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78,400 | In virtual space technology, a tracking system is generally a system capable of rendering virtual space to a human observer while tracking the observer's coordinates. For instance, in dynamic virtual auditory space simulations, a head tracker provides information to a central processor in real time and this enables the... | Tracking system | 0.785737 |
78,401 | chemist Min Enze, chemist Shi Jun (时钧), chemist Jin Baozhen (金宝桢), Mechanics Scientist Min Guirong (闵桂荣), aerospace engineer Ding Henggao (丁衡高), high-precision machinery expert Yang Huanming, Geneticist He Lin (贺林), Geneticist Zhengxu Zhao (赵正旭), Chief scientist of space mission visualization & control, Professor & Fel... | Southeast University | 0.785736 |
78,402 | Zhang Zhushan, Chemist Wu Chien-Shiung, physicist, known as the "Oriental Marie Curie", with β-decay experiments demonstrating that in the weak interaction, symmetry is not conserved Huang Weilu, missile engineer, recipient of the Two Bombs, One Satellite Medal Ren Xinmin, missile engineer, recipient of the Two Bombs, ... | Southeast University | 0.785736 |
78,403 | Yung Ho Chang (张永和), Owner of 'Architecture Prize' awarded by American Academy of Arts, Professor of the U.S. Massachusetts Institute of Technology (MIT), Department of Architecture (Department of Architecture, 81) Yuan Chun: Graduate from Southeast University, studied in Germany, a pioneer to promote the militarizatio... | Southeast University | 0.785736 |
78,404 | They are: Nanjing Railway Medical College, Nanjing College of Advanced Transportation, as well as Nanjing Advanced School of Geology. Nanjing Railway Medical College became the School of Medicine at Southeast University after it merged with SEU. The medical school is located in Dingjiaqiao. | Southeast University | 0.785736 |
78,405 | In 1952, the People's Republic of China began a national adjustment of its colleges. In Nanjing, the adjustment was mainly on Nanjing University and University of Nanking. Nanjing Institute of Technology was formed in the original site of National Central University from the Engineering School (at the time, the biggest... | Southeast University | 0.785736 |
78,406 | Due to the ambiguous meaning of the college name which led to several disputes, the Sanjiang Normal College was named as Liangjiang Normal College in 1905. The year after, Li Ruiqing was nominated as the principal, who closed the junior normal subjects, and added the public subjects, professional subjects, and also cre... | Southeast University | 0.785736 |
78,407 | Chiang Kai-shek (蔣介石), President of Republic of China Huang Wei (黄卫), vice chairman of Xinjiang Uygur Autonomous Region, the former Vice Minister of Construction (Civil Engineering) Zhenya Wang, Australian senator | Southeast University | 0.785736 |
78,408 | Most students are recruited by engineering or some big schools such as School of Mechanical Engineering, School of Energy & Environmental Engineering, School of Information Science & Engineering, School of Civil Engineering, School of Computer Science & Engineering, School of Economics & Management, as well as School o... | Southeast University | 0.785736 |
78,409 | Office of President Education Foundation University history Chien-Shiung Wu Memorial Hall Galileo training and application research center General Alumni Association of Southeast University School of Architecture School of Mechanical Engineering School of Energy & Environment Engineering School of Information Science &... | Southeast University | 0.785736 |
78,410 | The FETI-DP method is hybrid between a dual and a primal method. Non-overlapping domain decomposition methods are also called iterative substructuring methods. Mortar methods are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains. | Domain decomposition | 0.785733 |
78,411 | In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A coarse problem with one or few unknowns... | Domain decomposition | 0.785733 |
78,412 | In theoretical physics, the term dressed particle refers to a bare particle together with some excitations of other quantum fields that are physically inseparable from the bare particle. For example, a dressed electron includes the cloud of virtual electron–positron pairs and photons surrounding the original electron. ... | Dressed particle | 0.785733 |
78,413 | Satisfiability of a modal μ-calculus formula is EXPTIME-complete. Like for linear temporal logic, the model checking, satisfiability and validity problems of linear modal μ-calculus are PSPACE-complete. | Modal μ-calculus | 0.785733 |
78,414 | The 12 family uses a nonseparable (N in MN) functional form aiming to provide balanced performance for both chemistry and solid-state physics applications. It is composed by: MN12-L: A local functional, 0% HF exchange. The aim of the functional was to be very versatile and provide good computational performance and acc... | Minnesota functionals | 0.785732 |
78,415 | Intended for main group thermochemistry, kinetics and non-covalent interactions, with an intended performance comparable to that of M06-2X, and for TD-DFT applications, with an intended performance comparable to M06-HF. revM11: Range-separated hybrid functional with 22.5% HF exchange in the short-range and 100% in the ... | Minnesota functionals | 0.785732 |
78,416 | The '08 family was created with the primary intent to improve the M06-2X functional form, retaining the performances for main group thermochemistry, kinetics and non-covalent interactions. This family is composed by two functionals with a high percentage of HF exchange, with performances similar to those of M06-2X: M08... | Minnesota functionals | 0.785732 |
78,417 | It is the top performer within the 06 functionals for main group thermochemistry, kinetics and non-covalent interactions, however it cannot be used for cases where multi-reference species are or might be involved, such as transition metal thermochemistry and organometallics. M06-HF: Global hybrid functional with 100% H... | Minnesota functionals | 0.785732 |
78,418 | revM06: Global hybrid functional with 40.4% HF exchange. Intended for a broad range of applications on main-group chemistry, transition-metal chemistry, and molecular structure prediction to replace M06 and M06-2X. M06-2X: Global hybrid functional with 54% HF exchange. | Minnesota functionals | 0.785732 |
78,419 | M06: Global hybrid functional with 27% HF exchange. Intended for main group thermochemistry and non-covalent interactions, transition metal thermochemistry and organometallics. It is usually the most versatile of the 06 functionals, and because of this large applicability it can be slightly worse than M06-2X for specif... | Minnesota functionals | 0.785732 |
78,420 | A recent study has found this to be the case: for Minnesota functionals (which are very popular in computational chemistry for calculating energy-related quantities), the errors in atomic densities and in energetics are indeed decoupled, and the Minnesota functionals perform better for diatomic densities than for the a... | Minnesota functionals | 0.785732 |
78,421 | In this view, because Minnesota functionals are aiming for a balanced description for both main-group and transition-metal chemistry, the studies assessing Minnesota functionals solely based on the performance on main-group databases yield biased information, as the functionals that work well for main-group chemistry m... | Minnesota functionals | 0.785732 |
78,422 | These functionals can be used for traditional quantum chemistry and solid-state physics calculations. The Myz functionals are widely used and tested in the quantum chemistry community.Independent evaluations of the strengths and limitations of the Minnesota functionals with respect to various chemical properties have, ... | Minnesota functionals | 0.785732 |
78,423 | {\displaystyle s_{\beta }=\liminf\{s_{\alpha }:\alpha <\beta \}=\sup\{\inf\{s_{\alpha }:\delta \leq \alpha <\beta \}:\delta <\beta \}\,.} Alternatively, if s is an increasing function then s is continuous if s: γ → range(s) is a continuous function when the sets are each equipped with the order topology. These continuo... | Continuous function (set theory) | 0.785731 |
78,424 | Installation of the first 4 MeV clinical linear accelerator began in June 1952 in the Medical Research Council (MRC) Radiotherapeutic Research Unit at the Hammersmith Hospital, London. The system was handed over for physics and other testing in February 1953 and began to treat patients on 7 September that year. Meanwhi... | Gamma Knife | 0.785731 |
78,425 | The theorem was conjectured and proven for special cases, such as Banach spaces, by Juliusz Schauder in 1930. His conjecture for the general case was published in the Scottish book. In 1934, Tychonoff proved the theorem for the case when K is a compact convex subset of a locally convex space. This version is known as t... | Schauder fixed-point theorem | 0.785731 |
78,426 | The Schauder fixed-point theorem is an extension of the Brouwer fixed-point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if K {\displaystyle K} is a nonempty convex closed subset of a Hausdorff topological vector space V {\displaystyle V} and f {\displaystyle f} is a continu... | Schauder fixed-point theorem | 0.78573 |
78,427 | As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. | Local maxima | 0.785729 |
78,428 | The position, C {\displaystyle C} , of the camera expressed in world coordinates is C = − R − 1 T = − R T T {\displaystyle C=-R^{-1}T=-R^{T}T} (since R {\displaystyle R} is a rotation matrix). Camera calibration is often used as an early stage in computer vision. | Geometric camera calibration | 0.785729 |
78,429 | In this context, we use T {\displaystyle ^{T}} to represent a 2D point position in pixel coordinates and T {\displaystyle ^{T}} is used to represent a 3D point position in world coordinates. In both cases, they are represented in homogeneous coordinates (i.e. they have an additional last component, which is initially... | Geometric camera calibration | 0.785728 |
78,430 | As a result, a number of electrons are transferred from the valence band to the conduction band, and an equal number of holes are created in the valence band. Under the influence of an electric field, electrons and holes travel to the electrodes, where they result in a pulse that can be measured in an outer circuit, as... | Semiconductor detector | 0.785727 |
78,431 | Several practices are recommended to reduce risk based on theoretical arguments, but the value of many of these practices in reducing risk is uncertain, particularly in combinations. The vast majority of professional and recreational diving is done under low risk conditions and without recognised symptoms, but in spite... | Decompression table | 0.785726 |
78,432 | Single-crystal X-ray studies indicate that the PF5 has trigonal bipyramidal geometry. Thus it has two distinct types of P−F bonds (axial and equatorial): the length of an axial P−F bond is distinct from the equatorial P−F bond in the solid phase, but not the liquid or gas phases due to Berry pseudo rotation. Fluorine-1... | F5P | 0.785725 |
78,433 | Lower switching latency means that more aggressive regulation can be employed. Support for SSE2 and SSE3 extended instructions. NX bit in PAE mode that prevents buffer overflow software bugs from being exploitable by viruses or attackers. Hardware support for SHA-1 and SHA-256 hashing. Hardware based "Montgomery multip... | VIA C7 | 0.785725 |
78,434 | The top of this layer is called the water table. Calculations show that the water table on Mars was for a time 600 meters below the surface.The InSight lander uncovered in September 2019 unexplained magnetic pulses, and magnetic oscillations consistent with an existing planet-wide reservoir of liquid water deep undergr... | Groundwater on Mars | 0.785725 |
78,435 | In systems engineering, information systems and software engineering, the systems development life cycle (SDLC), also referred to as the application development life cycle, is a process for planning, creating, testing, and deploying an information system. The SDLC concept applies to a range of hardware and software con... | Systems development life-cycle | 0.785724 |
78,436 | In theoretical physics, Van der Waerden notation refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard in twistor theory and supersymmetry. It is named after Bartel Leendert van der Waerden. | Van der Waerden notation | 0.785724 |
78,437 | Additionally, in 2017, the Romanian Society for Cultural Astronomy ex was founded. It holds an annual international conference and has published the first monograph on archaeo- and ethnoastronomy in Romania (2019).Additionally the Journal for the History of Astronomy publishes many archaeoastronomical papers. | Archaeoastronomy | 0.785724 |
78,438 | There is also SIAC – La Sociedad Interamericana de Astronomía en la Cultura, primarily a Latin American organisation which was founded in 2003. In 2009, the Society for Cultural Astronomy in the American Southwest (SCAAS) was founded, a regional organisation focusing on the astronomies of the native peoples of the Sout... | Archaeoastronomy | 0.785724 |
78,439 | There are currently three academic organisations for scholars of archaeoastronomy. ISAAC – the International Society for Archaeoastronomy and Astronomy in Culture – was founded in 1995 and now sponsors the Oxford conferences and Archaeoastronomy – the Journal of Astronomy in Culture. SEAC – La Société Européenne pour l... | Archaeoastronomy | 0.785724 |
78,440 | In eastern Asia archaeoastronomy has developed from the history of astronomy and much archaeoastronomy is searching for material correlates of the historical record. This is due to the rich historical record of astronomical phenomena which, in China, stretches back into the Han dynasty, in the second century BC.A criti... | Archaeoastronomy | 0.785724 |
78,441 | In their discussion of the credibility of archaeoastronomical sites, Cotte and Ruggles considered the interpretation that the Caracol is an observatory site was debated among specialists, meeting the second of their four levels of site credibility.Aveni states that one of the strengths of the brown methodology is that ... | Archaeoastronomy | 0.785724 |
78,442 | In contrast to the largely alignment-oriented statistically led methods of green archaeoastronomy, brown archaeoastronomy has been identified as being closer to the history of astronomy or to cultural history, insofar as it draws on historical and ethnographic records to enrich its understanding of early astronomies an... | Archaeoastronomy | 0.785724 |
78,443 | For a long time I have believed that such diversity requires the invention of some all-embracing theory. I think I was very naïve in thinking that such a thing was ever possible. There is no one way to do archaeoastronomy. The divisions between archaeoastronomers tend not to be between the physical scientists and the s... | Archaeoastronomy | 0.785724 |
78,444 | Because archaeoastronomy is about the many and various ways people interacted with the sky, there are a diverse range of sources giving information about astronomical practices. | Archaeoastronomy | 0.785724 |
78,445 | Ruggles and Saunders proposed Cultural Astronomy as a unifying term for the various methods of studying folk astronomies. Others have argued that astronomy is an inaccurate term, what are being studied are cosmologies and people who object to the use of logos have suggested adopting the Spanish cosmovisión.When debates... | Archaeoastronomy | 0.785724 |
78,446 | Since archaeoastronomers disagree so widely on the characterization of the discipline, they even dispute its name. All three major international scholarly associations relate archaeoastronomy to the study of culture, using the term Astronomy in Culture or a translation. Michael Hoskin sees an important part of the disc... | Archaeoastronomy | 0.785724 |
78,447 | Some expressed incomprehension or even hostility, varying from a rejection by the archaeological mainstream of what they saw as an archaeoastronomical fringe to an incomprehension between the cultural focus of archaeologists and the quantitative focus of early archaeoastronomers. Yet archaeologists have increasingly co... | Archaeoastronomy | 0.785724 |
78,448 | Only rarely did they describe their work as astronomical, and then only as a secondary category.Both practicing archaeoastronomers and observers of the discipline approach it from different perspectives. Other researchers relate archaeoastronomy to the history of science, either as it relates to a culture's observation... | Archaeoastronomy | 0.785724 |
78,449 | ...ne of the most endearing characteristics of archaeoastronomy is its capacity to set academics in different disciplines at loggerheads with each other. Archaeoastronomy has long been seen as an interdisciplinary field that uses written and unwritten evidence to study the astronomies of other cultures. As such, it can... | Archaeoastronomy | 0.785724 |
78,450 | Since the 19th century, numerous scholars have sought to use archaeoastronomical calculations to demonstrate the antiquity of Ancient Indian Vedic culture, computing the dates of astronomical observations ambiguously described in ancient poetry to as early as 4000 BC. David Pingree, a historian of Indian astronomy, con... | Archaeoastronomy | 0.785724 |
78,451 | In recent years, new research has suggested that the Lascaux cave paintings in France may incorporate prehistoric star charts. Michael Rappenglueck of the University of Munich argues that some of the non-figurative dot clusters and dots within some of the figurative images correlate with the constellations of Taurus, t... | Archaeoastronomy | 0.785724 |
78,452 | What has astronomy brought into the lives of cultural groups throughout history? The answers are many and varied... | Archaeoastronomy | 0.785724 |
78,453 | For twenty-seven volumes (from 1979 to 2002) it published an annual supplement Archaeoastronomy. The Journal of Astronomical History and Heritage (National Astronomical Research Institute of Thailand), Culture & Cosmos (University of Wales, UK) and Mediterranean Archaeology and Archaeometry (University of Aegean, Greec... | Archaeoastronomy | 0.785724 |
78,454 | The concentration on historical data led to some claims of high accuracy that were comparatively weak when compared to the statistically led investigations in Europe.This came to a head at a meeting sponsored by the International Astronomical Union (IAU) in Oxford in 1981. The methodologies and research questions of th... | Archaeoastronomy | 0.785724 |
78,455 | The approach in the New World, where anthropologists began to consider more fully the role of astronomy in Amerindian civilizations, was markedly different. They had access to sources that the prehistory of Europe lacks such as ethnographies and the historical records of the early colonizers. Following the pioneering e... | Archaeoastronomy | 0.785724 |
78,456 | In contrast a re-evaluation of Thom's fieldwork by Clive Ruggles argued that Thom's claims of high accuracy astronomy were not fully supported by the evidence. Nevertheless, Thom's legacy remains strong, Edwin C. Krupp wrote in 1979, "Almost singlehandedly he has established the standards for archaeo-astronomical field... | Archaeoastronomy | 0.785724 |
78,457 | Euan MacKie would place the origin even later, stating: "...the genesis and modern flowering of archaeoastronomy must surely lie in the work of Alexander Thom in Britain between the 1930s and the 1970s". In the 1960s the work of the engineer Alexander Thom and that of the astronomer Gerald Hawkins, who proposed that St... | Archaeoastronomy | 0.785724 |
78,458 | Late in the nineteenth century astronomers such as Richard Proctor and Charles Piazzi Smyth investigated the astronomical orientations of the pyramids.The term archaeoastronomy was advanced by Elizabeth Chesley Baity (following the suggestion of Euan MacKie) in 1973, but as a topic of study it may be much older, depend... | Archaeoastronomy | 0.785724 |
78,459 | In his short history of 'Astro-archaeology' John Michell argued that the status of research into ancient astronomy had improved over the past two centuries, going 'from lunacy to heresy to interesting notion and finally to the gates of orthodoxy.' Nearly two decades later, we can still ask the question: Is archaeoastro... | Archaeoastronomy | 0.785724 |
78,460 | Because of the wide variety of evidence, which can include artefacts as well as sites, there is no one way to practice archaeoastronomy. Despite this it is accepted that archaeoastronomy is not a discipline that sits in isolation. Because archaeoastronomy is an interdisciplinary field, whatever is being investigated sh... | Archaeoastronomy | 0.785724 |
78,461 | Others have noted that the accuracy of horizon astronomy is limited by variations in refraction near the horizon. A deeper criticism of Green archaeoastronomy is that while it can answer whether there was likely to be an interest in astronomy in past times, its lack of a social element means that it struggles to answer... | Archaeoastronomy | 0.785724 |
78,462 | While not all these conclusions have been accepted, it has had an enduring influence on archaeoastronomy, especially in Europe. Euan MacKie has supported Thom's analysis, to which he added an archaeological context by comparing Neolithic Britain to the Mayan civilization to argue for a stratified society in this period... | Archaeoastronomy | 0.785724 |
78,463 | He believed that by using horizon astronomy, observers could make estimates of dates in the year to a specific day. The observation required finding a place where on a specific date the Sun set into a notch on the horizon. A common theme is a mountain that blocked the Sun, but on the right day would allow the tiniest f... | Archaeoastronomy | 0.785724 |
78,464 | Green archaeoastronomy is named after the cover of the book Archaeoastronomy in the Old World. It is based primarily on statistics and is particularly apt for prehistoric sites where the social evidence is relatively scant compared to the historic period. The basic methods were developed by Alexander Thom during his ex... | Archaeoastronomy | 0.785724 |
78,465 | Instead, it tends to depend on the location and/or kind of data available to the researcher. In the Old World, there is little data but the sites themselves; in the New World, the sites were supplemented by ethnographic and historic data. The effects of the isolated development of archaeoastronomy in different places c... | Archaeoastronomy | 0.785724 |
78,466 | Clive Ruggles and Michel Cotte recently edited a book on heritage sites of astronomy and archaeoastronomy which discussed a worldwide sample of astronomical and archaeoastronomical sites and provided criteria for the classification of archaeoastronomical sites. At Stonehenge in England and at Carnac in France, in Egypt... | Archaeoastronomy | 0.785724 |
78,467 | At least now we have all the archaeological facts to go along with the astronomers, the Druids, the Flat Earthers and all the rest. Archaeoastronomy owes something of this poor reputation among scholars to its occasional misuse to advance a range of pseudo-historical accounts. During the 1930s, Otto S. Reuter compiled ... | Archaeoastronomy | 0.785724 |
78,468 | It has been argued by some astronomers that this is a record of the 1054 Supernova. However recent reexaminations of related 'supernova petroglyphs' raises questions about such sites in general. Cotte and Ruggles used the Supernova petroglyph as an example of a completely refuted site and anthropological evidence sugge... | Archaeoastronomy | 0.785724 |
78,469 | Material evidence and its connection to the sky can reveal how a wider landscape can be integrated into beliefs about the cycles of nature, such as Mayan astronomy and its relationship with agriculture. Other examples which have brought together ideas of cognition and landscape include studies of the cosmic order embed... | Archaeoastronomy | 0.785724 |
78,470 | Archaeoastronomy uses a variety of methods to uncover evidence of past practices including archaeology, anthropology, astronomy, statistics and probability, and history. Because these methods are diverse and use data from such different sources, integrating them into a coherent argument has been a long-term difficulty ... | Archaeoastronomy | 0.785724 |
78,471 | Archaeoastronomy (also spelled archeoastronomy) is the interdisciplinary or multidisciplinary study of how people in the past "have understood the phenomena in the sky, how they used these phenomena and what role the sky played in their cultures". Clive Ruggles argues it is misleading to consider archaeoastronomy to be... | Archaeoastronomy | 0.785724 |
78,472 | The chaos, monsters and violence in ancient myths are representative of the forces that shape each age. They believed that ancient myths are the remains of preliterate astronomy that became lost with the rise of the Greco-Roman civilization. Santillana and von Dechend in their book Hamlet's Mill, An Essay on Myth and t... | Archaeoastronomy | 0.785724 |
78,473 | A common source of data for archaeoastronomy is the study of alignments. This is based on the assumption that the axis of alignment of an archaeological site is meaningfully oriented towards an astronomical target. Brown archaeoastronomers may justify this assumption through reading historical or ethnographic sources, ... | Archaeoastronomy | 0.785724 |
78,474 | A common justification for the need for astronomy is the need to develop an accurate calendar for agricultural reasons. Ancient texts like Hesiod's Works and Days, an ancient farming manual, would appear to partially confirm this: astronomical observations are used in combination with ecological signs, such as bird mig... | Archaeoastronomy | 0.785724 |
78,475 | It is this roofbox which strongly indicates that the tomb was built with an astronomical aspect in mind. In their discussion of the credibility of archaeoastronomical sites, Cotte and Ruggles gave Newgrange as an example of a Generally accepted site, the highest of their four levels of credibility. Clive Ruggles notes:... | Archaeoastronomy | 0.785724 |
78,476 | The rotation of the swing plane of Foucault pendulum can be treated as a result of parallel transport of the pendulum in a 2-dimensional sphere of Euclidean space. The hyperbolic space of velocities in Minkowski spacetime represents a 3-dimensional (pseudo-) sphere with imaginary radius and imaginary timelike coordinat... | Thomas precession | 0.785723 |
78,477 | Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer. pp. 38–43. ISBN 978-3211834435. | Thomas precession | 0.785723 |
78,478 | (2002) . The Classical Theory of Fields. Course of Theoretical Physics. | Thomas precession | 0.785723 |
78,479 | In the limit the time interval tends to zero, the accelerated frame will rotate at every instant, so the accelerated frame rotates with an angular velocity. The precession can be understood geometrically as a consequence of the fact that the space of velocities in relativity is hyperbolic, and so parallel transport of ... | Thomas precession | 0.785723 |
78,480 | In physics, the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital moti... | Thomas precession | 0.785723 |
78,481 | In quantum mechanics Thomas precession is a correction to the spin-orbit interaction, which takes into account the relativistic time dilation between the electron and the nucleus in hydrogenic atoms. Basically, it states that spinning objects precess when they accelerate in special relativity because Lorentz boosts do ... | Thomas precession | 0.785723 |
78,482 | A simplicial map (also called simplicial mapping) is a function between two simplicial complexes, with the property that the images of the vertices of a simplex always span a simplex. Simplicial maps can be used to approximate continuous functions between topological spaces that can be triangulated; this is formalized ... | Simplicial map | 0.785722 |
78,483 | Let f: | K | → | L | {\displaystyle f\colon |K|\to |L|} be a continuous map between the underlying polyhedra of simplicial complexes and let us write st ( v ) {\displaystyle {\text{st}}(v)} for the star of a vertex. A simplicial map f △: K → L {\displaystyle f_{\triangle }\colon K\to L} such that f ( st ( v ) ) ⊆ st ( ... | Simplicial map | 0.785722 |
78,484 | The Biometrical Journal figured in the 2007 comparison of statistics journals, according to which it is indexed in the Current Index to Statistics, Zentralblatt MATH, and Medline. Its impact factor was close to the median of indexed journals. The journal home page additionally lists CompuMath Citation Index, EORTC Bibl... | Biometrical Journal | 0.785721 |
78,485 | Now the entries of the matrix φ I n − A {\displaystyle \varphi I_{n}-A} all lie in the subring R generated by the identity and φ, which is commutative. Then a determinant map M(n, R) → R is defined, and det ( φ I n − A ) {\displaystyle \det(\varphi I_{n}-A)} evaluates to the value p(φ) of the characteristic polynomial ... | Hamilton-Cayley theorem | 0.785721 |
78,486 | As was mentioned above, the matrix p(A) in statement of the theorem is obtained by first evaluating the determinant and then substituting the matrix A for t; doing that substitution into the matrix t I n − A {\displaystyle tI_{n}-A} before evaluating the determinant is not meaningful. Nevertheless, it is possible to gi... | Hamilton-Cayley theorem | 0.785721 |
78,487 | All proofs below use the notion of the adjugate matrix adj(M) of an n × n matrix M, the transpose of its cofactor matrix. This is a matrix whose coefficients are given by polynomial expressions in the coefficients of M (in fact, by certain (n − 1) × (n − 1) determinants), in such a way that the following fundamental re... | Hamilton-Cayley theorem | 0.785721 |
78,488 | The above proofs show that the Cayley–Hamilton theorem holds for matrices with entries in any commutative ring R, and that p(φ) = 0 will hold whenever φ is an endomorphism of an R-module generated by elements e1,...,en that satisfies This more general version of the theorem is the source of the celebrated Nakayama lemm... | Hamilton-Cayley theorem | 0.785721 |
78,489 | The Cayley–Hamilton theorem is an effective tool for computing the minimal polynomial of algebraic integers. For example, given a finite extension Q {\displaystyle \mathbb {Q} } of Q {\displaystyle \mathbb {Q} } and an algebraic integer α ∈ Q {\displaystyle \alpha \in \mathbb {Q} } which is a non-zero linear combinat... | Hamilton-Cayley theorem | 0.785721 |
78,490 | The product-to-sum identities or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas, after Johannes Werner who used them for astronomical calculations. See amplitude modulation for an applic... | Trigonometric identity | 0.78572 |
78,491 | The quadrilateral's other diagonal is the diameter of length 1, so the product of the diagonals' lengths is also sin ( α + β ) {\displaystyle \sin(\alpha +\beta )} . When these values are substituted into the statement of Ptolemy's theorem that | A C ¯ | ⋅ | B D ¯ | = | A B ¯ | ⋅ | C D ¯ | + | A D ¯ | ⋅ | B C ¯ | {\d... | Trigonometric identity | 0.78572 |
78,492 | By the inscribed angle theorem, the central angle subtended by the chord A C ¯ {\displaystyle {\overline {AC}}} at the circle's center is twice the angle ∠ A D C {\displaystyle \angle ADC} , i.e. 2 ( α + β ) {\displaystyle 2(\alpha +\beta )} . Therefore, the symmetrical pair of red triangles each has the angle α + β {\... | Trigonometric identity | 0.78572 |
78,493 | By Thales's theorem, ∠ D A B {\displaystyle \angle DAB} and ∠ D C B {\displaystyle \angle DCB} are both right angles. The right-angled triangles D A B {\displaystyle DAB} and D C B {\displaystyle DCB} both share the hypotenuse B D ¯ {\displaystyle {\overline {BD}}} of length 1. Thus, the side A B ¯ = sin α {\displays... | Trigonometric identity | 0.78572 |
78,494 | Ptolemy's theorem is important in the history of trigonometric identities, as it is how results equivalent to the sum and difference formulas for sine and cosine were first proved. It states that in a cyclic quadrilateral A B C D {\displaystyle ABCD} , as shown in the accompanying figure, the sum of the products of the... | Trigonometric identity | 0.78572 |
78,495 | Obtained by solving the second and third versions of the cosine double-angle formula. In general terms of powers of sin θ {\displaystyle \sin \theta } or cos θ {\displaystyle \cos \theta } the following is true, and can be deduced using De Moivre's formula, Euler's formula and the binomial theorem. | Trigonometric identity | 0.78572 |
78,496 | In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates"). The matching is stable if... | Stable roommates problem | 0.785719 |
78,497 | The EF hand is a helix–loop–helix structural domain or motif found in a large family of calcium-binding proteins. The EF-hand motif contains a helix–loop–helix topology, much like the spread thumb and forefinger of the human hand, in which the Ca2+ ions are coordinated by ligands within the loop. The motif takes its na... | EF hand | 0.785719 |
78,498 | EF hands have very high selectivity for calcium. For example, the dissociation constant of alpha parvalbumin for Ca2+ is ~1000 times lower than that for the similar ion Mg2+. This high selectivity is due to the relatively rigid coordination geometry, the presence of multiple charged amino acid side chains in the bindin... | EF hand | 0.785719 |
78,499 | Let H be a Hilbert space and L(H) the set of bounded operators on H. The following is the classical definition of a Fredholm operator: an operator T ∈ L(H) is said to be a Fredholm operator if the kernel Ker(T) is finite-dimensional, Ker(T*) is finite-dimensional (where T* denotes the adjoint of T), and the range Ran(T... | Atkinson's theorem | 0.785718 |
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