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87,300 | Henry Draper's Henry Draper Catalogue, published between 1918 and 1924, lists more than 225,000 of the brightest stars, named using HD followed by a 6-digit number. Sir Patrick Moore compiled the Caldwell catalogue in 1995 to complement the Messier catalog, listing 109 bright star clusters, nebulae, and galaxies named ... | Astronomical catalog | 0.782122 |
87,301 | Azophi's Book of Fixed Stars, published in 964, describes more than a thousand stars in detail and provides the first descriptions of the Andromeda Galaxy and the Large Magellanic Cloud. Tycho Brahe completed his catalogue with the positions and magnitudes of 1004 fixed stars in 1598. It was the major achievement in as... | Astronomical catalog | 0.782122 |
87,302 | Ptolemy's Almagest is published in 1st century AD. It remained the most authoritative text on astronomy for over 1500 years. It details over 1022 stars, constellations, galaxies and nebulae along with their positions, ecliptic coordinates and magnitudes. It also describes in detail the construction of instruments to ai... | Astronomical catalog | 0.782122 |
87,303 | In order to work out why menstrual synchrony might have evolved, it is necessary to investigate why individuals who synchronized their cycles might have had increased survival and reproduction in the evolutionary past. The relevant field in this case is behavioral ecology. In mammalian mating systems generally, and amo... | McClintock effect | 0.782122 |
87,304 | These use wet chemistry (for CQD) and subsequent solution processing. Concentrated nanoparticle solutions are stabilized by long hydrocarbon ligands that keep the nanocrystals suspended in solution. To create a solid, these solutions are cast down and the long stabilizing ligands are replaced with short-chain crosslink... | Quantum dot solar cell | 0.782121 |
87,305 | The rate of MEG can be optimized by tailoring quantum dot ligand chemistry, as well as by changing the quantum dot material and geometry. In 2004, Los Alamos National Laboratory reported spectroscopic evidence that several excitons could be efficiently generated upon absorption of a single, energetic photon in a quantu... | Quantum dot solar cell | 0.782121 |
87,306 | In typical wet chemistry preparations, the tuning is accomplished by varying the synthesis duration or temperature. The ability to tune the bandgap makes quantum dots desirable for solar cells. For the sun's photon distribution spectrum, the Shockley-Queisser limit indicates that the maximum solar conversion efficiency... | Quantum dot solar cell | 0.782121 |
87,307 | Quantum dots are semiconducting particles that have been reduced below the size of the Exciton Bohr radius and due to quantum mechanics considerations, the electron energies that can exist within them become finite, much alike energies in an atom. Quantum dots have been referred to as "artificial atoms". These energy l... | Quantum dot solar cell | 0.782121 |
87,308 | According to Felson and Cohen, the reason for the increase is that the prosperity of contemporary society offers more opportunities for crime to occur. For example, the use of automobiles, on one hand, enables offenders to move more freely to conduct their violations and, on the other hand, provide more targets for the... | Routine activity theory | 0.782121 |
87,309 | In physics, natural abundance (NA) refers to the abundance of isotopes of a chemical element as naturally found on a planet. The relative atomic mass (a weighted average, weighted by mole-fraction abundance figures) of these isotopes is the atomic weight listed for the element in the periodic table. The abundance of an... | Isotopic abundance | 0.782119 |
87,310 | In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization. The rotation direction in the circle depends on which of the two-phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization.In all oth... | Optical component | 0.782117 |
87,311 | Δ o ⟶ S 1 Fin ∗ ⟶ F k -mod . {\displaystyle \Delta ^{o}{\overset {S^{1}}{\longrightarrow }}\operatorname {Fin} _{*}{\overset {F}{\longrightarrow }}k{\text{-mod}}.} The homology of this simplicial module is the Hochschild homology of the functor F. The above definition of Hochschild homology of commutative algebras is t... | Hochschild cohomology | 0.782117 |
87,312 | The examples of Hochschild homology computations can be stratified into a number of distinct cases with fairly general theorems describing the structure of the homology groups and the homology ring H H ∗ ( A ) {\displaystyle HH_{*}(A)} for an associative algebra A {\displaystyle A} . For the case of commutative algebra... | Hochschild cohomology | 0.782117 |
87,313 | "Lectures on Noncommutative Geometry". arXiv:math/0506603. Topological Hochschild homology in arithmetic geometry Hochschild cohomology at the nLab | Hochschild cohomology | 0.782117 |
87,314 | Dylan G.L. Allegretti, Differential Forms on Noncommutative Spaces. An elementary introduction to noncommutative geometry which uses Hochschild homology to generalize differential forms). Ginzburg, Victor (2005). | Hochschild cohomology | 0.782117 |
87,315 | The Hochschild homology of a commutative algebra A with coefficients in a symmetric A-bimodule M is the homology associated to the composition Δ o ⟶ S 1 Fin ∗ ⟶ L ( A , M ) k -mod , {\displaystyle \Delta ^{o}{\overset {S^{1}}{\longrightarrow }}\operatorname {Fin} _{*}{\overset {{\mathcal {L}}(A,M)}{\longrightarrow }}k{... | Hochschild cohomology | 0.782117 |
87,316 | One simple example is to compute the Hochschild homology of a polynomial ring of Q {\displaystyle \mathbb {Q} } with n {\displaystyle n} -generators. The HKR theorem gives the isomorphism where the algebra ⋀ ( d x 1 , … , d x n ) {\displaystyle \bigwedge (dx_{1},\ldots ,dx_{n})} is the free antisymmetric algebra over Q... | Hochschild cohomology | 0.782117 |
87,317 | Let k be a field, A an associative k-algebra, and M an A-bimodule. The enveloping algebra of A is the tensor product A e = A ⊗ A o {\displaystyle A^{e}=A\otimes A^{o}} of A with its opposite algebra. Bimodules over A are essentially the same as modules over the enveloping algebra of A, so in particular A and M can be c... | Hochschild cohomology | 0.782117 |
87,318 | Tensoring this algebra with F p {\displaystyle \mathbb {F} _{p}} over F p ⊗ Z L F p {\displaystyle \mathbb {F} _{p}\otimes _{\mathbb {Z} }^{\mathbf {L} }\mathbb {F} _{p}} givessince ε {\displaystyle \varepsilon } multiplied with any element in F p {\displaystyle \mathbb {F} _{p}} is zero. The algebra structure comes fr... | Hochschild cohomology | 0.782117 |
87,319 | Then, because we have to resolve the kernel ε ⋅ F p ⊗ Z L F p {\displaystyle \varepsilon \cdot \mathbb {F} _{p}\otimes _{\mathbb {Z} }^{\mathbf {L} }\mathbb {F} _{p}} , we can take a copy of F p ⊗ Z L F p {\displaystyle \mathbb {F} _{p}\otimes _{\mathbb {Z} }^{\mathbf {L} }\mathbb {F} _{p}} shifted in degree 2 {\displa... | Hochschild cohomology | 0.782117 |
87,320 | Then, the Hochschild complex is given byIn order to compute this, we must resolve F p {\displaystyle \mathbb {F} _{p}} as an F p ⊗ Z L F p {\displaystyle \mathbb {F} _{p}\otimes _{\mathbb {Z} }^{\mathbf {L} }\mathbb {F} _{p}} -algebra. Observe that the algebra structure F p / ( ε 2 ) → F p {\displaystyle \mathbb {F} _... | Hochschild cohomology | 0.782117 |
87,321 | In the characteristic p case, there is a userful counter-example to the Hochschild-Kostant-Rosenberg theorem which elucidates for the need of a theory beyond simplicial algebras for defining Hochschild homology. Consider the Z {\displaystyle \mathbb {Z} } -algebra F p {\displaystyle \mathbb {F} _{p}} . We can compute a... | Hochschild cohomology | 0.782117 |
87,322 | In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Hochschild cohomology was introduced by Gerhard Hochschild (1945) for algebras over a field, and extended to algebras over more general rings... | Hochschild cohomology | 0.782117 |
87,323 | For a simplicial resolution P ∙ → A {\displaystyle P_{\bullet }\to A} , we set L A / k i = Ω P ∙ / k i ⊗ P ∙ A {\displaystyle \mathbb {L} _{A/k}^{i}=\Omega _{P_{\bullet }/k}^{i}\otimes _{P_{\bullet }}A} . Then, there exists a descending N {\displaystyle \mathbb {N} } -filtration F ∙ {\displaystyle F_{\bullet }} on H H ... | Hochschild cohomology | 0.782117 |
87,324 | In the case of commutative algebras A / k {\displaystyle A/k} where Q ⊆ k {\displaystyle \mathbb {Q} \subseteq k} , the Hochschild homology has two main theorems concerning smooth algebras, and more general non-flat algebras A {\displaystyle A} ; but, the second is a direct generalization of the first. In the smooth ca... | Hochschild cohomology | 0.782117 |
87,325 | Measurements made above and below the canopy are used to determine canopy light interception at five angles, from which LAI is computed using a model of radiative transfer in vegetative canopies based on Beer's law . The LP-80 calculates LAI by means of measuring the difference between light levels above the canopy and... | Leaf Area Index | 0.782117 |
87,326 | LAI is a measure for the total area of leaves per unit ground area and directly related to the amount of light that can be intercepted by plants. It is an important variable used to predict photosynthetic primary production, evapotranspiration and as a reference tool for crop growth. As such, LAI plays an essential rol... | Leaf Area Index | 0.782117 |
87,327 | LAI can be determined directly by taking a statistically significant sample of foliage from a plant canopy, measuring the leaf area per sample plot and dividing it by the plot land surface area. Indirect methods measure canopy geometry or light extinction and relate it to LAI. | Leaf Area Index | 0.782117 |
87,328 | University of California, Berkeley The National Radio Astronomy Observatory University of Pennsylvania The Square Kilometre Array (SKA South Africa) == References == | Precision Array for Probing the Epoch of Reionization | 0.782116 |
87,329 | PAPER began as a collaboration between Don Backer of the UC Berkeley Radio Astronomy Laboratory and Richard Bradley of the National Radio Astronomy Observatory. With Backer's passing in 2010, Aaron Parsons has assumed leadership of PAPER on the side of UC Berkeley. The two fundamental concerns that most influence the d... | Precision Array for Probing the Epoch of Reionization | 0.782116 |
87,330 | The theorem is named after German mathematician Herbert Grötzsch, who published its proof in 1959. Grötzsch's original proof was complex. Berge (1960) attempted to simplify it but his proof was erroneous.In 2003, Carsten Thomassen derived an alternative proof from another related theorem: every planar graph with girth ... | Grötzsch's theorem | 0.782116 |
87,331 | In particular, the Grötzsch graph and the Chvátal graph are triangle-free graphs requiring four colors, and the Mycielskian is a transformation of graphs that can be used to construct triangle-free graphs that require arbitrarily high numbers of colors. The theorem cannot be generalized to all planar K4-free graphs, ei... | Grötzsch's theorem | 0.782116 |
87,332 | A slightly more general result is true: if a planar graph has at most three triangles then it is 3-colorable. However, the planar complete graph K4, and infinitely many other planar graphs containing K4, contain four triangles and are not 3-colorable. In 2009, Dvořák, Kráľ, and Thomas announced a proof of another gener... | Grötzsch's theorem | 0.782116 |
87,333 | A result of de Castro et al. (2002) combines Grötzsch's theorem with Scheinerman's conjecture on the representation of planar graphs as intersection graphs of line segments. They proved that every triangle-free planar graph can be represented by a collection of line segments, with three slopes, such that two vertices o... | Grötzsch's theorem | 0.782116 |
87,334 | A 3-coloring of a graph G may be described by a graph homomorphism from G to a triangle K3. In the language of homomorphisms, Grötzsch's theorem states that every triangle-free planar graph has a homomorphism to K3. Naserasr showed that every triangle-free planar graph also has a homomorphism to the Clebsch graph, a 4-... | Grötzsch's theorem | 0.782116 |
87,335 | In the mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. According to the four-color theorem, every graph that can be drawn in the plane without edge crossings can have its vertices colored using at most four different co... | Grötzsch's theorem | 0.782116 |
87,336 | An action bilinear in Weyl fields.A short proof by contradiction points out that the Noether current acquired from some of assumptions is conserved, while other assumptions imply that it is not. Every regularization scheme must violate one or more of the conditions. For lattice regularization the Nielsen–Ninomiya theor... | Nielsen-Ninomiya theorem | 0.782116 |
87,337 | The Nielsen–Ninomiya theorem can be generalized to all possible regularization schemes, not just lattice regularization. This general no-go theorem states that no regularized chiral fermion theory can satisfy all the following conditions Invariance under at least the global part of the gauge group. Different number of ... | Nielsen-Ninomiya theorem | 0.782116 |
87,338 | The MIT Lincoln Laboratory TX-2 computer was the successor to the Lincoln TX-0 and was known for its role in advancing both artificial intelligence and human–computer interaction. Wesley A. Clark was the chief architect of the TX-2. | TX-2 | 0.782114 |
87,339 | In molecular biology, the cohesin domain is a protein domain. It interacts with a complementary domain, termed the dockerin domain. The cohesin-dockerin interaction is the crucial interaction for complex formation in the cellulosome.The scaffolding component of the cellulolytic bacterium Clostridium thermocellum is a n... | Cohesin domain | 0.782113 |
87,340 | The convolution theorem for the discrete-time Fourier transform (DTFT) indicates that a convolution of two sequences can be obtained as the inverse transform of the product of the individual transforms. An important simplification occurs when one of sequences is N-periodic, denoted here by y N , {\displaystyle y_{_{N}}... | Discrete Fourier Transform | 0.782111 |
87,341 | When data is convolved with a function with wide support, such as for downsampling by a large sampling ratio, because of the Convolution theorem and the FFT algorithm, it may be faster to transform it, multiply pointwise by the transform of the filter and then reverse transform it. Alternatively, a good filter is obtai... | Discrete Fourier Transform | 0.782111 |
87,342 | The discrete Fourier transform is widely used with spatial frequencies in modeling the way that light, electrons, and other probes travel through optical systems and scatter from objects in two and three dimensions. The dual (direct/reciprocal) vector space of three dimensional objects further makes available a three d... | Discrete Fourier Transform | 0.782111 |
87,343 | The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware. These implementations usually ... | Discrete Fourier Transform | 0.782111 |
87,344 | Some specific examples of current applications include: Architecture student Magnus Larsson won the 2008 Holcim Award "Next Generation" first prize for region Africa Middle East for his project "Dune anti-desertification architecture, Sokoto, Nigeria" and his design of a habitable wall. Larssons also presented the prop... | Bacillus pasteurii | 0.78211 |
87,345 | For instance, for L2 functions, Carleson's theorem states that they have a pointwise (Lebesgue) almost everywhere convergent Fourier series. Fourier series can only be used for periodic functions, or for functions on a bounded (compact) interval. If f {\displaystyle f} is a periodic function with period P {\displaystyl... | Aperiodic function | 0.782109 |
87,346 | Mimer SQL is a proprietary SQL-based relational database management system produced by the Swedish company Mimer Information Technology AB (Mimer AB), formerly known as Upright Database Technology AB. It was originally developed as a research project at the Uppsala University, Uppsala, Sweden in the 1970s before being ... | Mimer SQL | 0.782109 |
87,347 | The edges extracted from a two-dimensional image of a three-dimensional scene can be classified as either viewpoint dependent or viewpoint independent. A viewpoint independent edge typically reflects inherent properties of the three-dimensional objects, such as surface markings and surface shape. A viewpoint dependent ... | Edge filter | 0.782109 |
87,348 | The phase stretch transform or PST is a physics-inspired computational approach to signal and image processing. One of its utilities is for feature detection and classification. PST is a spin-off from research on the time stretch dispersive Fourier transform. | Edge filter | 0.782109 |
87,349 | If Hough transforms are used to detect lines and ellipses, then thinning could give much better results. If the edge happens to be the boundary of a region, then thinning could easily give the image parameters like perimeter without much algebra.There are many popular algorithms used to do this, one such is described b... | Edge filter | 0.782109 |
87,350 | Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of fi... | Edge filter | 0.782109 |
87,351 | Canny also introduced the notion of non-maximum suppression, which means that given the presmoothing filters, edge points are defined as points where the gradient magnitude assumes a local maximum in the gradient direction. Looking for the zero crossing of the 2nd derivative along the gradient direction was first propo... | Edge filter | 0.782109 |
87,352 | The Anger and Weber functions satisfy these homogeneous forms of delay differential equations J ν − 1 ( z ) − J ν + 1 ( z ) = 2 ∂ ∂ z J ν ( z ) , {\displaystyle \mathbf {J} _{\nu -1}(z)-\mathbf {J} _{\nu +1}(z)=2{\dfrac {\partial }{\partial z}}\mathbf {J} _{\nu }(z),} E ν − 1 ( z ) − E ν + 1 ( z ) = 2 ∂ ∂ z E ν ( z ) .... | Anger function | 0.782109 |
87,353 | Gram-Schmidt theorem. If {v1, v2,...,vn} is a linearly independent list of vectors in an inner-product space V {\displaystyle {\mathcal {V}}} , then there exists an orthonormal list {e1, e2,...,en} of vectors in V {\displaystyle {\mathcal {V}}} such that span(e1, e2,...,en) = span(v1, v2,...,vn).Proof of the Gram-Schmi... | Orthonormality | 0.782109 |
87,354 | In Cartesian space, the norm of a vector is the square root of the vector dotted with itself. That is, ‖ x ‖ = x ⋅ x {\displaystyle \|\mathbf {x} \|={\sqrt {\mathbf {x} \cdot \mathbf {x} }}} Many important results in linear algebra deal with collections of two or more orthogonal vectors. | Orthonormality | 0.782109 |
87,355 | Research in intelligent user interfaces is published in general Human-Computer Interaction conferences and journals such as CHI or UIST as well as in some artificial intelligence research channels such as those hosted by the AAAI, but most importantly there are the dedicated conference series on Intelligent User Interf... | Intelligent user interface | 0.782108 |
87,356 | The International Geophysical Year (IGY; French: Année géophysique internationale), also referred to as the third International Polar Year, was an international scientific project that lasted from 1 July 1957 to 31 December 1958. It marked the end of a long period during the Cold War when scientific interchange between... | International Geophysical Year | 0.782106 |
87,357 | In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample. For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the a... | Median absolute deviation | 0.782106 |
87,358 | Suppose that X is a vector space and X# is the algebraic dual space of X (i.e. the vector space of all linear functionals on X). If X is endowed with the weak topology induced by X# then the continuous dual space of X is X#, every bounded subset of X is contained in a finite-dimensional vector subspace of X, every vect... | Weak topology (polar topology) | 0.782106 |
87,359 | The weak topology is characterized by the following condition: a net ( x λ ) {\displaystyle (x_{\lambda })} in X converges in the weak topology to the element x of X if and only if ϕ ( x λ ) {\displaystyle \phi (x_{\lambda })} converges to ϕ ( x ) {\displaystyle \phi (x)} in R {\displaystyle \mathbb {R} } or C {\displa... | Weak topology (polar topology) | 0.782105 |
87,360 | For example, the strong operator topology on L(X,Y) is the topology of pointwise convergence. For instance, if Y is a normed space, then this topology is defined by the seminorms indexed by x ∈ X: f ↦ ‖ f ( x ) ‖ Y . {\displaystyle f\mapsto \|f(x)\|_{Y}.} More generally, if a family of seminorms Q defines the topology ... | Weak topology (polar topology) | 0.782105 |
87,361 | If X and Y are topological vector spaces, the space L(X,Y) of continuous linear operators f: X → Y may carry a variety of different possible topologies. The naming of such topologies depends on the kind of topology one is using on the target space Y to define operator convergence (Yosida 1980, IV.7 Topologies of linear... | Weak topology (polar topology) | 0.782105 |
87,362 | For sake of simplicity, unless otherwise stated, the projective spaces considered in this article are supposed to be defined over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results remain true, or may be generalized to projective geo... | Fundamental theorem of projective geometry | 0.782105 |
87,363 | These constructions divide into two classes that have been shown to be equivalent. A projective space may be constructed as the set of the lines of a vector space over a given field (the above definition is based on this version); this construction facilitates the definition of projective coordinates and allows using t... | Fundamental theorem of projective geometry | 0.782105 |
87,364 | Historically, homographies (and projective spaces) have been introduced to study perspective and projections in Euclidean geometry, and the term homography, which, etymologically, roughly means "similar drawing", dates from this time. At the end of the 19th century, formal definitions of projective spaces were introduc... | Fundamental theorem of projective geometry | 0.782105 |
87,365 | In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of pr... | Fundamental theorem of projective geometry | 0.782105 |
87,366 | Every homography is the composition of a finite number of perspectivities. In particular, if the dimension of the implied projective space is at least two, every homography is the composition of a finite number of central collineations.If projective spaces are defined by means of axioms (synthetic geometry), the third ... | Fundamental theorem of projective geometry | 0.782105 |
87,367 | There are collineations besides the homographies. In particular, any field automorphism σ of a field F induces a collineation of every projective space over F by applying σ to all homogeneous coordinates (over a projective frame) of a point. These collineations are called automorphic collineations. The fundamental theo... | Fundamental theorem of projective geometry | 0.782105 |
87,368 | More generally there is a moduli stack M g , n {\displaystyle {\mathcal {M}}_{g,n}} of genus g {\displaystyle g} curves with n {\displaystyle n} marked points. In general this is an algebraic stack, and is a Deligne–Mumford stack for g ≥ 2 {\displaystyle g\geq 2} or g = 1 , n ≥ 1 {\displaystyle g=1,n\geq 1} or g = 0 , ... | Artin stack | 0.782105 |
87,369 | Mumford (1965) studied the moduli stack M1,1 of elliptic curves, and showed that its Picard group is cyclic of order 12. For elliptic curves over the complex numbers the corresponding stack is similar to a quotient of the upper half-plane by the action of the modular group. The moduli space of algebraic curves M g {\di... | Artin stack | 0.782105 |
87,370 | If A is a quasi-coherent sheaf of algebras in an algebraic stack X over a scheme S, then there is a stack Spec(A) generalizing the construction of the spectrum Spec(A) of a commutative ring A. An object of Spec(A) is given by an S-scheme T, an object x of X(T), and a morphism of sheaves of algebras from x*(A) to the co... | Artin stack | 0.782105 |
87,371 | The Wellcome Centre for Human Genetics is a human genetics research centre of the Nuffield Department of Medicine in the Medical Sciences Division, University of Oxford, funded by the Wellcome Trust among others. | Wellcome Centre for Human Genetics | 0.782104 |
87,372 | The WHG has been involved in many international statistical genetics advances including the Wellcome Trust Case Control Consortia (WTCCC, WTCCC2), the 1000 Genomes Project and the International HapMap Project. == References == | Wellcome Centre for Human Genetics | 0.782104 |
87,373 | ISBN 3-540-58713-6 Ramsay JG & Huber MI. (1987). The Techniques of Modern Structural Geology. | Shear zone | 0.782102 |
87,374 | In geology, a shear zone is a thin zone within the Earth's crust or upper mantle that has been strongly deformed, due to the walls of rock on either side of the zone slipping past each other. In the upper crust, where rock is brittle, the shear zone takes the form of a fracture called a fault. In the lower crust and ma... | Shear zone | 0.782102 |
87,375 | For a commutative ring, the four following properties are equivalent: being a semisimple ring; being artinian and reduced; being a reduced Noetherian ring of Krull dimension 0; and being isomorphic to a finite direct product of fields. If K is a field and G is a finite group of order n, then the group ring K is semisim... | Semisimple local ring | 0.782101 |
87,376 | Furthermore, every simple (left) R-module is isomorphic to a minimal left ideal of R, that is, R is a left Kasch ring. Semisimple rings are both Artinian and Noetherian. From the above properties, a ring is semisimple if and only if it is Artinian and its Jacobson radical is zero. If an Artinian semisimple ring contain... | Semisimple local ring | 0.782101 |
87,377 | Since "projective" implies "flat", a semisimple ring is a von Neumann regular ring. Semisimple rings are of particular interest to algebraists. For example, if the base ring R is semisimple, then all R-modules would automatically be semisimple. | Semisimple local ring | 0.782101 |
87,378 | A ring is said to be (left)-semisimple if it is semisimple as a left module over itself. Surprisingly, a left-semisimple ring is also right-semisimple and vice versa. The left/right distinction is therefore unnecessary, and one can speak of semisimple rings without ambiguity. A semisimple ring may be characterized in t... | Semisimple local ring | 0.782101 |
87,379 | One should beware that despite the terminology, not all simple rings are semisimple. The problem is that the ring may be "too big", that is, not (left/right) Artinian. In fact, if R is a simple ring with a minimal left/right ideal, then R is semisimple. Classic examples of simple, but not semisimple, rings are the Weyl... | Semisimple local ring | 0.782101 |
87,380 | As with the multidimensional central limit theorem, there is a multidimensional version of the Berry–Esseen theorem.Let X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} be independent R d {\displaystyle \mathbb {R} ^{d}} -valued random vectors each having mean zero. Write S n = ∑ i = 1 n X i n {\displaystyle S_{n}={\fr... | Berry–Esseen theorem | 0.7821 |
87,381 | In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases to infinity. Under stronger assumptions, the Berry–Esseen theorem, or Berry–Esseen inequality, giv... | Berry–Esseen theorem | 0.7821 |
87,382 | Statements of the theorem vary, as it was independently discovered by two mathematicians, Andrew C. Berry (in 1941) and Carl-Gustav Esseen (1942), who then, along with other authors, refined it repeatedly over subsequent decades. | Berry–Esseen theorem | 0.7821 |
87,383 | Kepler-90, also designated 2MASS J18574403+4918185, is an F-type star located about 2,790 light-years (855 pc) from Earth in the constellation of Draco. It is notable for possessing a planetary system that has the same number of observed planets as the Solar System. On 14 December 2017, NASA and Google announced the di... | Kepler-90 | 0.782099 |
87,384 | The capacitive gap structure consists of sections of line about λ/2 in length which act as resonators and are coupled "end-on" by gaps in the transmission line. It is particularly suitable for planar formats, is easily implemented with printed circuit technology and has the advantage of taking up no more space than a p... | Distributed-element filter | 0.782098 |
87,385 | Crusher is a 13,200-pound (6,000 kg) autonomous off-road Unmanned Ground Combat Vehicle developed by researchers at the Carnegie Mellon University's National Robotics Engineering Center for DARPA. It is a follow-up on the previous Spinner vehicle. DARPA's technical name for the Crusher is Unmanned Ground Combat Vehicle... | Autonomous foraging | 0.782097 |
87,386 | UGV Interoperability Profile (UGV IOP), Robotics and Autonomous Systems – Ground IOP (RAS-G IOP), was originally a research program started by the United States Department of Defense (DoD) to organize and maintain open architecture interoperability standards for Unmanned Ground Vehicles (UGV). The IOP was initially cre... | Autonomous foraging | 0.782097 |
87,387 | Sophia imitates human gestures and facial expressions and is able to answer certain questions and to make simple conversations on predefined topics (e.g. on the weather). The AI program analyses conversations and extracts data that allows it to improve responses in the future. Nine other robot humanoid "siblings" who w... | Autonomous foraging | 0.782097 |
87,388 | The Seekur robot was the first commercially available robot to demonstrate MDARS-like capabilities for general use by airports, utility plants, corrections facilities and Homeland Security.The DARPA Grand Challenge and DARPA Urban Challenge have encouraged development of even more autonomous capabilities for ground veh... | Autonomous foraging | 0.782097 |
87,389 | Construction robots are used directly on job sites and perform work such as building, material handling, earthmoving, and surveillance. Numerous companies have robotics applications in stages ranging from R&D to fully-commercialized. ASI Robots: heavy equipment automation and autonomy platform Builder: heavy equipment ... | Autonomous foraging | 0.782097 |
87,390 | All major reactors that produce technetium-99m were built in the 1960s and are close to the end of life. The two new Canadian Multipurpose Applied Physics Lattice Experiment reactors planned and built to produce 200% of the demand of technetium-99m relieved all other producers from building their own reactors. With the... | Technetium | 0.782097 |
87,391 | The discovery of element 43 was finally confirmed in a 1937 experiment at the University of Palermo in Sicily by Carlo Perrier and Emilio Segrè. In mid-1936, Segrè visited the United States, first Columbia University in New York and then the Lawrence Berkeley National Laboratory in California. He persuaded cyclotron in... | Technetium | 0.782097 |
87,392 | Technetium could be immobilized by some environments, such as microbial activity in lake bottom sediments, and the environmental chemistry of technetium is an area of active research.An alternative disposal method, transmutation, has been demonstrated at CERN for technetium-99. In this process, the technetium (techneti... | Technetium | 0.782096 |
87,393 | Technetium-99m ("m" indicates that this is a metastable nuclear isomer) is used in radioactive isotope medical tests. For example, Technetium-99m is a radioactive tracer that medical imaging equipment tracks in the human body. It is well suited to the role because it emits readily detectable 140 keV gamma rays, and its... | Technetium | 0.782096 |
87,394 | The binary tetrahalides can be converted to the hexahalides 2− (X = F, Cl, Br, I), which adopt octahedral molecular geometry. More reduced halides form anionic clusters with Tc–Tc bonds. The situation is similar for the related elements of Mo, W, Re. | Technetium | 0.782096 |
87,395 | In Book VIII of his Physics, Aristotle examines the notions of change or motion, and attempts to show by a challenging argument, that the mere supposition of a 'before' and an 'after', requires a first principle. He argues that in the beginning, if the cosmos had come to be, its first motion would lack an antecedent st... | Prime mover theory | 0.782095 |
87,396 | John Burnet (1892) noted The Neoplatonists were quite justified in regarding themselves as the spiritual heirs of Pythagoras; and, in their hands, philosophy ceased to exist as such, and became theology. And this tendency was at work all along; hardly a single Greek philosopher was wholly uninfluenced by it. Perhaps Ar... | Prime mover theory | 0.782095 |
87,397 | The most commonly recognized and used β-galactoside in biochemistry is lactose. However, other chemicals, such as ONPG, are known, but these are typically synthesized for biochemical assays. | Galactoside | 0.782094 |
87,398 | Microwave measurement techniques based on cavity perturbation theory are generally used to determine the dielectric and magnetic parameters of materials and various circuit components such as dielectric resonators. Since ex-ante knowledge of the resonant frequency, resonant frequency shift and electromagnetic fields is... | Cavity Perturbation Theory | 0.78209 |
87,399 | Castings can be made from an original wax model (the direct method) or from wax replicas of an original pattern that need not be made from wax (the indirect method). The following steps describe the indirect process, which can take two to seven days to complete. Produce a master pattern: An artist or mould-maker create... | Investment Casting | 0.78209 |
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