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79,100 | In addition, film thickness and fuel vapor are important parameters in many applications. Advances in computational fluid dynamics modeling, such as RANS or LES, and specialized codes (based on the volume of fluid method, level-set method or lattice Boltzmann methods) developed to simulate the atomization and drop tran... | Institute for Liquid Atomization and Spray Systems | 0.785507 |
79,101 | Swift, a NASA spacecraft, was launched in 2004 and carries the BAT instrument for gamma-ray burst observations. Following BeppoSAX and HETE-2, it has observed numerous X-ray and optical counterparts to bursts, leading to distance determinations and detailed optical follow-up. These have established that most bursts ori... | Gamma-ray astronomy | 0.785506 |
79,102 | Given a differentiable real dynamical system defined on an open subset of the plane, every non-empty compact ω-limit set of an orbit, which contains only finitely many fixed points, is either a fixed point, a periodic orbit, or a connected set composed of a finite number of fixed points together with homoclinic and het... | Poincaré–Bendixson theorem | 0.785506 |
79,103 | The condition that the dynamical system be on the plane is necessary to the theorem. On a torus, for example, it is possible to have a recurrent non-periodic orbit. In particular, chaotic behaviour can only arise in continuous dynamical systems whose phase space has three or more dimensions. However the theorem does no... | Poincaré–Bendixson theorem | 0.785506 |
79,104 | In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere. | Poincaré–Bendixson theorem | 0.785506 |
79,105 | One important implication is that a two-dimensional continuous dynamical system cannot give rise to a strange attractor. If a strange attractor C did exist in such a system, then it could be enclosed in a closed and bounded subset of the phase space. By making this subset small enough, any nearby stationary points coul... | Poincaré–Bendixson theorem | 0.785506 |
79,106 | The JPL Small-Body Database (SBDB) is an astronomy database about small Solar System bodies. It is maintained by Jet Propulsion Laboratory (JPL) and NASA and provides data for all known asteroids and several comets, including orbital parameters and diagrams, physical diagrams, close approach details, radar astrometry, ... | JPL Small-Body Database | 0.785505 |
79,107 | A mainframe computer, informally called a mainframe or big iron, is a computer used primarily by large organizations for critical applications like bulk data processing for tasks such as censuses, industry and consumer statistics, enterprise resource planning, and large-scale transaction processing. A mainframe compute... | Mainframe server | 0.785505 |
79,108 | Certain oracle problems like Simon's problem and the Bernstein–Vazirani problem do give provable speedups, though this is in the quantum query model, which is a restricted model where lower bounds are much easier to prove and doesn't necessarily translate to speedups for practical problems. Other problems, including th... | Quantum processor | 0.785505 |
79,109 | Such tasks can in theory be solved on a large-scale quantum computer whereas classical computers would not finish computations in any reasonable amount of time. However, quantum speedup is not universal or even typical across computational tasks, since basic tasks such as sorting are proven to not allow any asymptotic ... | Quantum processor | 0.785505 |
79,110 | Moreover, scalable quantum computers do not hold promise for many practical tasks, and for many important tasks quantum speedups are proven impossible. The basic unit of information in quantum computing is the qubit, similar to the bit in traditional digital electronics. Unlike a classical bit, a qubit can exist in a s... | Quantum processor | 0.785505 |
79,111 | A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and ... | Quantum processor | 0.785505 |
79,112 | In 2013, Nuance confirmed that its natural language processing algorithms supported Apple's Siri voice assistant. | Nuance Communications | 0.785505 |
79,113 | Nuance Communications, Inc. owned by Microsoft is an American multinational computer software technology corporation, headquartered in Burlington, Massachusetts, that markets speech recognition and artificial intelligence software. Nuance merged with its competitor in the commercial large-scale speech application busin... | Nuance Communications | 0.785505 |
79,114 | In mathematics, the Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by Charles W. Curtis (1980) and studied by his student Dean Alvis (1979). Kawanaka (1981, 1982) introduced a similar duality operation for Lie algebras. Alvis–Curtis duality has order 2... | Alvis–Curtis dual | 0.785504 |
79,115 | In neutron time-of-flight scattering, a form of inelastic neutron scattering, the initial position and velocity of a pulse of neutrons is fixed, and their final position and the time after the pulse that the neutrons are detected are measured. By the principle of conservation of momentum, these pairs of coordinates may... | Neutron time-of-flight scattering | 0.785503 |
79,116 | Imry, Y. (1997). Introduction to Mesoscopic Physics. Oxford University Press. | Dephasing | 0.785501 |
79,117 | When the temperature is lowered and the dimensions of the device are meaningfully reduced, this classical behaviour should disappear and the laws of quantum mechanics should govern the behavior of conducting electrons seen as waves that move ballistically inside the conductor without any kind of dissipation. Most of th... | Dephasing | 0.785501 |
79,118 | In physics, dephasing is a mechanism that recovers classical behaviour from a quantum system. It refers to the ways in which coherence caused by perturbation decays over time, and the system returns to the state before perturbation. It is an important effect in molecular and atomic spectroscopy, and in the condensed ma... | Dephasing | 0.785501 |
79,119 | In classical physics, the behavior of the electric and magnetic field is described by a system of equations known as Maxwell's equations. Working in the language of vector calculus and assuming that no electric charges or currents are present, these equations can be written ∇ ⋅ E = 0 , ∇ ⋅ B = 0 , ∇ × E = − ∂ B ∂ t , ∇... | Strong-weak duality | 0.785501 |
79,120 | Another realization of S-duality in quantum field theory is Seiberg duality, first introduced by Nathan Seiberg around 1995. Unlike Montonen–Olive duality, which relates two versions of the maximally supersymmetric gauge theory in four-dimensional spacetime, Seiberg duality relates less symmetric theories called N=1 su... | Strong-weak duality | 0.785501 |
79,121 | In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult t... | Strong-weak duality | 0.785501 |
79,122 | SGA5 Cohomologie l-adique et fonctions L, 1965–1966 (l-adic cohomology and L-functions), Lecture Notes in Mathematics 589, 1977 SGA6 Théorie des intersections et théorème de Riemann-Roch, 1966–1967 (Intersection theory and the Riemann–Roch theorem), Lecture Notes in Mathematics 225, 1971 SGA7 Groupes de monodromie en g... | Séminaire de Géométrie Algébrique du Bois Marie | 0.785501 |
79,123 | The volumes of the SGA series are the following: SGA1 Revêtements étales et groupe fondamental, 1960–1961 (Étale coverings and the fundamental group), Lecture Notes in Mathematics 224, 1971 SGA2 Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, 1961–1962 (Local cohomology of cohere... | Séminaire de Géométrie Algébrique du Bois Marie | 0.785501 |
79,124 | As a first step, the entire work was scanned and made available on-line (see the links section below) by Frank Calegari, Jim Borger and William Stein. The job of typesetting the text anew and proofreading it was then distributed among dozens of volunteers (most of them junior French mathematicians, because of the requi... | Séminaire de Géométrie Algébrique du Bois Marie | 0.785501 |
79,125 | In the 1990s, it became obvious that the lack of availability of the SGA was becoming more and more of a problem to researchers and graduate students in algebraic geometry: not only are the copies in book form too few for the growing number of researchers, but they are also difficult to read because of the way they are... | Séminaire de Géométrie Algébrique du Bois Marie | 0.785501 |
79,126 | Foldit is an online puzzle video game about protein folding. It is part of an experimental research project developed by the University of Washington, Center for Game Science, in collaboration with the UW Department of Biochemistry. The objective of Foldit is to fold the structures of selected proteins as perfectly as ... | Foldit | 0.785499 |
79,127 | Four player-designed proteins were successfully grown in E. coli and then "solved" via X-ray crystallography. The proteins were added to the Protein Data Bank as 6MRR, 6MRS, 6MSP, and 6NUK. In November 2019, an article in PLOS Biology reported how Foldit players were able to "build protein structures into crystallograp... | Foldit | 0.785499 |
79,128 | In January 2012, Scientific American reported that Foldit gamers achieved the first crowdsourced redesign of a protein, an enzyme that catalysed the Diels–Alder reactions widely used in synthetic chemistry. A team including David Baker in the Center for Game Science at University of Washington in Seattle computationall... | Foldit | 0.785499 |
79,129 | Protein structure prediction is important in several fields of science, including bioinformatics, molecular biology, and medicine. Identifying natural proteins' structural configurations enables scientists to understand them better. This can lead to creating novel proteins by design, advances in treating disease, and s... | Foldit | 0.785499 |
79,130 | Prof. David Baker, a protein research scientist at the University of Washington, founded the Foldit project. Seth Cooper was the lead game designer. Before starting the project, Baker and his laboratory coworkers relied on another research project named Rosetta to predict the native structures of various proteins using... | Foldit | 0.785499 |
79,131 | A Semispray structure on a smooth manifold M is by definition a smooth vector field H on TM \0 such that JH=V. An equivalent definition is that j(H)=H, where j:TTM→TTM is the canonical flip. A semispray H is a spray, if in addition, =H. Spray and semispray structures are invariant versions of second order ordinary diff... | Double tangent bundle | 0.785498 |
79,132 | In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of a smooth manifold M . A note on notation: in this article, we denote projection maps by their domains, e.g., πTT... | Double tangent bundle | 0.785498 |
79,133 | A second spontaneous electrocyclization, this time a 6π-disrotatory ring closure, converted 41 to the bicyclic species 42, the geometry and stereochemistry of which favored a subsequent intramolecular Diels-Alder reaction. The methyl ester of endiandric acid B (43) was thus obtained in 23% overall yield. A pericyclic s... | Cascade reaction | 0.785496 |
79,134 | These incidents often lead to significant economic losses.The Committee on Enhancing the Resilience of the Nation's Electric Power Transmission and Distribution System has developed strategies that seek to reduce the impact of large-scale, long-duration outages. Resilience is not just about preventing these outages fro... | Resilience (power system) | 0.785496 |
79,135 | Rapid Control Prototyping is involved in various fields of engineering, for instance: Mechatronics, robotics Power electronics, motor drives, motion control Automotive, aerospace Military | Rapid control prototyping | 0.785495 |
79,136 | The Pauli vector is defined by where x ^ 1 {\displaystyle {\hat {x}}_{1}} , x ^ 2 {\displaystyle {\hat {x}}_{2}} , and x ^ 3 {\displaystyle {\hat {x}}_{3}} are an equivalent notation for the more familiar x ^ {\displaystyle {\hat {x}}} , y ^ {\displaystyle {\hat {y}}} , and z ^ {\displaystyle {\hat {z}}} . The Pauli ve... | Pauli spin matrices | 0.785495 |
79,137 | I denotes the 2 × 2 identity matrix. These anti-commutation relations make the Pauli matrices the generators of a representation of the Clifford algebra for R 3 , {\displaystyle \ \mathbb {R} ^{3}\ ,} denoted C l 3 ( R ) . {\displaystyle \ \mathrm {Cl} _{3}(\mathbb {R} )~.} The usual construction of generators σ i j = ... | Pauli spin matrices | 0.785495 |
79,138 | The Pauli matrices obey the following commutation relations: = 2 i ε i j k σ k , {\displaystyle =2i\varepsilon _{ijk}\,\sigma _{k}\ ,} where the structure constant εijk is the Levi-Civita symbol and Einstein summation notation is used. These commutation relations make the Pauli matrices the generators of a representat... | Pauli spin matrices | 0.785495 |
79,139 | The group SU(2) is the Lie group of unitary 2 × 2 matrices with unit determinant; its Lie algebra is the set of all 2 × 2 anti-Hermitian matrices with trace 0. Direct calculation, as above, shows that the Lie algebra s u 2 {\displaystyle {\mathfrak {su}}_{2}} is the 3-dimensional real algebra spanned by the set {iσk}. ... | Pauli spin matrices | 0.785495 |
79,140 | It follows from this definition that the Σ k {\displaystyle \ {\mathsf {\Sigma }}_{k}\ } matrices have the same algebraic properties as the σk matrices. However, relativistic angular momentum is not a three-vector, but a second order four-tensor. Hence Σ k {\displaystyle \ {\mathsf {\Sigma }}_{k}\ } needs to be replace... | Pauli spin matrices | 0.785495 |
79,141 | In relativistic quantum mechanics, the spinors in four dimensions are 4 × 1 (or 1 × 4) matrices. Hence the Pauli matrices or the Sigma matrices operating on these spinors have to be 4 × 4 matrices. They are defined in terms of 2 × 2 Pauli matrices as Σ k = ( σ k 0 0 σ k ) . {\displaystyle {\mathsf {\Sigma }}_{k}={\begi... | Pauli spin matrices | 0.785495 |
79,142 | By taking Kronecker products of this representation with itself repeatedly, one may construct all higher irreducible representations. That is, the resulting spin operators for higher spin systems in three spatial dimensions, for arbitrarily large j, can be calculated using this spin operator and ladder operators. They ... | Pauli spin matrices | 0.785495 |
79,143 | In quantum mechanics, each Pauli matrix is related to an angular momentum operator that corresponds to an observable describing the spin of a spin 1⁄2 particle, in each of the three spatial directions. As an immediate consequence of the Cartan decomposition mentioned above, iσj are the generators of a projective repres... | Pauli spin matrices | 0.785495 |
79,144 | Each of the tensors S, E, and W has the same algebraic symmetries as the Riemann tensor. That is: S i j k l = − S j i k l = − S i j l k = S k l i j E i j k l = − E j i k l = − E i j l k = E k l i j W i j k l = − W j i k l = − W i j l k = W k l i j {\displaystyle {\begin{aligned}S_{ijkl}&=-S_{jikl}=-S_{ijlk}=S_{klij}\\E... | Ricci decomposition | 0.785494 |
79,145 | In the mathematical fields of Riemannian and pseudo-Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a Riemannian or pseudo-Riemannian manifold into pieces with special algebraic properties. This decomposition is of fundamental importance in Riemannian and pseudo-Riem... | Ricci decomposition | 0.785494 |
79,146 | Conversely, given a pair of symmetric 2-forms h and k, the Kulkarni–Nomizu product of h and k ( h ∧ ◯ k ) ( x , y , z , w ) = h ( x , z ) k ( y , w ) + h ( y , w ) k ( x , z ) − h ( x , w ) k ( y , z ) − h ( y , z ) k ( x , w ) {\displaystyle (h{~\wedge \!\!\!\!\!\!\!\!\;\bigcirc ~}k)(x,y,z,w)=h(x,z)k(y,w)+h(y,w)k(x,z)... | Ricci decomposition | 0.785494 |
79,147 | The Ricci contraction mapping c: S 2 Λ 2 V → S 2 V {\displaystyle c:S^{2}\Lambda ^{2}V\to S^{2}V} is given by c ( R ) ( x , y ) = tr R ( x , ⋅ , y , ⋅ ) . {\displaystyle c(R)(x,y)=\operatorname {tr} R(x,\cdot ,y,\cdot ).} This associates a symmetric 2-form to an algebraic curvature tensor. | Ricci decomposition | 0.785494 |
79,148 | As a result, R is an element of the subspace S 2 Λ 2 V {\displaystyle S^{2}\Lambda ^{2}V} , the second symmetric power of the second exterior power of V. A curvature tensor must also satisfy the Bianchi identity, meaning that it is in the kernel of the linear map b: S 2 Λ 2 V → Λ 4 V {\displaystyle b:S^{2}\Lambda ^{2}V... | Ricci decomposition | 0.785494 |
79,149 | As stated, this is vacuous since it is just a reorganization of the definition of W. The importance of the decomposition is in the properties of the three new tensors S, E, and W. Terminological note. The tensor W is called the Weyl tensor. The notation W is standard in mathematics literature, while C is more common in... | Ricci decomposition | 0.785494 |
79,150 | Their secondary analysis bioinformatics product for the RS, called “SMRT Analysis”, was open source. For the Sequel system the secondary analysis software was reorganized as the "SMRT Link" application. In 2013, the company released new bioinformatics tools for automated genome assembly (HGAP) and finishing (Quiver). | Pacific Biosciences | 0.785493 |
79,151 | The company was founded based on research done at Cornell University that combined semiconductor processing and photonics with biotechnology research. Three graduate students in the lab of Professors Watt W. Webb — Jonas Korlach — and Harold Craighead — Steve Turner and Mathieu Foquet — became the first employees. It b... | Pacific Biosciences | 0.785493 |
79,152 | Pacific Biosciences of California, Inc. (aka PacBio) is an American biotechnology company founded in 2004 that develops and manufactures systems for gene sequencing and some novel real time biological observation. PacBio has two principal sequencing platforms: single-molecule real-time sequencing (SMRT), based on the p... | Pacific Biosciences | 0.785493 |
79,153 | On 3 August 2021, Circulomics Inc. was acquired by PacBio to expand offerings in high-molecular weight DNA extraction sample preparation. The acquisition led to the development of the high throughput Nanobind DNA extraction kits which were later introduced in April, 2023. Omniome, Inc. was acquired by PacBio on 20 Sept... | Pacific Biosciences | 0.785493 |
79,154 | In astronomy, an epoch specifies a precise moment in time. The positions of celestial objects and events, as measured from Earth, change over time, so when measuring or predicting celestial positions, the epoch to which they pertain must be specified. A new standard epoch is chosen about every 50 years. | Julian year (astronomy) | 0.785492 |
79,155 | In astronomy, a Julian year (symbol: a or aj) is a unit of measurement of time defined as exactly 365.25 days of 86400 SI seconds each. The length of the Julian year is the average length of the year in the Julian calendar that was used in Western societies until the adoption of the Gregorian Calendar, and from which t... | Julian year (astronomy) | 0.785492 |
79,156 | A Julian year should not be confused with the Julian day, which is also used in astronomy (more properly called the Julian day number or JDN). The JDN uniquely specifies a place in time, without becoming bogged down in its date-in-month, week, month, or year in any particular calendar. Despite the similarity of names, ... | Julian year (astronomy) | 0.785492 |
79,157 | The Julian year is not a unit of measurement in the International System of Units (SI), but it is recognized by the International Astronomical Union (IAU) as a non-SI unit for use in astronomy. Before 1984, both the Julian year and the mean tropical year were used by astronomers. In 1898, Simon Newcomb used both in his... | Julian year (astronomy) | 0.785492 |
79,158 | Enzymes are classified based on recommendations from the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology and are given an enzyme commission number, commonly referred to as an EC number. Each distinct enzymatic activity is given a recommended name and EC number. To be classified a... | Non-homologous isofunctional enzymes | 0.785491 |
79,159 | Non-Homologous Isofunctional Enzymes (NISE) are two evolutionarily unrelated enzymes that catalyze the same chemical reaction. Enzymes that catalyze the same reaction are sometimes referred to as analogous as opposed to homologous (Homology (biology)), however it is more appropriate to name them as Non-homologous Isofu... | Non-homologous isofunctional enzymes | 0.785491 |
79,160 | A media processor, mostly used as an image/video processor, is a microprocessor-based system-on-a-chip which is designed to deal with digital streaming data in real-time (e.g. display refresh) rates. These devices can also be considered a class of digital signal processors (DSPs). Unlike graphics processing units (GPUs... | Media Processing Engine | 0.785489 |
79,161 | The Trinder glucose activity test is a diagnostic test used in medicine to determine the presence of glucose or glucose oxidase. The test employs the Trinder reagent, and is a colour change test resulting from the Trinder reaction. The Trinder reagent, named after P. Trinder of the Biochemistry Department of the Royal ... | Trinder glucose activity test | 0.785489 |
79,162 | Hayden said, "There are those out there who can take a look at this... and maybe even attempt to turn it to their own purposes". In the same report, Sean McGurk, a former cybersecurity official at the Department of Homeland Security noted that the Stuxnet source code could now be downloaded online and modified to be di... | Stuxnet | 0.785489 |
79,163 | and Israel reportedly did to Iran with Stuxnet, it could convince the leaders of that country that they were being attacked with nuclear weapons when they weren't. This could lead them to start a nuclear war by mistake, believing that they could lose the ability to respond appropriately if they waited for more informat... | Stuxnet | 0.785489 |
79,164 | Former U.S. Secretary of Defense William J. Perry and Tom Z. Collina, Director of Policy at the Ploughshares Fund, wrote that there are thousand and maybe millions of attacks each day on the U.S. military's use of the internet and similar DoD-only communications. If a cybersecurity attack on any nuclear-weapon state do... | Stuxnet | 0.785489 |
79,165 | According to the Israeli newspaper Haaretz, in September 2010 experts on Iran and computer security specialists were increasingly convinced that Stuxnet was meant "to sabotage the uranium enrichment facility at Natanz – where the centrifuge operational capacity had dropped over the past year by 30 percent." On 23 Novem... | Stuxnet | 0.785489 |
79,166 | On 1 September 2011, a new worm was found, thought to be related to Stuxnet. The Laboratory of Cryptography and System Security (CrySyS) of the Budapest University of Technology and Economics analyzed the malware, naming the threat Duqu. Symantec, based on this report, continued the analysis of the threat, calling it "... | Stuxnet | 0.785489 |
79,167 | Wired speculated that the assassinations could indicate that whoever was behind Stuxnet felt that it was not sufficient to stop the nuclear program. That same Wired article suggested the Iranian government could have been behind the assassinations. In January 2010, another Iranian nuclear scientist, a physics professor... | Stuxnet | 0.785489 |
79,168 | Empirical findings support the predictions: in all cases that were investigated (birds, fish, amphibians, aquatic insects, zooplankton) generation times are negatively correlated with temperature. Brown et al.(2004) further developed these findings to a general metabolic theory of ecology. | Effective evolutionary time | 0.785487 |
79,169 | Roger L. Easton of the Naval Research Laboratory, Ivan A. Getting of The Aerospace Corporation, and Bradford Parkinson of the Applied Physics Laboratory are credited with inventing it. The work of Gladys West is credited as instrumental in the development of computational techniques for detecting satellite positions wi... | Global Positioning System | 0.785487 |
79,170 | In particle physics, isoscalar refers to the scalar transformation of a particle or field under the SU(2) group of isospin. Isoscalars are a singlet state, with total isospin 0 and the third component of isospin 0, much like a singlet state in a 2-particle addition of spin. Mesons which have all flavor quantum numbers ... | Isoscalar | 0.785485 |
79,171 | Amazon's developers opted for "just works" design patterns with S3 and SimpleDB. While these systems had noticeable design flaws, they did not demand the overhead of provisioning hardware and scaling and re-partitioning data. Amazon's next iteration of NoSQL technology, DynamoDB, automated these database management ope... | Amazon DynamoDB | 0.785485 |
79,172 | Still, third-party relational database management systems struggled to handle Amazon's client base. This culminated during the 2004 holiday season, when several technologies failed under high traffic. Engineers were normalizing these relational systems to reduce data redundancy, a design that optimizes for storage. | Amazon DynamoDB | 0.785485 |
79,173 | Suppose that a DynamoDB user issues a write operation (a Put, Update, or Delete). While a typical relational system would convert the SQL query to relational algebra and run optimization algorithms, DynamoDB skips both processes and gets right to work. The request arrives at the DynamoDB request router, which authentic... | Amazon DynamoDB | 0.785485 |
79,174 | A physical unclonable function (sometimes also called physically unclonable function, which refers to a weaker security metric than a physical unclonable function), or PUF, is a physical object that for a given input and conditions (challenge), provides a physically defined "digital fingerprint" output (response) that ... | Physically unclonable function | 0.785485 |
79,175 | However, to do so requires some moderately advanced calculus. A much simpler approach considers the ant's position as a proportion of the distance from the starting-point to the target-point.Consider coordinates ψ {\displaystyle \psi } measured along the rope with the starting-point at ψ = 0 {\displaystyle \psi =0} and... | Ant on a rubber rope | 0.785484 |
79,176 | In the mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing a single vertex from G is Hamiltonian. | Hypohamiltonian graph | 0.785483 |
79,177 | The INET models are licensed under the LGPL or GPL. NED (NEtwork Description) is the topology description language of OMNeT++. To manage and reduce the time to carry out large-scale simulations, additional tools have been developed, for example, based on Python. | OMNeT++ | 0.785483 |
79,178 | NovoGen is a proprietary form of 3D printing technology that allows scientists to assemble living tissue cells into a desired pattern. When combined with an extracellular matrix, the cells can be arranged into complex structures, such as organs. Designed by Organovo, the NovoGen technology has been successfully integra... | NovoGen | 0.785482 |
79,179 | The dimensions of compliance in respiratory physiology are inconsistent with the dimensions of compliance in physics-based applications. In physiology, = = L 3 M L − 1 T − 2 = L 4 T 2 M , {\displaystyle ={\frac {}{}}={\frac {L^{3}}{ML^{-1}T^{-2}}}={\frac {L^{4}T^{2}}{M}},} whereas in newtonian physics, compliance is... | Lung compliance | 0.785481 |
79,180 | In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in sym... | Almost complex manifold | 0.78548 |
79,181 | The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece. It is one of several definitions of hardness in materials science. | Brinell scale | 0.785479 |
79,182 | The Radio Neutrino Observatory Greenland (or RNO-G) is a neutrino observatory deployed near Summit Camp on top of the Greenland ice sheet. The goal of the RNO-G experiment is detecting ultra-high energy neutrinos and estimating their flux. These particles could help to better understand the most violent events in the u... | Radio Neutrino Observatory Greenland | 0.785479 |
79,183 | A harmonic gear or strain wave gear is a specialized gearing mechanism often used in industrial motion control, robotics and aerospace for its advantages over traditional gearing systems, including lack of backlash, compactness and high gear ratios. Though the diagram does not demonstrate the correct configuration, it ... | Gear teeth | 0.785479 |
79,184 | The conclusion of Myers' theorem says that for any p , q ∈ M , {\displaystyle p,q\in M,} one has dg(p,q) ≤ π/√k. In 1975, Shiu-Yuen Cheng proved: Let ( M , g ) {\displaystyle (M,g)} be a complete and smooth Riemannian manifold of dimension n. If k is a positive number with Ricg ≥ (n-1)k, and if there exists p and q in ... | Myers's theorem | 0.785479 |
79,185 | Myers's theorem, also known as the Bonnet–Myers theorem, is a celebrated, fundamental theorem in the mathematical field of Riemannian geometry. It was discovered by Sumner Byron Myers in 1941. It asserts the following: In the special case of surfaces, this result was proved by Ossian Bonnet in 1855. For a surface, the ... | Myers's theorem | 0.785479 |
79,186 | Much of the underlying physics of the Portevin-Le Chatelier effect lies in a specific case of solute drag creep. Adding solute atoms to a pure crystal introduces a size misfit into the system. This size misfit leads to restriction of dislocation motion. At low temperature, these solute atoms are immobile within the lat... | Portevin–Le Chatelier effect | 0.785476 |
79,187 | For certain theories, S-duality provides a way of doing computations at strong coupling by translating these computations into different computations in a weakly coupled theory. S-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two seemingly differ... | S-duality | 0.785472 |
79,188 | In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory to the branch of mathematics known as representation theory. Formulated by Robert Langlands in the late 1960s, the Langlands correspondence is related to important conjectures in number theory such a... | S-duality | 0.785472 |
79,189 | Mechanically interlocked molecular architectures consist of molecules that are linked only as a consequence of their topology. Some non-covalent interactions may exist between the different components (often those that were utilized in the construction of the system), but covalent bonds do not. Supramolecular chemistry... | Template-directed synthesis | 0.785472 |
79,190 | Macrocycles are very useful in supramolecular chemistry, as they provide whole cavities that can completely surround guest molecules and may be chemically modified to fine-tune their properties. Cyclodextrins, calixarenes, cucurbiturils and crown ethers are readily synthesized in large quantities, and are therefore con... | Template-directed synthesis | 0.785472 |
79,191 | If a Riemannian manifold M (of any dimension) is almost flat (more precisely, M is a region of R n {\displaystyle \mathbb {R} ^{n}} with a Riemannian metric that is C 2 {\displaystyle C^{2}} -near the standard Euclidean metric), then M is a volume minimizer: it cannot be replaced by an orientable Riemannian manifold th... | Gromov's filling conjecture | 0.785471 |
79,192 | Thus the minimum area that the isometric filling M {\displaystyle M} can have is equal to the minimum area that a Riemannian projective plane of systole L {\displaystyle L} can have. But then Pu's systolic inequality asserts precisely that a Riemannian projective plane of given systole has minimum area if and only if i... | Gromov's filling conjecture | 0.785471 |
79,193 | The corresponding simply connected group is SU(2); it has center of order 2 and trivial outer automorphism group, and is a spin group.The classification of 3-dimensional complex Lie algebras is similar except that types VIII and IX become isomorphic, and types VI and VII both become part of a single family of Lie algeb... | Bianchi classification | 0.785471 |
79,194 | Historically these four types of homogeneous spaces have been classified as: B i a n c h i V: n 1 = 0 , ( a , n 2 , n 3 ) = ( 1 , 0 , 0 ) , B i a n c h i I V: n 1 = 0 , ( a , n 2 , n 3 ) = ( 1 , 0 , 1 ) , B i a n c h i V I I: n 1 = 0 , ( a , n 2 , n 3 ) = ( a , 1 , 1 ) , B i a n c h i I I I: n 1 = 0 , ( a , n 2 , n 3 )... | Bianchi classification | 0.785471 |
79,195 | Type V (a=1, n(1)=0, n(2)=0) is the interval (0,1] along the axis a and type IV (a=1, n(1)=1, n(2)=0) is the vertical open face between the first and fourth quadrants of the a = 0 plane with the latter giving the class A limit of each type. The Einstein equations for a universe with a homogeneous space can reduce to a ... | Bianchi classification | 0.785471 |
79,196 | However, the dynamics near the singularity is approximately governed by a series of successive Kasner (Bianchi I) periods. The complicated dynamics, which essentially amounts to billiard motion in a portion of hyperbolic space, exhibits chaotic behaviour, and is named Mixmaster; its analysis is referred to as the BKL a... | Bianchi classification | 0.785471 |
79,197 | (2) The solvable Lie algebra of 2×2 upper triangular matrices of trace 0. It has trivial center and trivial outer automorphism group. The associated simply connected Lie group is the affine group of the line. | Bianchi classification | 0.785471 |
79,198 | Dimension 0: The only Lie algebra is the abelian Lie algebra R0. Dimension 1: The only Lie algebra is the abelian Lie algebra R1, with outer automorphism group the multiplicative group of non-zero real numbers. Dimension 2: There are two Lie algebras: (1) The abelian Lie algebra R2, with outer automorphism group GL2(R)... | Bianchi classification | 0.785471 |
79,199 | The simply connected group is not a matrix group; it is denoted by SL ( 2 , R ) ¯ {\displaystyle {\overline {{\mbox{SL}}(2,\mathbf {R} )}}} , has center Z and its outer automorphism group has order 2. Type IX: The Lie algebra of the orthogonal group O3(R). It is denoted by 𝖘𝖔(3) and is simple and unimodular. | Bianchi classification | 0.785471 |
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