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19,800 | The Hurewicz theorems are a key link between homotopy groups and homology groups. | Hurewicz homomorphism | 0.811312 |
19,801 | Rational Hurewicz theorem: Let X be a simply connected topological space with π i ( X ) ⊗ Q = 0 {\displaystyle \pi _{i}(X)\otimes \mathbb {Q} =0} for i ≤ r {\displaystyle i\leq r} . Then the Hurewicz map h ⊗ Q: π i ( X ) ⊗ Q ⟶ H i ( X ; Q ) {\displaystyle h\otimes \mathbb {Q} \colon \pi _{i}(X)\otimes \mathbb {Q} \long... | Hurewicz homomorphism | 0.811312 |
19,802 | The invariance principle generalizes the Berry–Esseen theorem to non-linear functions. The Berry–Esseen theorem states (among else) that if f = ∑ i = 1 n c i x i {\displaystyle f=\sum _{i=1}^{n}c_{i}x_{i}} and no c i {\displaystyle c_{i}} is too large compared to the rest, then the distribution of f {\displaystyle f} o... | Analysis of Boolean functions | 0.811301 |
19,803 | {\displaystyle \|f\|_{\infty }=\max _{x\in \{-1,1\}^{n}}|f(x)|.} The hypercontractivity theorem states that for any q > 2 {\displaystyle q>2} and q ′ = 1 / ( 1 − 1 / q ) {\displaystyle q'=1/(1-1/q)} , ‖ T ρ f ‖ q ≤ ‖ f ‖ 2 and ‖ T ρ f ‖ 2 ≤ ‖ f ‖ q ′ . {\displaystyle \|T_{\rho }f\|_{q}\leq \|f\|_{2}\quad {\text{and}}\q... | Analysis of Boolean functions | 0.811301 |
19,804 | Friedgut's sharp threshold theorem states, roughly speaking, that a monotone graph property (a graph property is a property which doesn't depend on the names of the vertices) has a sharp threshold unless it is correlated with the appearance of small subgraphs. This theorem has been widely applied to analyze random grap... | Analysis of Boolean functions | 0.811301 |
19,805 | The Russo–Margulis formula (also called the Margulis–Russo formula) states that for monotone Boolean functions f: { 0 , 1 } n → { 0 , 1 } {\displaystyle f\colon \{0,1\}^{n}\to \{0,1\}} , d d p E x ∼ μ p = Inf p ( 1 − p ) = ∑ i = 1 n Pr . {\displaystyle {\frac {d}{dp}}\operatorname {E} _{x\sim \mu _{p}}={\frac {\... | Analysis of Boolean functions | 0.811301 |
19,806 | The first proof of this theorem used the invariance principle in conjunction with an isoperimetric theorem of Borell in Gaussian space; since then more direct proofs were devised.Majority is Stablest implies that the Goemans–Williamson approximation algorithm for MAX-CUT is optimal, assuming the unique games conjecture... | Analysis of Boolean functions | 0.811301 |
19,807 | For example, a dictatorship x i {\displaystyle x_{i}} has noise stability ρ {\displaystyle \rho } . The Majority is Stablest theorem states, informally, then the only functions having noise stability larger than majority have influential coordinates. Formally, for every ε > 0 {\displaystyle \varepsilon >0} there exists... | Analysis of Boolean functions | 0.811301 |
19,808 | If f: { − 1 , 1 } n → { − 1 , 1 } {\displaystyle f\colon \{-1,1\}^{n}\to \{-1,1\}} is an M {\displaystyle M} -junta (a function depending on at most M {\displaystyle M} coordinates) then Inf ≤ M {\displaystyle \operatorname {Inf} \leq M} according to the Poincaré inequality. Friedgut's theorem is a converse to this ... | Analysis of Boolean functions | 0.811301 |
19,809 | Quantitatively, if f: { − 1 , 1 } n → { − 1 , 1 } {\displaystyle f\colon \{-1,1\}^{n}\to \{-1,1\}} and ‖ f > 1 ‖ 2 < ε {\displaystyle \|f^{>1}\|^{2}<\varepsilon } , then f {\displaystyle f} is O ( ε ) {\displaystyle O(\varepsilon )} -close to a dictatorship, that is, ‖ f − g ‖ 2 = O ( ε ) {\displaystyle \|f-g\|^{2}=O(\... | Analysis of Boolean functions | 0.811301 |
19,810 | If f: { − 1 , 1 } n → { − 1 , 1 } {\displaystyle f\colon \{-1,1\}^{n}\to \{-1,1\}} has degree at most 1, then f {\displaystyle f} is either constant, equal to a coordinate, or equal to the negation of a coordinate. In particular, f {\displaystyle f} is a dictatorship: a function depending on at most one coordinate. The... | Analysis of Boolean functions | 0.811301 |
19,811 | Arrow's impossibility theorem states that for three and more candidates, the only unanimous voting rule for which there is always a Condorcet winner is a dictatorship. The usual proof of Arrow's theorem is combinatorial. Kalai gave an alternative proof of this result in the case of three candidates using Fourier analys... | Analysis of Boolean functions | 0.811301 |
19,812 | The bound given by the Kahn–Kalai–Linial theorem is tight, and is achieved by the Tribes function of Ben-Or and Linial: ( x 1 , 1 ∧ ⋯ ∧ x 1 , w ) ∨ ⋯ ∨ ( x 2 w , 1 ∧ ⋯ ∧ x 2 w , w ) . {\displaystyle (x_{1,1}\land \cdots \land x_{1,w})\lor \cdots \lor (x_{2^{w},1}\land \cdots \land x_{2^{w},w}).} The Kahn–Kalai–Linial t... | Analysis of Boolean functions | 0.811301 |
19,813 | The Poincaré inequality for the Boolean cube (which follows from formulas appearing above) states that for a function f: { − 1 , 1 } n → R {\displaystyle f\colon \{-1,1\}^{n}\to \mathbb {R} } , Var ≤ Inf ≤ deg f ⋅ Var . {\displaystyle \operatorname {Var} \leq \operatorname {Inf} \leq \deg f\cdot \operatornam... | Analysis of Boolean functions | 0.811301 |
19,814 | In mathematics and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} or { − 1 , 1 } n {\displaystyle \{-1,1\}^{n}} (such functions are sometimes known as pseudo-Boolean functions) from a spectral perspective. The functions studie... | Analysis of Boolean functions | 0.811301 |
19,815 | The mathematician Jerry P. King describes mathematics as an art, stating that "the keys to mathematics are beauty and elegance and not dullness and technicality", and that beauty is the motivating force for mathematical research. King cites the mathematician G. H. Hardy's 1940 essay A Mathematician's Apology. In it, Ha... | Mathematics and art | 0.811299 |
19,816 | Art has sometimes stimulated the development of mathematics, as when Brunelleschi's theory of perspective in architecture and painting started a cycle of research that led to the work of Brook Taylor and Johann Heinrich Lambert on the mathematical foundations of perspective drawing, and ultimately to the mathematics of... | Mathematics and art | 0.811299 |
19,817 | The astronomer Galileo Galilei in his Il Saggiatore wrote that " is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures." Artists who strive and seek to study nature must first, in Galileo's view, fully understand mathematics. Mathematicians, conversely, have s... | Mathematics and art | 0.811299 |
19,818 | The Platonic solids and other polyhedra are a recurring theme in Western art. They are found, for instance, in a marble mosaic featuring the small stellated dodecahedron, attributed to Paolo Uccello, in the floor of the San Marco Basilica in Venice; in Leonardo da Vinci's diagrams of regular polyhedra drawn as illustra... | Mathematics and art | 0.811299 |
19,819 | Sasho Kalajdzievski's Math and Art: An Introduction to Visual Mathematics takes a similar approach, looking at suitably visual mathematics topics such as tilings, fractals and hyperbolic geometry.Some of the first works of computer art were created by Desmond Paul Henry's "Drawing Machine 1", an analogue machine based ... | Mathematics and art | 0.811299 |
19,820 | Mathematics can be discerned in many of the arts, such as music, dance, painting, architecture, and sculpture. Each of these is richly associated with mathematics. Among the connections to the visual arts, mathematics can provide tools for artists, such as the rules of linear perspective as described by Brook Taylor an... | Mathematics and art | 0.811299 |
19,821 | In solid-state physics crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the associated wave vectors k {\displaystyle \mathbf {k} } of this lattice, according to p crystal ≡ ℏ k {\displaystyle {\mathbf {p} }_{\text{crystal}}\equiv \hbar {\mathbf... | Crystal momentum | 0.811298 |
19,822 | Crystal momentum also plays a seminal role in the semiclassical model of electron dynamics, where it follows from the acceleration theorem that it obeys the equations of motion (in cgs units):: 218 v n ( k ) = 1 ℏ ∇ k E n ( k ) , {\displaystyle {\mathbf {v} }_{n}({\mathbf {k} })={\frac {1}{\hbar }}\nabla _{\mathbf {k} ... | Crystal momentum | 0.811298 |
19,823 | For example, while regular momentum is completely conserved, crystal momentum is only conserved to within a lattice vector. For example, an electron can be described not only by the wave vector k {\displaystyle \mathbf {k} } , but also with any other wave vector k ′ {\displaystyle \mathbf {k'} } such that k ′ = k + K ,... | Crystal momentum | 0.811298 |
19,824 | : 134 These conditions imply Bloch's theorem, which states ψ n ( x ) = e i k ⋅ x u n k ( x ) , u n k ( x + a ) = u n k ( x ) {\displaystyle \psi _{n}({\mathbf {x} })=e^{i{\mathbf {k} {\mathbf {\cdot x} }}}u_{n{\mathbf {k} }}({\mathbf {x} }),\qquad u_{n{\mathbf {k} }}({\mathbf {x} }+{\mathbf {a} })=u_{n{\mathbf {k} }}({... | Crystal momentum | 0.811298 |
19,825 | The maximum modulus principle has many uses in complex analysis, and may be used to prove the following: The fundamental theorem of algebra. Schwarz's lemma, a result which in turn has many generalisations and applications in complex analysis. The Phragmén–Lindelöf principle, an extension to unbounded domains. The Bore... | Maximum modulus principle | 0.811296 |
19,826 | Another proof works by using Gauss's mean value theorem to "force" all points within overlapping open disks to assume the same value as the maximum. The disks are laid such that their centers form a polygonal path from the value where f ( z ) {\displaystyle f(z)} is maximized to any other point in the domain, while bei... | Maximum modulus principle | 0.811296 |
19,827 | Let f {\displaystyle f} be a holomorphic function on some connected open subset D {\displaystyle D} of the complex plane C {\displaystyle \mathbb {C} } and taking complex values. If z 0 {\displaystyle z_{0}} is a point in D {\displaystyle D} such that | f ( z 0 ) | ≥ | f ( z ) | {\displaystyle |f(z_{0})|\geq |f(z)|} fo... | Maximum modulus principle | 0.811296 |
19,828 | Optical character recognition or optical character reader (OCR) is the electronic or mechanical conversion of images of typed, handwritten or printed text into machine-encoded text, whether from a scanned document, a photo of a document, a scene photo (for example the text on signs and billboards in a landscape photo) ... | Character recognition | 0.811295 |
19,829 | Reference ranges for TSH may vary slightly, depending on the method of analysis, and do not necessarily equate to cut-offs for diagnosing thyroid dysfunction. In the UK, guidelines issued by the Association for Clinical Biochemistry suggest a reference range of 0.4–4.0 µIU/mL (or mIU/L). The National Academy of Clinica... | Thyroid-stimulating hormone | 0.811286 |
19,830 | Roberts worked with the Bureau of Standards, "forecasting radio conditions on the basis of solar observations". Such studies of the upper atmosphere were critical for predicting conditions for radio communication, guided missiles, and supersonic aircraft and, as a result, solar observations "became essential to the war... | Sunspot Solar Observatory | 0.811281 |
19,831 | The origins of Sunspot as a Solar Observatory date back to the sudden increased interest of solar physics to the US military during the Second World War. In 1940, the High Altitude Observatory (HAO) was established in 1940 in Climax, Colorado, by Walter Orr Roberts and Donald Menzel. It was associated with both Harvard... | Sunspot Solar Observatory | 0.811281 |
19,832 | The Sunspot Solar Observatory (SSO) is an astronomical observatory designed for the study of the Sun. The observatory is operated by New Mexico State University (NMSU) and the U.S. National Solar Observatory (NSO). It is split between operations at the telescope facility at Sunspot, New Mexico, and data and management ... | Sunspot Solar Observatory | 0.811281 |
19,833 | The Sunspot Astronomy and Visitor Center provides an interactive astronomical experience through activities, displays, and informational exhibits. The Center is operated by New Mexico State University through support from the state of New Mexico and provides guided tours of the site and the telescope for the public on ... | Sunspot Solar Observatory | 0.811281 |
19,834 | The CLEVER (Cross Lipschitz Extreme Value for nEtwork Robustness) score is a way of measuring the robustness of an artificial neural network towards adversarial attacks. It was developed by a team at the MIT-IBM Watson AI Lab in IBM Research and first presented at the 2018 International Conference on Learning Represent... | CLEVER score | 0.81128 |
19,835 | The Green Paradox's line of reasoning starts by recognizing a fundamental, unavoidable fact: every carbon atom in the gas, coal or oil extracted from the ground to be used as fuel ends up in the atmosphere, in particular if high efficiency combustion processes ensure that no part of it ends up as soot. About a quarter ... | Green paradox | 0.811279 |
19,836 | In the basic electroforming process, an electrolytic bath is used to deposit nickel or other electroformable metal onto a conductive surface of a model (mandrel). Once the deposited material has been built up to the desired thickness, the electroform is parted from the substrate. This process allows precise replication... | Electroforming | 0.811278 |
19,837 | In 2012 AlexNet, a deep learning network, outperformed all other programs in classifying images on ImageNet by a substantial margin. In the years since, deep learning has proved to be much more successful in many domains than symbolic AI. | Physical symbol systems hypothesis | 0.811277 |
19,838 | If sub-symbolic AI programs, such as deep learning, can intelligently solve problems, then this is evidence that the necessary side of the PSSH is false. If hybrid approaches that combine symbolic AI with other approaches can efficiently solve a wider range of problems than either technique alone, this is evidence that... | Physical symbol systems hypothesis | 0.811277 |
19,839 | Examples of physical symbol systems include: Formal logic: the symbols are words like "and", "or", "not", "for all x" and so on. The expressions are statements in formal logic which can be true or false. The processes are the rules of logical deduction. Algebra: the symbols are "+", "×", "x", "y", "1", "2", "3", etc. T... | Physical symbol systems hypothesis | 0.811277 |
19,840 | Two lines of evidence suggested to Allen Newell and Herbert A. Simon that "symbol manipulation" was the essence of both human and machine intelligence: psychological experiments on human beings and the development of artificial intelligence programs. | Physical symbol systems hypothesis | 0.811277 |
19,841 | The processes are the rules of algebra, that allow one to manipulate a mathematical expression and retain its truth. Chess: the symbols are the pieces, the processes are the legal chess moves, the expressions are the positions of all the pieces on the board. A computer running a program: the symbols and expressions are... | Physical symbol systems hypothesis | 0.811277 |
19,842 | The PSSH refers to "general intelligent action" -- that is, to every activity that we would consider "intelligent". Thus it is the claim that artificial general intelligence can be achieved using only symbolic methods. It does not refer to "narrow" applications. Artificial intelligence research has succeeded in develop... | Physical symbol systems hypothesis | 0.811277 |
19,843 | In the early decades of AI research there were many very successful programs that used high level symbol processing. These programs were very successful, demonstrating skills that many people at the time had assumed were impossible for machines, such as solving algebra word problems (STUDENT), proving theorems in logic... | Physical symbol systems hypothesis | 0.811277 |
19,844 | Allow hardware vendors and others to improve the performance of artificial neural networks of multiple frameworks at once by targeting the ONNX representation. | Open Neural Network Exchange | 0.811276 |
19,845 | The Open Neural Network Exchange (ONNX) is an open-source artificial intelligence ecosystem of technology companies and research organizations that establish open standards for representing machine learning algorithms and software tools to promote innovation and collaboration in the AI sector. ONNX is available on Git... | Open Neural Network Exchange | 0.811276 |
19,846 | In 1897 an additional section for the book and illustration trade was opened, the school called "KK Graphische Lehr- und Versuchsanstalt" was then divided into four sections: Section I: Institute for Photography and Reproduction (corresponds to the former Institute for Photography and Reproduction Processes) Section II... | Höhere Graphische Bundes-Lehr- und Versuchsanstalt | 0.811272 |
19,847 | The GLV was instituted on August 27, 1887 "by the highest resolution to approve the activation of this teaching and research institute in Vienna on March 1, 1888". The aim of the institute was the “training of specialist photographers, retouchers, collotype printers, photolithographers, etc., the instruction of artists... | Höhere Graphische Bundes-Lehr- und Versuchsanstalt | 0.811272 |
19,848 | Originally set up as a photographic research institute by the President of the Photographic Society, the graphic teaching and research institute (GLV) was created through the incorporation of the photographic school (a department for photographic reproduction processes connected to the Salzburg State Building School) a... | Höhere Graphische Bundes-Lehr- und Versuchsanstalt | 0.811272 |
19,849 | Let Z*(X) := Z be the free abelian group on the algebraic cycles of X. Then an adequate equivalence relation is a family of equivalence relations, ∼X on Z*(X), one for each smooth projective variety X, satisfying the following three conditions: (Linearity) The equivalence relation is compatible with addition of cycles.... | Numerical equivalence | 0.811272 |
19,850 | {\displaystyle \left\{z=(z_{1},\dots ,z_{n});z=a+\left(z^{0}-a\right)e^{i\theta },\ 0\leq \theta <2\pi \right\}.} A Reinhardt domain D is called a complete Reinhardt domain with centre at a point a if together with all point z 0 ∈ D {\displaystyle z^{0}\in D} it also contains the polydisc { z = ( z 1 , … , z n ) ; | z ... | Two complex variables | 0.81127 |
19,851 | In polydisks, the Cauchy's integral formula holds and the power series expansion of holomorphic functions is defined, but polydisks and open unit balls are not biholomorphic mapping because the Riemann mapping theorem does not hold, and also, polydisks was possible to separation of variables, but it doesn't always hold... | Two complex variables | 0.81127 |
19,852 | For one complex variable, every domain( D ⊂ C {\displaystyle D\subset \mathbb {C} } ), is the domain of holomorphy of some function, in other words every domain has a function for which it is the domain of holomorphy. For several complex variables, this is not the case; there exist domains ( D ⊂ C n , n ≥ 2 {\displayst... | Two complex variables | 0.81127 |
19,853 | In probability theory, the points of the standard n-simplex in (n + 1)-space form the space of possible probability distributions on a finite set consisting of n + 1 possible outcomes. The correspondence is as follows: For each distribution described as an ordered (n + 1)-tuple of probabilities whose sum is (necessaril... | Unit simplex | 0.811269 |
19,854 | Limnological Review (ISSN 1642-5952) is an official journal of Polish Limnological Society and publishes original papers that deal with theoretical and applied freshwater research, including such topics as limnology, ecohydrology, chemistry, physics, aquatic biology, aquatic ecology, ecotoxicology, sedimentology, hydro... | Limnological Review | 0.811267 |
19,855 | Society for Laboratory Automation & Screening (SLAS) American Association for Clinical Chemistry (AACC) Laboratory Informatics Institute | Laboratory informatics | 0.811263 |
19,856 | Laboratory informatics is the specialized application of information technology aimed at optimizing and extending laboratory operations. It encompasses data acquisition (e.g. through sensors and hardware or voice), instrument interfacing, laboratory networking, data processing, specialized data management systems (such... | Laboratory informatics | 0.811263 |
19,857 | Among the students was John W. Mauchly. Eckert and Mauchly then teamed in developing the Electronic Numerical Integrator And Computer (ENIAC), America's first large-scale digital computer. Courses in industrial chemistry and metallurgy were in great demand. | Engineering, Science, and Management War Training | 0.811259 |
19,858 | From June 23 to August 29, 1941, electrical engineering student J. Presper Eckert assisted in teaching a 10-week ESMDT course in electronics at the University of Pennsylvania's Moore School of Electrical Engineering. The course had 30 students, 16 of whom held Ph.D. degrees. | Engineering, Science, and Management War Training | 0.811259 |
19,859 | It was somewhat the same in many undergraduate physics and chemistry programs. Although there might be progressively higher-level courses in a subject, each ESMWT course was to be complete in itself and designed to convey some stated, applicable knowledge set. While prerequisites were listed for courses, these were mai... | Engineering, Science, and Management War Training | 0.811259 |
19,860 | The primary objective of the program was to prepare persons for professional positions in defense activities. The authorization required the courses to be of "an academic standard customarily demanded of engineering-school students", distinguishing them from offerings of trade or technical schools. They were limited to... | Engineering, Science, and Management War Training | 0.811259 |
19,861 | As an example, at North Carolina State University the Chancellor often personally awarded certificates to the graduates. The Office of Education requirements were that students of any race would be admitted to ESMDT courses. Unfortunately, African-Americans were not well represented either in the participating institut... | Engineering, Science, and Management War Training | 0.811259 |
19,862 | During the remainder of the Fiscal Year ending June 30, 1941, about 120,800 individuals enrolled in 2,260 courses offered by 144 institutions. In July 1941, the Labor-Federal Security Appropriations Act, authorized the addition of chemistry, physics, and production-related courses to form an integrated ESMDT program. F... | Engineering, Science, and Management War Training | 0.811259 |
19,863 | VIB has established several core facilities focused on advanced technologies, which make high through-flow technologies available to academic and industrial researchers in Flanders. VIB BioInformatics Training and Service facility VIB Compound Screening service Facility, UGent VIB Genetic Service Facility, University o... | Vlaams Instituut voor Biotechnologie | 0.811257 |
19,864 | The VIB scientist works on the normal and abnormal or pathological processes occurring in a cell, an organ and an organism (humans, plants, micro organisms). Instead of relocating scientists to a new campus, the VIB researchers work in research departments on six Flemish campuses: Ghent University, KU Leuven, Universit... | Vlaams Instituut voor Biotechnologie | 0.811257 |
19,865 | The relatively low cost of the electrathon racing has made the sport a popular activity for high school age students worldwide who learn skills related to design, problem-solving, teamwork, mathematics, physics, and electricity. Prizes are awarded for high school, college and open divisions, and there are separate clas... | Electrathon | 0.811255 |
19,866 | Other battery chemistries are allowed but the weights are restricted accordingly to maintain the 1kwh capacity limit. This type of lightweight car appeared in Australia in the late 1970s and was warmly embraced and introduced into American culture as early as 1980.The current official record is 62.05 miles (99.86 km) a... | Electrathon | 0.811255 |
19,867 | A nontrivial representation of 0 as a sum of three cubes would give a counterexample to Fermat's Last Theorem for the exponent three, as one of the three cubes would have the opposite sign as the other two and its negation would equal the sum of the other two. Therefore, by Leonhard Euler's proof of that case of Fermat... | Sum of three cubes | 0.811254 |
19,868 | In 1992, Roger Heath-Brown conjectured that every n {\displaystyle n} unequal to 4 or 5 modulo 9 has infinitely many representations as sums of three cubes. The case n = 33 {\displaystyle n=33} of this problem was used by Bjorn Poonen as the opening example in a survey on undecidable problems in number theory, of which... | Sum of three cubes | 0.811254 |
19,869 | Supermetric is a mathematical concept used in a number of fields in physics. | Supermetric | 0.811252 |
19,870 | Kernel function depends on geometry of the body. In above equation K(r,r′) is the kernel function for the integral, which for 3-D problems takes the following form where F assumes a value of one when the surface element I sees the surface element J, otherwise it is zero if the ray is blocked and θr is the angle at poin... | Kernel function for solving integral equation of surface radiation exchanges | 0.811251 |
19,871 | Kernel functions provide a way to manipulate data as though it were projected into a higher dimensional space, by operating on it in its original space. So that data in higher-dimensional space become more easily separable. Kernel function is also used in integral equation for surface radiation exchanges. Kernel functi... | Kernel function for solving integral equation of surface radiation exchanges | 0.811251 |
19,872 | In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The rel... | Kernel function for solving integral equation of surface radiation exchanges | 0.811251 |
19,873 | Organic synthesis is a special type of chemical synthesis dealing with the synthesis of organic compounds. For the total synthesis of a complex product, multiple procedures in sequence may be required to synthesize the product of interest, requiring a large amount of time. Skill in organic synthesis is prized among che... | Chemical Synthesis | 0.811251 |
19,874 | In chemistry, chemical synthesis (chemical combination) is the artificial execution of chemical reactions to obtain one or several products. This occurs by physical and chemical manipulations usually involving one or more reactions. In modern laboratory uses, the process is reproducible and reliable. | Chemical Synthesis | 0.811251 |
19,875 | The four-acceleration of a particle executing geodesic motion is zero. This corresponds to gravity not being a force. Four-acceleration is different from what we understand by acceleration as defined in Newtonian physics, where gravity is treated as a force. | Four-acceleration | 0.811249 |
19,876 | In non-inertial coordinates, which include accelerated coordinates in special relativity and all coordinates in general relativity, the acceleration four-vector is related to the four-velocity through an absolute derivative with respect to proper time. In inertial coordinates the Christoffel symbols Γ λ μ ν {\displayst... | Four-acceleration | 0.811249 |
19,877 | Especially infrared (IR) spectroscopy, which is used to investigate molecular vibration, benefits from the matrix isolation technique. For example, in the gas-phase IR spectrum of fluoroethane some spectral regions are very difficult to interpret, as vibrational quantum states heavily overlap with multiple rotational-v... | Inert gas matrix | 0.811243 |
19,878 | Matrix isolation is an experimental technique used in chemistry and physics. It generally involves a material being trapped within an unreactive matrix. A host matrix is a continuous solid phase in which guest particles (atoms, molecules, ions, etc.) are embedded. The guest is said to be isolated within the host matrix... | Inert gas matrix | 0.811243 |
19,879 | Radical materials advances can drive the creation of new products or even new industries, but stable industries also employ materials scientists to make incremental improvements and troubleshoot issues with currently used materials. Industrial applications of materials science include materials design, cost-benefit tra... | Materials Engineering | 0.811242 |
19,880 | Nanomaterials describe, in principle, materials of which a single unit is sized (in at least one dimension) between 1 and 1000 nanometers (10−9 meter), but is usually 1 nm – 100 nm. Nanomaterials research takes a materials science based approach to nanotechnology, using advances in materials metrology and synthesis, wh... | Materials Engineering | 0.811242 |
19,881 | The DB-Engines Ranking ranks database management systems by popularity, covering over 380 systems. The ranking criteria include number of search engine results when searching for the system names, Google Trends, Stack Overflow discussions, job offers with mentions of the systems, number of profiles in professional netw... | DB-Engines ranking | 0.811242 |
19,882 | At the same time, distant objects appear larger than they really are because the photons observed were emitted at a time when the object was closer. Adding these effects together, the surface brightness in a simple expanding universe (flat geometry and uniform expansion over the range of redshifts observed) should decr... | Tolman surface brightness test | 0.811236 |
19,883 | In molecular biology, a cap-independent translation element (CITE or 3'CITE) is an RNA sequence found in the 3'UTR of many RNA plant viruses. Eukaryotic mRNAs contain a 5' cap structure which is required for efficient binding of translation initiation factors. Many viral mRNAs lack the 5' cap, animal virus mRNAs often ... | Cap-independent translation element | 0.811236 |
19,884 | One area of research in which attenuation plays a prominent role, is in ultrasound physics. Attenuation in ultrasound is the reduction in amplitude of the ultrasound beam as a function of distance through the imaging medium. Accounting for attenuation effects in ultrasound is important because a reduced signal amplitud... | Attenuation (electromagnetic radiation) | 0.811236 |
19,885 | The lone pairs on transition metal atoms are usually stereochemically inactive, meaning that their presence does not change the molecular geometry. For example, the hexaaquo complexes M(H2O)6 are all octahedral for M = V3+, Mn3+, Co3+, Ni2+ and Zn2+, despite the fact that the electronic configurations of the central me... | Molecule shape | 0.811235 |
19,886 | Some transition metal complexes with low d electron count have unusual geometries, which can be ascribed to d subshell bonding interaction. Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere. This phenomenon is an electronic effec... | Molecule shape | 0.811235 |
19,887 | There are groups of compounds where VSEPR fails to predict the correct geometry. | Molecule shape | 0.811235 |
19,888 | Lone pair–lone pair (lp–lp) repulsions are considered stronger than lone pair–bonding pair (lp–bp) repulsions, which in turn are considered stronger than bonding pair–bonding pair (bp–bp) repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible. : 41... | Molecule shape | 0.811235 |
19,889 | The overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. The bonding electron pair shared in a sigma bond with an adjacent atom lies further from the central atom than a nonbonding (lone) pair of that atom, which is held close to its positively charged nucleus. VSEPR theo... | Molecule shape | 0.811235 |
19,890 | Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n 1 {\displaystyle n_{1}} and another med... | Optics | 0.811231 |
19,891 | Additionally, computer engineers have taken an interest in integrated optics, machine vision, and photonic computing as possible components of the "next generation" of computers.Today, the pure science of optics is called optical science or optical physics to distinguish it from applied optical sciences, which are refe... | Optics | 0.811231 |
19,892 | Light-emitting diodes and photovoltaic cells, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics.Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics and metamateri... | Optics | 0.811231 |
19,893 | Light detectors, such as photomultipliers and channeltrons, respond to individual photons. Electronic image sensors, such as CCDs, exhibit shot noise corresponding to the statistics of individual photon events. | Optics | 0.811231 |
19,894 | Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics, quantum optics, deals with specifically qu... | Optics | 0.811231 |
19,895 | Perhaps one of the more innovative solutions is millipede memory, developed by IBM. Millipede is, in essence, a punched card rendered using nanotechnology in order to dramatically increase areal density. Although it was planned to introduce Millipede as early as 2003, unexpected problems in development delayed this unt... | Non-volatile random-access memory | 0.81123 |
19,896 | SimTK – a collection of biological modelling resources made available by The National NIH Center for Biomedical Computing. E-Cell System – a simulation and modelling environment for biological systems offered by Keio University in Tokyo, Japan.Tools such as these are developed using markup languages specific to bioinfo... | Physiomics | 0.81123 |
19,897 | Collaborative physiomics research is promoted in part by the open availability of bioinformatics software such as simulation programs and modelling environments. There are many institutions and research groups that make their software available to the public. Examples of openly available software include: JSim and Syst... | Physiomics | 0.81123 |
19,898 | Physiomics is a systematic study of physiome in biology. Physiomics employs bioinformatics to construct networks of physiological features that are associated with genes, proteins and their networks. A few of the methods for determining individual relationships between the DNA sequence and physiological function includ... | Physiomics | 0.81123 |
19,899 | Physiomics arose from the imbalance between the amount of data being generated by genome projects and the technological ability to analyze the data on a large scale. As technologies such as high-throughput sequencing were being used to generate large amounts of genomic data, effective methods needed to be designed to e... | Physiomics | 0.81123 |
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