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82,200 | Safe primes are also important in cryptography because of their use in discrete logarithm-based techniques like Diffie–Hellman key exchange. If 2p + 1 is a safe prime, the multiplicative group of integers modulo 2p + 1 has a subgroup of large prime order. It is usually this prime-order subgroup that is desirable, and t... | Safe prime | 0.784266 |
82,201 | {\displaystyle \displaystyle {\pi _{ij}(xy)=\pi _{ij}(x)\pi _{ij}(y),\,\,\,\pi _{ij}(1)=I.}} Since every x in O has a right inverse y with xy = 1, the map πij is injective. On the other hand, it is an algebra homomorphism from the nonassociative algebra O into the associative algebra End Vi, a contradiction. | Symmetric cone | 0.784266 |
82,202 | The same is therefore true of any special algebra. On the other hand, as Albert (1934) showed, the Albert algebra H3(O) cannot be realized as a subalgebra of Hn(R) for any n.Indeed, let π is a real-linear map of E = H3(O) into the self-adjoint operators on V = Rn with π(ab) = 1/2(π(a)π(b) + π(b)π(a)) and π(1) = I. If e... | Symmetric cone | 0.784266 |
82,203 | If 1 - e1 is a primitive idempotent, the subalgebra must be proper, by the properties of the rank in E. A Euclidean algebra is said to be special if its central decomposition contains no copies of the Albert algebra. Since the Albert algebra cannot be generated by two elements, it follows that a Euclidean Jordan algebr... | Symmetric cone | 0.784266 |
82,204 | {\displaystyle \displaystyle {Y_{1}={\begin{pmatrix}0&0&0\\0&0&y_{1}\\0&y_{1}^{*}&0\end{pmatrix}},\,\,\,Y_{2}={\begin{pmatrix}0&0&y_{2}^{*}\\0&0&0\\y_{2}&0&0\end{pmatrix}},\,\,\,Y_{3}={\begin{pmatrix}0&y_{3}&0\\y_{3}^{*}&0&0\\0&0&0\end{pmatrix}}.}} It is straightforward to verify that the real linear span of the diagon... | Symmetric cone | 0.784266 |
82,205 | For in that case g and its inverse preserve D so must be surjective. If u = eix with x = Σ ξiei in E, then gu lies in ⊕ C ei. This is a commutative associative algebra and the spectral norm is the supremum norm. | Symmetric cone | 0.784266 |
82,206 | In fact in this case the relations for a quadratic Jordan algebra imply R ( a , b ) = 2 Q ( a ) Q ( a − 1 , b ) = 2 Q ( a , b − 1 ) Q ( b ) {\displaystyle \displaystyle {R(a,b)=2Q(a)Q(a^{-1},b)=2Q(a,b^{-1})Q(b)}} so that B ( a , b ) = Q ( a ) Q ( a − 1 − b ) = Q ( b − 1 − a ) Q ( b ) . {\displaystyle \displaystyle {B(a... | Symmetric cone | 0.784266 |
82,207 | {\displaystyle \displaystyle {\mathrm {Im} \,C(U)=(2i)^{-1}=(1-U^{*})^{-1}(I-U)^{-1}.}} Since the Cayley transform and its inverse commute with the transpose, they also establish a bijection for symmetric matrices. This corresponds to the Jordan algebra of symmetric complex matrices, the complexification of Hn(R). | Symmetric cone | 0.784266 |
82,208 | For matrices this follows because unitary and self-adjoint matrices can be diagonalized and their eigenvalues lie on the unit circle or real line. In this finite-dimensional setting the Cayley transform and its inverse establish a bijection between the matrices of operator norm less than one and operators with imaginar... | Symmetric cone | 0.784266 |
82,209 | Let E be a simple Euclidean Jordan algebra with inner product given by the trace form τ(a)= Tr L(a). The proof that E has the above form rests on constructing an analogue of matrix units for a Jordan frame in E. The following properties of idempotents hold in E. An idempotent e is minimal in E if and only if E1(e) has ... | Symmetric cone | 0.784266 |
82,210 | In their classic paper, Jordan, von Neumann & Wigner (1934) studied and completely classified a class of finite-dimensional Jordan algebras, that are now called either Euclidean Jordan algebras or formally real Jordan algebras. | Symmetric cone | 0.784266 |
82,211 | By the spectral theorem for self-adjoint operators, T = ∑ λ i P i {\displaystyle \displaystyle {T=\sum \lambda _{i}P_{i}}} where the Pi are orthogonal projections on E0 with sum I and the λi's are the distinct real eigenvalues of T. Since the Pi's commute with T and are self-adjoint, they are given by multiplication el... | Symmetric cone | 0.784266 |
82,212 | The spectral theorem states that any element a can be uniquely written as a = ∑ λ i e i , {\displaystyle \displaystyle {a=\sum \lambda _{i}e_{i},}} where the idempotents ei's are a partition of 1 and the λi, the eigenvalues of a, are real and distinct. In fact let E0 = R and let T be the restriction of L(a) to E0. T is... | Symmetric cone | 0.784266 |
82,213 | The analysis in Springer & Veldkamp (2000) then shows that the unital Jordan subalgebra generated by X and Y is proper. Indeed, if 1 − e1 is the sum of two primitive idempotents in the subalgebra, then, after applying an automorphism of E if necessary, the subalgebra will be generated by the diagonal matrices and a mat... | Symmetric cone | 0.784266 |
82,214 | The exceptional Euclidean Jordan algebra E= H3(O) is called the Albert algebra. The Cohn–Shirshov theorem implies that it cannot be generated by two elements (and the identity). This can be seen directly. For by Freudenthal's diagonalization theorem one element X can be taken to be a diagonal matrix with real entries a... | Symmetric cone | 0.784266 |
82,215 | Let E be a Euclidean Jordan algebra. The complexification EC = E ⊕ iE has a natural conjugation operation (a + ib)* = a − ib and a natural complex inner product and norm. The Jordan product on E extends bilinearly to EC, so that (a + ib)(c + id) = (ac − bd) + i(ad + bc). If multiplication is defined by L(a)b = ab then ... | Symmetric cone | 0.784266 |
82,216 | For each operator ideal J {\displaystyle {\mathcal {J}}} , every component of the form J ( X ) := J ( X , X ) {\displaystyle {\mathcal {J}}(X):={\mathcal {J}}(X,X)} forms an ideal in the algebraic sense.Furthermore, some very well-known classes are norm-closed operator ideals, i.e., operator ideals whose components are... | Operator ideal | 0.784266 |
82,217 | They are, for example, based on mixtures of alumina powder with the liquids tetra-ethyl-orthosilicate (as Si donor) and aluminium-butylate (as Al donor), which yield a mullite matrix. Other techniques, such as sol–gel process chemistry, are also used. CMCs obtained with this process usually have a high porosity of abou... | Ceramic Matrix Composite | 0.784266 |
82,218 | In materials science, ceramic matrix composites (CMCs) are a subgroup of composite materials and a subgroup of ceramics. They consist of ceramic fibers embedded in a ceramic matrix. The fibers and the matrix both can consist of any ceramic material, whereby carbon and carbon fibers can also be regarded as a ceramic mat... | Ceramic Matrix Composite | 0.784266 |
82,219 | The United States Air Force and Navy were both seeking new aircraft when Robert McNamara was appointed U.S. Secretary of Defense in January 1961. The aircraft sought by the two armed services shared the need to carry heavy armament and fuel loads, feature high supersonic speed, twin engines and two seats, and probably ... | TFX Program | 0.784266 |
82,220 | A virtual camera can be then be positioned relative to the 3D roadway surface. Physical evidence is then mapped from the photos onto the 3D roadway to create a three dimensional accident scene drawing. Photogrammetry: Photogrammetry is used to determine the three-dimensional geometry of an object on the accident scene ... | Accident analysis | 0.784265 |
82,221 | Near the end of the scheduled run time, data suggested tantalizing but inconclusive hints that the Higgs particle of a mass around 115 GeV might have been observed, a sort of Holy Grail of current high-energy physics. The run-time was extended for a few months, to no avail. The strength of the signal remained at 1.7 st... | Large Electron–Positron Collider | 0.784265 |
82,222 | The shape of the collider is also important. High energy physics colliders collect particles into bunches, and then collide the bunches together. However, only a very tiny fraction of particles in each bunch actually collide. | Large Electron–Positron Collider | 0.784265 |
82,223 | OPAL stands for Omni-Purpose Apparatus for LEP. The name of the experiment was a play on words, as some of the founding members of the scientific collaboration which first proposed the design had previously worked on the JADE detector at DESY in Hamburg. OPAL was a general-purpose detector designed to collect a broad r... | Large Electron–Positron Collider | 0.784265 |
82,224 | (2019). "Axial-anomaly in noncommutative QED and Pauli–Villars regularization". International Journal of Modern Physics A. | Adler–Bell–Jackiw anomaly | 0.784264 |
82,225 | (2004). "Trace anomalies and chiral Ward identities". Chinese Physics Letters. | Adler–Bell–Jackiw anomaly | 0.784264 |
82,226 | "Chiral Anomalies via Classical and Quantum Functional Methods". International Journal of Modern Physics A. 20 (20–21): 5009. arXiv:hep-th/0410129. | Adler–Bell–Jackiw anomaly | 0.784264 |
82,227 | It is possible that other imbalances have been caused by breaking of a chiral law of this kind. Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly. Research into chiral symmetry breaking laws is a major endeavor in particle physics resea... | Adler–Bell–Jackiw anomaly | 0.784264 |
82,228 | In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa. Such events are expected to be prohibited... | Adler–Bell–Jackiw anomaly | 0.784264 |
82,229 | Isopsephy (; ἴσος isos meaning "equal" and ψῆφος psephos meaning "pebble") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number. The total number is then used as a metaphorical bridge to other words evaluating the equal number, which satisfies isos or "equal" in... | Isopsephy | 0.784264 |
82,230 | Nicon of Pergamon, the Greek architect and builder described by his son, the famous physician Galen, as having "mastered all there was to know of the science of geometry and numbers", was a master in composing isopsephic works. | Isopsephy | 0.784264 |
82,231 | In another of his distichs, the hexameter line is equal in number to its corresponding pentameter: Εἱς προς ἑνα ψηφοισιν ισαζεται, ου δυο δοιοις, Ου γαρ ετι στεργω την δολιχογραφιην.Which translates to: "One line is made equal in number to one, not two to two; for I no longer approve of long epigrams." Here each line t... | Isopsephy | 0.784264 |
82,232 | In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the radioactive decay of atoms or the decay of elementary particles. It... | Branching rate | 0.784263 |
82,233 | The decomposition process described (below) can be carried through on the product of two pure Lorentz transformations to obtain explicitly the rotation of the coordinate axes resulting from the two successive "boosts". In general, the algebra involved is quite forbidding, more than enough, usually, to discourage any ac... | Wigner rotation | 0.784261 |
82,234 | {\displaystyle E(\gamma _{1},\gamma _{2})=E(F\circ \gamma _{1},F\circ \gamma _{2}).} This condition is called the conformal invariance property of the Möbius cross energy. Main Theorem. | Möbius energy | 0.784261 |
82,235 | Proof of Theorem A. Let T {\displaystyle T} be a Möbius transformation sending a point of γ {\displaystyle \gamma } to infinity. The energy E ( T ( γ ) ) ≥ 0 {\displaystyle E(T(\gamma ))\geq 0} with equality holding if and only if T ( γ ) {\displaystyle T(\gamma )} is a straight line. Apply the Möbius invariance proper... | Möbius energy | 0.784261 |
82,236 | Let γ {\displaystyle \gamma } be a closed curve in R 3 {\displaystyle \mathbb {R} ^{3}} and T {\displaystyle T} a Möbius transformation of S 3 = R 3 ∪ ∞ {\displaystyle S^{3}=\mathbb {R} ^{3}\cup \infty } . If T ( γ ) {\displaystyle T(\gamma )} is contained in R 3 {\displaystyle \mathbb {R} ^{3}} then E ( T ( γ ) ) = E ... | Möbius energy | 0.784261 |
82,237 | Environmental lawyers and policymakers work to define legislation with the intention that water is maintained at an appropriate quality for its identified use. Another general perception of water quality is that of a simple property that tells whether water is polluted or not. In fact, water quality is a complex subjec... | Drinking water pollution | 0.784261 |
82,238 | In molecular biology, the haemagglutination activity domain is a conserved protein domain found near the N terminus of a number of large, repetitive bacterial proteins, including many proteins of over 2500 amino acids. A number of the members of this family have been designated adhesins, filamentous haemagglutinins, ha... | Haemagglutination activity domain | 0.784258 |
82,239 | These certificates can then be sold and transferred to liable entities (usually electricity retailers) to meet their obligations under this tradeable certificates scheme. However, as this legislation is technology neutral in its operation, it tends to favour more established RE technologies with a lower levelised cost ... | Solar Turbine Plants | 0.784255 |
82,240 | Another promising application for CSP in Australia are mines that need 24/7 electricity but often have no grid connection. Vast Solar a startup company aiming to commercialize a novel modular third generation CSP design is looking to start construction of a 50MW combines CSP and PV facility in Mt. Isa of North-West Que... | Solar Turbine Plants | 0.784255 |
82,241 | Of late China has been aggressive in developing CSP technology to compete with other electricity generation methods based on renewable and non-renewable energy sources. In the current 14th Five-Year Plan CSP projects are developed in several provinces alongside large GW sized solar PV and wind projects.In 2016 China an... | Solar Turbine Plants | 0.784255 |
82,242 | MET technology had its origins in the 1950s, when it was discovered that very sensitive, low-power, low-noise detectors and control devices could be made based on specially designed electrochemical cells (which were referred to as “solions”, derived from the words solution and ions). Up through the 1970s, the US Navy a... | Molecular electronic transducers | 0.784254 |
82,243 | Large rivers have comparatively more species than small streams. Many relate this pattern to the greater area and volume of larger systems, as well as an increase in habitat diversity. Some systems, however, show a poor fit between system size and species richness. In these cases, a combination of factors such as histo... | Lotic ecosystems | 0.784253 |
82,244 | Prestacks may be studied on their own or passed to stacks. Since a stack is a prestack, all the results on prestacks are valid for stacks as well. Throughout the article, we work with a fixed base category C; for example, C can be the category of all schemes over some fixed scheme equipped with some Grothendieck topolo... | Prestack | 0.784252 |
82,245 | In algebraic geometry, a prestack F over a category C equipped with some Grothendieck topology is a category together with a functor p: F → C satisfying a certain lifting condition and such that (when the fibers are groupoids) locally isomorphic objects are isomorphic. A stack is a prestack with effective descents, mea... | Prestack | 0.784252 |
82,246 | Given prestacks p: F → C , q: G → C {\displaystyle p:F\to C,q:G\to C} over the fixed base category C, a morphism f: F → G {\displaystyle f:F\to G} is a functor such that (1) q ∘ f = p {\displaystyle q\circ f=p} and (2) it maps cartesian morphisms to cartesian morphisms. Note (2) is automatic if G is fibered in groupoid... | Prestack | 0.784252 |
82,247 | On the morphism-level, while X has only identity morphisms as morphisms, the prestack p r e {\displaystyle ^{pre}} have additional morphisms δ {\displaystyle \delta } specified by the equivalence pre-relation f. One importance of this construction is that it provides an atlas for an algebraic space: every algebraic sp... | Prestack | 0.784252 |
82,248 | Let X be a scheme in the base category C. By definition, an equivalence pre-relation is a morphism R → X × X {\displaystyle R\to X\times X} in C such that, for each scheme T in C, the function f ( T ): R ( T ) = Hom ( T , R ) → X ( T ) × X ( T ) {\displaystyle f(T):R(T)=\operatorname {Hom} (T,R)\to X(T)\times X(T)} h... | Prestack | 0.784252 |
82,249 | Let G be an algebraic group acting from the right on a scheme X of finite type over a field k. Then the group action of G on X determines a prestack (but not a stack) over the category C of k-schemes, as follows. Let F be the category where an object is a pair ( U , x ) {\displaystyle (U,x)} consisting of a scheme U in... | Prestack | 0.784252 |
82,250 | In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. In detail, if p {\displaystyle p} is a prime num... | Chowla–Mordell theorem | 0.784252 |
82,251 | In molecular biology, the trappin protein transglutaminase binding domain or cementoin is a protein domain found at the N-terminus of Whey Acidic Protein (WAP) domain-containing protease inhibitors such as trappin-2. This N-terminal domain enables it to become cross-linked to extracellular matrix proteins by transgluta... | Trappin protein transglutaminase binding domain | 0.784249 |
82,252 | In number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture, hence the name. The conjecture states that the equation has only finitely many solutions (a,b,c,m,n,k) with distinct triplets of values (am, bn, ck) where a, b, c are positive coprime integers and m... | Fermat–Catalan conjecture | 0.784248 |
82,253 | Suppose i: X → Y {\displaystyle i:X\to Y} is an embedding. This can be deformed to the embedding of X {\displaystyle X} inside the normal cone C X / Y {\displaystyle C_{X/Y}} (as the zero section) in the following sense:: 6 there is a flat family with generic fiber Y {\displaystyle Y} and special fiber C X / Y {\displa... | Deformation to normal cone | 0.784246 |
82,254 | Underfunding is particularly acute in the least developed countries, which are not attractive to the private sector.The United Nations Framework Convention on Climate Change estimates that climate financing totalled $681 billion in 2016. Most of this is private-sector investment in renewable energy deployment, public-s... | Green energy | 0.784246 |
82,255 | Traditionally, most district heating systems have used fossil fuels, but modern and cold district heating systems are designed to use high shares of renewable energy.Cooling of buildings can be made more efficient through passive building design, planning that minimises the urban heat island effect, and district coolin... | Green energy | 0.784246 |
82,256 | Standard monolayer cell culturing on tissue culture plastic has notably improved our understanding of basic cell biology, but it does not replicate the complex 3D architecture of in vivo tissue, and it can significantly modify cell properties. This often compromises experiments in basic life science, leads to misleadin... | 3D Cell Culturing by Magnetic Levitation | 0.784246 |
82,257 | Shown in the picture above is an invasion assay of magnetically levitated multicellular spheroids. Fluorescence images of human glioblastoma (GBM) cells (green; GFP-expressing cells) and normal human astrocytes (NHA) (red; mCherry-labelled) cultured separately and then magnetically guided together (left, time 0). Invas... | 3D Cell Culturing by Magnetic Levitation | 0.784246 |
82,258 | The standard test used to detect this gene in tumor samples is fluorescence in situ hybridization (FISH) by a US FDA approved kit. Recently Roche Ventana obtained approval in China and European Union countries to test this mutation by immunohistochemistry. Other techniques like reverse-transcriptase PCR (RT-PCR) can al... | Anaplastic lymphoma kinase | 0.784245 |
82,259 | Modern science treats lamprophyres as a catch-all term for ultrapotassic mafic igneous rocks which have primary mineralogy consisting of amphibole or biotite, and with feldspar in the groundmass. Lamprophyres are not amenable to classification according to modal proportions, such as the system QAPF due to peculiar mine... | Lamprophyre | 0.784243 |
82,260 | Either scheme may apply to some, but not all, occurrences and variations of the broader group of rocks known as lamprophyres and melilitic rocks. Leaving aside complex petrogenetic arguments, it is fair to say that the essential components in lamprophyre genesis are; high depth of melting, which yields more mafic magma... | Lamprophyre | 0.784243 |
82,261 | Penn received a B.S. in mathematics from the University of Chicago and Ph.D. in computer science from Carnegie Mellon University. His Ph.D. thesis was nominated by Carnegie Mellon School of Computer Science for the ACM Doctoral Dissertation Award. | Gerald Penn (computer scientist) | 0.784242 |
82,262 | Penn is a past recipient of the Ontario Early Researcher Award. His joint work with Geoffrey Hinton and Hui Jiang on signal processing with neural networks revolutionized acoustic modelling for speech recognition systems, and received the Best Paper Award from IEEE Signal Processing Society. He has led numerous researc... | Gerald Penn (computer scientist) | 0.784242 |
82,263 | Gerald Penn is an American computer scientist specializing in mathematical linguistics and speech processing. He is a Professor of Computer Science at the University of Toronto, a senior member of IEEE and AAAI, and a past chair of Association for Mathematics of Language. | Gerald Penn (computer scientist) | 0.784242 |
82,264 | In software engineering, the composite pattern is a partitioning design pattern. The composite pattern describes a group of objects that are treated the same way as a single instance of the same type of object. The intent of a composite is to "compose" objects into tree structures to represent part-whole hierarchies. I... | Composite pattern | 0.784241 |
82,265 | Sir John Frederick William Herschel, 1st Baronet (; 7 March 1792 – 11 May 1871) was an English polymath active as a mathematician, astronomer, chemist, inventor, experimental photographer who invented the blueprint and did botanical work.Herschel originated the use of the Julian day system in astronomy. He named seven ... | John Herschel | 0.784239 |
82,266 | Herschel wrote many papers and articles, including entries on meteorology, physical geography and the telescope for the eighth edition of the Encyclopædia Britannica. He also translated the Iliad of Homer. In 1823, Herschel published his findings on the optical spectra of metal salts.Herschel invented the actinometer i... | John Herschel | 0.784239 |
82,267 | He left Cambridge in 1816 and started working with his father. He took up astronomy in 1816, building a reflecting telescope with a mirror 18 inches (460 mm) in diameter, and with a 20-foot (6.1 m) focal length. Between 1821 and 1823 he re-examined, with James South, the double stars catalogued by his father. | John Herschel | 0.784239 |
82,268 | Intrigued by the ideas of gradual formation of landscapes set out in Charles Lyell's Principles of Geology, he wrote to Lyell on 20 February 1836 praising the book as a work that would bring "a complete revolution in subject, by altering entirely the point of view in which it must thenceforward be contemplated" and op... | John Herschel | 0.784239 |
82,269 | Most uses of microtasking services involve processing data, especially online. These include driving traffic to websites, gathering data like email addresses, and labelling or tagging data online. They are also used to accurately translate or transcribe audio clips and pictures, since these are activities that are bett... | Microwork | 0.784239 |
82,270 | These are mecha that have the ability to be self-aware, think, and sometimes feel emotion. The source of sentience varies from aliens, such as the titular characters of American-produced and Japanese-animated series, The Transformers (1984), to artificial intelligence or synthetic intelligence, such as the robots of Dr... | Super Robot | 0.784237 |
82,271 | Mecha anime and manga, known in Japan as robot anime (ロボットアニメ, robotto anime) and robot manga (ロボット漫画, robotto manga), are anime and manga that feature robots (mecha) in battle. The genre is broken down into two subcategories; "super robot", featuring super-sized, implausible robots, and "real robot", where robots are ... | Super Robot | 0.784237 |
82,272 | For solid materials, Raman scattering is used as a tool to detect high-frequency phonon and magnon excitations. Raman lidar is used in atmospheric physics to measure the atmospheric extinction coefficient and the water vapour vertical distribution. Stimulated Raman transitions are also widely used for manipulating a tr... | Raman Effect | 0.784237 |
82,273 | The Long Michelson Interferometer was a radio telescope interferometer built by Martin Ryle and co-workers in the late 1940s beside a rifle range to the west of Cambridge, England. The interferometer consisted of 2 fixed elements 440m apart to survey the sky using Earth rotation. It produced the Preliminary survey of t... | Long Michelson Interferometer | 0.784236 |
82,274 | {\displaystyle |A(t,y_{1},h,f)-A(t,y_{2},h,f)|\leq L|y_{1}-y_{2}|.} Then the global error satisfies the bound | e n | ≤ max j τ j h L ( e L ( t n − t 0 ) − 1 ) . {\displaystyle |e_{n}|\leq {\frac {\max _{j}\tau _{j}}{hL}}\left(\mathrm {e} ^{L(t_{n}-t_{0})}-1\right).} It follows from the above bound for the global error... | Truncation error (numerical integration) | 0.784236 |
82,275 | Process manufacturing is a branch of manufacturing that is associated with formulas and manufacturing recipes, and can be contrasted with discrete manufacturing, which is concerned with discrete units, bills of materials and the assembly of components. Process manufacturing is also referred to as a 'process industry' w... | Process Manufacturing | 0.784236 |
82,276 | In probability theory and statistics, the beta rectangular distribution is a probability distribution that is a finite mixture distribution of the beta distribution and the continuous uniform distribution. The support is of the distribution is indicated by the parameters a and b, which are the minimum and maximum value... | Beta rectangular distribution | 0.784235 |
82,277 | Preservation of photographic plates is a particular need in astronomy, where changes often occur slowly and the plates represent irreplaceable records of the sky and astronomical objects that extend back over 100 years. The method of digitization of astronomical plates enables free and easy access to those unique astro... | Photographic plate | 0.784235 |
82,278 | Photographic plates were also an important tool in early high-energy physics, as they are blackened by ionizing radiation. Ernest Rutherford was one of the first to study the absorption, in various materials, of the rays produced in radioactive decay, by using photographic plates to measure the intensity of the rays. D... | Photographic plate | 0.784235 |
82,279 | 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 | 0.784235 |
82,280 | In particular, the convolutional neural network lends itself to eye-tracking, as it is designed for image-centric tasks. With AI, eye-tracking tasks and studies can yield additional information that may not have been detected by human observers. The practice of deep learning also allows for a given neural network to im... | Commercial eye tracking | 0.784235 |
82,281 | Thanks to advancement in portable electronic devices, portable head-mounted eye trackers currently can achieve excellent performance and are being increasingly used in research and market applications targeting daily life settings. These same advances have led to increases in the study of small eye movements that occur... | Commercial eye tracking | 0.784235 |
82,282 | In a 2019 study, a Convolutional Neural Network (CNN) was constructed with the ability to identify individual chess pieces the same way other CNNs can identify facial features. It was then fed eye-tracking input data from 30 chess players of various skill levels. With this data, the CNN used gaze estimation to determin... | Commercial eye tracking | 0.784235 |
82,283 | The DINN was trained on data from over 2,400 subjects and correctly diagnosed their states 96%-99.5% of the time. Most other artificial intelligence models performed at rates above 90%. This technology could ideally provide another avenue for driver drowsiness detection. | Commercial eye tracking | 0.784235 |
82,284 | Scientists in 2017 constructed a Deep Integrated Neural Network (DINN) out of a Deep Neural Network and a convolutional neural network. The goal was to use deep learning to examine images of drivers and determine their level of drowsiness by "classify eye states." With enough images, the proposed DINN could ideally det... | Commercial eye tracking | 0.784235 |
82,285 | In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. : 9–11 It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. : 9–11 The stochastic matrix wa... | Right stochastic matrix | 0.784234 |
82,286 | A planetarium (PL: planetariums or planetaria) is a theatre built primarily for presenting educational and entertaining shows about astronomy and the night sky, or for training in celestial navigation.A dominant feature of most planetariums is the large dome-shaped projection screen onto which scenes of stars, planets,... | Planetarium | 0.784233 |
82,287 | Equational logic was common before Principia Mathematica (e.g., Peirce,1,2,3 Johnson 1892), and has present-day advocates (Gries and Schneider 1993). Conventional mathematical logic consists of tautological formulae, signalled by a prefixed turnstile. To denote that the primary algebra formula A is a tautology, simply ... | Laws of Form | 0.784233 |
82,288 | R1 and R2 enable transforming one equation into another. Hence the primary algebra is an equational formal system, like the many algebraic structures, including Boolean algebra, that are varieties. | Laws of Form | 0.784233 |
82,289 | A demonstration by calculation is often little more than: Invoking T13 repeatedly to eliminate redundant subformulae; Erasing any subformulae having the form .The last step of a calculation always invokes J1a. LoF includes elegant new proofs of the following standard metatheory: Completeness: all primary algebra conseq... | Laws of Form | 0.784233 |
82,290 | LoF (T14–15) proves the primary algebra analog of the well-known Boolean algebra theorem that every formula has a normal form. Let A be a subformula of some formula B. When paired with C3, J1a can be viewed as the closure condition for calculations: B is a tautology if and only if A and (A) both appear in depth 0 of B.... | Laws of Form | 0.784233 |
82,291 | primary algebra demonstrations and calculations often require no more than J1a, J2, C2, and the consequences (C3 in LoF), (C1), and AA=A (C5). The consequence , C7' in LoF, enables an algorithm, sketched in LoFs proof of T14, that transforms an arbitrary primary algebra formula to an equivalent formula whose depth does... | Laws of Form | 0.784233 |
82,292 | Let A and B be primary algebra formulas. A demonstration of A=B may proceed in either of two ways: Modify A in steps until B is obtained, or vice versa; Simplify both and to . This is known as a "calculation".Once A=B has been demonstrated, A=B can be invoked to justify steps in subsequent demonstrations. | Laws of Form | 0.784233 |
82,293 | Demonstrations and proofs invoke an initial as if it were an axiom.The distinction between consequence and theorem holds for all formal systems, including mathematics and logic, but is usually not made explicit. A demonstration or decision procedure can be carried out and verified by computer. The proof of a theorem ca... | Laws of Form | 0.784233 |
82,294 | The primary algebra contains three kinds of proved assertions: Consequence is a primary algebra equation verified by a demonstration. A demonstration consists of a sequence of steps, each step justified by an initial or a previously demonstrated consequence. Theorem is a statement in the metalanguage verified by a proo... | Laws of Form | 0.784233 |
82,295 | By virtue of J1a, it is a complemented lattice whose upper bound is . By J0, is the corresponding lower bound and identity element. J0 is also an algebraic version of A2 and makes clear the sense in which aliases with the blank page. | Laws of Form | 0.784233 |
82,296 | An initial is a primary algebra equation verifiable by a decision procedure and as such is not an axiom. LoF lays down the initials: The absence of anything to the right of the "=" above, is deliberate. J2 is the familiar distributive law of sentential logic and Boolean algebra. Another set of initials, friendlier to c... | Laws of Form | 0.784233 |
82,297 | Some of these authors have modified the primary algebra in a variety of interesting ways. LoF claimed that certain well-known mathematical conjectures of very long standing, such as the four color theorem, Fermat's Last Theorem, and the Goldbach conjecture, are provable using extensions of the primary algebra. Spencer-... | Laws of Form | 0.784233 |
82,298 | Indeed, the two-element Boolean algebra 2 can be seen as the intended interpretation of the primary algebra. Yet the notation of the primary algebra: Fully exploits the duality characterizing not just Boolean algebras but all lattices; Highlights how syntactically distinct statements in logic and 2 can have identical s... | Laws of Form | 0.784233 |
82,299 | Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic: it was praised by Heinz von Foerster when he reviewed it for the Whole Earth Catalog. Those who agree point to LoF as embodying an enigmatic "mathematics of consciousness", its algebraic symbolism capturing an (perhaps even ... | Laws of Form | 0.784233 |
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