text stringlengths 14 4.79k | source stringlengths 13 304 | tokens float64 75 1.06k ⌀ | char_length float64 106 4.79k ⌀ | article_title stringlengths 16 300 ⌀ |
|---|---|---|---|---|
A study comparing film/screen and digital imaging demonstrates that a digital system with high DQE can improve one's ability to detect small, low-contrast objects – even though the digital system may have substantially lower Limiting Spatial Resolution (LSR) than film. Reducing radiation dose is another potential advan... | Wikipedia - Detective quantum efficiency | null | null | null |
Compared with film/screen imaging, a digital detector with high DQE has the potential to deliver significant object-detectability improvements at an equivalent dose, or to permit object detectability comparable to film's at reduced dose. Equally important, high DQE provides the requisite foundation for advanced digital... | Wikipedia - Detective quantum efficiency | null | null | null |
It's worth pointing out that finding even a single eigenvector of a symmetric matrix is not computable (in exact real arithmetic according to the definitions in computable analysis). This difficulty exists whenever the multiplicities of a matrix's eigenvalues are not knowable. On the other hand, the same problem does n... | Wikipedia - QR algorithm | null | null | null |
We will now discuss how these difficulties manifest in the basic QR algorithm. This is illustrated in Figure 2. | Wikipedia - QR algorithm | null | null | null |
Recall that the ellipses represent positive-definite symmetric matrices. As the two eigenvalues of the input matrix approach each other, the input ellipse changes into a circle. A circle corresponds to a multiple of the identity matrix. | Wikipedia - QR algorithm | null | null | null |
A near-circle corresponds to a near-multiple of the identity matrix whose eigenvalues are nearly equal to the diagonal entries of the matrix. Therefore the problem of approximately finding the eigenvalues is shown to be easy in that case. But notice what happens to the semi-axes of the ellipses. | Wikipedia - QR algorithm | null | null | null |
An iteration of QR (or LR) tilts the semi-axes less and less as the input ellipse gets closer to being a circle. The eigenvectors can only be known when the semi-axes are parallel to the x-axis and y-axis. The number of iterations needed to achieve near-parallelism increases without bound as the input ellipse becomes m... | Wikipedia - QR algorithm | null | null | null |
While it may be impossible to compute the eigendecomposition of an arbitrary symmetric matrix, it is always possible to perturb the matrix by an arbitrarily small amount and compute the eigendecomposition of the resulting matrix. In the case when the matrix is depicted as a near-circle, the matrix can be replaced with ... | Wikipedia - QR algorithm | null | null | null |
Italian colonello > Middle French coronnelThis example of a relatively old case of phonetic dissimilation has been artificially undone in the spelling of English colonel, whose standard pronunciation is /ˈkɝnəl/ (with the r sound) in North-American English, or /ˈkɜːnəl/ in RP. It was formerly spelt coronel and is a bor... | Wikipedia - Liquid consonant | null | null | null |
Italian philosopher Gianni Vattimo and Spanish philosopher Santiago Zabala in their book Hermeneutic Communism, when discussing contemporary capitalist regimes, stated that, "A politics of descriptions does not impose power in order to dominate as a philosophy; rather, it is functional for the continued existence of a ... | Wikipedia - Radical hermeneutics | null | null | null |
Italian physicists Roberto Car and Michele Parrinello invent the Car–Parrinello method. Swendsen–Wang algorithm is invented in the field of Monte Carlo simulations. Fast multipole method is invented by Vladimir Rokhlin and Leslie Greengard (voted one of the top 10 algorithms of the 20th century). Ullli Wolff invents th... | Wikipedia - Timeline of computational physics | null | null | null |
Italian radiologists complete a four-year residency program after completing the six-year MD program. | Wikipedia - Radiology | null | null | null |
Italian theoretical physicist Carlo Rovelli writes: Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton theory is an approximation of Einstein's theory. Aristotelian physics lasted long not because ... | Wikipedia - Physics (Aristotle) | null | null | null |
Items on norm-referenced tests have been tried out on a norming group and scores on the test can be classified as high, medium, or low and the gradations in between. These tests allow for the study of individual differences. Scores on norm-referenced achievement tests are associated with percentile ranks vis-á-vis othe... | Wikipedia - Psychological tests | null | null | null |
Iterated functions crop up in the series expansion of combined functions, such as g(f(x)). Given the iteration velocity, or beta function (physics), v ( x ) = ∂ f n ( x ) ∂ n | n = 0 {\displaystyle v(x)=\left. {\frac {\partial f^{n}(x)}{\partial n}}\right|_{n=0}} for the nth iterate of the function f, we have g ( f ( x... | Wikipedia - Function iteration | null | null | null |
For example, for rigid advection, if f(x) = x + t, then v(x) = t. Consequently, g(x + t) = exp(t ∂/∂x) g(x), action by a plain shift operator. Conversely, one may specify f(x) given an arbitrary v(x), through the generic Abel equation discussed above, f ( x ) = h − 1 ( h ( x ) + 1 ) , {\displaystyle f(x)=h^{-1}(h(x)+1)... | Wikipedia - Function iteration | null | null | null |
This is evident by noting that f n ( x ) = h − 1 ( h ( x ) + n ) . {\displaystyle f^{n}(x)=h^{-1}(h(x)+n)~.} For continuous iteration index t, then, now written as a subscript, this amounts to Lie's celebrated exponential realization of a continuous group, e t ∂ ∂ h ( x ) g ( x ) = g ( h − 1 ( h ( x ) + t ) ) = g ( f t... | Wikipedia - Function iteration | null | null | null |
{\displaystyle e^{t~{\frac {\partial ~~}{\partial h(x)}}}g(x)=g(h^{-1}(h(x)+t))=g(f_{t}(x)).} The initial flow velocity v suffices to determine the entire flow, given this exponential realization which automatically provides the general solution to the translation functional equation, f t ( f τ ( x ) ) = f t + τ ( x ) ... | Wikipedia - Function iteration | null | null | null |
Iterations of continuous maps serve as the simplest examples of models for dynamical systems. Named after mathematical physicist Mitchell Feigenbaum, the two Feigenbaum constants appear in such iterative processes: they are mathematical invariants of logistic maps with quadratic maximum points and their bifurcation dia... | Wikipedia - Mathematical constant | null | null | null |
The map was popularized in a seminal 1976 paper by the Australian biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. The difference equation is intended to capture the two effects of reproduction and starvation. The numeric va... | Wikipedia - Mathematical constant | null | null | null |
Iterative algorithms solve the eigenvalue problem by producing sequences that converge to the eigenvalues. Some algorithms also produce sequences of vectors that converge to the eigenvectors. Most commonly, the eigenvalue sequences are expressed as sequences of similar matrices which converge to a triangular or diagona... | Wikipedia - Matrix eigenvalue problem | null | null | null |
Iterative self-organizing data analysis technique (ISODATA) – In this approach, the classifier automatically groups a number of closely related image pixels into clusters, and then computes the mean clusters and classifies land cover based on a series of repeated iterations. K-means clustering – An approach in which th... | Wikipedia - Land cover maps | null | null | null |
Its Director until March 2013 was Dame Celia Hoyles, Professor of Mathematics Education at the Institute of Education, University of London and former chief adviser on mathematics education for the government. She was succeeded by the current Director, Charlie Stripp. An innovative NCETM development is the MatheMaPedia... | Wikipedia - National Centre for Excellence in the Teaching of Mathematics | null | null | null |
Its Earth equivalents are the Neoproterozoic era of the Proterozoic eon and the whole of the Phanerozoic eon. So, while animal life bloomed on Earth, the Moon's geologic activity was coming to an end. | Wikipedia - Copernican period | null | null | null |
Its Weyl/Coxeter group G = W ( G 2 ) {\displaystyle G=W(G_{2})} is the dihedral group D 6 {\displaystyle D_{6}} of order 12. It has minimal faithful degree μ ( G ) = 5 {\displaystyle \mu (G)=5} . | Wikipedia - G2 (mathematics) | null | null | null |
Its Weyl/Coxeter group G = W(F4) is the symmetry group of the 24-cell: it is a solvable group of order 1152. It has minimal faithful degree μ(G) = 24, which is realized by the action on the 24-cell. | Wikipedia - F4 (mathematics) | null | null | null |
Its book information is collected from the Library of Congress, other libraries, and Amazon.com, as well as from user contributions through a wiki-like interface. If books are available in digital form, a button labeled "Read" appears next to its catalog listing. Digital copies of the contents of each scanned book are ... | Wikipedia - Open library | null | null | null |
There are different entities in the database: authors works (which are the aggregate of all books with the same title and text) editions (which are different publications of the corresponding works)Open Library claims to have over 20 million records in its database. Copies of the contents of tens of thousands of modern... | Wikipedia - Open library | null | null | null |
Its chemical formula is CF3-CHF-CF3, or C3HF7. With a boiling point of −16.4 °C, it is a gas at room temperature. It is slightly soluble in water (260 mg/L). | Wikipedia - 1,1,1,2,3,3,3-Heptafluoropropane | null | null | null |
Its chief aim is to interest children in science, technology, engineering and mathematics. Primary school children can start to have an interest in these subjects, leading secondary school pupils to choose science A levels, which will lead to a science career. It supports the After School Science and Engineering Clubs ... | Wikipedia - Science, Technology, Engineering and Mathematics Network | null | null | null |
Its critical point is at 178.5 °C (451.7 K) and 5.17 MPa (51.7 bar). At temperatures from 5 K to 105 K, it has one phase in the space group Pbca. | Wikipedia - Dichlorofluoromethane | null | null | null |
Its critical point is at 54.8 °C (328 K) and 5.24 MPa. Its molecular dipole moment is 1.4 Debye and heat of vaporization is 361 kJ/kg. | Wikipedia - C2H3F | null | null | null |
Its crystal structure is monoclinic with space group P21 and lattice constants a = 6.7676, b = 4.1477, c = 5.0206 (0.10−1 nm), β = 108.205°.At an altitude of 22 km, traces of chlorofluoromethane occur (148 ppt). | Wikipedia - Chlorofluoromethane | null | null | null |
Its derivatives include colforsin daropate, NKH477, and FSK88, which may be more potent than forskolin at raising cAMP. These derivatives may have pharmaceutical utility against bronchoconstriction and heart failure. | Wikipedia - Forskolin | null | null | null |
Its development provides the ability of internet applications to send data over the Internet. There are some well-established transport protocols such as TCP (Transmission Control Protocol) and UDP (User Datagram Protocol) which are continuously getting extended and refined to meet the needs of the global Internet. | Wikipedia - Internet Engineering Task Force | null | null | null |
Its diet consists mainly of fruit and arthropods. The female lays one to two pale cream eggs with brown and grey spots. | Wikipedia - Black-billed sicklebill | null | null | null |
Its essential part is a quasigroup of order 10 (i.e. having a 10 × 10 Latin square as the body of its operation table) with the special feature of being weakly totally anti-symmetric. Damm revealed several methods to create totally anti-symmetric quasigroups of order 10 and gave some examples in his doctoral dissertati... | Wikipedia - Damm algorithm | null | null | null |
Its faces are hexagonal stars with two short and four long edges. Denoting the golden ratio by ϕ {\displaystyle \phi } and putting ξ = 1 4 + 1 4 1 + 4 ϕ ≈ 0.933 380 199 59 {\displaystyle \xi ={\frac {1}{4}}+{\frac {1}{4}}{\sqrt {1+4\phi }}\approx 0.933\,380\,199\,59} , the stars have five equal angles of arccos ( ξ )... | Wikipedia - Small hexagrammic hexecontahedron | null | null | null |
Its factorization as 13 × 17 makes 221 the product of two consecutive prime numbers, the sixth smallest such product.221 is a centered square number. | Wikipedia - 221 (number) | null | null | null |
Its factorization makes it a sphenic number. Since 255 = 28 – 1, it is a Mersenne number (though not a pernicious one), and the fourth such number not to be a prime number. It is a perfect totient number, the smallest such number to be neither a power of three nor thrice a prime. Since 255 is the product of the first t... | Wikipedia - 255 (number) | null | null | null |
In base 10, it is a self number. 255 is a repdigit in base 2 (11111111), in base 4 (3333), and in base 16 (FF). { 9 2 } = 255. {\displaystyle \left\{{9 \atop 2}\right\}=255.} | Wikipedia - 255 (number) | null | null | null |
Its foundational concepts are open science and the Bermuda Principles.Open science is the idea that scientific research should be openly shared to enable massive collaboration (e.g., the Polymath Project). The Bermuda Principles is a private accord declaring that all DNA sequence data should be released in publicly acc... | Wikipedia - Open synthetic biology | null | null | null |
Its founder, Gustav Theodor Fechner defined the mission of the discipline of psychophysics as the functional relationship between the mental and material worlds—in this particular case, the visual and object spaces—but he acknowledged an intermediate step, which has since blossomed into the major enterprise of modern n... | Wikipedia - Visual space | null | null | null |
Its main function is enabling MSTP to select its root bridges for the proper CIST and each MSTI. MSTP includes all its spanning tree information in a single BPDU format. Not only does reduce the number of BPDUs required on a LANs to communicate spanning tree information for each VLAN, but it also ensures backward compa... | Wikipedia - Multiple Spanning Tree Protocol | null | null | null |
Its main purpose is to promote the development of educational research in the field of Natural Science. Among other studies the institute carried out the Programme for International Student Assessment 2003 and 2006, SINUS, ChiK, LeLa, LLL, LUV, System Earth as well as the GLOBE Program.The IPN is engaged in various Ger... | Wikipedia - Leibniz Institute for Science and Mathematics Education at Kiel University | null | null | null |
Its multi-disciplinary engineering approach is what differentiates architectural engineering from architecture (the field of the architect): which is an integrated, separate and single, field of study when compared to other engineering disciplines. Through training in and appreciation of architecture, the field seeks i... | Wikipedia - Building technology | null | null | null |
Its phosphorylated form, dihydroxyacetone phosphate (DHAP), takes part in glycolysis, and it is an intermediate product of fructose metabolism. | Wikipedia - Dihydroxyacetone | null | null | null |
Its predators are not well-documented, but may include avian species such as the long-tailed hawk. It has a diverse array of parasites, including such ectoparasites as the bat fly (Nycteribiidae) Dipseliopoda arcuata, the spinturnicid mite Ancystropus aethiopicus, the gastronyssid mite Mycteronyssus polli, and the tein... | Wikipedia - Hammer-headed bat | null | null | null |
Its product lines included servers, desktop computers, notebooks and the Belinea series of monitors. == References == | Wikipedia - Maxdata | null | null | null |
Its rapid growth and its ability to reproduce from buried rhizomes and tubers facilitates the Jerusalem artichoke's uncontrolled spread. The vegetative propagules can be transported via rivers and water streams and begin a new population on riverbanks. Dispersal by animal is also possible, as animals feed on tubers and... | Wikipedia - Jerusalem Artichoke | null | null | null |
With humans' cultivation, there is also a risk of the plant's unintended escape into the wild. It can also be propagated by seed. Its relatively long flower period enables the Jerusalem artichoke to increase its reproductive potential. | Wikipedia - Jerusalem Artichoke | null | null | null |
Its research interests involve nuclear astrophysics, stellar evolution, chemical composition of stars, binary stars, neutron stars and modified Newtonian dynamics. | Wikipedia - Institute for Astronomy and Astrophysics | null | null | null |
Its role in Friedrich Bachmann's absolute geometry based on line-reflections, in the absence of order or free mobility (the theory of metric planes) was studied in and in. | Wikipedia - Lotschnittaxiom | null | null | null |
Its science payload would be a novel detector of solar energetic neutral atoms (ENA), as well as an array of waves and other Solar energetic particles (SEP) that erupt from the Sun. The instrument is called the HELio Energetic Neutral Atom (HELENA) detector. This technology could enable advanced warnings of potential s... | Wikipedia - Science-Enabling Technologies for Heliophysics | null | null | null |
Its structure incorporates the backbone of amphetamine, the prototypical CNS stimulant which, like phenmetrazine, is a releasing agent of dopamine and norepinephrine. The molecule also loosely resembles ethcathinone, the active metabolite of popular anorectic amfepramone (diethylpropion). Unlike phenmetrazine, ethcathi... | Wikipedia - Phenmetrazine | null | null | null |
Its structure is almost similar to voacangine, an alkaloid used in semi-synthesis of ibogaine. Compared to voacangine, it has an extra O-atom. When it is degraded, iboxygaine and ibogaine are formed. | Wikipedia - Voacristine | null | null | null |
Its two vertex configurations are shared with two 1-uniform tilings: | Wikipedia - 33344-33434 tiling | null | null | null |
Its two vertex configurations are shared with two 1-uniform tilings: It can be seen as a type of diminished rhombitrihexagonal tiling, with dodecagons replacing periodic sets of hexagons and surrounding squares and triangles. This is similar to the Johnson solid, a diminished rhombicosidodecahedron, which is a rhombico... | Wikipedia - 3-4-6-12 tiling | null | null | null |
Itô's lemma is the version of the chain rule or change of variables formula which applies to the Itô integral. It is one of the most powerful and frequently used theorems in stochastic calculus. For a continuous n-dimensional semimartingale X = (X1,...,Xn) and twice continuously differentiable function f from Rn to R, ... | Wikipedia - Itō process | null | null | null |
Iu-h Interface - Residing between an HNB and HNB-GW, the Iu-h interface defines the security architecture used to provide a secure, scalable communications over the Internet. The Iu-h interface also defines an efficient, reliable method for transporting Iu-based traffic as well as a new protocol (HNBAP) for enabling hi... | Wikipedia - Home NodeB | null | null | null |
Ivan Cherednik introduced generalizations of affine Hecke algebras, the so-called double affine Hecke algebra (usually referred to as DAHA). Using this he was able to give a proof of Macdonald's constant term conjecture for Macdonald polynomials (building on work of Eric Opdam). Another main inspiration for Cherednik t... | Wikipedia - Affine Hecke algebra | null | null | null |
Ivor Grattan-Guinness states that the French word 'Logistique' was "introduced by Couturat and others at the 1904 International Congress of Philosophy, and was used by Russell and others from then on, in versions appropriate for various languages." (G-G 2000:501). Apparently the first (and only) usage by Russell appear... | Wikipedia - Logicism | null | null | null |
7). Apart from the misrepresentation (which Russell partly rectified by explaining his own view of the role of arithmetic in mathematics), the passage is notable for the word which he put in quotation marks, but their presence suggests nervousness, and he never used the word again, so that 'logicism' did not emerge unt... | Wikipedia - Logicism | null | null | null |
263)" (G-G 2002:269). Carnap used a slightly different word 'Logistik'; Behmann complained about its use in Carnap's manuscript so Carnap proposed the word 'Logizismus', but he finally stuck to his word-choice 'Logistik' (G-G 2002:501). Ultimately "the spread was mainly due to Carnap, from 1930 onwards." (G-G 2000:502)... | Wikipedia - Logicism | null | null | null |
Iwahori–Hecke algebra Quantum affine algebra Quantum enveloping algebra Quantum group | Wikipedia - List of q-analogs | null | null | null |
Iwahori–Hecke algebras first appeared as an important special case of a very general construction in group theory. Let (G,K) be a pair consisting of a unimodular locally compact topological group G and a closed subgroup K of G. Then the space of K-biinvariant continuous functions of compact support, Cc(K\G/K), can be e... | Wikipedia - Hecke algebra of a Coxeter group | null | null | null |
More generally if (G,K) is a Gelfand pair then the resulting algebra turns out to be commutative. Example: If G = SL(2,Q) and K = SL(2,Z) we get the abstract ring behind Hecke operators in the theory of modular forms, which gave the name to Hecke algebras in general. The case leading to the Hecke algebra of a finite We... | Wikipedia - Hecke algebra of a Coxeter group | null | null | null |
Iwahori showed that the Hecke ring H(G//B) is obtained from the generic Hecke algebra Hq of the Weyl group W of G by specializing the indeterminate q of the latter algebra to pk, the cardinality of the finite field. George Lusztig remarked in 1984 (Characters of reductive groups over a finite field, xi, footnote): I th... | Wikipedia - Hecke algebra of a Coxeter group | null | null | null |
These ideas were taken much further in Colin Bushnell and Philip Kutzko's theory of types, allowing them to complete the classification in the general linear case. Many of the techniques can be extended to other reductive groups, which remains an area of active research. It has been conjectured that all Hecke algebras ... | Wikipedia - Hecke algebra of a Coxeter group | null | null | null |
Iwasawa theory Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem Euler system p-adic L-function | Wikipedia - List of algebraic number theory topics | null | null | null |
Ixodidae ticks have three different life cycles. Depending on the species, Ixodids can either possess a one-host life cycle, two-host life cycle, or three-host life cycle. | Wikipedia - Tick bites | null | null | null |
Iyanaga, Shōkichi, ed. (1954), Iwanami Sūgaku Jiten (in Japanese) (1st ed. ), Tokyo: Iwanami Shoten, MR 0062668 Iyanaga, Shōkichi, ed. (1960), Iwanami mathematical dictionary, Edited by the Mathematical Society of Japan. | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
Revised and enlarged (in Japanese), Tokyo: Iwanami Shoten, MR 0130788 Iyanaga, Shōkichi, ed. (1968), Iwanami Sūgaku Jiten (in Japanese) (2nd ed. ), Iwanami Shoten Publishers, Tokyo, MR 0241228 Iyanaga, Shōkichi, ed. | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
(1977), Encyclopedic Dictionary of Mathematics, Volumes I, II, hardback, translated from the 2nd Japanese edition (1st ed. ), MIT Press, pp. 1750, ISBN 978-0-262-09016-2, MR 0490100 Iyanaga, Shōkichi; Kawada, Yukiyosi, eds. | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
(1980) , Encyclopedic Dictionary of Mathematics, Volumes I, II, Translated from the 2nd Japanese edition, paperback version of the 1977 edition (1st ed. ), MIT Press, ISBN 978-0-262-59010-5, MR 0591028 Sūgaku Jiten (in Japanese) (3rd ed. ), Tokyo: Iwanami Shoten, 1985, ISBN 978-4-00-080016-7, MR 0924841 Itô, Kiyosi, ed... | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
(1987), Encyclopedic Dictionary of Mathematics. Vol. I--IV, Hardback, Translated from the Japanese 3rd edition (2nd ed. | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
), MIT Press, p. 2148, ISBN 978-0-262-09026-1, MR 0901762, archived from the original on 2011-06-29 Itô, Kiyosi, ed. (1993), Encyclopedic Dictionary of Mathematics. | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
Vol. I--II, Paperback, Translated from the Japanese 3rd edition (2nd ed. ), MIT Press, p. 2148, ISBN 0-262-59020-4; paperback version of the 1987 edition Iwanami Sūgaku Jiten (in Japanese) (Fourth ed. ), Tokyo: Iwanami Shoten, 2007, ISBN 978-4-00-080309-0, MR 2383190 | Wikipedia - Encyclopedic Dictionary of Mathematics | null | null | null |
J ( x ) = ( x − x b ) T B − 1 ( x − x b ) + ( y − H ) T R − 1 ( y − H ) , {\displaystyle J(\mathbf {x} )=(\mathbf {x} -\mathbf {x} _{b})^{\mathrm {T} }\mathbf {B} ^{-1}(\mathbf {x} -\mathbf {x} _{b})+(\mathbf {y} -{\mathit {H}})^{\mathrm {T} }\mathbf {R} ^{-1}(\mathbf {y} -{\mathit {H}}),} where B {\displaystyle \mat... | Wikipedia - Data assimilation | null | null | null |
J ( x ) = ( x − x b ) T B − 1 ( x − x b ) + ∑ i = 0 n ( y i − H i ) T R i − 1 ( y i − H i ) {\displaystyle J(\mathbf {x} )=(\mathbf {x} -\mathbf {x} _{b})^{\mathrm {T} }\mathbf {B} ^{-1}(\mathbf {x} -\mathbf {x} _{b})+\sum _{i=0}^{n}(\mathbf {y} _{i}-{\mathit {H}}_{i})^{\mathrm {T} }\mathbf {R} _{i}^{-1}(\mathbf {y} ... | Wikipedia - Data assimilation | null | null | null |
J represents: the unit joule of energy the current density in electromagnetism denoted J {\displaystyle {\boldsymbol {J}}} the radiosity in thermal mechanics the moment of inertia Total angular momentum quantum number Bessel function of the first kind Impulse J represents: the scheme of a diagram in category theory j r... | Wikipedia - Latin letters used in mathematics, science, and engineering | null | null | null |
J supports three simple types: Numeric Literal (Character) BoxedOf these, numeric has the most variants. One of J's numeric types is the bit. There are two bit values: 0, and 1. Also, bits can be formed into lists. | Wikipedia - J programming language | null | null | null |
For example, 1 0 1 0 1 1 0 0 is a list of eight bits. Syntactically, the J parser treats that as one word. (The space character is recognized as a word-forming character between what would otherwise be numeric words.) | Wikipedia - J programming language | null | null | null |
Lists of arbitrary length are supported. Further, J supports all the usual binary operations on these lists, such as and, or, exclusive or, rotate, shift, not, etc. For example, 1 0 0 1 0 0 1 0 +. 0 1 0 1 1 0 1 0 NB. | Wikipedia - J programming language | null | null | null |
or 1 1 0 1 1 0 1 0 3 |. 1 0 1 1 0 0 1 1 1 1 1 NB. | Wikipedia - J programming language | null | null | null |
rotate 1 0 0 1 1 1 1 1 1 0 1 J also supports higher order arrays of bits. They can be formed into two-dimensional, three-dimensional, etc. arrays. The above operations perform equally well on these arrays. | Wikipedia - J programming language | null | null | null |
Other numeric types include integer (e.g., 3, 42), floating point (3.14, 8.8e22), complex (0j1, 2.5j3e88), extended precision integer (12345678901234567890x), and (extended precision) rational fraction (1r2, 3r4). As with bits, these can be formed into lists or arbitrarily dimensioned arrays. As with bits, operations a... | Wikipedia - J programming language | null | null | null |
Lists of bits can be converted to integer using the #. verb. Integers can be converted to lists of bits using the #: verb. | Wikipedia - J programming language | null | null | null |
(When parsing J, . (period) and: (colon) are word-forming characters. | Wikipedia - J programming language | null | null | null |
They are never tokens alone, unless preceded by whitespace characters.) J also supports the literal (character) type. Literals are enclosed in quotes, for example, 'a' or 'b'. | Wikipedia - J programming language | null | null | null |
Lists of literals are also supported using the usual convention of putting multiple characters in quotes, such as 'abcdefg'. Typically, individual literals are 8-bits wide (ASCII), but J also supports other literals (Unicode). Numeric and boolean operations are not supported on literals, but collection-oriented operati... | Wikipedia - J programming language | null | null | null |
Finally, there is a boxed data type. Typically, data is put in a box using the < operation (with no left argument; if there's a left argument, this would be the less than operation). This is analogous to C's & operation (with no left argument). | Wikipedia - J programming language | null | null | null |
However, where the result of C's & has reference semantics, the result of J's < has value semantics. In other words, < is a function and it produces a result. The result has 0 dimensions, regardless of the structure of the contained data. | Wikipedia - J programming language | null | null | null |
From the viewpoint of a J programmer, < puts the data into a box and allows working with an array of boxes (it can be assembled with other boxes, and/or more copies can be made of the box). <1 0 0 1 0 +---------+ |1 0 0 1 0| +---------+ The only collection type offered by J is the arbitrarily dimensioned array. Most al... | Wikipedia - J programming language | null | null | null |
J's arrays are homogeneously typed, for example the list 1 2 3 is a list of integers despite 1 being a bit. For the most part, these sorts of type issues are transparent to programmers. Only certain specialized operations reveal differences in type. | Wikipedia - J programming language | null | null | null |
For example, the list 1.0 0.0 1.0 0.0 would be treated exactly the same, by most operations, as the list 1 0 1 0 . J also supports sparse numeric arrays where non-zero values are stored with their indices. This is an efficient mechanism where relatively few values are non-zero. | Wikipedia - J programming language | null | null | null |
J also supports objects and classes, but these are an artifact of the way things are named, and are not data types. Instead, boxed literals are used to refer to objects (and classes). J data has value semantics, but objects and classes need reference semantics.Another pseudo-type—associated with name, rather than value... | Wikipedia - J programming language | null | null | null |
J. B. S. Haldane – W. D. Hamilton – Hardy–Weinberg principle – heredity – hierarchy of life – history of evolutionary thought – history of speciation – homologous chromosomes – homology (biology) – horizontal gene transfer – human evolution – human evolutionary genetics – human vestigiality – Julian Huxley – Thomas Hen... | Wikipedia - Index of evolutionary biology articles | null | null | null |
J. Barkley Rosser defined an "effective method" in the following manner (italicization added): "'Effective method' is used here in the rather special sense of a method each step of which is precisely determined and which is certain to produce the answer in a finite number of steps. With this special meaning, three dif... | Wikipedia - Mathematical algorithm | null | null | null |
All three definitions are equivalent, so it doesn't matter which one is used. Moreover, the fact that all three are equivalent is a very strong argument for the correctness of any one." (Rosser 1939:225–226)Rosser's footnote No. 5 references the work of (1) Church and Kleene and their definition of λ-definability, in p... | Wikipedia - Mathematical algorithm | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.