \Sigma _{0}} , μ 0 ( A ) = + ∞ {\displaystyle \mu _{0}(A)=+\infty } Now, let Σ {\displaystyle \Sigma } be the σ {\displaystyle \sigma } -algebra generated by Σ 0 {\displaystyle \Sigma _{0}... | Carathéodory extension theorem | 0.784676 |
81,197 | This example is a more detailed variation of the above. The rational closed-open interval is any subset of Q {\displaystyle \mathbb {Q} } of the form [ a , b ) {\displaystyle [a,b)} , where a , b ∈ Q {\displaystyle a,b\in \mathbb {Q} } . Let X {\displaystyle X} be Q ∩ [ 0 , 1 ) {\displaystyle \mathbb {Q} \cap [0,1)} an... | Carathéodory extension theorem | 0.784676 |
81,198 | Think about the subset of P ( R ) {\displaystyle {\mathcal {P}}(\mathbb {R} )} defined by the set of all half-open intervals [ a , b ) {\displaystyle [a,b)} for a and b reals. This is a semi-ring, but not a ring. Stieltjes measures are defined on intervals; the countable additivity on the semi-ring is not too difficult... | Carathéodory extension theorem | 0.784676 |
81,199 | Take the algebra generated by all half-open intervals [a,b) on the real line, and give such intervals measure infinity if they are non-empty. The Carathéodory extension gives all non-empty sets measure infinity. Another extension is given by the counting measure. | Carathéodory extension theorem | 0.784676 |
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