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91,700 | Incidence and Symmetry in Design and Architecture is divided into two parts of roughly equal length, each divided into four chapters. The first part, "Incidence", is primarily on graph theory. Its topics include the basic definitions of directed graphs and undirected graphs, homeomorphisms of graphs, Dijkstra's algorit... | Incidence and Symmetry in Design and Architecture | 0.780461 |
91,701 | Incidence and Symmetry in Design and Architecture is a book on symmetry, graph theory, and their applications in architecture, aimed at architecture students. It was written by Jenny Baglivo and Jack E. Graver and published in 1983 by Cambridge University Press in their Cambridge Urban and Architectural Studies book se... | Incidence and Symmetry in Design and Architecture | 0.780461 |
91,702 | Whereas Greek astronomers expressed "prejudice in favor of circles or spheres rotating with uniform motion", such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits. There is no evidence that the celestial bodies moved in uniform circular... | Babylonian astronomy | 0.78046 |
91,703 | Though there is a lack of surviving material on Babylonian planetary theory, it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. It had been thought that most of the predictive Babylonian planetary models that have survived were usually strictly empirical and arithmet... | Babylonian astronomy | 0.78046 |
91,704 | Only fragments of Babylonian astronomy have survived, consisting largely of contemporary clay tablets containing astronomical diaries, ephemerides and procedure texts, hence current knowledge of Babylonian planetary theory is in a fragmentary state. Nevertheless, the surviving fragments show that Babylonian astronomy w... | Babylonian astronomy | 0.78046 |
91,705 | This was an important contribution to astronomy and the philosophy of science, and some modern scholars have thus referred to this novel approach as the first scientific revolution. This approach to astronomy was adopted and further developed in Greek and Hellenistic astrology. Classical Greek and Latin sources frequen... | Babylonian astronomy | 0.78046 |
91,706 | This system simplified the calculating and recording of unusually great and small numbers. The modern practices of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians.During the 8th and 7th centuries BC, Babylonian astronomers developed a new empirical approach to astronomy. They began stud... | Babylonian astronomy | 0.78046 |
91,707 | Babylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia. Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations may have been collected from various earlier sources. The earliest catalogue,... | Babylonian astronomy | 0.78046 |
91,708 | astronomers, or astronomical concepts and practices through the documentation by Xenophon of Socrates telling his students to study astronomy to the extent of being able to tell the time of night from the stars. This skill is referenced in the poem of Aratos, which discusses telling the time of night from the zodiacal ... | Babylonian astronomy | 0.78046 |
91,709 | So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it i... | Babylonian astronomy | 0.78046 |
91,710 | "Old" Babylonian astronomy was practiced during and after the First Babylonian dynasty (ca. 1830 BC) and before the Neo-Babylonian Empire (ca. 626 BC). The Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. | Babylonian astronomy | 0.78046 |
91,711 | Both of these tablets were translated and transcribed by Weidner. During the reign of Hammurabi these three separate traditions were combined. This combining also ushered in a more scientific approach to astronomy as connections to the original three traditions weakened. The increased use of science in astronomy is evi... | Babylonian astronomy | 0.78046 |
91,712 | The astrolabes (not to be mistaken for the later astronomical measurement device of the same name) are one of the earliest documented cuneiform tablets that discuss astronomy and date back to the Old Babylonian Kingdom. They are a list of thirty-six stars connected with the months in a year, generally considered to be ... | Babylonian astronomy | 0.78046 |
91,713 | The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323–60 BC). In the 3rd century BC, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous ph... | Babylonian astronomy | 0.78046 |
91,714 | Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Achaemenid, Seleucid, and Parthian periods of Mesopotamian history. A significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar (747–734 BC). The syste... | Babylonian astronomy | 0.78046 |
91,715 | Most known astronomical tablets have been described by Abraham Sachs and later published by Otto Neugebauer in the Astronomical Cuneiform Texts (ACT). Herodotus writes that the Greeks learned such aspects of astronomy as the gnomon and the idea of the day being split into two halves of twelve from the Babylonians. Othe... | Babylonian astronomy | 0.78046 |
91,716 | Many of the works of ancient Greek and Hellenistic writers (including mathematicians, astronomers, and geographers) have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by earlier ancient Near Eastern civili... | Babylonian astronomy | 0.78046 |
91,717 | MUL.APIN is a collection of two cuneiform tablets (Tablet 1 and Tablet 2) that document aspects of Babylonian astronomy such as the movement of celestial bodies and records of solstices and eclipses. Each tablet is also split into smaller sections called Lists. It was comprised in the general time frame of the astrolab... | Babylonian astronomy | 0.78046 |
91,718 | It was a common Mesopotamian belief that gods could and did indicate future events to mankind through omens; sometimes through animal entrails, but most often they believed omens could be read through astronomy and astrology. Since omens via the planets were produced without any human action, they were seen as more pow... | Babylonian astronomy | 0.78046 |
91,719 | In contrast to the world view presented in Mesopotamian and Assyro-Babylonian literature, particularly in Mesopotamian and Babylonian mythology, very little is known about the cosmology and world view of the ancient Babylonian astrologers and astronomers. This is largely due to the current fragmentary state of Babyloni... | Babylonian astronomy | 0.78046 |
91,720 | The Littlewood–Richardson rule was first stated by D. E. Littlewood and A. R. Richardson (1934, theorem III p. 119) but though they claimed it as a theorem they only proved it in some fairly simple special cases. Robinson (1938) claimed to complete their proof, but his argument had gaps, though it was so obscurely writ... | Littlewood–Richardson coefficient | 0.78046 |
91,721 | The ARRPOF RNA motif is a conserved RNA structure that was discovered by bioinformatics.Most ARRPOF motif examples are found in environmental DNA samples, and the host organism is unknown. The only classified organism with an ARRPOF motif is Fusobacterium nucleatum, and the ARRPOF motif instance is found in the pKH9 pl... | ARRPOF RNA motif | 0.78046 |
91,722 | In natural science, subaerial (literally "under the air") has been used since 1833, notably in geology and botany, to describe features and events occurring or formed on or near the Earth's land surface. They are thus exposed to Earth's atmosphere. This may be contrasted with subaqueous events or features located below... | Subaerial | 0.780458 |
91,723 | In neuroscience and psychophysics, an absolute threshold was originally defined as the lowest level of a stimulus – light, sound, touch, etc. – that an organism could detect. Under the influence of signal detection theory, absolute threshold has been redefined as the level at which a stimulus will be detected a specifi... | Absolute threshold | 0.780457 |
91,724 | Recallpg 59 that the Steenrod algebra A p ∗ {\displaystyle {\mathcal {A}}_{p}^{*}} (also denoted A ∗ {\displaystyle {\mathcal {A}}^{*}} ) is a graded noncommutative Hopf algebra which is cocommutative, meaning its comultiplication is cocommutative. This implies if we take the dual Hopf algebra, denoted A p , ∗ {\displa... | Dual Steenrod algebra | 0.780453 |
91,725 | In this case, the dual Steenrod algebra is a graded commutative polynomial algebra A ∗ = Z / 2 {\displaystyle {\mathcal {A}}_{*}=\mathbb {Z} /2} where the degree deg ( ξ n ) = 2 n − 1 {\displaystyle \deg(\xi _{n})=2^{n}-1} . Then, the coproduct map is given by Δ: A ∗ → A ∗ ⊗ A ∗ {\displaystyle \Delta :{\mathcal {A}}... | Dual Steenrod algebra | 0.780453 |
91,726 | (Several other scientists, including Ralph Cicerone, Richard Stolarski, Michael McElroy, and Steven Wofsy had independently proposed that chlorine could catalyze ozone loss, but none had realized that CFCs were a potentially large source of chlorine.) Crutzen, Molina and Rowland were awarded the 1995 Nobel Prize for Ch... | Montreal Protocol | 0.780453 |
91,727 | The rest of the Hopf algebra structures can be described exactly the same in both cases. There is both a unit map η {\displaystyle \eta } and counit map ε {\displaystyle \varepsilon } η: Z / p → A ∗ ε: A ∗ → Z / p {\displaystyle {\begin{aligned}\eta &:\mathbb {Z} /p\to {\mathcal {A}}_{*}\\\varepsilon &:{\mathcal {A}}_{... | Dual Steenrod algebra | 0.780453 |
91,728 | In algebraic topology, through an algebraic operation (dualization), there is an associated commutative algebra from the noncommutative Steenrod algebras called the dual Steenrod algebra. This dual algebra has a number of surprising benefits, such as being commutative and provided technical tools for computing the Adam... | Dual Steenrod algebra | 0.780453 |
91,729 | The portfolio obeys the stochastic differential equation d X ( t ) = Δ ( t ) d S ( t ) + r ( t ) ( X ( t ) − Δ ( t ) S ( t ) ) d t {\displaystyle dX(t)=\Delta (t)\ dS(t)+r(t)(X(t)-\Delta (t)S(t))\ dt} One will then attempt to apply Girsanov theorem by first computing d P ~ d P {\displaystyle {\frac {d{\tilde {\mathbb {... | Martingale pricing | 0.780451 |
91,730 | Silicotungstic acid is used to manufacture ethyl acetate by the alkylation of acetic acid by ethylene: C2H4 + CH3CO2H → CH3CO2C2H5It has also been commercialized for the oxidation of ethylene to acetic acid: C2H4 + O2 → CH3CO2HThis route is claimed as a "greener" than methanol carbonylation. The heteropoly acid is disp... | Silicotungstic acid | 0.78045 |
91,731 | In this form it was used by many large UK users, an example being the Pay-As-You-Earn system operated by Inland Revenue. Many of these IDMSX systems for UK Government were still running in 2013. In the early to mid-1980s, relational database management systems started to become more popular, encouraged by increasing ha... | IDMS | 0.780449 |
91,732 | The roots of IDMS go back to the pioneering database management system called Integrated Data Store (IDS), developed at General Electric by a team led by Charles Bachman and first released in 1964. In the early 1960s IDS was taken from its original form, by the computer group of the B.F. Goodrich Chemical Division, and... | IDMS | 0.780449 |
91,733 | The Integrated Database Management System (IDMS) is a network model (CODASYL) database management system for mainframes. It was first developed at B.F. Goodrich and later marketed by Cullinane Database Systems (renamed Cullinet in 1983). Since 1989 the product has been owned by Computer Associates (now CA Technologies)... | IDMS | 0.780449 |
91,734 | Welsh has led teams at Google and Apple Inc., and served a Professor of Computer Science at Harvard University. In November 2010, five months after being granted tenure, Welsh announced that he was leaving Harvard. | Matt Welsh (computer scientist) | 0.780447 |
91,735 | Matthew David Welsh is a computer scientist and software engineer and is currently the CEO and co-founder of Fixie.ai, which he started after stints at Google, xnor.ai, and Apple. He was the Gordon McKay Professor of Computer Science at Harvard University and author of several books about the Linux operating system, se... | Matt Welsh (computer scientist) | 0.780447 |
91,736 | By setting pi = λn/n, we see that this generalizes the usual Poisson limit theorem. When λ n {\displaystyle \lambda _{n}} is large a better bound is possible: ∑ k = 0 ∞ | Pr ( S n = k ) − λ n k e − λ n k ! | < 2 ( 1 ∧ 1 λ n ) ( ∑ i = 1 n p i 2 ) . | Le Cam's theorem | 0.780444 |
91,737 | In probability theory, Le Cam's theorem, named after Lucien Le Cam (1924 – 2000), states the following.Suppose: X 1 , X 2 , X 3 , … {\displaystyle X_{1},X_{2},X_{3},\ldots } are independent random variables, each with a Bernoulli distribution (i.e., equal to either 0 or 1), not necessarily identically distributed. Pr (... | Le Cam's theorem | 0.780444 |
91,738 | The first director of the Cyclotron Research Centre was Yves Jongen, from Nivelles, who studied electronic engineering at the Catholic University of Louvain in the 1960s, extending his studies with a specialization in nuclear physics. In August 1970, Jongen moved to a house located near the future centre of the new cit... | Louvain-la-Neuve Cyclotron | 0.780443 |
91,739 | The eastern tower, located in front of the headquarters of Ion Beam Applications, goes lower than the North Tower, with only three floors. It also houses multiple services, both in the domains of physics and of entrepreneurship & business management, projects associated with the Louvain School of Management: the Radiat... | Louvain-la-Neuve Cyclotron | 0.780443 |
91,740 | The North Tower, called after Marc de Heptinne, one of the university's most famous physicists, is the highest of the three and one of Louvain-la-Neuve's largest buildings. Its five floors and adjacent wings currently house: the Cyclotron Resource Centre, which tests components with heavy ion, proton, neutron and Cobal... | Louvain-la-Neuve Cyclotron | 0.780443 |
91,741 | The Louvain-la-Neuve Cyclotron is a brutalist architectural complex of the University of Louvain built from 1970 to 1972 in Louvain-la-Neuve, Walloon Brabant, Belgium, notably holding UCLouvain's CYCLONE particle accelerators. It is the first building completed by the university when it moved following the Leuven crisi... | Louvain-la-Neuve Cyclotron | 0.780443 |
91,742 | The Cyclotron Research Centre was equipped in the early 1970s with a first particle accelerator called CYCLONE110, built by Thomson-CSF in collaboration with the Ateliers de constructions électriques de Charleroi (ACEC) and used for nuclear physics, isotope production, medical and technological applications. A second a... | Louvain-la-Neuve Cyclotron | 0.780443 |
91,743 | It considers the layout of the watershed, geology, soils, vegetation, nutrients, energy and wildlife. Modelled aspects include precipitation, the interception of rain water by vegetation or artificial structures, evaporation, the runoff function and the soil-surface system itself.When surface water seeps into the groun... | Surface-water hydrology | 0.780443 |
91,744 | In mathematics, Fuchs' theorem, named after Lazarus Fuchs, states that a second-order differential equation of the form has a solution expressible by a generalised Frobenius series when p ( x ) {\displaystyle p(x)} , q ( x ) {\displaystyle q(x)} and g ( x ) {\displaystyle g(x)} are analytic at x = a {\displaystyle x=a}... | Fuchs's theorem | 0.780442 |
91,745 | Then the condition for ρ ∞ {\displaystyle \rho _{\infty }} to be a Gibbs state is L = 0 {\displaystyle L=0} .In physics there may be several physically distinct Gibbs states in which a system may be trapped, particularly at lower temperatures. They are named after Josiah Willard Gibbs, for his work in determining equi... | Gibbs state | 0.780442 |
91,746 | In probability theory and statistical mechanics, a Gibbs state is an equilibrium probability distribution which remains invariant under future evolution of the system. For example, a stationary or steady-state distribution of a Markov chain, such as that achieved by running a Markov chain Monte Carlo iteration for a su... | Gibbs state | 0.780442 |
91,747 | Department of Energy's effort to make data open, is in the public domain under the CC0 public domain dedication.Users search, edit, add and access data in OpenEI for free. OpenEI serves researchers, entrepreneurs, policy makers, students, and more generally, consumers interested in renewable energy. Region-specific dat... | OpenEI | 0.78044 |
91,748 | OpenEI provides two primary mechanisms for sharing structured information: a semantic wiki (using MediaWiki and the Semantic MediaWiki extension) for collaboratively-managed resources, and a dataset upload mechanism for contributor-controlled resources. In both cases, the resulting data is made available via Linked Dat... | OpenEI | 0.78044 |
91,749 | The formula has applications, for example, in the path integral formulation of quantum mechanics. It allows one to separate the Schrödinger evolution operator (propagator) into alternating increments of kinetic and potential operators (the Suzuki–Trotter decomposition, after Trotter and Masuo Suzuki). The same idea is ... | Lie product formula | 0.780439 |
91,750 | In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula, named after Hale Trotter, states that for arbitrary m × m real or complex matrices A and B, e A + B = lim n → ∞ ( e A / n e B / n ) n , {\displaystyle e^{A+B}=\lim _{n\rightarrow \infty }(e^{A/n}e^{... | Lie product formula | 0.780439 |
91,751 | Artificial intelligence has also been used to predict MSI from the appearance of tumors under the microscope. Digital pathology can be submitted to machine learning techniques and predictions about MSI can be made without any molecular testing. These methods have not yet shown results that are sufficient to incorporate... | Microsatellite instability | 0.780439 |
91,752 | In 1912, Alfred Fowler managed to produce similar lines from a hydrogen-helium mixture, and supported Pickering's conclusion as to their origin. Bohr's model does not allow for half-integer transitions (nor does quantum mechanics) and Bohr concluded that Pickering and Fowler were wrong, and instead assigned these spect... | Superfluid helium | 0.780439 |
91,753 | In the perspective of quantum mechanics, helium is the second simplest atom to model, following the hydrogen atom. Helium is composed of two electrons in atomic orbitals surrounding a nucleus containing two protons and (usually) two neutrons. As in Newtonian mechanics, no system that consists of more than two particles... | Superfluid helium | 0.780439 |
91,754 | Helium liquifies when cooled below 4.2 K at atmospheric pressure. Unlike any other element, however, helium remains liquid down to a temperature of absolute zero. This is a direct effect of quantum mechanics: specifically, the zero point energy of the system is too high to allow freezing. Pressures above about 25 atmos... | Superfluid helium | 0.780439 |
91,755 | A 3D graphics programmer must have a firm grasp of advanced mathematical concepts such as vector and matrix math, quaternions and linear algebra. Skilled programmers specializing in this area of game development can demand high wages and are usually a scarce commodity. Their skills can be used for video games on any pl... | Video game programmer | 0.780438 |
91,756 | Historically, this title usually belonged to a programmer who developed specialized blitter algorithms and clever optimizations for 2D graphics. Today, however, it is almost exclusively applied to programmers who specialize in developing and modifying complex 3D graphic renderers. Some 2D graphics skills have just rece... | Video game programmer | 0.780438 |
91,757 | A game's physics programmer is dedicated to developing the physics a game will employ. Typically, a game will only simulate a few aspects of real-world physics. For example, a space game may need simulated gravity, but would not have any need for simulating water viscosity. | Video game programmer | 0.780438 |
91,758 | In the early days of video games (from the early 1970s to mid-1980s), a game programmer also took on the job of a designer and artist. This was generally because the abilities of early computers were so limited that having specialized personnel for each function was unnecessary. Game concepts were generally light and g... | Video game programmer | 0.780438 |
91,759 | Since processing cycles are always at a premium, physics programmers may employ "shortcuts" that are computationally inexpensive, but look and act "good enough" for the game in question. In other cases, unrealistic physics are employed to allow easier gameplay or for dramatic effect. Sometimes, a specific subset of sit... | Video game programmer | 0.780438 |
91,760 | A contemporary video game may include advanced physics, artificial intelligence, 3D graphics, digitised sound, an original musical score, complex strategy and may use several input devices (such as mice, keyboards, gamepads and joysticks) and may be playable against other people via the Internet or over a LAN. Each asp... | Video game programmer | 0.780438 |
91,761 | The Berlin experimental accelerator uses superconducting niobium cavity resonators of the type mentioned above. In 2014, three free-electron lasers based on Energy Recovery Linacs were in operation worldwide: in the Jefferson Lab (USA), in the Budker Institute of Nuclear Physics (Russia) and at JAEA (Japan). At the Uni... | Linear particle accelerator | 0.780438 |
91,762 | In mathematics, Janiszewski's theorem, named after the Polish mathematician Zygmunt Janiszewski, is a result concerning the topology of the plane or extended plane. It states that if A and B are closed subsets of the extended plane with connected intersection, then any two points that can be connected by paths avoiding... | Janiszewski's theorem | 0.780435 |
91,763 | In probability theory and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and upper limit b. f ( x | a , b , α , β ) = α ( x − β ) 2 , for x ∈ . {\displaystyle f(x|a,b,\alpha ,\beta )=\alpha \left(x-\beta \right)^{2},\qu... | U-quadratic distribution | 0.780435 |
91,764 | Next Limit has actively participated in various research projects throughout Europe as well as Spain. It is currently the leader of the European project, SAFECITI (Safe Citizen), which aims to create a simulation system for analysts that would predict the behavior of large crowds in urban environments in moments of pan... | Next Limit Technologies | 0.780433 |
91,765 | In fact, since the pushout is the colimit of a span and the pullback is the limit of a cospan, we can think of the tensor product of rings and the fibered product of rings (see the examples section) as dual notions to each other. In particular, let A, B, and C be objects (commutative rings with identity) in CRing and l... | Pushout (category theory) | 0.780433 |
91,766 | It shows up in the Seifert–van Kampen theorem of algebraic topology (see below). In CRing, the category of commutative rings (a full subcategory of the category of rings), the pushout is given by the tensor product of rings A ⊗ C B {\displaystyle A\otimes _{C}B} with the morphisms g ′: A → A ⊗ C B {\displaystyle g':A\r... | Pushout (category theory) | 0.780433 |
91,767 | Of course, X is the pushout of the two inclusion maps of D into A and B. Thus we may interpret the theorem as confirming that the fundamental group functor preserves pushouts of inclusions. We might expect this to be simplest when D is simply connected, since then both homomorphisms above have trivial domain. Indeed, t... | Pushout (category theory) | 0.780433 |
91,768 | The Seifert–van Kampen theorem answers the following question. Suppose we have a path-connected space X, covered by path-connected open subspaces A and B whose intersection D is also path-connected. (Assume also that the basepoint * lies in the intersection of A and B.) If we know the fundamental groups of A, B, and th... | Pushout (category theory) | 0.780433 |
91,769 | The answer is yes, provided we also know the induced homomorphisms π 1 ( D , ∗ ) → π 1 ( A , ∗ ) {\displaystyle \pi _{1}(D,*)\to \pi _{1}(A,*)} and π 1 ( D , ∗ ) → π 1 ( B , ∗ ) . {\displaystyle \pi _{1}(D,*)\to \pi _{1}(B,*).} The theorem then says that the fundamental group of X is the pushout of these two induced ma... | Pushout (category theory) | 0.780433 |
91,770 | The micro-level influences of symbolic interaction, exchange, and rational choice, along with the micro-level focus of computational political scientists, such as Robert Axelrod, helped to develop computational sociology's bottom-up, agent-based approach to modeling complex systems. This is what Joshua M. Epstein calls... | Sociology and complexity science | 0.780432 |
91,771 | In molecular biology, the BmKK2 toxins are a family of scorpion toxins. They belong to the scorpion toxin subfamily alpha-KTx 14. They include a novel short-chain peptide from the Asian scorpion Mesobuthus martensii Karsch, a potassium channel blocker composed of 31 amino acid residues. The peptide adopts a classical a... | BmKK2 toxin | 0.780431 |
91,772 | Because of this homeomorphism, some authors call affine line the spectrum of k. If k is not algebraically closed, for example the field of the real numbers, the picture becomes more complicated because of the existence of non-linear irreducible polynomials. In this case, the spectrum consists of one closed point for ea... | Zariski dense | 0.780429 |
91,773 | Spec k, the spectrum of a field k is the topological space with one element. Spec ℤ, the spectrum of the integers has a closed point for every prime number p corresponding to the maximal ideal (p) ⊂ ℤ, and one non-closed generic point (i.e., whose closure is the whole space) corresponding to the zero ideal (0). So the ... | Zariski dense | 0.780429 |
91,774 | Since as shown above, the classical definition is essentially the modern definition with only maximal ideals considered, this shows that the interpretation of the modern definition as "zero sets of functions" agrees with the classical definition where they both make sense. Just as Spec replaces affine varieties, the Pr... | Zariski dense | 0.780429 |
91,775 | Another way, perhaps more similar to the original, to interpret the modern definition is to realize that the elements of A can actually be thought of as functions on the prime ideals of A; namely, as functions on Spec A. Simply, any prime ideal P has a corresponding residue field, which is the field of fractions of the... | Zariski dense | 0.780429 |
91,776 | In modern algebraic geometry, an algebraic variety is often represented by its associated scheme, which is a topological space (equipped with additional structures) that is locally homeomorphic to the spectrum of a ring. The spectrum of a commutative ring A, denoted Spec A, is the set of the prime ideals of A, equipped... | Zariski dense | 0.780429 |
91,777 | Another approach to the harmonic conjugate is through the concept of a complete quadrangle such as KLMN in the above diagram. Based on four points, the complete quadrangle has pairs of opposite sides and diagonals. In the expression of harmonic conjugates by H. S. M. Coxeter, the diagonals are considered a pair of oppo... | Projective harmonic conjugates | 0.780429 |
91,778 | In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM ... | Projective harmonic conjugates | 0.780429 |
91,779 | "Longitudinal waves" and "transverse waves" have been abbreviated by some authors as "L-waves" and "T-waves", respectively, for their own convenience. While these two abbreviations have specific meanings in seismology (L-wave for Love wave or long wave) and electrocardiography (see T wave), some authors chose to use "l... | Compressional wave | 0.780428 |
91,780 | 1790s: The first evidence of electrical activity in the nervous system was observed by Luigi Galvani in the 1790s with his studies on dissected frogs. He discovered that you can induce a dead frog leg to twitch with a spark. 1888: Santiago Ramón y Cajal, a Spanish neuroscientist, revolutionized neuroscience with his ne... | Single-unit recording | 0.780428 |
91,781 | The plant feeds a compressed natural gas station and injects methane into a natural gas boiler.The Sabatier reaction has been used in renewable-energy-dominated energy systems to use the excess electricity generated by wind, solar photovoltaic, hydro, marine current, etc. to make methane from hydrogen from water electr... | Sabatier process | 0.780428 |
91,782 | The rigging process can be sped up through the use of adaptable biped and quadruped rigs, FaceRobot for facial rigs and automatic lip syncing. Animation features include layers and a mixer, which allows combining animation clips non-linearly. Animation operators are tracked in a construction history stack that is separ... | Autodesk Softimage | 0.780428 |
91,783 | Autodesk Softimage is a 3D animation application comprising a suite of computer graphics tools. Modeling tools allow the generation of polygonal or NURBS models. Subdivision modeling requires no additional operators and works directly on the polygonal geometry. Each modeling operation is tracked by a construction histo... | Autodesk Softimage | 0.780428 |
91,784 | Compounds can also be shared between installations because their entire functionality is stored in XML files. The graph-based approach of ICE allows for the creation of effects previously attainable only through the use of scripting and/or compiled code. Due to its visual nature and interactivity, it is very accessible... | Autodesk Softimage | 0.780428 |
91,785 | The screenshot on the right shows an example of a simple geometry deformation ICE graph. In a practical scenario, one would collapse the graph into a compound and expose important parameters, for instance the deformation intensity. After adding the tool to the user interface it can easily be applied to other objects. | Autodesk Softimage | 0.780428 |
91,786 | Theoretical physics continues to strive toward a theory of everything, a theory that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle. In practical terms the immediate goal in this regard is to develop a theory which would ... | Physics beyond the Standard Model | 0.780427 |
91,787 | The CKM matrix, if interpreted as a rotation matrix in a 3-dimensional vector space, "rotates" a vector composed of square roots of down-type quark masses ( m d , m s , m b ) {\displaystyle ({\sqrt {m_{d}}},{\sqrt {m_{s}}},{\sqrt {m_{b}}}{\big )}} into a vector of square roots of up-type quark masses ( m u , m c , m t ... | Physics beyond the Standard Model | 0.780427 |
91,788 | In molecular biology, the CAT RNA-binding domain (Co-AntiTerminator RNA-binding domain) is a protein domain found at the amino terminus of a family of transcriptional antiterminator proteins. This domain forms a dimer in the crystal structure. Transcriptional antiterminators of the BglG/SacY family are regulatory prote... | CAT RNA-binding domain | 0.780423 |
91,789 | Stannabenzene (C5H6Sn) is the parent representative of a group of organotin compounds that are related to benzene with a carbon atom replaced by a tin atom. Stannabenzene itself has been studied by computational chemistry, but has not been isolated. | Stannabenzene | 0.780423 |
91,790 | Wet deposition of acids occurs when any form of precipitation (rain, snow, and so on) removes acids from the atmosphere and delivers it to the Earth's surface. This can result from the deposition of acids produced in the raindrops (see aqueous phase chemistry above) or by the precipitation removing the acids either in ... | Acid rain | 0.780421 |
91,791 | The hydronium ions of acid rain also mobilize toxins, such as aluminium, and leach away essential nutrients and minerals such as magnesium. 2 H+ (aq) + Mg2+ (clay) ⇌ 2 H+ (clay) + Mg2+ (aq)Soil chemistry can be dramatically changed when base cations, such as calcium and magnesium, are leached by acid rain, thereby affe... | Acid rain | 0.780421 |
91,792 | Soil biology and chemistry can be seriously damaged by acid rain. Some microbes are unable to tolerate changes to low pH and are killed. The enzymes of these microbes are denatured (changed in shape so they no longer function) by the acid. | Acid rain | 0.780421 |
91,793 | The ability to image single-cell migration in real time is expected to be important to several research areas such as embryogenesis, cancer metastasis, stem cell therapeutics, and lymphocyte immunology. One application of quantum dots in biology is as donor fluorophores in Förster resonance energy transfer, where the l... | Quantum dot dye | 0.780421 |
91,794 | The journal is abstracted and indexed in Academic Search Premier, Current Contents, the Material Science Citation Index, Mechanical Engineering Abstracts, Scopus, and the Science Citation Index Expanded. According to the Journal Citation Reports, its 2019 impact factor is 3.125 (2 years), ranking it 126 out of 314 jour... | International Journal of Damage Mechanics | 0.78042 |
91,795 | The International Journal of Damage Mechanics is a peer-reviewed scientific journal covering the fields of engineering and materials science. The editor-in-chief is Chi L. Chow (University of Michigan). It was established in 1992 and is published by SAGE Publications. | International Journal of Damage Mechanics | 0.78042 |
91,796 | The prime-counting function π ( n ) {\displaystyle \pi (n)} is defined as the number of primes not greater than n {\displaystyle n} . For example, π ( 11 ) = 5 {\displaystyle \pi (11)=5} , since there are five primes less than or equal to 11. Methods such as the Meissel–Lehmer algorithm can compute exact values of π ( ... | Odd prime | 0.780419 |
91,797 | Another optimization is to check only primes as factors in this range. For instance, to check whether 37 is prime, this method divides it by the primes in the range from 2 to 37 {\displaystyle {\sqrt {37}}} , which are 2, 3, and 5. | Odd prime | 0.780419 |
91,798 | The growth rate of this sum is described more precisely by Mertens' second theorem. For comparison, the sum 1 1 2 + 1 2 2 + 1 3 2 + ⋯ + 1 n 2 {\displaystyle {\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots +{\frac {1}{n^{2}}}} does not grow to infinity as n {\displaystyle n} goes to infinity (see the Bas... | Odd prime | 0.780419 |
91,799 | The original proof of the prime number theorem was based on a weak form of this hypothesis, that there are no zeros with real part equal to 1, although other more elementary proofs have been found. The prime-counting function can be expressed by Riemann's explicit formula as a sum in which each term comes from one of t... | Odd prime | 0.780419 |
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