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The topology of the AS-Interface is arbitrary, but without a repeater or extender, the cable length must not exceed 100 m. Due to a special terminating resistor (a combination of resistive and capacitive load), however, it is possible to increase the maximum cable length up to 300 m. Diagnostic devices or masters with ...
AS-Interface
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Calculus Lite. Third edition. A K Peters/CRC Press, Natick, MA, 2001. ISBN 1-56881-157-8 Geometric measure theory.
Frank Morgan (mathematician)
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Depending on the counting geometry of the system, count times can be from 1 minute to about 30 minutes. The sensitivity of a counter does depend on counting time so the longer the count, for the same system, the better the detection limit. The detection limit, often referred to as the Minimum Detectable Activity (MDA),...
Whole body counting
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Protic solvents often undergo some autoionization (in this case autoprotolysis): 2 H 2 O ↽ − − ⇀ H 3 O + + OH − {\displaystyle {\ce {2 H2O <=> H3O+ + OH-}}} The self-ionization of water is particularly well studied, due to its implications for acid-base chemistry of aqueous solutions. 2 NH 3 ↽ − − ⇀ NH 4 + + NH 2 − {\d...
Molecular autoionization
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This is an expanding field and there is room for greater application to mental health disorders and brain malfunction, in which current research is building on neural networks and the psychopathology involved.The human connectome can be viewed as a graph, and the rich tools, definitions and algorithms of the Graph theo...
Connectomics
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In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object along with the object itself. For example, a 1-dimensional line ( l ) {\displaystyle (l)} may be studied in isolation —in which case the ambient space of l {\displaystyle l} is l {\displaystyle l} , or i...
Ambient space (mathematics)
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In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection between the three perpendicular bisectors...
Circumcircle
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Marine engineering is the engineering of boats, ships, submarines, and any other marine vessel. Here it is also taken to include the engineering of other ocean systems and structures – referred to in certain academic and professional circles as “ocean engineering.” Marine engineering applies a number of engineering sci...
Ocean engineering
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The US Recommended Dietary Allowance for vitamin C for adult women is 76 mg/day and for adult men 90 mg/day. Although Linus Pauling was known for highly respectable research in chemistry and biochemistry, he was also known for promoting the consumption of vitamin C in large doses. Although he claimed and stood firm in ...
Megavitamin therapy
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In computer science, a finger tree is a purely functional data structure that can be used to efficiently implement other functional data structures. A finger tree gives amortized constant time access to the "fingers" (leaves) of the tree, which is where data is stored, and concatenation and splitting logarithmic time i...
Finger tree
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ReH2−9 is sometimes described as having a capped square antiprismatic geometry, although its geometry is most often described as tricapped trigonal prismatic. 4+2, a lanthanum(III) complex with a La–La bond. == References ==
Capped square antiprismatic molecular geometry
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Renaissance mathematicians Lodovico Ferrari, Gerolamo Cardano and Niccolò Fontana Tartaglia and others were able to show in the 16th century that any ruler-and-compass construction could be accomplished with a straightedge and a fixed-width compass (i.e. a rusty compass).Motivated by Mascheroni's result, in 1822 Jean V...
Mohr–Mascheroni theorem
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Software sizing or software size estimation is an activity in software engineering that is used to determine or estimate the size of a software application or component in order to be able to implement other software project management activities (such as estimating or tracking). Size is an inherent characteristic of a...
Software Sizing
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As for all digital codes, the error detection and correction abilities of polynomial codes are determined by the minimum Hamming distance of the code. Since polynomial codes are linear codes, the minimum Hamming distance is equal to the minimum weight of any non-zero codeword. In the example above, the minimum Hamming ...
Polynomial code
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The Research Institute for Symbolic Computation (RISC Linz) is a research institute in the area of symbolic computation, including automated theorem proving and computer algebra. It is located in Schloß Hagenberg in Hagenberg near Linz in Austria. RISC was founded in 1987 under Bruno Buchberger and moved to Hagenberg i...
Research Institute for Symbolic Computation
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It offers academic courses in Fire Fighter I, Fire Fighter II, EMT1, Paramedic, Cosmetology, Information Technology, Business, Community Development, Vocational Training, and Disaster Management. ICT Schools and Departments School of Emergency Medical Services Fire Fighting Academy School of Information Technology Scho...
International Centre of Technology
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Thus the question arose whether the Electromagnetic conception of the world (compatible with Abraham's theory) or the Relativity Principle (compatible with Lorentz's Theory) was correct.In a September 1904 lecture in St. Louis named The Principles of Mathematical Physics, Poincaré drew some consequences from Lorentz's ...
History of special relativity
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If A n ≃ M k n ( C ) , {\displaystyle A_{n}\simeq M_{k_{n}}(\mathbb {C} ),} then rkn = kn + 1 for some integer r and ϕ n ( a ) = a ⊗ I r , {\displaystyle \phi _{n}(a)=a\otimes I_{r},} where Ir is the identity in the r × r matrices. The sequence ...kn|kn + 1|kn + 2... determines a formal product δ ( A ) = ∏ p p t p {\di...
Uniformly hyperfinite algebra
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George Pólya (; Hungarian: Pólya György, pronounced ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysi...
George Pólya
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The DTMs are capable of identifying the structural parameters of geological features(tilt angle of a fold limb). For example, dip and dip directions of rock planes can be derived from DTM. The general methodology has the following steps: 1) Obtain LiDAR data of a targeted slope2) Noise cleaning and filtering of point d...
Geological structure measurement by LiDAR
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It was reviewed in Mathematical Reviews by J. Eells, who interpreted it as a three-term textbook for a sequence in abstract algebra, geometric algebra, and differential calculus in Euclidean and Banach spaces and on manifolds. Eells says "Surely this book is the product of substantial thought and care, both from the st...
Ian R. Porteous
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In 2016, Mission Neutral Park has acquired specialized R&D assets in Genome Valley from U.S.-based Alexandria REIT and rechristened it as MN Park. It is a collaborative life sciences ecosystem in Genome Valley, Hyderabad consisting of Grade A R&D facilities. MN Park is spread over 400 acres including build-up facilitie...
Genome Valley
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Common uses for metamodels are: As a schema for semantic data that needs to be exchanged or stored As a language that supports a particular method or process As a language to express additional semantics of existing information As a mechanism to create tools that work with a broad class of models at run time As a schem...
Meta-modeling technique
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In physics, drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero. Applying an electric field adds to this random moti...
Electron velocity
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Prosen earned his Diploma in Physics in 1991, and a Doctorate of Science in 1995, both from the University of Ljubljana. He finished both at a significantly younger age than usual. ISI named him a ‘Citation Superstar’ as one of the most cited young scientists in Slovenia in 2000. He was made a Full Professor at the Uni...
Tomaž Prosen
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His early education was obtained at Worthing High School for Boys. After serving in the Czech Airforce Training Unit during the war, he moved to London to study for undergraduate and postgraduate degrees in chemistry at Imperial College London. His PhD was awarded in 1951, under the supervision of Professor Herrington,...
Martin Fleischmann
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Vieta's formulas are simpler in the case of monic polynomials: The ith elementary symmetric function of the roots of a monic polynomial of degree n equals ( − 1 ) i c n − i , {\displaystyle (-1)^{i}c_{n-i},} where c n − i {\displaystyle c_{n-i}} is the coefficient of the (n−i)th power of the indeterminate. Euclidean di...
Monic polynomial
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The physical similarities suggest that there is a similar underlying biology between ESCO2 and thalidomide. As a result, it is speculated that thalidomide affects chromosomes and cell division in a similar manner to ESCO2. For this reason, Roberts syndrome is sometimes called Pseudothalidomide Syndrome.
Roberts syndrome
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In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map f: X → Y {\displaystyle f:X\to Y} , the inverse image functor is a functor from the category of sheaves on Y to the category of sh...
Inverse image functor
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Bioelectrochemistry is a bimonthly peer-reviewed scientific journal covering research on the electrochemistry of biological systems. The current editor-in-chief is E. Neumann (Bielefeld University). It was established in 1974 as Bioelectrochemistry and Bioenergetics (ISSN 0302-4598) and obtained its current title in 20...
Bioelectrochemistry (journal)
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A number of HOL systems (sharing essentially the same logic) remain active and in use: HOL4 — the only presently maintained and developed system stemming from the HOL88 system, which was the culmination of the original HOL implementation effort, led by Mike Gordon. HOL88 included its own ML implementation, which was in...
HOL theorem prover
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Astropulse and its older partner, SETI@home, offer a concrete way for secondary school science teachers to involve their students with astronomy and computing. A number of schools maintain volunteer computing class projects.
Astropulse
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Richard Walter Conway (born December 12, 1931) is an American industrial engineer and computer scientist who is the Emerson Electric Company Professor of Manufacturing Management, Emeritus in the Johnson Graduate School of Management at Cornell University. Conway has spent his entire academic career, both as a student ...
Richard W. Conway
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In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. It was popularized in English by Hugo Steinhaus in the 1950 edition of ...
Pick's theorem
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Since every infinite well-ordered set is Dedekind-infinite, and since the AC is equivalent to the well-ordering theorem stating that every set can be well-ordered, clearly the general AC implies that every infinite set is Dedekind-infinite. However, the equivalence of the two definitions is much weaker than the full st...
Dedekind finite ring
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For all compact K ⊆ U , {\displaystyle K\subseteq U,} the interior of C k ( K ) {\displaystyle C^{k}(K)} in C c k ( U ) {\displaystyle C_{c}^{k}(U)} is empty so that C c k ( U ) {\displaystyle C_{c}^{k}(U)} is of the first category in itself. It follows from Baire's theorem that C c k ( U ) {\displaystyle C_{c}^{k}(U)}...
Spaces of test functions and distributions
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000 Generalities 000 Special collections 010 Bibliography; Literacy (Documentation) 020 Library and information science; Archive management 030 Sinology 040 General encyclopedia 050 Serial publications; Periodicals 060 General organization; Museology 070 General collected essays 080 General series 090 Collected Chinese...
New Classification Scheme for Chinese Libraries
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They are generalizations of the hyperplane separation theorem, which states that two disjoint nonempty convex subsets of a finite-dimensional space R n {\displaystyle \mathbb {R} ^{n}} can be separated by some affine hyperplane, which is a fiber (level set) of the form f − 1 ( s ) = { x: f ( x ) = s } {\displaystyle f^...
Hahn–Banach theorem
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The word syzygy came into mathematics with the work of Arthur Cayley. In that paper, Cayley used it in the theory of resultants and discriminants. As the word syzygy was used in astronomy to denote a linear relation between planets, Cayley used it to denote linear relations between minors of a matrix, such as, in the c...
Linear relation
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In terms of aperture, the largest aircraft-borne instrument to date is a 2.7 m (110 in) reflector telescope carried by a modified Boeing 747 for the Stratospheric Observatory for Infrared Astronomy (SOFIA) project. This instrument was put into use for astronomical observation in 2010. On 29 June 2015, the dwarf planet ...
Airborne telescope
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With rising concern for environmental ramifications of plastic waste, researchers have been exploring the application of genetic engineering and synthetic biology for optimizing biodegradable plastic production. This involves altering the endogenous genetic makeup or other biological systems of organisms.In 1995, an ar...
Compostable plastics
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In geometry, a limaçon or limacon , also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle...
Limaçon
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In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(m,n) is the nm × mn matrix which, for any m × n matrix A, transforms vec(A) into vec(AT): K(m,...
Commutation matrix
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The NTN has over 250 sites that focus on wet deposition chemistry by collecting weekly precipitation samples nationwide. The samples are sent to the Central Analytical Laboratory (The Wisconsin State Lab of Hygiene) for analysis and are then used to determine geographic distribution and annual trends. The sample collec...
National Atmospheric Deposition Program
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in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry.Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago instead.
Leonard Eugene Dickson
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Let V denote a topological vector space over the field F. A Schauder basis is a sequence {bn} of elements of V such that for every element v ∈ V there exists a unique sequence {αn} of scalars in F so that The convergence of the infinite sum is implicitly that of the ambient topology, i.e., but can be reduced to only we...
Schauder basis
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Recent updates to APT include the ability to read FITS image files which use a Pixel Coordinate matrix (PCM), such as that used by the Panoramic Survey Telescope and Rapid Response System.APT calculates geometric image distortion only for the tangent projection at this time. Two distortion conventions are supported, wh...
Aperture Photometry Tool
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Canadian Association for Clinical Microbiology and Infectious Diseases (CACMID) - Patron (former). Canadian Association of Emergency Physicians (CAEP) - Corporate partner. Canadian Association of Medical Oncologists - Annual meeting sponsor.
Pfizer
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In addition to proving the theorem, the above argument tells us that the coefficients Bi of B are polynomials in A, while from the second proof we only knew that they lie in the centralizer Z of A; in general Z is a larger subring than R, and not necessarily commutative. In particular the constant term B0 = adj(−A) lie...
Cayley–Hamilton theorem
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This is because surface waves are a created as a consequence of an interface between two media having dissimilar refractive indices. Depending on the application of the system that includes the two media, there may be a need to attenuate surface waves or utilize them.An FSS based metamaterial employs a (miniature) mode...
Tunable metamaterial
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95,650
In the field of molecular biology, gene expression profiling is the measurement of the activity (the expression) of thousands of genes at once, to create a global picture of cellular function. These profiles can, for example, distinguish between cells that are actively dividing, or show how the cells react to a particu...
Digital gene expression profiling
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95,651
According to Helmholtz's theorems, a vortex line cannot start or end in the fluid – except momentarily, in non-steady flow, while the vortex is forming or dissipating. In general, vortex lines (in particular, the axis line) are either closed loops or end at the boundary of the fluid. A whirlpool is an example of the la...
Vortex
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95,652
Square-free factorization is the first step of the polynomial factorization algorithms that are implemented in computer algebra systems. Therefore, the algorithm of square-free factorization is basic in computer algebra. Over a field of characteristic 0, the quotient of f {\displaystyle f} by its GCD with its derivativ...
Square-free factorization
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95,653
A different response, advocated by physicist Max Tegmark, is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. The same interpretation had been advanced some years pre...
Wigner's Puzzle
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95,654
Drawing upon fundamental works in classical homogenization theory, Berlyand advanced the methods of homogenization in many versatile applications. He obtained mathematical results applicable to diverse scientific areas including biology, fluid mechanics, superconductivity, elasticity, and material science. His mathemat...
Leonid Berlyand
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Electron diffraction patterns emerge when energetic electrons reflect or penetrate ordered solids; analysis of the patterns leads to models of the atomic arrangement in the solids. They are used for imaging from the micron to atomic scale using electron microscopes, in transmission, using scanning, and for surfaces at ...
DeBroglie hypothesis
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Over the field of real numbers R {\displaystyle \mathbb {R} } there are exactly (up to isomorphism) two tori of rank 1: the split torus R × {\displaystyle \mathbb {R} ^{\times }} the compact form, which can be realised as the unitary group U ( 1 ) {\displaystyle \mathbf {U} (1)} or as the special orthogonal group S O (...
Algebraic torus
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95,657
For the same reason, a minimally imperfect graph whose complement has a 2-join cannot be Berge.A skew partition is a partition of a graph's vertices into two subsets, one of which induces a disconnected subgraph and the other of which has a disconnected complement; Chvátal (1985) had conjectured that no minimal counter...
Strong perfect graph conjecture
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He was the inventor of the trie data structure, radio transponders for vehicle identification, the concept of computer navigation for automobiles, the Fredkin gate, and the Billiard-Ball Computer Model for reversible computing. He has also been involved in computer vision, chess, and other areas of Artificial Intellige...
Edward Fredkin
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Voytek's primary scientific interests are biogeochemistry and aquatic microbial ecology; more particularly, environmental controls on microbial transformations of nutrients, xenobiotics, and metals in freshwater and marine systems. She has worked in several extreme environments, including Antarctica, hypersaline lakes,...
Mary Voytek
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It is unique (up to isomorphism).The separable closure is the full algebraic closure if and only if K is a perfect field. For example, if K is a field of characteristic p and if X is transcendental over K, K ( X ) ( X p ) ⊃ K ( X ) {\displaystyle K(X)({\sqrt{X}})\supset K(X)} is a non-separable algebraic field extensio...
Separable closure
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There is a vast body of methods for solving various kinds of differential equations, both numerically and analytically. A particular class of problem that can be considered to belong here is integration, and the analytic methods for solving this kind of problems are now called symbolic integration. Solutions of differe...
Solving equations
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This era of the observatory was made famous by the work of Cecelia Payne-Gaposchkin, who became the first woman to earn a PhD in astronomy from Radcliffe College (a short walk from the observatory). Payne-Gapochkin's 1925 thesis proposed that stars were composed primarily of hydrogen and helium, an idea thought ridicul...
Harvard–Smithsonian Center for Astrophysics
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The International Conference on Future Applications of AI, Sensors, and Robotics in Society explore the state of the art research, highlighting the future challenges as well as the hidden potential behind the technologies. The accepted contributions to this conference will be published annually in the special edition o...
Human–robot interaction
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Many pediatric endocrinologists have interests and expertise in bone metabolism, lipid metabolism, adolescent gynecology, or inborn errors of metabolism.In the United States and Canada, pediatric endocrinology is a subspecialty of the American Board of Pediatrics or the American Osteopathic Board of Pediatrics, with bo...
Pediatric endocrinology
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In the mathematical field of graph theory, a icosidodecahedral graph is the graph of vertices and edges of the icosidodecahedron, one of the Archimedean solids. It has 30 vertices and 60 edges, and is a quartic graph Archimedean graph.
Icosidodecahedral graph
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Data in the NVO Closeout Repository are available from a variety of observatories and wavelengths, including NSF's National Optical Astronomy Observatory (NOAO), National Radio Astronomy Observatory (NRAO), the Sloan Digital Sky Survey (SDSS), and the 2 Micron All Sky Survey (2MASS). Also found in the NVO are NASA's ri...
National Virtual Observatory
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The assertion of B ⟹ A {\displaystyle B\implies A} is captured by certainty of the conditional, the assertion of P ( A | B ) = 1 {\displaystyle P(A\vert B)=1} . Relating the directions of implication, Bayes' theorem represents a generalization of the contraposition law, which in classical propositional logic can be exp...
Bayes' Theorem
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To build an artificial brain requires formulas, knowledge and sufficient computational power, explains Kurzweil. He says "by around the year 2020" a $1,000 personal computer will have enough speed and memory to match the human brain, based on the law of accelerating returns and his own estimates of the computational sp...
The Age of Spiritual Machines
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In quantum mechanics, the four-probability current or probability four-current is analogous to the electromagnetic four-current: where ρ is the probability density function corresponding to the time component, and j is the probability current vector. In non-relativistic quantum mechanics, this current is always well de...
Position four-vector
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The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references (Antman 1983, pp. 282–284) and (Fichera 1995): the first papers of the theory were (Fichera 1963) and (Fichera 1964a), (Fichera 1964b). La...
Variational inequality
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Sociobiology is based upon two fundamental premises: Certain behavioral traits are inherited, Inherited behavioral traits have been honed by natural selection. Therefore, these traits were probably "adaptive" in the environment in which the species evolved.Sociobiology uses Nikolaas Tinbergen's four categories of quest...
Sociobiology
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In civil engineering "rough grading" is performed by heavy equipment such as wheel tractor-scrapers and bulldozers. Graders are used to "finish grade", with the angle, tilt (or pitch), and height of their blade capable of being adjusted to a high level of precision. Graders are commonly used in the construction and mai...
Grader
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In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Hexagon
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ERP Cybersecurity survey revealed that organizations running ERP systems "lack both awareness and actions taken towards ERP security". ISACA states that "there is a shortage of staff members trained in ERP security" and security services have the superficial understanding of risks and threats associated with ERP system...
ERP security
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Let Χ be a set of objects called names. The abstract syntax for the π-calculus is built from the following BNF grammar (where x and y are any names from Χ): P , Q ::= x ( y ) . P Receive on channel x , bind the result to y , then run P | x ¯ ⟨ y ⟩ . P Send the value y over channel x , then run P | P | Q Run P and Q sim...
Π-calculus
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The analogue of this result for primes other than 2 was known as the Bloch–Kato conjecture. Work of Voevodsky and Markus Rost yielded a complete proof of this conjecture in 2009; the result is now called the norm residue isomorphism theorem.
Milnor conjecture
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The topology and dynamics of CNN processors closely resembles that of CA. Like most CNN processors, CA consists of a fixed-number of identical processors that are spatially discrete and topologically uniform. The difference is that most CNN processors are continuous-valued whereas CA have discrete-values. Furthermore, ...
Cellular neural network
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Q (cipher) • Qrpff • QUAD (cipher) • Quadratic sieve • Quantum coin flipping • Quantum cryptography • Quantum digital signature • Quantum fingerprinting • Quantum key distribution
Index of cryptography articles
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It is a model system that like WRF can be run in many configurations, including at high resolution with the non-hydrostatic Arome physics or at lower resolutions with hydrostatic physics based on the ALADIN physical schemes. It has mostly been used in Europe and the Arctic for climate studies including 3km downscaling ...
Atmospheric modelling
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In polygons, the turning number is referred to as the polygon density. For convex polygons, and more generally simple polygons (not self-intersecting), the density is 1, by the Jordan curve theorem. By contrast, for a regular star polygon {p/q}, the density is q.
Winding number
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Clinical Biochemistry is a peer-reviewed scientific journal covering the analytical and clinical investigation of laboratory tests in humans used for diagnosis, molecular biology and genetics, prognosis, treatment and therapy, and monitoring of disease ; the discipline of clinical biochemistry. It is the official journ...
Clinical Biochemistry
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A pebble-bed power plant combines a gas-cooled core and a novel packaging of the fuel that dramatically reduces complexity while improving safety.The uranium, thorium or plutonium nuclear fuels are in the form of a ceramic (usually oxides or carbides) contained within spherical pebbles a little smaller than the size of...
Pebble Bed Reactor
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As long as the function in question is reasonably well-behaved, it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these points. By the central limit theorem, this method displays 1 / N {\displaystyle \scriptstyle 1/{\sqrt {N}}} convergen...
Monte Carlo Simulation
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Robert Louis Griess, Jr. (born 1945, Savannah, Georgia) is a mathematician working on finite simple groups and vertex algebras. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan.
Robert Griess
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Something that is quantized, as the energy of Planck's harmonic oscillators, can only take specific values. For example, in most countries, money is effectively quantized, with the quantum of money being the lowest-value coin in circulation. Mechanics is the branch of science that deals with the action of forces on obj...
Modern quantum theory
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Atiyah's works on K-theory, including his book on K-theory are reprinted in volume 2 of his collected works.The simplest nontrivial example of a vector bundle is the Möbius band (pictured on the right): a strip of paper with a twist in it, which represents a rank 1 vector bundle over a circle (the circle in question be...
Michael Atiyah
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Taylor diagrams are mathematical diagrams designed to graphically indicate which of several approximate representations (or models) of a system, process, or phenomenon is most realistic. This diagram, invented by Karl E. Taylor in 1994 (published in 2001) facilitates the comparative assessment of different models. It i...
Taylor diagram
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The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI). Suborder Roseiflexineae Gupta et al. 2013 Family Roseiflexaceae Gupta et al. 2013 Genus "Kouleothrix" Kohno et al. 2002 Genus Heliothrix Pierson et al...
Green non-sulfur bacteria
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Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping e: G 1 × G 2 → G T {\displaystyle e:G_{1}\times G_{2}\to G_{T}} to construct or analyze cryptographic systems.
Pairing-based cryptography
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The AP Physics 2 classes began in the fall of 2014, with the first AP exams administered in May 2015. The courses were formed through collaboration between current Advanced Placement teachers and The College Board, with the guidance from the National Research Council and the National Science Foundation. As of August 20...
AP Physics 2
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(1972), "The Theorems of Bony and Brezis on Flow-Invariant Sets", The American Mathematical Monthly, 79 (7): 740–747, doi:10.2307/2316263, JSTOR 2316263 Crandall, Michael G. (1972), "A generalization of Peano's existence theorem and flow invariance", Proceedings of the American Mathematical Society, 36 (1): 151–155, do...
Bony–Brezis theorem
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In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathematical formulation. There are multiple possible alternative ways to express ...
Weak energy condition
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Glymour, in collaboration with Peter Spirtes and Richard Scheines, also developed an automated causal inference algorithm implemented as software named TETRAD. Using multivariate statistical data as input, TETRAD rapidly searches from among all possible causal relationship models and returns the most plausible causal m...
Clark Glymour
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Proposed in early 2007, DARPA came to believe that a visual warning system could be produced and developed via an integration of technology and artificial intelligence. By combining discoveries in flat-field, wide-angle optics, large pixel-count digital imagers, ultra-low power analog-digital hybrid signal processing e...
Cognitive Technology Threat Warning System
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A ring is called local if it has only a single maximal ideal, denoted by m. For any (not necessarily local) ring R, the localization at a prime ideal p is local. This localization reflects the geometric properties of Spec R "around p". Several notions and problems in commutative algebra can be reduced to the case when ...
Commutative ring
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By the secant-tangent theorem, the square of this tangent length equals the power of the point P in the circle C. This power equals the product of distances from P to any two intersection points of the circle with a secant line passing through P. The tangent line t and the tangent point T have a conjugate relationship ...
Tangent lines to circles
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Although ultimately every mathematical argument must meet a high standard of precision, mathematicians use descriptive but informal statements to discuss recurring themes or concepts with unwieldy formal statements. Note that many of the terms are completely rigorous in context. almost all A shorthand term for "all exc...
Deep result
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First-order methods for conic optimization avoid computing, storing and factorizing a large Hessian matrix and scale to much larger problems than interior point methods, at some cost in accuracy. A first-order method is implemented in the Splitting Cone Solver (SCS). Another first-order method is the alternating direct...
Semidefinite program
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Glass-backed plates, rather than film, were generally used in astronomy because they do not shrink or deform noticeably in the development process or under environmental changes. Several important applications of astrophotography, including astronomical spectroscopy and astrometry, continued using plates until digital ...
Photographic plate
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