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85,400 | The theory of the Selberg trace formula, as applied by others, showed the considerable depth of the theory. Robert Langlands showed how (in generality, many particular cases being known) the Riemann–Roch theorem could be applied to the calculation of dimensions of automorphic forms; this is a kind of post hoc check on ... | Automorphic representation | 0.782924 |
85,401 | One of Poincaré's first discoveries in mathematics, dating to the 1880s, was automorphic forms. He named them Fuchsian functions, after the mathematician Lazarus Fuchs, because Fuchs was known for being a good teacher and had researched on differential equations and the theory of functions. Poincaré actually developed ... | Automorphic representation | 0.782924 |
85,402 | A predisposition for bladder infections may run in families. This is believed to be related to genetics. Other risk factors include diabetes, being uncircumcised, and having a large prostate. In children UTIs are associated with vesicoureteral reflux (an abnormal movement of urine from the bladder into ureters or kidne... | Urinary tract infections | 0.782922 |
85,403 | This has altered surface water levels. Climate change also enhances the existing challenges we face in water quality. The quality of surface water is based on the chemical inputs from the surrounding elements such as the air and the nearby landscape. When these elements are polluted due to human activity, it alters the... | Surface water | 0.782922 |
85,404 | Semi-permanent (ephemeral) surface water refers to bodies of water that are only present at certain times of the year including seasonally dry channels such as creeks, lagoons and waterholes. Human-made surface water is water that can be continued by infrastructures that humans have assembled. This would be dammed arti... | Surface water | 0.782922 |
85,405 | This in turn has provided to date records and documents of water data over the years. Management teams that oversee the distribution of water are then able to make decisions of adequate water supply to sectors. These include municipal, industrial, agricultural, renewable energy (hydropower), and storage in reservoirs. | Surface water | 0.782922 |
85,406 | In mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states: Every solution of a system (in general, overdetermined) of homogeneous partial differential equations with constant coefficients can be represented as the integral with respect to an appropriate Radon measure over the c... | Ehrenpreis's fundamental principle | 0.782919 |
85,407 | Symplectic geometry is the study of symplectic manifolds. The tangent space at any point on a symplectic manifold is a symplectic vector space. As noted earlier, structure preserving transformations of a symplectic vector space form a group and this group is Sp(2n, F), depending on the dimension of the space and the fi... | Unitary symplectic group | 0.782916 |
85,408 | Some main subgroups are: Sp ( n ) ⊃ Sp ( n − 1 ) {\displaystyle \operatorname {Sp} (n)\supset \operatorname {Sp} (n-1)} Sp ( n ) ⊃ U ( n ) {\displaystyle \operatorname {Sp} (n)\supset \operatorname {U} (n)} Sp ( 2 ) ⊂ O ( 4 ) {\displaystyle \operatorname {Sp} (2)\subset \operatorname {O} (4)} Conversely it ... | Unitary symplectic group | 0.782916 |
85,409 | Rather, it is isomorphic to a subgroup of Sp(2n, C), and so does preserve a complex symplectic form in a vector space of twice the dimension. As explained below, the Lie algebra of Sp(n) is the compact real form of the complex symplectic Lie algebra sp(2n, C). Sp(n) is a real Lie group with (real) dimension n(2n + 1). ... | Unitary symplectic group | 0.782916 |
85,410 | Mathematically, these charges are eigenvalues of the Cartan subalgebra generators, and are called roots or weights of a representation. In the Standard Model of particle physics, each different kind of elementary particle has four different charges, corresponding to twists along directions of a four-dimensional maximal... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,411 | For a Lie group of rank R, one can choose at most R orthogonal circles that do not twist around each other, and so form a maximal torus within the Lie group, corresponding to a collection of R mutually-commuting Lie algebra generators, spanning a Cartan subalgebra. Each elementary particle state can be thought of as a ... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,412 | The goal of E8 Theory is to describe all elementary particles and their interactions, including gravitation, as quantum excitations of a single Lie group geometry—specifically, excitations of the noncompact quaternionic real form of the largest simple exceptional Lie group, E8. A Lie group, such as a one-dimensional ci... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,413 | In December 2011, in a paper for a special issue of the journal Foundations of Physics, Michael Duff argued against Lisi's theory and the attention it has received in the popular press. Duff states that Lisi's paper was incorrect, citing Distler and Garibaldi's proof, and criticizes the press for giving Lisi uncritical... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,414 | In a joint paper with Lee Smolin and Simone Speziale, published in Journal of Physics A, Lisi proposed a new action and symmetry-breaking mechanism. In 2008, FQXi awarded Lisi a grant for further development of E8 Theory.In September 2010, Scientific American reported on a conference inspired by Lisi's work. Shortly th... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,415 | Lee Smolin's "The Plebanski action extended to a unification of gravity and Yang–Mills theory" proposes a symmetry-breaking mechanism to go from an E8 symmetric action to Lisi's action for the Standard Model and gravity. Roberto Percacci's "Mixing internal and spacetime transformations: some examples and counterexample... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,416 | Addressing the one generation case, in June 2010 Lisi posted a new paper on E8 Theory, "An Explicit Embedding of Gravity and the Standard Model in E8", eventually published in a conference proceedings, describing how the algebra of gravity and the Standard Model with one generation of fermions embeds in the E8 Lie alge... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,417 | These arguments were distilled in a paper written jointly with Skip Garibaldi, "There is no 'Theory of Everything' inside E8", published in Communications in Mathematical Physics. In this paper, Distler and Garibaldi offer a proof that it is impossible to embed all three generations of fermions in E8, or to obtain even... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,418 | Lisi's paper spawned a variety of reactions and debates across various physics blogs and online discussion groups. The first to comment was Sabine Hossenfelder, summarizing the paper and noting the lack of a dynamical symmetry-breaking mechanism. | An Exceptionally Simple Theory of Everything | 0.782916 |
85,419 | Lisi made a further presentation for the International Loop Quantum Gravity Seminar on November 13, 2007, and responded to press inquiries on an FQXi forum. He presented his work at the TED Conference on February 28, 2008.Numerous news sites reported on the new theory in 2007 and 2008, noting Lisi's personal history an... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,420 | Before writing his 2007 paper, Lisi discussed his work on a Foundational Questions Institute (FQXi) forum, at an FQXi conference, and for an FQXi article. Lisi gave his first talk on E8 Theory at the Loops '07 conference in Morelia, Mexico, soon followed by a talk at the Perimeter Institute. John Baez commented on Lisi... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,421 | The theory received a flurry of media coverage, but was also met with widespread skepticism. Scientific American reported in March 2008 that the theory was being "largely but not entirely ignored" by the mainstream physics community, with a few physicists picking up the work to develop it further. In July 2009, Jacques... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,422 | "An Exceptionally Simple Theory of Everything" is a physics preprint proposing a basis for a unified field theory, often referred to as "E8 Theory", which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physics arXiv by Anto... | An Exceptionally Simple Theory of Everything | 0.782916 |
85,423 | In graph theory, the Lovász–Woodall conjecture is a long-standing problem on cycles in graphs. It says: If G is a k-connected graph and L is a set of k independent edges in G, then G has a cycle containing L, unless k is odd and L is an edge cut.It was proposed independently by László Lovász in 1974 and by D. R. Woodal... | Lovász–Woodall conjecture | 0.782916 |
85,424 | As mentioned above, the k = 2 case of the Lovász–Woodall conjecture follows from Menger's theorem. The k = 3 case was given as an exercise by Lovász. After the conjecture was made, it was proven for k = 4 by Péter L. Erdős and E. Győri and independently by Michael V. Lomonosov., and for k = 5 by Daniel P. Sanders.Other... | Lovász–Woodall conjecture | 0.782916 |
85,425 | Many results in graph theory, starting with Menger's theorem, guarantee the existence of paths or cycles in a k-connected graph. For 2-connected graphs, Menger's theorem is equivalent to the statement that any two vertices lie on a common cycle. A theorem of G. A. Dirac generalizes this claim: if a graph is k-connected... | Lovász–Woodall conjecture | 0.782916 |
85,426 | Sodium dithionate Na2S2O6 is an important compound for inorganic chemistry. It is also known under names disodium dithionate, sodium hyposulfate, and sodium metabisulfate. The sulfur can be considered to be in its +5 oxidation state. It should not be confused with sodium dithionite, Na2S2O4, which is a very different c... | Sodium dithionate | 0.782915 |
85,427 | Alkenyl hydroperoxides (R1 = H) have been postulated as reactive intermediates in atmospheric chemistry. They are formed via ozonolysis of alkenes in the atmosphere and form hydroxyl radicals upon decay, which play an important role in the decomposition of pollutants in the air. During day-time, hydroxyl radicals form ... | Alkenyl peroxides | 0.782914 |
85,428 | In organic chemistry, alkenyl peroxides are organic compounds bearing an alkene (R2C=CR2) residue directly at the peroxide (R−O−O−R) group, resulting in the general formula R2C=C(R)OOR. They have very weak O-O bonds and are thus generally unstable compounds. | Alkenyl peroxides | 0.782914 |
85,429 | In fact, Goodale's problem was essentially the same as Reichenbach's had been, but applied to botany rather than marine biology for, in both cases, the practiced method of exhibition robbed the specimens of color and three-dimensional form. Moreover and also like Prof. Reichenbach, Prof. Goodale first learned of Leopol... | Glass sea creatures | 0.782913 |
85,430 | Bonnet's theorem can be naturally formulated for hypersurfaces in a Euclidean space of any dimension, and the result remains true in this context. Furthermore, the theorem can be extended from Bonnet's local formulation to a global formulation, allowing D to be any connected and simply-connected smooth manifold, with t... | Bonnet theorem | 0.782913 |
85,431 | Any surface in three-dimensional Euclidean space has a first and second fundamental form, which automatically are interrelated by the Gauss–Codazzi equations. Bonnet's theorem asserts a local converse to this result.Given an open region D in R2, let g and h be symmetric 2-tensors on D, with g additionally required to b... | Bonnet theorem | 0.782913 |
85,432 | In the mathematical field of differential geometry, the fundamental theorem of surface theory deals with the problem of prescribing the geometric data of a submanifold of Euclidean space. Originally proved by Pierre Ossian Bonnet in 1867, it has since been extended to higher dimensions and non-Euclidean contexts. | Bonnet theorem | 0.782913 |
85,433 | FIDES . The FIDES methodology (UTE-C 80-811) is based on the physics of failures and supported by the analysis of test data, field returns and existing modelling. UTE-C 80–810 or RDF2000 . The RDF2000 methodology is based on the French telecom experience. | Reliability theory | 0.782912 |
85,434 | Some universities offer graduate degrees in reliability engineering. Other reliability professionals typically have a physics degree from a university or college program. Many engineering programs offer reliability courses, and some universities have entire reliability engineering programs. A reliability engineer must ... | Reliability theory | 0.782912 |
85,435 | Unlike hardware, performing exactly the same test on exactly the same software configuration does not provide increased statistical confidence. Instead, software reliability uses different metrics, such as code coverage. The Software Engineering Institute's capability maturity model is a common means of assessing the o... | Reliability theory | 0.782912 |
85,436 | Software reliability engineering relies heavily on a disciplined software engineering process to anticipate and design against unintended consequences. There is more overlap between software quality engineering and software reliability engineering than between hardware quality and reliability. A good software developme... | Reliability theory | 0.782912 |
85,437 | Software reliability engineering must take this into account. Despite this difference in the source of failure between software and hardware, several software reliability models based on statistics have been proposed to quantify what we experience with software: the longer software is run, the higher the probability th... | Reliability theory | 0.782912 |
85,438 | The input for the models can come from many sources including testing; prior operational experience; field data; as well as data handbooks from similar or related industries. Regardless of source, all model input data must be used with great caution, as predictions are only valid in cases where the same product was use... | Reliability theory | 0.782912 |
85,439 | In practice, most failures can be traced back to some type of human error, for example in: Management decisions (e.g. in budgeting, timing, and required tasks) Systems Engineering: Use studies (load cases) Systems Engineering: Requirement analysis / setting Systems Engineering: Configuration control Assumptions Calcula... | Reliability theory | 0.782912 |
85,440 | The Chemical Pioneer Award, established in 1966, is awarded by the American Institute of Chemists to recognize chemists or chemical engineers who have made outstanding contributions to advances in chemistry or the chemical profession. | Chemical Pioneer Award | 0.78291 |
85,441 | . . d ω M {\displaystyle \sum _{n_{1}=-\infty }^{\infty }...\sum _{n_{M}=-\infty }^{\infty }|x_{1}(n_{1},...,n_{M})|^{2}{=}{\frac {1}{(2\pi )^{M}}}\int \limits _{-\pi }^{\pi }...\int \limits _{-\pi }^{\pi }|X_{1}(\omega _{1},...,\omega _{M})|^{2}d\omega _{1}...d\omega _{M}} A special case of the Parseval's theorem is w... | Multidimensional transform | 0.782908 |
85,442 | Discrete Fourier transforms are often used to solve partial differential equations, where again the DFT is used as an approximation for the Fourier series (which is recovered in the limit of infinite N). The advantage of this approach is that it expands the signal in complex exponentials einx, which are eigenfunctions ... | Multidimensional transform | 0.782908 |
85,443 | A fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. An FFT computes the DFT and produces exactly the same result as evaluating the DFT definition directly; the only difference is that an FFT is much faster. (In the presence of round-off error, many FFT algorit... | Multidimensional transform | 0.782908 |
85,444 | The multidimensional Laplace transform is useful for the solution of boundary value problems. Boundary value problems in two or more variables characterized by partial differential equations can be solved by a direct use of the Laplace transform. The Laplace transform for an M-dimensional case is defined as F ( s 1 , s... | Multidimensional transform | 0.782908 |
85,445 | Such an approach is called a spectral method. DCTs are also widely employed in solving partial differential equations by spectral methods, where the different variants of the DCT correspond to slightly different even/odd boundary conditions at the two ends of the array. Laplace transforms are used to solve partial diff... | Multidimensional transform | 0.782908 |
85,446 | A linear differential equation with constant coefficients is transformed into an easily solvable algebraic equation. One then uses the inverse DFT to transform the result back into the ordinary spatial representation. | Multidimensional transform | 0.782908 |
85,447 | The DCT and DFT are often used in signal processing and image processing, and they are also used to efficiently solve partial differential equations by spectral methods. The DFT can also be used to perform other operations such as convolutions or multiplying large integers. The DFT and DCT have seen wide usage across a... | Multidimensional transform | 0.782908 |
85,448 | The set M(n, R) (also denoted Mn(R)) of all square n-by-n matrices over R is a ring called matrix ring, isomorphic to the endomorphism ring of the left R-module Rn. If the ring R is commutative, that is, its multiplication is commutative, then the ring M(n, R) is also an associative algebra over R. The determinant of s... | Principal submatrix | 0.782907 |
85,449 | Wherever eigenvalues are considered, as these are roots of a polynomial they may exist only in a larger field than that of the entries of the matrix; for instance, they may be complex in the case of a matrix with real entries. The possibility to reinterpret the entries of a matrix as elements of a larger field (for exa... | Principal submatrix | 0.782907 |
85,450 | A square matrix A that is equal to its transpose, that is, A = AT, is a symmetric matrix. If instead, A is equal to the negative of its transpose, that is, A = −AT, then A is a skew-symmetric matrix. In complex matrices, symmetry is often replaced by the concept of Hermitian matrices, which satisfy A∗ = A, where the st... | Principal submatrix | 0.782907 |
85,451 | In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimension. Matrices are used in most areas of mathematics and most scientific fields, either directly, or through their use in geometry and numerical analysis. ... | Principal submatrix | 0.782907 |
85,452 | Square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. The determinant of a square matrix is a number associated to the matrix, which is fundamental for the study of a square matrix; for example, a square matrix is invertible if and only if it... | Principal submatrix | 0.782907 |
85,453 | This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. This article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square matrices, matrices with the same number of rows and columns, p... | Principal submatrix | 0.782907 |
85,454 | Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents the composition of linear maps. Not all matrices are related to linear algebra. | Principal submatrix | 0.782907 |
85,455 | In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by... | Principal submatrix | 0.782907 |
85,456 | There are three equivalent ways to define X {\displaystyle X} being Markov with initial distribution λ {\displaystyle \lambda } and rate matrix Q {\displaystyle Q}: via transition probabilities or via the jump chain and holding times.As a prelude to a transition-probability definition, we first motivate the definition ... | Continuous-time Markov process | 0.782907 |
85,457 | In the field of remote sensing the geotagging goal is to store coordinates of every pixel in the image. One approach is used with the orthophotos where we store coordinates of four corners and all the other pixels can be georeferenced by interpolation. The four corners are stored using GeoTIFF or World file standards. ... | Geotagging | 0.782906 |
85,458 | In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known as the multivariate constraint (Garner 1962) or multiinformation (Studený & Vejnarová 1999). It quantifies the redundancy or dependency among a s... | Total Correlation | 0.782904 |
85,459 | M m {\displaystyle M_{\mathfrak {m}}} is free as R m {\displaystyle R_{\mathfrak {m}}} -module for every maximal ideal m {\displaystyle {\mathfrak {m}}} of R. M p {\displaystyle M_{\mathfrak {p}}} is free as R p {\displaystyle R_{\mathfrak {p}}} -module for every prime ideal p {\displaystyle {\mathfrak {p}}} of R. Ther... | Finitely generated projective module | 0.782904 |
85,460 | The quality of MMIR Systems depends heavily on the quality of the training data. Discriminative descriptions can be extracted from media sources in various forms. Machine learning provides categorization methods for all types of data. | Multimedia information retrieval | 0.782903 |
85,461 | Multimedia information retrieval (MMIR or MIR) is a research discipline of computer science that aims at extracting semantic information from multimedia data sources. Data sources include directly perceivable media such as audio, image and video, indirectly perceivable sources such as text, semantic descriptions, biosi... | Multimedia information retrieval | 0.782903 |
85,462 | Generally, all forms of machine learning can be employed for the categorization of multimedia descriptions: 125 though some methods are more frequently used in one area than another. For example, hidden Markov models are state-of-the-art in speech recognition, while dynamic time warping – a semantically related method ... | Multimedia information retrieval | 0.782903 |
85,463 | In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R-module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as Z ( M ) = { m ∈ M ∣ a n n ( m ) ⊆ e R } {\displaystyle ... | Singular submodule | 0.782903 |
85,464 | Some publishers of open-access journals have argued that data from food science and gastronomy studies should be freely available to aid reproducibility. A number of people have published creative commons licensed recipe books. Open-source colas – cola soft drinks, similar to Coca-Cola and Pepsi, whose recipe is open s... | Open source technology | 0.782902 |
85,465 | The C1-FFL with an AND gate was shown to have a function of a 'sign-sensitive delay' element and a persistence detector both theoretically and experimentally with the arabinose system of E. coli. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but per... | Network motif | 0.7829 |
85,466 | A Lie group integrator is a numerical integration method for differential equations built from coordinate-independent operations such as Lie group actions on a manifold. They have been used for the animation and control of vehicles in computer graphics and control systems/artificial intelligence research. These tasks a... | Lie group integrator | 0.782899 |
85,467 | On the other hand, high altitude does not offer as significant an advantage for radio astronomy at longer wavelengths, so relatively few radio telescopes are located at such sites. At the far end of the spectrum, for the extremely short wavelengths of x-ray and gamma ray astronomy, along with high-energy cosmic rays, h... | List of highest astronomical observatories | 0.782897 |
85,468 | In particular, sites on mountaintops within about 80 km (50 mi) of the ocean often have excellent observing conditions above a stable inversion layer throughout much of the year. High altitude sites are also above most of atmosphere's water vapor, making them ideal for infrared astronomy and submillimeter astronomy as ... | List of highest astronomical observatories | 0.782897 |
85,469 | In the first decade of the 21st century, there has been a new wave of observatory construction at very high altitudes above 4,500 m (14,800 ft), with such observatories constructed in India, Mexico, and most notably the Atacama Desert in northern Chile, now the site of several of the world's highest observatories. The ... | List of highest astronomical observatories | 0.782897 |
85,470 | Prominent features of MySQL Workbench are: General Database Connection & Instance Management Wizard driven action items Fully scriptable with Python and Lua Support for custom plugins MSAA (Windows Accessibility API) compliant Supports MySQL Enterprise features (Audit Log, Firewall, and Enterprise Backup) SQL Editor Sc... | MySQL Workbench | 0.782897 |
85,471 | On August 19, 2014, the MySQL Workbench Team announced its first public beta release of Version 6.2. The first general-availability release was made on September 23, 2014. New features are shortcut buttons for common operations, "pinning" of the results tab, Microsoft Access Migration, MySQL Fabric Integration, Spatial... | MySQL Workbench | 0.782897 |
85,472 | Researchers have demonstrated a quantum-like computing method using acoustic metamaterials. Recently operations similar to the Controlled-NOT (CNOT) gate, a key component in quantum computing, have been demonstrated. By employing a nonlinear acoustic metamaterial, consisting of three elastically coupled waveguides, the... | Acoustic metamaterial | 0.782897 |
85,473 | Phononic crystals are synthetic materials formed by periodic variation of the acoustic properties of the material (i.e., elasticity and mass). One of their main properties is the possibility of having a phononic band gap. A phononic crystal with phononic band gap prevents phonons of selected ranges of frequencies from ... | Acoustic metamaterial | 0.782897 |
85,474 | Thus, by the properties of inversive geometry, since the figure traced by point D is the inverse of the figure traced by point B, if B traces a circle passing through the center of inversion O, then D is constrained to trace a straight line. But if B traces a straight line not passing through O, then D must trace an ar... | Peaucellier–Lipkin linkage | 0.782896 |
85,475 | \ell _{OB}\cdot \ell _{OD}=k^{2}} and since points O, B, D are collinear, then D is the inverse of B with respect to the circle (O,k) with center O and radius k. | Peaucellier–Lipkin linkage | 0.782896 |
85,476 | Therefore, angle ∠BPA = angle ∠DPA. But since ∠BPA + ∠DPA = 180°, then 2 × ∠BPA = 180°, ∠BPA = 90°, and ∠DPA = 90°. Let: x = ℓ B P = ℓ P D y = ℓ O B h = ℓ A P {\displaystyle {\begin{aligned}&x=\ell _{BP}=\ell _{PD}\\&y=\ell _{OB}\\&h=\ell _{AP}\end{aligned}}} Then: ℓ O B ⋅ ℓ O D = y ( y + 2 x ) = y 2 + 2 x y {\displays... | Peaucellier–Lipkin linkage | 0.782896 |
85,477 | The NRAO VLA Sky Survey (NVSS) was an astronomical survey of the Northern Hemisphere carried out by the Very Large Array (VLA) of the National Radio Astronomy Observatory (NRAO), resulting in an astronomical catalogue. It was led by James J. Condon.The survey covers 82% sky, consisting of everything north of declinatio... | NRAO VLA Sky Survey | 0.782896 |
85,478 | A balloon-borne telescope is a type of airborne telescope, a sub-orbital astronomical telescope that is suspended below one or more stratospheric balloons, allowing it to be lifted above the lower, dense part of the Earth's atmosphere. This has the advantage of improving the resolution limit of the telescope at a much ... | Balloon-borne telescope | 0.782894 |
85,479 | In quantum information theory and quantum optics, the Schrödinger–HJW theorem is a result about the realization of a mixed state of a quantum system as an ensemble of pure quantum states and the relation between the corresponding purifications of the density operators. The theorem is named after physicists and mathemat... | Schrödinger–HJW theorem | 0.782894 |
85,480 | It is also taught at Harvard, most recently as Astronomy 2.Celestial navigation continues to be used by private yachtsmen, and particularly by long-distance cruising yachts around the world. For small cruising boat crews, celestial navigation is generally considered an essential skill when venturing beyond visual range... | Astronomical navigation | 0.782892 |
85,481 | The Opto Semiconductors Business Unit provides opto semiconductors, which are crucial elements in lighting, visualization, and sensor technology. Osram Opto Semiconductors offers a wide range of LEDs in the low-power, mid-power, high-power, and ultra-high-power classes that are used in general lighting, automotive, con... | Osram | 0.782892 |
85,482 | OSRAM Licht AG is a German company that makes electric lights, headquartered in Munich and Premstätten (Austria). OSRAM positions itself as a high-tech photonics company that is increasingly focusing on sensor technology, visualization and treatment by light. The company serves customers in the consumer, automotive, he... | Osram | 0.782892 |
85,483 | The cross product has applications in various contexts. For example, it is used in computational geometry, physics and engineering. A non-exhaustive list of examples follows. | Cross product matrix | 0.78289 |
85,484 | In vector calculus, the cross product is used to define the formula for the vector operator curl. The trick of rewriting a cross product in terms of a matrix multiplication appears frequently in epipolar and multi-view geometry, in particular when deriving matching constraints. | Cross product matrix | 0.78289 |
85,485 | Like other boranes, the structure of tetraborane involves multicenter bonding, with hydrogen bridges or protonated double bonds. According to its formula, B4H10, it is classified as an arachno-cluster and has a butterfly geometry, which can be rationalized by Wade's rules. Each boron is sp3 hybridized, and “the configu... | B4H10 | 0.78289 |
85,486 | There are many examples of when a particular idea, almost on the same period, arises in different disciplines. One case is the shift from the approach of focusing on "specialized segments of attention" (adopting one particular perspective), to the idea of "instant sensory awareness of the whole", an attention to the "t... | Interdisciplinary research | 0.782889 |
85,487 | The epidemiology of HIV/AIDS or global warming requires understanding of diverse disciplines to solve complex problems. Interdisciplinary may be applied where the subject is felt to have been neglected or even misrepresented in the traditional disciplinary structure of research institutions, for example, women's studie... | Interdisciplinary research | 0.782889 |
85,488 | If the theory is renormalizable (see below for more on this), as it is in QED, the divergent parts of loop diagrams can all be decomposed into pieces with three or fewer legs, with an algebraic form that can be canceled out by the second term (or by the similar counterterms that come from Z0 and Z3). The diagram with t... | Renormalization | 0.782889 |
85,489 | Rivasseau, Vincent; An introduction to renormalization, Poincaré Seminar (Paris, Oct. 12, 2002), published in: Duplantier, Bertrand; Rivasseau, Vincent (Eds. ); Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003) ISBN 3-7643-0579-7. | Renormalization | 0.782889 |
85,490 | In more technical terms, let us assume that we have a theory described by a certain function Z {\displaystyle Z} of the state variables { s i } {\displaystyle \{s_{i}\}} and a certain set of coupling constants { J k } {\displaystyle \{J_{k}\}} . This function may be a partition function, an action, a Hamiltonian, etc. ... | Renormalization | 0.782889 |
85,491 | (See also regularization (physics) for an alternative way to remove infinities from this classical problem, assuming new physics exists at small scales.) When calculating the electromagnetic interactions of charged particles, it is tempting to ignore the back-reaction of a particle's own field on itself. (Analogous to ... | Renormalization | 0.782889 |
85,492 | If the cutoff is a real, physical quantity—that is, if the theory is only an effective description of physics up to some maximum energy or minimum distance scale—then these additional terms could represent real physical interactions. Assuming that the dimensionless constants in the theory do not get too large, one can ... | Renormalization | 0.782889 |
85,493 | The Standard Model of particle physics contains only renormalizable operators, but the interactions of general relativity become nonrenormalizable operators if one attempts to construct a field theory of quantum gravity in the most straightforward manner (treating the metric in the Einstein–Hilbert Lagrangian as a pert... | Renormalization | 0.782889 |
85,494 | "A hint of renormalization". American Journal of Physics. 72 (2): 170–184. | Renormalization | 0.782889 |
85,495 | DeDeo, Simon; Introduction to Renormalization (2017). Santa Fe Institute Complexity Explorer MOOC. Renormalization from a complex systems point of view, including Markov Chains, Cellular Automata, the real space Ising model, the Krohn-Rhodes Theorem, QED, and rate distortion theory. Delamotte, Bertrand (2004). | Renormalization | 0.782889 |
85,496 | (Ed. ); Renormalization: From Lorentz to Landau (and Beyond), Springer-Verlag (New York-1993) ISBN 0-387-97933-6. Cardy, John; Scaling and Renormalization in Statistical Physics, Cambridge University Press (1996) ISBN 0-521-49959-3. | Renormalization | 0.782889 |
85,497 | Zinn-Justin, Jean; Phase Transitions & Renormalization Group: from Theory to Numbers, Poincaré Seminar (Paris, Oct. 12, 2002), published in: Duplantier, Bertrand; Rivasseau, Vincent (Eds. ); Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003) ISBN 3-7643-0579-7. | Renormalization | 0.782889 |
85,498 | After canceling out these terms with the contributions from cutoff-dependent counterterms, the cutoff is taken to infinity and finite physical results recovered. If physics on scales we can measure is independent of what happens at the very shortest distance and time scales, then it should be possible to get cutoff-ind... | Renormalization | 0.782889 |
85,499 | Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormal... | Renormalization | 0.782889 |
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