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Adducts are not necessarily molecular in nature. A good example from solid-state chemistry is the adducts of ethylene or carbon monoxide of CuAlCl4. The latter is a solid with an extended lattice structure. Upon formation of the adduct, a new extended phase is formed in which the gas molecules are incorporated (inserte...
Addition compound
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Auburn University - Multiscale Tribology Laboratory and the Undergraduate Tribology Minor Georgia Institute of Technology - Tribology Research Group George Mason University - Tribology and Surface Mechanics (TSM) Group Gonzaga University - Tribology Research Laboratory Iowa State University - Convergent Manufacturing, ...
List of tribology organizations
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In a neural network, batch normalization is achieved through a normalization step that fixes the means and variances of each layer's inputs. Ideally, the normalization would be conducted over the entire training set, but to use this step jointly with stochastic optimization methods, it is impractical to use the global ...
Batch normalization
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Advocates of NCT, in contrast, are part of a sizable minority of evolutionary biologists that conceive of evolutionary processes more broadly, as anything that systematically biases the direction or rate of evolution, a criterion that they (but not the skeptics) feel niche construction meets." The authors conclude that...
Niche construction
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Self-Reconfiguring and Modular Technology is a group for discussion of the perception and understanding of the developing field.robotics. Modular Robotics Google Group is an open public forum dedicated to announcements of events in the field of Modular Robotics. This medium is used to disseminate calls to workshops, sp...
Self-Reconfiguring Modular Robotics
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In the 17th century, Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry. Further steps in abstraction were taken by Lobachevsky, Bolyai, Riemann and Gauss, who generalised the concepts of geometry to develop non-Euclidean geometries. Later in the 19th century, mathematicians ...
Mathematical abstraction
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Aflatoxin total synthesis concerns the total synthesis of a group of organic compounds called aflatoxins. These compounds occur naturally in several fungi. As with other chemical compound targets in organic chemistry, the organic synthesis of aflatoxins serves various purposes.
Aflatoxin total synthesis
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NETtalk is an artificial neural network. It is the result of research carried out in the mid-1980s by Terrence Sejnowski and Charles Rosenberg. The intent behind NETtalk was to construct simplified models that might shed light on the complexity of learning human level cognitive tasks, and their implementation as a conn...
NETtalk (artificial neural network)
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Scott Eric Denmark is an American chemist who is the Reynold C. Fuson Professor of Chemistry at the University of Illinois at Urbana-Champaign (UIUC). Denmark received an S.B. degree from MIT in 1975 and the D.Sc.Tech.
Scott E. Denmark
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Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz – died 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis.
Gottfried Köthe
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Long before the discovery of water on asteroids, on comets, and on dwarf planets beyond Neptune, the Solar System's circumstellar disks, beyond the snow line, including the asteroid belt and the Kuiper Belt were thought to contain large amounts of water and these were believed to be the Origin of water on Earth. Given ...
Extraterrestrial liquid water
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H. Amann and E. Zehnder. Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann.
Eduard Zehnder
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Later, Kai Simons at the European Molecular Biology Laboratory (EMBL) in Germany and Gerrit van Meer from the University of Utrecht, Netherlands refocused interest on these membrane microdomains, enriched with lipids and cholesterol, glycolipids, and sphingolipids, present in cell membranes. Subsequently, they called t...
Lipid rafts
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The nature of chemical reactions and their description is one of the most fundamental problems in chemistry. The concepts of covalent and ionic bonds which emerged in the beginning of the 20th century specify the profound differences between their electronic structures. These differences, in turn, lead to dramatically ...
Ioliomics
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The internal graph model is close to RDF* which is used in Blazegraph and Amazon Neptune. That allows it to treat the internal data graph both as RDF graph and as Property Graph, performing queries both in SPARQL and Gremlin-style languages. Instead of indexes based on B+-trees traditionally used in graph databases, Ni...
NitrosBase
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F-distribution, arises frequently as the null distribution of a test statistic, most notably in the analysis of variance Fisher–Tippett–Gnedenko theorem: Fisher's contribution to this was made in 1927 Fisher–Tippett distribution Fisher-Yates shuffle algorithm Von Mises–Fisher distribution Inverse probability, a term Fi...
Ronald Fisher
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Kircher's work in geology included studies of volcanoes and fossils. One of the first researchers to observe microbes through a microscope, Kircher was ahead of his time in proposing that the plague was caused by an infectious microorganism and in suggesting effective measures to prevent its spread. Kircher also displa...
Athanasius Kircher
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Bicomplex number appears as the center of CAPS (complexified algebra of physical space), which is Clifford algebra C l ( 3 , C ) {\displaystyle Cl(3,\mathbb {C} )} . Since the linear space of CAPS can be viewed as the four dimensional space span { 1 , e 1 , e 2 , e 3 {\displaystyle 1,e_{1},e_{2},e_{3}} } over { 1 , i ,...
Bicomplex number
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In mathematics, more specifically sheaf theory, a branch of topology and algebraic geometry, the exceptional inverse image functor is the fourth and most sophisticated in a series of image functors for sheaves. It is needed to express Verdier duality in its most general form.
Exceptional inverse image functor
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Let X be a scheme over a field k (for example, an algebraic variety) with a line bundle L. (A line bundle may also be called an invertible sheaf.) Let a 0 , . .
Very ample line bundle
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The International Society of Electrochemistry (ISE) is a global scientific society founded in 1949. The Head Office of ISE is located now in Lausanne, Switzerland. ISE is a Member Organization of IUPAC.
International Society of Electrochemistry
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In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter. It is in this essay that the term 'potential function' first occurs. Herein also his remarkable theorem in pure mathematics, since universally k...
An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism
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Cellular automata are used in the field of artificial life, the most famous example being John Conway's Game of Life. Some other examples which could be explained using automata theory in biology include mollusk and pine cone growth and pigmentation patterns. Going further, a theory suggesting that the whole universe i...
Analog automata
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The company developed enzyme-based reagent kits made by Promega Corporation, and in the new field of bioinformatics, licensed with TRW Inc. Also, joint marketing began with Perkin-Elmer Corporation and Cetus Corporation (formerly of instruments and reagents for DNA replication, the fastest growing segment in biotechnol...
Applied Biosystems
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The statement is relative easy to prove by induction on the dimension of Z (even for Y=Z, X=0, c=1) with a K that depends only on N; the point of the theorem is that K is independent of N. In fact, the constant c can be made arbitrarily close to 1, at the expense of the constant K becoming large. The original proof all...
Quotient of subspace theorem
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In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at ...
Rule of Succession
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Non-linear neural networks are a network of complex neurons that have many connections with one another such as the neuronal systems found within our brains. Comparatively, linear networks are an experimental view of analyzing a neural system by placing neurons in series with each other. Initially, noise in complex com...
Neuronal noise
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Wide-field Infrared Survey Explorer (WISE, observatory code C51, Explorer 92 and SMEX-6) is a NASA infrared astronomy space telescope in the Explorers Program. It was launched in December 2009, and placed in hibernation mode in February 2011, before being re-activated in 2013 and renamed the Near-Earth Object Wide-fiel...
WISE mission
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In biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a stimulus. Reflexes are found with varying levels of complexity in organisms with a nervous system. A reflex occurs via neural pathways in the nervous system called reflex arcs.
Involuntary action
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In 2013 a fairly short, fully formal proof using homotopy type theory as a mathematical foundation and an Agda variant as a proof assistant was announced by Peter LeFanu Lumsdaine; this became Theorem 8.10.2 of Homotopy Type Theory – Univalent Foundations of Mathematics. This induces an internal proof for any infinity-...
Blakers–Massey theorem
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"What the Tortoise Said to Achilles", written in 1895 by Lewis Carroll, was an attempt to reveal an analogous paradox in the realm of pure logic. If Carroll's argument is valid, the implication is that Zeno's paradoxes of motion are not essentially problems of space and time, but go right to the heart of reasoning itse...
Dichotomy paradox
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Rado (1949) proves the following theorem, which may be seen as a generalization of the De Bruijn–Erdős theorem. Let V {\displaystyle V} be an infinite set, for instance the set of vertices in an infinite graph. For each element v {\displaystyle v} of V {\displaystyle V} , let c v {\displaystyle c_{v}} be a finite set o...
De Bruijn–Erdős theorem (graph theory)
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Like human eyes, robots' "eyes" must also be able to focus on a particular area of interest, and also adjust to variations in light intensities. There is a subfield within computer vision where artificial systems are designed to mimic the processing and behavior of biological system, at different levels of complexity. ...
Robotics
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The Von Neumann-Morgenstern utility theorem, which assumes that individuals make decisions that maximise utility, had been proven 6 years prior to the Allais paradox, in 1947.Thirdly, In 1979, Allais's work was noticed and cited by Amos Tversky and Daniel Kahneman in their paper introducing Prospect Theory, titled Pros...
Allais paradox
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Francisco Ernesto (Tito) Baralle (born 26 October 1943, in Buenos Aires) is an Argentinian geneticist best known for his innovations in molecular biology and in particular the discovery of how genes are processed and mechanisms in mRNA splicing.
Francisco Ernesto Baralle
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The double negation introduction rule may be written in sequent notation: P ⊢ ¬ ¬ P {\displaystyle P\vdash \neg \neg P} The double negation elimination rule may be written as: ¬ ¬ P ⊢ P {\displaystyle \neg \neg P\vdash P} In rule form: P ¬ ¬ P {\displaystyle {\frac {P}{\neg \neg P}}} and ¬ ¬ P P {\displaystyle {\frac {...
Double negation elimination
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BRIDGE collected and compiled: multibeam bathymetry, sonar imagery, seismic data, electromagnetic data, gravimetry, petrology (including rock sections, cores, sediments and analytical data), chemical and physical oceanography (samples and analytical data), macro- and microbiology (specimens, film and analytical data); ...
British Mid-Ocean Ridge Initiative
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Like Earth's, Mercury's magnetic field is tilted, meaning that the magnetic poles are not located in the same area as the geographic poles. As a result of the north-south asymmetry in Mercury's internal magnetic field, the geometry of magnetic field lines is different in Mercury's north and south polar regions. In part...
Mercury's magnetic field
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In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given ...
Xyzzy (mnemonic)
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E-science tends toward inter- and multidisciplinary approaches that depend on computation and computer science. Research libraries have traditionally been discipline focused and, although increasingly technologically sophisticated, do not have systems of the scale or complexity of the e-science environment. E-science i...
E-Science librarianship
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There are many examples of symmetric tensors. Some include, the metric tensor, g μ ν {\displaystyle g_{\mu \nu }} , the Einstein tensor, G μ ν {\displaystyle G_{\mu \nu }} and the Ricci tensor, R μ ν {\displaystyle R_{\mu \nu }} . Many material properties and fields used in physics and engineering can be represented as...
Symmetric tensor
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The Louvain method for community detection is a method to extract non-overlapping communities from large networks created by Blondel et al. from the University of Louvain (the source of this method's name). The method is a greedy optimization method that appears to run in time O ( n ⋅ log ⁡ n ) {\displaystyle O(n\cdot ...
Louvain modularity
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The contingent world must have some necessary reason for its existence. Leibniz uses a geometry book as an example to explain his reasoning. If this book was copied from an infinite chain of copies, there must be some reason for the content of the book.
Well-founded phenomenon
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The curl of the gradient of any continuously twice-differentiable scalar field φ {\displaystyle \varphi } (i.e., differentiability class C 2 {\displaystyle C^{2}} ) is always the zero vector: It can be easily proved by expressing ∇ × ( ∇ φ ) {\displaystyle \nabla \times (\nabla \varphi )} in a Cartesian coordinate syst...
Vector calculus identity
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"The distribution, diversity, and importance of 16S rRNA gene introns in the order Thermoproteales". Biology Direct. 10 (35): 35. doi:10.1186/s13062-015-0065-6.
Caldivirga
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Model obfuscation is a technique to hide the internal structure of a machine learning model. Obfuscation turns a model into a black box. It is contrary to explainable AI.
Software obfuscation
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In organic chemistry, acid hydrolysis is a hydrolysis process in which a protic acid is used to catalyze the cleavage of a chemical bond via a nucleophilic substitution reaction, with the addition of the elements of water (H2O). For example, in the conversion of cellulose or starch to glucose. For the case of esters an...
Acid hydrolysis
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Self-organizing maps (SOMs) were described by Teuvo Kohonen in 1982. SOMs are neurophysiologically inspired artificial neural networks that learn low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using competitive learning. SOMs create inte...
History of artificial neural networks
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A superior approach for modelling daily or monthly weather variable time series is to combine statistical and physical weather models using time-horizon varying weight which are obtained after optimization of those based on historical out-of-sample evaluation of the combined model scheme performance.
Weather derivatives
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As used in biology, the indifference curve is a model for how animals 'decide' whether to perform a particular behavior, based on changes in two variables which can increase in intensity, one along the x-axis and the other along the y-axis. For example, the x-axis may measure the quantity of food available while the y-...
Indifference curves
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87,350
Coalescent theory relates genetic diversity in a sample to demographic history of the population from which it was taken. It normally assumes neutrality, and so sequences from more neutrally evolving portions of genomes are therefore selected for such analyses. It can be used to infer the relationships between species ...
Evolutionary genetics
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An element of the center of an extended supersymmetry algebra. ZEUS zino A hypothetical supersymmetric partner of the Z-boson. zweibein A frame in 2 dimensions
Glossary of string theory
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The terminology used for types of stationarity other than strict stationarity can be rather mixed. Some examples follow. Priestley uses stationary up to order m if conditions similar to those given here for wide sense stationarity apply relating to moments up to order m. Thus wide sense stationarity would be equivalent...
Wide-sense stationary process
0.7984
87,353
The notion of intersex individuals can be understood in the context of sexual system biology that varies across different types of organisms. Most animal species (~95%, including humans) are gonochoric, in which individuals are of either a female or male sex. Hermaphroditic species (some animals and most flowering plan...
Intersex
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To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as "an act of desperation". One of his new boundary conditions was to interpret UN not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of fin...
Reduced Planck Constant
0.7984
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In July 2018, Google announced the Edge TPU. The Edge TPU is Google's purpose-built ASIC chip designed to run machine learning (ML) models for edge computing, meaning it is much smaller and consumes far less power compared to the TPUs hosted in Google datacenters (also known as Cloud TPUs). In January 2019, Google made...
Tensor Processing Unit
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Materiomics is the holistic study of material systems. Materiomics examines links between physicochemical material properties and material characteristics and function. The focus of materiomics is system functionality and behavior, rather than a piecewise collection of properties, a paradigm similar to systems biology.
Materiomics
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87,357
and ""The GSA Division with the biggest field area! "Major centers for planetary science research include the Lunar and Planetary Institute, Applied Physics Laboratory, Planetary Science Institute, Jet Propulsion Laboratory, Southwest Research Institute, and Johnson Space Center. Additionally, several universities cond...
Planetary geology
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87,358
By solving Apollonius' problem repeatedly to find the inscribed circle, the interstices between mutually tangential circles can be filled arbitrarily finely, forming an Apollonian gasket, also known as a Leibniz packing or an Apollonian packing. This gasket is a fractal, being self-similar and having a dimension d that...
Apollonius pursuit problem
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In 1937 he married Sherna Shalett. He obtained his Ph.D. in chemistry in 1940 with Professor James W. McBain at Stanford University with research on physical and colloid chemistry.
Jerome Vinograd
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Dlab was a postdoctoral student of renowned Czech mathematician Eduard Čech. While in Canada, Dlab worked as the editor-of-chief of mathematical journals and chairman of assorted organizations and institutions. In 1977, he was elected a fellow of the Royal Society of Canada. Claus Michael Ringel was the co-author of so...
Vlastimil Dlab
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87,361
History of FIB technology 1975: The first FIB systems based on field emission technology were developed by Levi-Setti and by Orloff and Swanson and used gas field ionization sources (GFISs). 1978: The first FIB based on an LMIS was built by Seliger et al.Physics of LMIS 1600: Gilbert documented that fluid under high te...
Focused ion beam
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Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra Symmetric algebra Clifford algebra Geometric algebra
Outline of linear algebra
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The pseudocircle is the finite topological space X consisting of four distinct points {a,b,c,d } with the following non-Hausdorff topology: This topology corresponds to the partial order a < c , b < c , a < d , b < d {\displaystyle a
Pseudocircle
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Molecular Aspects of Medicine is a bimonthly peer-reviewed medical journal covering molecular medicine. It is published by Elsevier on behalf of the International Union of Biochemistry and Molecular Biology.
Molecular Aspects of Medicine
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Wadler received a Bachelor of Science degree in mathematics from Stanford University in 1977, and a Master of Science degree in computer science from Carnegie Mellon University in 1979. He completed his Doctor of Philosophy in computer science at Carnegie Mellon University in 1984. His thesis was entitled "Listlessness...
Philip Wadler
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Areas where DAI have been applied are: Electronic commerce, e.g. for trading strategies the DAI system learns financial trading rules from subsamples of very large samples of financial data Networks, e.g. in telecommunications the DAI system controls the cooperative resources in a WLAN network Routing, e.g. model vehic...
Distributed Artificial Intelligence
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87,367
The second early 19th century development, that of Abelian integrals, would lead Bernhard Riemann to the development of Riemann surfaces. In the same period began the algebraization of the algebraic geometry through commutative algebra. The prominent results in this direction are Hilbert's basis theorem and Hilbert's N...
Algebraic Geometry
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87,368
Physical Chemistry (originally the department of Colloid Science led by Eric Rideal) had left the old Cavendish site, subsequently locating as the Department of Physical Chemistry (under RG Norrish) in the then new chemistry building with the Department of Chemistry (led by Lord Todd) in Lensfield Road: both chemistry ...
Theory of Condensed Matter
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87,369
In theoretical computer science, a small-bias sample space (also known as ϵ {\displaystyle \epsilon } -biased sample space, ϵ {\displaystyle \epsilon } -biased generator, or small-bias probability space) is a probability distribution that fools parity functions. In other words, no parity function can distinguish betwee...
Small-bias sample space
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87,370
Roy Patrick Kerr (; born 16 May 1934) is a New Zealand mathematician who discovered the Kerr geometry, an exact solution to the Einstein field equation of general relativity. His solution models the gravitational field outside an uncharged rotating massive object, including a rotating black hole. His solution to Einste...
Roy Kerr
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The singular computer algebra system for commutative algebra smooth A smooth morphism of rings is a homomorphism that is formally smooth and finitely presented. These are analogous to submersions in differential topology. An algebra over a ring is called smooth if the corresponding morphism is smooth.
Formally equidimensional
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In his book The Global Genome: Biotechnology, Politics, and Culture, Thacker looks to developments in tissue engineering where techno-mechanical apparatuses disappear altogether so that it appears as though technology is the natural body. In Thacker's words, "biotechnology is thus invisible yet immanent. "In 2013 Thack...
Eugene Thacker
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radio astronomy The subfield of astronomy that studies astronomical objects at radio frequencies, using large radio antennas known as radio telescopes. radio source Any astronomical object that emits strong radio waves into space. These objects are the basis for radio astronomy.
Hydrogen burning limit
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This change has resulted in several mistranslations: For example, Saint Augustine's warning that Christians should beware of mathematici, meaning "astrologers", is sometimes mistranslated as a condemnation of mathematicians.The apparent plural form in English goes back to the Latin neuter plural mathematica (Cicero), b...
Mathematical research
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87,375
Detractors say that the overall concept of dopamine fasting is unscientific since the chemical plays a vital role in everyday life; literally reducing it would not be good for a person, and removing a particular stimulus like social media would not reduce the levels of dopamine in the body, only the stimulation of it. ...
Dopamine fasting
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87,376
He found the existence of the infinitely many fixed points (equilibrium points) for the first two versions. He concluded that these versions of AFDEs are structurally unstable systems mathematically by using an extension of the Peixoto Theorem for two-dimensional manifolds to a four-dimensional manifold. Moreover, he o...
Quantitative behavioral finance
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87,377
However, as before, this topology is not necessarily compatible with the vector space structure of B ( X , Y ; Z ) {\displaystyle {\mathcal {B}}(X,Y;Z)} or of B ( X , Y ; Z ) {\displaystyle B(X,Y;Z)} without the additional requirement that for all bilinear maps, b {\displaystyle b} in this space (that is, in B ( X , Y ...
Space of linear maps
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87,378
Venkatraman Radhakrishnan FASc (son of C. V. Raman) was a distinguished astrophysicist credited with expanding the field of radio astronomy and for research in pulsars, interstellar clouds and various celestial bodies. Subrahmanyan Chandrasekhar FNA, FASc, FRS (nephew of C. V. Raman) was an Indian American astrophysici...
Chandrasekhar family
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For example, if x {\displaystyle {x}} and y {\displaystyle {y}} are fluents, then x ˙ {\displaystyle {\dot {x}}} and y ˙ {\displaystyle {\dot {y}}} are their respective fluxions. This revised calculus of ratios continued to be developed and was maturely stated in the 1676 text De Quadratura Curvarum where Newton came t...
History of calculus
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John of Dumbleton is recorded to have become a fellow at Merton College, Oxford (ca. 1338–9) and to have studied with the likes of William Heytesbury, Thomas Bradwardine, and Richard Swineshead. These four medieval scholastics held a common bond in that their study interests were in a similar field, but the method of s...
John Dumbleton
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The assays and other tests used in the commission's laboratory are all published, making the required standards known to both vendors and users of biological stains (Penney et al. 2002a,b). The commission's web site includes instructions for submitting samples of stains for testing and certification.Since 1925 the BSC ...
Biological Stain Commission
0.798394
87,382
In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional techniques of lower-order statistics, which use constant, linear, and quadratic terms (zeroth, first, and second powers). The third and higher moments, as used in th...
Higher-order statistics
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87,383
Physically speaking, a null dust describes either gravitational radiation, or some kind of nongravitational radiation which is described by a relativistic classical field theory (such as electromagnetic radiation), or a combination of these two. Null dusts include vacuum solutions as a special case. Phenomena which can...
Null dust solution
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87,384
Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety of computer architectures for use by the research community.
DiRAC
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87,385
In chemistry, a glycoside is a molecule in which a sugar is bound to another functional group via a glycosidic bond. Glycosides play numerous important roles in living organisms. Many plants store chemicals in the form of inactive glycosides. These can be activated by enzyme hydrolysis, which causes the sugar part to b...
Glycoside
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Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exa...
Numerical software
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87,387
The 2− ion adopts an eclipsed conformation as shown at left. The delta bonding orbital is then formed by overlap of the d orbitals on each rhenium atom, which are perpendicular to the Re–Re axis and lie in between the Re–Cl bonds. The d orbitals directed along the Re–Cl bonds are stabilized by interaction with chlorine...
Quadruple bond
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The following minerals are detectable in calculus by X-ray diffraction: brushite (CaHPO4 · 2 H2O), octacalcium phosphate (Ca8H2(PO4)6 · 5 H2O), magnesium-containing whitlockite (Ca9(Mg,Fe)(PO4)6(PO3OH)), and carbonate-containing hydroxyapatite (approximately Ca5(PO4)3OH but containing some carbonate).The reason fossili...
Dental calculus
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Convex optimization Quadratic programming Linear least squares (mathematics) Total least squares Frank–Wolfe algorithm Sequential minimal optimization — breaks up large QP problems into a series of smallest possible QP problems Bilinear program Basis pursuit — minimize L1-norm of vector subject to linear constraints Ba...
List of numerical analysis topics
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r = 2 {\displaystyle r=2} In the special case r = 2 {\displaystyle r=2} , we have a complete graph K n {\displaystyle K_{n}} on n {\displaystyle n} vertices, and we wish to color the edges with ( n 2 ) 2 n = n − 1 {\displaystyle {\binom {n}{2}}{\frac {2}{n}}=n-1} colors so that the edges of each color form a perfect ma...
Baranyai's theorem
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The features of the π-calculus that make these encodings possible are name-passing and replication (or, equivalently, recursively defined agents). In the absence of replication/recursion, the π-calculus ceases to be Turing-complete. This can be seen by the fact that bisimulation equivalence becomes decidable for the re...
Pi calculus
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87,392
The momentum equation (3) can also be cast in the so-called conservation form, through some algebraic manipulations on the Saint-Venant equations, (1) and (3). In terms of the discharge Q = Au: where A, I1 and I2 are functions of the channel geometry, described in the terms of the channel width B(σ,x). Here σ is the he...
Shallow-water equations
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87,393
The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose symmetry algebra is the Virasoro algebra with the central charge c = 1 2 {\displaystyle c={\tfrac {1}{2}}} . Correlation functions of the spin and energy operators ar...
Two-dimensional critical Ising model
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87,394
Casio had used different product names in France, following their French predecessors. The Graph 100 and the Graph 100+ were respectively the Algebra FX 2.0 and the Algebra FX 2.0 Plus. The Algebra FX 2.0 Plus was discontinued in 2003 and succeeded by the Casio ClassPad series, where the calculators have stylus-based t...
Casio Algebra FX Series
0.798392
87,395
On January 11, 2023, the James Webb Space Telescope reported the discovery of its first exoplanet LHS 475 b On April 3, 2023, a study published by the Nature Astronomy discovers bursts of radiation in radio wavelengths from YZ Ceti, which may be associated with interaction of the innermost planet, YZ Ceti b. A study pu...
Discoveries of extrasolar planets
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Muhammad ibn Mūsā al-Khwārizmī originated the word "algebra" in 830 AD, but his work was entirely rhetorical algebra. Fully symbolic algebra did not appear until François Viète's 1591 New Algebra, and even this had some spelled out words that were given symbols in Descartes's 1637 La Géométrie. The formal study of solv...
Abstract Algebra
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Studies have proven that genetic variations and differences in our neurobiology can alter an individual's vulnerability to developing an addiction. Estimates have shown that around 40%-60% of the susceptibility of an individual to develop an addiction to drugs, nicotine, and alcohol is allotted to genetic variables. Th...
Addiction psychology
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As the example below shows, regardless of whether or not a space is Hausdorff or already complete, every topological vector space (TVS) has infinitely many non-isomorphic completions.However, every Hausdorff TVS has a Hausdorff completion that is unique up to TVS-isomorphism. But nevertheless, every Hausdorff TVS still...
Complete TVS
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As early as the 4th century BC, Hippocrates suggested in his essay "On Airs, Waters, and Places" that factors such as behavior and environment may play a role in disease. Epidemiology entered a more systematic phase with the work of John Graunt, who in 1662 tried to quantify mortality in London using a statistical appr...
Genetic epidemiology
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