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Not much about the exact toxicity of phantasmidine is known; however, epibatidines in general are 200 times more potent than morphine (Riley 21). Phantasmidine interacts with the body's stimulation of the parasympathetic nervous system, making it a dangerous inhibitory poison. Symptoms of phantasmidine poisoning may in... | Wikipedia - Phantasmidine | null | null | null |
Not much evidence has been able to support whether or not telehealth is more cost effective or not. There is some research showing that it can be a less expensive way for doctors to provide care because they aren’t using any of their physical resources on the patient. Sage journals published a case study researching if... | Wikipedia - Remote physiological monitoring | null | null | null |
Once EMS was on scene, they would pull up a virtual system putting them in direct contact with an emergency department provider at the hospital. The provider was then able to triage the patient at the scene of the call and determine the best course of treatment potentially being no transport to the hospital. This in tu... | Wikipedia - Remote physiological monitoring | null | null | null |
Not much is known about Qin dynasty mathematics, or before, due to the burning of books and burying of scholars, circa 213–210 BC. Knowledge of this period can be determined from civil projects and historical evidence. The Qin dynasty created a standard system of weights. Civil projects of the Qin dynasty were signific... | Wikipedia - Chinese mathematics | null | null | null |
Emperor Qin Shihuang (秦始皇) ordered many men to build large, lifesize statues for the palace tomb along with other temples and shrines, and the shape of the tomb was designed with geometric skills of architecture. It is certain that one of the greatest feats of human history, the Great Wall of China, required many mathe... | Wikipedia - Chinese mathematics | null | null | null |
Not needed for only primary loading that meets static loading requirements. Needed for cyclic thermal loading plus primary loading with a mean. | Wikipedia - Shakedown (continuum mechanics) | null | null | null |
Not only can SEOP be used to hyperpolarize noble gases, but a more recent development is SEOP on solids. It was first performed in 2007 and was used to polarize nuclei in a solid, allowing for nuclei that cannot be polarized by other methods to become hyperpolarized. For example, nuclear polarization of 133Cs in the fo... | Wikipedia - Hyperpolarization (physics) | null | null | null |
Unreacted hydrogen was removed, and the process was repeated several times to increase the thickness of the CsH film, then pressurized with nitrogen gas. Usually, SEOP experiments are done with the cell centered in Helmholtz or electromagnetic coils, as previously described, but these experiments were done in a superco... | Wikipedia - Hyperpolarization (physics) | null | null | null |
In the future, it may be possible to use this technique to transfer polarization to 6Li or 7Li, leading to even more applications since the T1 is expected to be longer. Since the discovery of this technique that allows solids to be characterized, it has been improved in such a way where polarized light is not necessary... | Wikipedia - Hyperpolarization (physics) | null | null | null |
Not only logic, but the whole of philosophy is given a dialogical treatment by Lorenz. Only in the mirror of a relative Other is it possible to reflect upon oneself. Lorenz developed a dialogical constructivism from the focus on the dialogical principle (Martin Buber) and the process of language games of the later Ludw... | Wikipedia - Kuno Lorenz | null | null | null |
Not surprisingly, metadata sharing processes yearn to be automated. Every metadata file that is statically configured into the SAML application by an administrator incurs technical debt. The accumulation of this debt prevents the SAML deployment from scaling to its potential. | Wikipedia - SAML metadata | null | null | null |
To avoid excessive technical debt, the metadata sharing process must be automated. One approach is to enlist the help of a trusted third party whose responsibility it is to collect, curate, and distribute metadata across the network. Curated metadata is consistently formatted, more likely to be free of vulnerabilities ... | Wikipedia - SAML metadata | null | null | null |
In the case of SAML metadata, this trusted third party is called a SAML federation. The community of SAML deployers comprising the federation willingly conform to one or more profiles of SAML to promote interoperability and trust. To that end, federation participants often share a central infrastructure for metadata sh... | Wikipedia - SAML metadata | null | null | null |
Not used in this table.Holman, S. W.; Lawrence, R. R.; Barr, L. (1 January 1895). "Melting Points of Aluminum, Silver, Gold, Copper, and Platinum". Proceedings of the American Academy of Arts and Sciences. | Wikipedia - Melting points of the elements (data page) | null | null | null |
31: 218–233. doi:10.2307/20020628. JSTOR 20020628. | Wikipedia - Melting points of the elements (data page) | null | null | null |
Notable People associated with NCRA: Govind Swarup, An Internationally renowned Radio Astronomer and Emeritus Professor of the Institute Rajaram Nityananda, former Director of the Institute Vijay Kumar Kapahi, former Director of the Institute Yashwant Gupta, radio astronomer and professor of astrophysics Nissim Kanekar... | Wikipedia - National Centre for Radio Astrophysics | null | null | null |
Notable academic and industry laboratories in the field are: Adobe Research IBM Research Google Research Microsoft Research Panopticon Software Scientific Computing and Imaging Institute Tableau Software University of Maryland Human-Computer Interaction Lab VviConferences in this field, ranked by significance in data v... | Wikipedia - Data visualisation | null | null | null |
EuroVis: An annual Europe-wide conference on data visualization, organized by the Eurographics Working Group on Data Visualization and supported by the IEEE Visualization and Graphics Technical Committee (IEEE VGTC). Conference is usually held in June. Conference on Human Factors in Computing Systems (CHI): An annual i... | Wikipedia - Data visualisation | null | null | null |
Conference is usually held in April or May. Eurographics: An annual Europe-wide computer graphics conference, held by the European Association for Computer Graphics. Conference is usually held in April or May. PacificVis: An annual visualization symposium held in the Asia-Pacific region, sponsored by the IEEE Visualiza... | Wikipedia - Data visualisation | null | null | null |
Notable algorithms include: Luhn algorithm (1954) Verhoeff algorithm (1969) Damm algorithm (2004) | Wikipedia - Check digit | null | null | null |
Notable alumni include House Democratic Whip Steny Hoyer; Google co-founder Sergey Brin; The Muppets creator Jim Henson; The Wire creator David Simon; Former NFL Quarterback Norman "Boomer" Esiason; CBS host Gayle King; journalist Connie Chung; and Seinfeld co-creator and Curb Your Enthusiasm creator Larry David. Promi... | Wikipedia - Center for Bioinformatics and Computational Biology | null | null | null |
Attendees within the fields of science and mathematics are Nobel laureates Raymond Davis Jr., 2002 winner in Physics; Herbert Hauptman, 1985 winner in Chemistry, and Fields Medal winner Charles Fefferman. Other alumni include George Dantzig, considered the father of linear programming; late NASA astronaut Judith Resnik... | Wikipedia - Center for Bioinformatics and Computational Biology | null | null | null |
Businessman Robert H. Smith, who graduated from the university in 1950 with a degree in accounting, has given over $45 million to the business school that now bears his name and to the Clarice Smith Performing Arts Center, which bears his wife's name. Construction entrepreneur A. James Clark, who graduated with an engi... | Wikipedia - Center for Bioinformatics and Computational Biology | null | null | null |
from the university in 1991 and gave $5 million for the construction of a state-of-the-art engineering building. Philip Merrill, a media figure, donated $10 million to the College of Journalism. Robert E. Fischell, physicist, inventor, and holder of more than 200 U.S. and foreign medical patents donated $30 million to ... | Wikipedia - Center for Bioinformatics and Computational Biology | null | null | null |
Notable derivative-free optimization algorithms include: Bayesian optimization Coordinate descent and adaptive coordinate descent Cuckoo search Beetle Antennae Search (BAS) DONE Evolution strategies, Natural evolution strategies (CMA-ES, xNES, SNES) Genetic algorithms MCS algorithm Nelder-Mead method Particle swarm opt... | Wikipedia - Derivative-free optimization | null | null | null |
Notable developments accomplished using the Nengo software have occurred in many fields, and Nengo has been used and cited in over 100 publications. An important development to note is Spaun, a network of 6.6 million artificial spiking neurons (a small number compared to the number in the human brain), which uses group... | Wikipedia - Neural Engineering Object | null | null | null |
Notable figures in the history and/or modern development of paraconsistent logic include: Alan Ross Anderson (United States, 1925–1973). One of the founders of relevance logic, a kind of paraconsistent logic. Florencio González Asenjo (Argentina, 1927-2013) Diderik Batens (Belgium) Nuel Belnap (United States, b. 1930) ... | Wikipedia - Paraconsistent logic | null | null | null |
Jean-Yves Béziau (France/Switzerland, b. 1965). Has written extensively on the general structural features and philosophical foundations of paraconsistent logics. | Wikipedia - Paraconsistent logic | null | null | null |
Ross Brady (Australia) Bryson Brown (Canada) Walter Carnielli (Brazil). The developer of the possible-translations semantics, a new semantics which makes paraconsistent logics applicable and philosophically understood. Newton da Costa (Brazil, b. | Wikipedia - Paraconsistent logic | null | null | null |
1929). One of the first to develop formal systems of paraconsistent logic. Itala M. L. D'Ottaviano (Brazil) J. Michael Dunn (United States). | Wikipedia - Paraconsistent logic | null | null | null |
An important figure in relevance logic. Carl Hewitt Stanisław Jaśkowski (Poland). One of the first to develop formal systems of paraconsistent logic. | Wikipedia - Paraconsistent logic | null | null | null |
R. E. Jennings (Canada) David Kellogg Lewis (USA, 1941–2001). Articulate critic of paraconsistent logic. Jan Łukasiewicz (Poland, 1878–1956) Robert K. Meyer (United States/Australia) Chris Mortensen (Australia). | Wikipedia - Paraconsistent logic | null | null | null |
Has written extensively on paraconsistent mathematics. Lorenzo Peña (Spain, b. 1944). | Wikipedia - Paraconsistent logic | null | null | null |
Has developed an original line of paraconsistent logic, gradualistic logic (also known as transitive logic, TL), akin to fuzzy logic. Val Plumwood (Australia, b. 1939). | Wikipedia - Paraconsistent logic | null | null | null |
Frequent collaborator with Sylvan. Graham Priest (Australia). Perhaps the most prominent advocate of paraconsistent logic in the world today. | Wikipedia - Paraconsistent logic | null | null | null |
Francisco Miró Quesada (Peru). Coined the term paraconsistent logic. B. H. Slater (Australia). | Wikipedia - Paraconsistent logic | null | null | null |
Another articulate critic of paraconsistent logic. Richard Sylvan (New Zealand/Australia, 1935–1996). Important figure in relevance logic and a frequent collaborator with Plumwood and Priest. Nicolai A. Vasiliev (Russia, 1880–1940). First to construct logic tolerant to contradiction (1910). | Wikipedia - Paraconsistent logic | null | null | null |
Notable free software for data analysis include: DevInfo – A database system endorsed by the United Nations Development Group for monitoring and analyzing human development. ELKI – Data mining framework in Java with data mining oriented visualization functions. KNIME – The Konstanz Information Miner, a user friendly an... | Wikipedia - Data Interpretation | null | null | null |
Pandas – Python library for data analysis. PAW – FORTRAN/C data analysis framework developed at CERN. R – A programming language and software environment for statistical computing and graphics. | Wikipedia - Data Interpretation | null | null | null |
ROOT – C++ data analysis framework developed at CERN. SciPy – Python library for data analysis. Julia – A programming language well-suited for numerical analysis and computational science. | Wikipedia - Data Interpretation | null | null | null |
Notable material science databases are combined under CSA Materials Research Database with METADEX. Contents up to the level of specialist are accessible, collected from the disciplines of materials science, metallurgy, ceramics, polymers, and composites used in engineering application. For all metals, alloys, polymers... | Wikipedia - Metals Abstracts | null | null | null |
The chain of processing continues with in depth coverage also of welding and fabrication developed for end uses. This is followed by performance, corrosion, and recycling, as related to all metals, alloys, polymers, ceramics, and composites. In addition, this database is indexed for more than 3,000 relevant publication... | Wikipedia - Metals Abstracts | null | null | null |
Notable members of the Lwów school of mathematics included: | Wikipedia - Lwów School of Mathematics | null | null | null |
Notable mixing engineers using SL 4000 Series consoles include Bob Clearmountain, Steve Lillywhite, Chris Lord-Alge, Tom Lord-Alge, Andy Wallace, Mark "Spike" Stent, Will Schillinge, Alan Moulder, and Trevor Horn. | Wikipedia - Solid State Logic SL 4000 | null | null | null |
Notable people associated with IUCAA: Jayant Narlikar, founding director Naresh Dadhich, physicist, Fellow of the Indian Academy of Sciences, 2nd Director Ajit Kembhavi, 3rd Director Thanu Padmanabhan, Padma Shri award-winning astrophysicist Somak Raychaudhury, 4th Director Sanjeev Dhurandhar, gravitational-wave physic... | Wikipedia - Inter-University Centre for Astronomy and Astrophysics | null | null | null |
Notable people include: Rudolf Diesel, inventor of the Diesel engine Claude Dornier, airplane designer Carl von Linde, discoverer of the refrigeration cycle Willy Messerschmitt, aircraft designer, known for the Messerschmitt fighters Oskar von Miller, engineer, founder of the Deutsches Museum | Wikipedia - TUM School of Engineering and Design | null | null | null |
Notable potentially viable pharmacological agents – as final products or as prototypes for similar ones – under early-stage research with potential for substantial effect sizes for specific purposes in specific situations (such as learning periods) also in healthy non-old humans but, in at least most cases, largely unk... | Wikipedia - Cognitive enhancement | null | null | null |
Notable projective configurations include the following: (11), the simplest possible configuration, consisting of a point incident to a line. Often excluded as being trivial. (32), the triangle. | Wikipedia - Geometric configuration | null | null | null |
Each of its three sides meets two of its three vertices, and vice versa. More generally any polygon of n sides forms a configuration of type (n2) (43 62) and (62 43), the complete quadrangle and complete quadrilateral respectively. (73), the Fano plane. | Wikipedia - Geometric configuration | null | null | null |
This configuration exists as an abstract incidence geometry, but cannot be constructed in the Euclidean plane. (83), the Möbius–Kantor configuration. This configuration describes two quadrilaterals that are simultaneously inscribed and circumscribed in each other. | Wikipedia - Geometric configuration | null | null | null |
It cannot be constructed in Euclidean plane geometry but the equations defining it have nontrivial solutions in complex numbers. (93), the Pappus configuration. (94 123), the Hesse configuration of nine inflection points of a cubic curve in the complex projective plane and the twelve lines determined by pairs of these ... | Wikipedia - Geometric configuration | null | null | null |
This configuration shares with the Fano plane the property that it contains every line through its points; configurations with this property are known as Sylvester–Gallai configurations due to the Sylvester–Gallai theorem that shows that they cannot be given real-number coordinates. (103), the Desargues configuration. ... | Wikipedia - Geometric configuration | null | null | null |
(125 302), the Schläfli double six, formed by 12 of the 27 lines on a cubic surface (153), the Cremona–Richmond configuration, formed by the 15 lines complementary to a double six and their 15 tangent planes (166), the Kummer configuration. (214), the Grünbaum–Rigby configuration. (273), the Gray configuration (354), D... | Wikipedia - Geometric configuration | null | null | null |
Notable theorems proved using homology include the following: The Brouwer fixed point theorem: If f is any continuous map from the ball Bn to itself, then there is a fixed point a ∈ B n {\displaystyle a\in B^{n}} with f ( a ) = a . {\displaystyle f(a)=a.} Invariance of domain: If U is an open subset of R n {\displaysty... | Wikipedia - Homology theories | null | null | null |
(Two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.) Invariance of dimension: if non-empty open subsets U ⊆ R m {\displaystyle U\subseteq \mathbb {R} ^{m}} and V ⊆ R n {\displaystyle V\subseteq \mathbb {R} ^{n}} are homeomorphic, then m = n . {\displaystyle ... | Wikipedia - Homology theories | null | null | null |
Notably, because of its potential in relevant antimicrobial, anti-tumor cell, and/or consumption of amino acids, the interest of researching sv-LAAOs has begun to grow. Many authors have investigated the mechanism of antibacterial action of sv-LAAO. It is well established that sv-LAAO kills and breaks down bacteria by ... | Wikipedia - L-amino-acid oxidase | null | null | null |
Notably, one of the ways animal nervous systems represent sensory and other information is through rate coding whereby the magnitude of the signal is related to the rate of firing of the sensory neuron. In direct analogy, each neural event – called an action potential – represents one bit (pulse), with the rate of firi... | Wikipedia - Pulse-density modulation | null | null | null |
Notation for half-reaction standard electrode potentials is as follows. The redox reaction split into: a reduction reaction: B + + e − ↽ − − ⇀ B {\displaystyle {\ce {B+ + e^- <=> B}}} and an oxidation reaction: A + + e − ↽ − − ⇀ A {\displaystyle {\ce {A+ + e^- <=> A}}} (written this way by convention) the electrode pot... | Wikipedia - Defining equation (physical chemistry) | null | null | null |
Notation used in this discussion is as in Flannery's original paper. | Wikipedia - Cayley–Purser algorithm | null | null | null |
Notational abuse to be found below includes eX for the exponential map exp given an argument, writing g for the element (g, eH) in a direct product G × H (eH is the identity in H), and analogously for Lie algebra direct sums (where also g + h and (g, h) are used interchangeably). Likewise for semidirect products and se... | Wikipedia - Lie algebra extension | null | null | null |
The default names for elements of g, h, ..., are G, H, ... (just like for the groups! ), partly to save scarce alphabetical resources but mostly to have a uniform notation. | Wikipedia - Lie algebra extension | null | null | null |
Lie algebras that are ingredients in an extension will, without comment, be taken to be over the same field. The summation convention applies, including sometimes when the indices involved are both upstairs or both downstairs. Caveat: Not all proofs and proof outlines below have universal validity. | Wikipedia - Lie algebra extension | null | null | null |
The main reason is that the Lie algebras are often infinite-dimensional, and then there may or may not be a Lie group corresponding to the Lie algebra. Moreover, even if such a group exists, it may not have the "usual" properties, e.g. the exponential map might not exist, and if it does, it might not have all the "usua... | Wikipedia - Lie algebra extension | null | null | null |
Note "treat separately" means to use the decision table on each component | Wikipedia - IUPAC nomenclature of inorganic chemistry 2005 | null | null | null |
Note (1): Recursive CTEs introduced in 11gR2 supersedes similar construct called CONNECT BY. | Wikipedia - Comparison of relational database management systems | null | null | null |
Note that Cohen's kappa measures agreement between two raters only. For a similar measure of agreement (Fleiss' kappa) used when there are more than two raters, see Fleiss (1971). The Fleiss kappa, however, is a multi-rater generalization of Scott's pi statistic, not Cohen's kappa. Kappa is also used to compare perform... | Wikipedia - Cohen's kappa | null | null | null |
Note that I − P {\displaystyle I-P} is also an oblique projection. The singular values of P {\displaystyle P} and I − P {\displaystyle I-P} can be computed by an orthonormal basis of A {\displaystyle A} . Let Q A {\displaystyle Q_{A}} be an orthonormal basis of A {\displaystyle A} and let Q A ⊥ {\displaystyle Q_{A}^{\p... | Wikipedia - Projection (linear algebra) | null | null | null |
Denote the singular values of the matrix Q A T A ( B T A ) − 1 B T Q A ⊥ {\displaystyle Q_{A}^{T}A(B^{T}A)^{-1}B^{T}Q_{A}^{\perp }} by the positive values γ 1 ≥ γ 2 ≥ … ≥ γ k {\displaystyle \gamma _{1}\geq \gamma _{2}\geq \ldots \geq \gamma _{k}} . With this, the singular values for P {\displaystyle P} are: and the sin... | Wikipedia - Projection (linear algebra) | null | null | null |
Note that Specification is an axiom schema. The theory given by these axioms is not finitely axiomatizable. Montague (1961) showed that ZFC is not finitely axiomatizable, and his argument carries over to GST. Hence any axiomatization of GST must include at least one axiom schema. | Wikipedia - General set theory | null | null | null |
With its simple axioms, GST is also immune to the three great antinomies of naïve set theory: Russell's, Burali-Forti's, and Cantor's. GST is Interpretable in relation algebra because no part of any GST axiom lies in the scope of more than three quantifiers. This is the necessary and sufficient condition given in Tarsk... | Wikipedia - General set theory | null | null | null |
Note that a "complex Lie group" is defined as a complex analytic manifold that is also a group whose multiplication and inversion are each given by a holomorphic map. The dimensions in the table below are dimensions over C. Note that every complex Lie group/algebra can also be viewed as a real Lie group/algebra of twic... | Wikipedia - Table of Lie groups | null | null | null |
Note that due to an overloading of the word "limit", the classical limit is not the opposite of the quantum limit. In "quantum limit", "limit" is being used in the sense of a physical limitation (e.g. the Armstrong limit). In "classical limit", "limit" is used in the sense of a limiting process. (Note that there is no ... | Wikipedia - Standard quantum limit | null | null | null |
Note that functions on a finite group can be identified with the group ring, though these are more naturally thought of as dual – the group ring consists of finite sums of elements, and thus pairs with functions on the group by evaluating the function on the summed elements. | Wikipedia - Antipode (algebra) | null | null | null |
Note that if x and y are spacelike-separated points, φ(x) and φ(y) neither commute nor anticommute unless p=1. The same comment applies to ψ(x) and ψ(y). So, if we have n spacelike separated points x1, ..., xn, ϕ ( x 1 ) ⋯ ϕ ( x n ) | Ω ⟩ {\displaystyle \phi (x_{1})\cdots \phi (x_{n})|\Omega \rangle } corresponds to cr... | Wikipedia - Parastatistics | null | null | null |
Because these fields neither commute nor anticommute ϕ ( x π ( 1 ) ) ⋯ ϕ ( x π ( n ) ) | Ω ⟩ {\displaystyle \phi (x_{\pi (1)})\cdots \phi (x_{\pi (n)})|\Omega \rangle } and ψ ( x π ( 1 ) ) ⋯ ψ ( x π ( n ) ) | Ω ⟩ {\displaystyle \psi (x_{\pi (1)})\cdots \psi (x_{\pi (n)})|\Omega \rangle } gives distinct states for each ... | Wikipedia - Parastatistics | null | null | null |
It is also unitary. Moreover, E {\displaystyle {\mathcal {E}}} is an operator-valued representation of the symmetric group Sn and as such, we can interpret it as the action of Sn upon the n-particle Hilbert space itself, turning it into a unitary representation. QCD can be reformulated using parastatistics with the qua... | Wikipedia - Parastatistics | null | null | null |
Note that in the theorem stated here, we have imposed the condition that if F {\displaystyle \mathbf {F} } is not defined on a bounded domain, then F {\displaystyle \mathbf {F} } shall decay faster than 1 / r {\displaystyle 1/r} . Thus, the Fourier transform of F {\displaystyle \mathbf {F} } , denoted as G {\displaysty... | Wikipedia - Longitudinal and transverse vector fields | null | null | null |
Note that in these experiments, the only quantity that affects the result is the difference in phase between the two parts of the electron wave. Suppose we imagine the two parts of the electron wave as tiny clocks, each with a single hand that sweeps around in a circle, keeping track of its own phase. Although this car... | Wikipedia - Introduction to gauge theory | null | null | null |
If both clocks are sped up by the same amount, the phase relationship between them is unchanged, and the results of experiments are the same. Not only that, but it is not even necessary to change the speed of each clock by a fixed amount. We could change the angle of the hand on each clock by a varying amount θ, where ... | Wikipedia - Introduction to gauge theory | null | null | null |
Note that not all of these satisfy the O ( n 3 ) {\displaystyle O(n^{3})} time complexity, even if they claim so. Some may contain errors, implement the slower O ( n 4 ) {\displaystyle O(n^{4})} algorithm, or have other inefficiencies. In the worst case, a code example linked from Wikipedia could later be modified to i... | Wikipedia - Hungarian algorithm | null | null | null |
Lua and Python versions of R.A. Pilgrim's code (claiming O ( n 3 ) {\displaystyle O(n^{3})} time complexity) Julia implementation C implementation claiming O ( n 3 ) {\displaystyle O(n^{3})} time complexity Java implementation claiming O ( n 3 ) {\displaystyle O(n^{3})} time complexity Python implementation Ruby implem... | Wikipedia - Hungarian algorithm | null | null | null |
Note that some of these terms are defined differently in older mathematical literature; see history of the separation axioms. T0 or Kolmogorov. A space is Kolmogorov if for every pair of distinct points x and y in the space, there is at least either an open set containing x but not y, or an open set containing y but no... | Wikipedia - Topological properties | null | null | null |
(Compare with T0; here, we are allowed to specify which point will be contained in the open set.) Equivalently, a space is T1 if all its singletons are closed. T1 spaces are always T0. | Wikipedia - Topological properties | null | null | null |
Sober. A space is sober if every irreducible closed set C has a unique generic point p. In other words, if C is not the (possibly nondisjoint) union of two smaller closed non-empty subsets, then there is a p such that the closure of {p} equals C, and p is the only point with this property. | Wikipedia - Topological properties | null | null | null |
T2 or Hausdorff. A space is Hausdorff if every two distinct points have disjoint neighbourhoods. T2 spaces are always T1. | Wikipedia - Topological properties | null | null | null |
T2½ or Urysohn. A space is Urysohn if every two distinct points have disjoint closed neighbourhoods. T2½ spaces are always T2. | Wikipedia - Topological properties | null | null | null |
Completely T2 or completely Hausdorff. A space is completely T2 if every two distinct points are separated by a function. Every completely Hausdorff space is Urysohn. | Wikipedia - Topological properties | null | null | null |
Regular. A space is regular if whenever C is a closed set and p is a point not in C, then C and p have disjoint neighbourhoods. T3 or Regular Hausdorff. | Wikipedia - Topological properties | null | null | null |
A space is regular Hausdorff if it is a regular T0 space. (A regular space is Hausdorff if and only if it is T0, so the terminology is consistent.) Completely regular. | Wikipedia - Topological properties | null | null | null |
A space is completely regular if whenever C is a closed set and p is a point not in C, then C and {p} are separated by a function. T3½, Tychonoff, Completely regular Hausdorff or Completely T3. A Tychonoff space is a completely regular T0 space. | Wikipedia - Topological properties | null | null | null |
(A completely regular space is Hausdorff if and only if it is T0, so the terminology is consistent.) Tychonoff spaces are always regular Hausdorff. Normal. | Wikipedia - Topological properties | null | null | null |
A space is normal if any two disjoint closed sets have disjoint neighbourhoods. Normal spaces admit partitions of unity. T4 or Normal Hausdorff. | Wikipedia - Topological properties | null | null | null |
A normal space is Hausdorff if and only if it is T1. Normal Hausdorff spaces are always Tychonoff. Completely normal. | Wikipedia - Topological properties | null | null | null |
A space is completely normal if any two separated sets have disjoint neighbourhoods. T5 or Completely normal Hausdorff. A completely normal space is Hausdorff if and only if it is T1. | Wikipedia - Topological properties | null | null | null |
Completely normal Hausdorff spaces are always normal Hausdorff. Perfectly normal. A space is perfectly normal if any two disjoint closed sets are precisely separated by a function. | Wikipedia - Topological properties | null | null | null |
A perfectly normal space must also be completely normal. T6 or Perfectly normal Hausdorff, or perfectly T4. A space is perfectly normal Hausdorff, if it is both perfectly normal and T1. | Wikipedia - Topological properties | null | null | null |
A perfectly normal Hausdorff space must also be completely normal Hausdorff. Discrete space. A space is discrete if all of its points are completely isolated, i.e. if any subset is open. Number of isolated points. The number of isolated points of a topological space. | Wikipedia - Topological properties | null | null | null |
Note that some texts use an alternative notation, in which the statistic S ∗ ( θ ) = S ( θ ) {\displaystyle S^{*}(\theta )={\sqrt {S(\theta )}}} is tested against a normal distribution. This approach is equivalent and gives identical results. | Wikipedia - Lagrange multiplier statistics | null | null | null |
Note that the accuracy with which a parameter distribution law of populations compatible with a sample is obtained is not a function of the sample size. Instead, it is a function of the number of seeds we draw. In turn, this number is purely a matter of computational time but does not require any extension of the obser... | Wikipedia - Bootstrapping populations | null | null | null |
Note that the decomposition obtained through this procedure is a Doolittle decomposition: the main diagonal of L is composed solely of 1s. If one would proceed by removing elements above the main diagonal by adding multiples of the columns (instead of removing elements below the diagonal by adding multiples of the rows... | Wikipedia - LU decomposition | null | null | null |
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