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81,700 | Therefore, S contains a nonzero integer point. Remarks: The argument above proves the theorem that any set of volume > det ( L ) {\textstyle >\!\det(L)} contains two distinct points that differ by a lattice vector. This is a special case of Blichfeldt's theorem. The argument above highlights that the term 2 n det ( L )... | Minkowski's theorem | 0.784482 |
81,701 | The following argument proves Minkowski's theorem for the specific case of L = ℤ2. Proof of the Z 2 {\textstyle \mathbb {Z} ^{2}} case: Consider the map f: S → R 2 / 2 L , ( x , y ) ↦ ( x mod 2 , y mod 2 ) {\displaystyle f:S\to \mathbb {R} ^{2}/2L,\qquad (x,y)\mapsto (x{\bmod {2}},y{\bmod {2}})} Intuitively, this map c... | Minkowski's theorem | 0.784482 |
81,702 | Another application of Minkowski's theorem is the result that every class in the ideal class group of a number field K contains an integral ideal of norm not exceeding a certain bound, depending on K, called Minkowski's bound: the finiteness of the class number of an algebraic number field follows immediately. | Minkowski's theorem | 0.784482 |
81,703 | The difficult implication in Fermat's theorem on sums of two squares can be proven using Minkowski's bound on the shortest vector. Theorem: Every prime with p ≡ 1 mod 4 {\textstyle p\equiv 1\mod 4} can be written as a sum of two squares. Additionally, the lattice perspective gives a computationally efficient approach t... | Minkowski's theorem | 0.784482 |
81,704 | The complexity of finding the point guaranteed by Minkowski's theorem, or the closely related Blichfeldt's theorem, have been studied from the perspective of TFNP search problems. In particular, it is known that a computational analogue of Blichfeldt's theorem, a corollary of the proof of Minkowski's theorem, is PPP-co... | Minkowski's theorem | 0.784482 |
81,705 | Minkowski's theorem is also useful to prove Lagrange's four-square theorem, which states that every natural number can be written as the sum of the squares of four natural numbers. | Minkowski's theorem | 0.784482 |
81,706 | Minkowski's theorem gives an upper bound for the length of the shortest nonzero vector. This result has applications in lattice cryptography and number theory. Theorem (Minkowski's bound on the shortest vector): Let L {\textstyle L} be a lattice. Then there is a x ∈ L ∖ { 0 } {\textstyle x\in L\setminus \{0\}} with ‖ x... | Minkowski's theorem | 0.784482 |
81,707 | Minkowski's theorem can be used to prove Dirichlet's theorem on simultaneous rational approximation. | Minkowski's theorem | 0.784482 |
81,708 | In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the origin and which has volume greater than 2 n {\displaystyle 2^{n}} contains a non-zero integer point (meaning a point in Z n {\displaystyle \mathbb {Z} ^{n}} that is ... | Minkowski's theorem | 0.784482 |
81,709 | Suppose that L is a lattice of determinant d(L) in the n-dimensional real vector space ℝn and S is a convex subset of ℝn that is symmetric with respect to the origin, meaning that if x is in S then −x is also in S. Minkowski's theorem states that if the volume of S is strictly greater than 2n d(L), then S must contain ... | Minkowski's theorem | 0.784482 |
81,710 | Source: American Society for Cell Biology 2020 James Olzmann 2019 Cignall Kadoch 2018 Sergiu Pasca 2017 Meng Wang 2016 Bo Huang;Valentina Greco 2015 Vladimir Denic 2014 Manuel Thery 2013 Douglas B. Weibel 2012 Iain Cheeseman 2012 Gia Voeltz 2011 Maxence V. Nachury 2010 Anna Kashina 2009 Martin W. Hetzer 2008 Arshad B. ... | Early Career Life Scientist Award | 0.784481 |
81,711 | The ASCB Early Career Life Scientist Award is awarded by the American Society for Cell Biology to an outstanding scientist who earned his doctorate no more than 12 years earlier and who has served as an independent investigator for no more than seven years. The winner speaks at the ASCB Annual Meeting and receives a mo... | Early Career Life Scientist Award | 0.784481 |
81,712 | The International Association for Statistical Education (IASE) is a section of the International Statistical Institute (ISI), a professional association of statisticians, devoted to statistics education. It was founded in 1991 as an outgrowth of the ISI Statistical Education Committee, which had operated since 1948.Sin... | International Association for Statistical Education | 0.78448 |
81,713 | Functionally, the subcutaneous fat insulates the body, absorbs trauma, and serves as a reserve energy source.Conditions of the human integumentary system constitute a broad spectrum of diseases, also known as dermatoses, as well as many nonpathologic states (like, in certain circumstances, melanonychia and racquet nail... | Skin conditions | 0.784479 |
81,714 | A Weil divisor D is effective if all the coefficients are non-negative. One writes D ≥ D′ if the difference D − D′ is effective. For example, a divisor on an algebraic curve over a field is a formal sum of finitely many closed points. | Effective divisor | 0.784479 |
81,715 | The R shears are then linked by a second set, the R' shears, that forms at about 75° to the main fault trace. These two fault orientations can be understood as conjugate fault sets at 30° to the short axis of the instantaneous strain ellipse associated with the simple shear strain field caused by the displacements appl... | Fault stepover | 0.784479 |
81,716 | Rabies virus is estimated to cause around 55,000 deaths per year across the world and has a death rate of nearly 100%. These statistics coupled with the fact that there is currently no specific treatment, or antiviral drug makes research on the virus of vital importance for the scientific community in order to possibly... | Rabies virus | 0.784478 |
81,717 | The central concepts in the analysis of linear multistep methods, and indeed any numerical method for differential equations, are convergence, order, and stability. | Adams-Moulton method | 0.784478 |
81,718 | The BDF methods are implicit methods with b s − 1 = ⋯ = b 0 = 0 {\displaystyle b_{s-1}=\cdots =b_{0}=0} and the other coefficients chosen such that the method attains order s (the maximum possible). These methods are especially used for the solution of stiff differential equations. | Adams-Moulton method | 0.784478 |
81,719 | The two-dimensional critical Ising model is the critical limit of the Ising model in two dimensions. It is a two-dimensional conformal field theory whose symmetry algebra is the Virasoro algebra with the central charge c = 1 2 {\displaystyle c={\tfrac {1}{2}}} . Correlation functions of the spin and energy operators ar... | Two-dimensional critical Ising model | 0.784476 |
81,720 | The Ising model has a description as a random cluster model due to Fortuin and Kasteleyn. In this description, the natural observables are connectivities of clusters, i.e. probabilities that a number of points belong to the same cluster. The Ising model can then be viewed as the case q = 2 {\displaystyle q=2} of the q ... | Two-dimensional critical Ising model | 0.784476 |
81,721 | In probability and statistics the extended negative binomial distribution is a discrete probability distribution extending the negative binomial distribution. It is a truncated version of the negative binomial distribution for which estimation methods have been studied.In the context of actuarial science, the distribut... | Extended negative binomial distribution | 0.784476 |
81,722 | 1985, c. S-16 Statistics Act, R.S.C. 1985, c. S-19Other legislation: Agricultural and Rural Development Act, R.S.C. 1985, c. A-3 Atlantic Canada Opportunities Agency Act, R.S.C. | Innovation, Science and Economic Development Canada | 0.784475 |
81,723 | ISED oversees 17 departments and agencies and is associated with an additional 4 organizations. Each of these organizations are related to one or more of the four focus areas of ISED: innovation in science and technology, trade and investment, growing small and medium-sized enterprises, and economic growth of Canadian ... | Innovation, Science and Economic Development Canada | 0.784475 |
81,724 | The Elo rating system has been used in soft biometrics, which concerns the identification of individuals using human descriptions. Comparative descriptions were utilized alongside the Elo rating system to provide robust and discriminative 'relative measurements', permitting accurate identification. The Elo rating syste... | Elo rating system | 0.784474 |
81,725 | In 2003 scientists from around Germany initiated the establishment of the German Society for Stem Cell Research with emphasis on basic research in stem cell biology. The society is a non-profit organisation, financially and politically autonomous, and is registered with the district court Cologne under the number VR 14... | German Society for Stem Cell Research | 0.78447 |
81,726 | The German Society for Stem Cell Research (Deutsche Gesellschaft für Stammzellforschung or GSZ), established in 2003 by Juergen Hescheler, brings scientists from around Germany together and has an emphasis on basic research in stem cell biology. The main purpose of the society is to promote stem cell research. In order... | German Society for Stem Cell Research | 0.78447 |
81,727 | The journal was founded by Gopal Kanji in 1974 as the Bulletin in Applied Statistics (BIAS). Kanji remained as editor until the end of 2007. | Journal of Applied Statistics | 0.784469 |
81,728 | The Journal of Applied Statistics or J.Appl.Stat. is a peer-reviewed scientific journal covering applied statistics that is published by Taylor & Francis. Its Journal Citation Reports impact factor was 1.013 in 2019. | Journal of Applied Statistics | 0.784469 |
81,729 | TLC is an instance of a more general class of models known as semantic networks. In a semantic network, each node is to be interpreted as representing a specific concept, word, or feature; each node is a symbol. Semantic networks generally do not employ distributed representations for concepts, as may be found in a neu... | Hyperspace Analogue to Language | 0.784469 |
81,730 | The cognitive neuroscience of semantic memory is a controversial issue with two dominant views. Many researchers and clinicians believe that semantic memory is stored by the same brain systems involved in episodic memory, that is, the medial temporal lobes, including the hippocampal formation. In this system, the hippo... | Hyperspace Analogue to Language | 0.784469 |
81,731 | Toxicology studies of nanomaterials are a key input into determining occupational exposure limits. The Royal Society identifies the potential for nanoparticles to penetrate the skin, and recommends that the use of nanoparticles in cosmetics be conditional upon a favorable assessment by the relevant European Commission ... | Nanotoxicology | 0.784466 |
81,732 | Nanomaterials have at least one primary dimension of less than 100 nanometers, and often have properties different from those of their bulk components that are technologically useful. Because nanotechnology is a recent development, the health and safety effects of exposures to nanomaterials, and what levels of exposure... | Nanotoxicology | 0.784466 |
81,733 | Metal based nanoparticles (NPs) are a prominent class of NPs synthesized for their functions as semiconductors, electroluminescents, and thermoelectric materials. Biomedically, these antibacterial NPs have been utilized in drug delivery systems to access areas previously inaccessible to conventional medicine. With the ... | Nanotoxicology | 0.784466 |
81,734 | They argued in 2007 that it would be necessary to increase funding to a minimum of $50 million in the following two years so as to fill the gaps in knowledge in these areas.The potential for workplace exposure was highlighted by the 2004 Royal Society report which recommended a review of existing regulations to assess ... | Nanotoxicology | 0.784466 |
81,735 | Lyapunov–Schmidt reduction has been used in economics, natural sciences, and engineering often in combination with bifurcation theory, perturbation theory, and regularization. LS reduction is often used to rigorously regularize partial differential equation models in chemical engineering resulting in models that are ea... | Lyapunov–Schmidt reduction | 0.784465 |
81,736 | In organic chemistry, α-keto halogenation is a special type of halogenation. The reaction may be carried out under either acidic or basic conditions in an aqueous medium with the corresponding elemental halogen. In this way, chloride, bromide, and iodide (but notably not fluoride) functionality can be inserted selectiv... | Ketone halogenation | 0.784465 |
81,737 | An experiment conducted by Meshram et al. in 2005 investigated making ketone halogenation a greener reaction, according to the principles of green chemistry. Meshram et al. investigated alternatives to the hazardous chemicals that are primarily used in ketone halogenation, finding that room temperature ionic liquids we... | Ketone halogenation | 0.784465 |
81,738 | The entry requirements for the BIG-NSE are: A Master‘s degree or German Diploma in chemistry, biology, physics or engineering. A Certificate of English Proficiency (TOEFL with a minimum of 550 - paper-based version, or equivalent) for applicants whose native language is neither English nor German. Two letters of recomm... | BIG-NSE | 0.784465 |
81,739 | The Berlin Graduate School of Natural Sciences and Engineering (BIG-NSE) is part of the Cluster of Excellence "Unifying Concepts in Catalysis" (UniCat) founded in November 2007 by the Technical University of Berlin and five further institutions in the Berlin area within the framework of the German government‘s Excellen... | BIG-NSE | 0.784465 |
81,740 | Oxidative addition proceeds with retention of stereochemistry with vinyl halides, while giving inversion of stereochemistry with allylic and benzylic halides. The oxidative addition initially forms the cis–palladium complex, which rapidly isomerizes to the trans-complex. The Suzuki Coupling occurs with retention of con... | Suzuki coupling | 0.784464 |
81,741 | Nevertheless, it was known that yeast extracts can ferment sugar even in the absence of living yeast cells. While studying this process in 1897, the German chemist and zymologist Eduard Buchner of Humboldt University of Berlin, Germany, found that sugar was fermented even when there were no living yeast cells in the mi... | Fermented food | 0.784463 |
81,742 | {\displaystyle p(t)=\det(t\delta _{ij}-a_{ij}).} To prove Nakayama's lemma from the Cayley–Hamilton theorem, assume that IM = M and take φ to be the identity on M. Then define a polynomial p(x) as above. Then r = p ( 1 ) = 1 + p 1 + p 2 + ⋯ + p n {\displaystyle r=p(1)=1+p_{1}+p_{2}+\cdots +p_{n}} has the required prope... | Nakayama lemma | 0.784462 |
81,743 | A standard proof of the Nakayama lemma uses the following technique due to Atiyah & Macdonald (1969). Let M be an R-module generated by n elements, and φ: M → M an R-linear map. If there is an ideal I of R such that φ(M) ⊂ IM, then there is a monic polynomial p ( x ) = x n + p 1 x n − 1 + ⋯ + p n {\displaystyle p(x)=x^... | Nakayama lemma | 0.784462 |
81,744 | The going up theorem is essentially a corollary of Nakayama's lemma. It asserts: Let R ↪ S {\displaystyle R\hookrightarrow S} be an integral extension of commutative rings, and p {\displaystyle {\mathfrak {p}}} a prime ideal of R {\displaystyle R} . Then there is a prime ideal q {\displaystyle {\mathfrak {q}}} in S {\d... | Nakayama lemma | 0.784462 |
81,745 | Nakayama's lemma is used to prove a version of the inverse function theorem in algebraic geometry: Let f: X → Y {\textstyle f:X\to Y} be a projective morphism between quasi-projective varieties. Then f {\textstyle f} is an isomorphism if and only if it is a bijection and the differential d f p {\textstyle df_{p}} is in... | Nakayama lemma | 0.784462 |
81,746 | Proof: Apply Statement 2 to M / N {\displaystyle M/N} .The following result manifests Nakayama's lemma in terms of generators.Statement 5: If M {\displaystyle M} is a finitely generated module over R {\displaystyle R} and the images of elements m {\displaystyle m} 1,..., m {\displaystyle m} n {\displaystyle n} of M {\d... | Nakayama lemma | 0.784462 |
81,747 | Many modern advancements in technology have been inspired by nature and natural systems, including aircraft, automobiles, architecture, and even industrial systems. Advancements in nanotechnology initiated the application of this technique to micro- and nano-scale problems, including tissue engineering. This technique ... | Tissue repair | 0.78446 |
81,748 | A further description goes on to say that an "underlying supposition of tissue engineering is that the employment of natural biology of the system will allow for greater success in developing therapeutic strategies aimed at the replacement, repair, maintenance, or enhancement of tissue function".Developments in the mul... | Tissue repair | 0.78446 |
81,749 | The Michigan Life Sciences Corridor (MLSC) is a $1 billion biotechnology initiative in the U.S. state of Michigan. The MLSC invests in biotech research at four Michigan institutions: the University of Michigan in Ann Arbor; Michigan State University in East Lansing; Wayne State University in Detroit; and the Van Andel ... | Michigan Life Sciences Corridor | 0.784458 |
81,750 | The bill appropriated money from the state's settlement with the tobacco industry to fund biotech research at four of Michigan's largest research institutions.Under the management of the Michigan Economic Development Corporation, the MLSC allocated $1 billion over the course of 20 years, including $50 million in 1999 t... | Michigan Life Sciences Corridor | 0.784458 |
81,751 | While digital patterns are becoming widespread, critics maintain that the pixellated look is a question of fashion rather than function.The design process involves trading-off different factors, including colour, contrast, and overall disruptive effect. A failure to consider all elements of pattern design tends to resu... | Digital camouflage | 0.784458 |
81,752 | According to Proclus, Pythagoreanism divided all mathematical sciences into four categories: arithmetic, music, geometry and astronomy. Boethius developed this theory further, arguing that a fourfold path led to the attainment of knowledge. Arithmetic, music, geometry and astronomy went on to become the essential parts... | Pythagorean doctrine | 0.784457 |
81,753 | The preparation and study of karyotypes is part of cytogenetics. The basic number of chromosomes in the somatic cells of an individual or a species is called the somatic number and is designated 2n. In the germ-line (the sex cells) the chromosome number is n (humans: n = 23).p28 Thus, in humans 2n = 46. | Karyotype | 0.784456 |
81,754 | The first-established prize is the Dirac Medal for the Advancement of Theoretical Physics, awarded by the University of New South Wales, Sydney, Australia, jointly with the Australian Institute of Physics on the occasion of the public Dirac Lecture. The Lecture and the Medal commemorate the visit to the university in 1... | Dirac Medal | 0.784456 |
81,755 | The Dirac Medal of the ICTP is given each year by the Abdus Salam International Centre for Theoretical Physics (ICTP) in honour of physicist Paul Dirac. The award, announced each year on 8 August (Dirac's birthday), was first awarded in 1985.An international committee of distinguished scientists selects the winners fro... | Dirac Medal | 0.784456 |
81,756 | The Dirac Medal is the name of four awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th century. | Dirac Medal | 0.784456 |
81,757 | The Dirac Medal is a gold medal awarded annually by the Institute of Physics (Britain's and Ireland's main professional body for physicists) for "outstanding contributions to theoretical (including mathematical and computational) physics". The award, which includes a £1000 prize, was decided upon by the Institute of Ph... | Dirac Medal | 0.784456 |
81,758 | Risk factors associated with the leading causes of preventable death worldwide as of the year 2001, according to researchers working with the Disease Control Priorities Network (DCPN): By contrast, the World Health Organization (WHO)'s 2008 statistics list only causes of death, and not the underlying risk factors. In 2... | Preventable death | 0.784456 |
81,759 | Arsenate readily reacts with metals to form arsenate metal compounds. Arsenate is a moderate oxidizer and an electron acceptor, with an electrode potential of +0.56 V for its reduction to arsenite. Due to arsenic having the same valency and similar atomic radius to phosphorus, arsenate shares similar geometry and react... | AsO4 | 0.784455 |
81,760 | The arsenate is an ion with the chemical formula AsO3−4. Bonding in arsenate consists of a central arsenic atom, with oxidation state +5, double bonded to one oxygen atom and single bonded to a further three oxygen atoms. The four oxygen atoms orient around the arsenic atom in a tetrahedral geometry. Resonance disperse... | AsO4 | 0.784455 |
81,761 | In statistics, the covariance matrix of a multivariate probability distribution is always positive semi-definite; and it is positive definite unless one variable is an exact linear function of the others. Conversely, every positive semi-definite matrix is the covariance matrix of some multivariate distribution. | Positive definite matrices | 0.784455 |
81,762 | {\displaystyle A=\mathrm {diag} (z_{1},\dots ,z_{n})+{\begin{pmatrix}1\\\vdots \\1\end{pmatrix}}\cdot \left(w_{1},\dots ,w_{n}\right).} From the transposed matrix case of the Gershgorin circle theorem it follows that all eigenvalues of A, that is, all roots of ƒ(X), are contained in the union of the disks D ( a k , k ,... | Durand–Kerner method | 0.784455 |
81,763 | In the quotient ring (algebra) of residue classes modulo ƒ(X), the multiplication by X defines an endomorphism that has the zeros of ƒ(X) as eigenvalues with the corresponding multiplicities. Choosing a basis, the multiplication operator is represented by its coefficient matrix A, the companion matrix of ƒ(X) for this ... | Durand–Kerner method | 0.784455 |
81,764 | MVA-B, or Modified Vaccinia Ankara B, is an HIV vaccine created to give immune resistance to infection by the human immunodeficiency virus. It was developed by a team of Spanish researchers at the Spanish National Research Council's Biotechnology National Centre headed by Dr. Mariano Esteban. The vaccine is based on th... | MVA-B | 0.784451 |
81,765 | The card catalog, or "catalog of characteristics," in cryptography, was a system designed by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski, and first completed about 1935 or 1936, to facilitate decrypting German Enigma ciphers. | Card catalog (cryptology) | 0.784451 |
81,766 | If the hypersurfaces are in relative general position, then there are d 1 ⋯ d n {\displaystyle d_{1}\cdots d_{n}} intersection points, all with multiplicity 1. There are various proofs of this theorem, which either are expressed in purely algebraic terms, or use the language or algebraic geometry. Three algebraic proof... | Bézout's theorem | 0.78445 |
81,767 | The generalization in higher dimension may be stated as: Let n projective hypersurfaces be given in a projective space of dimension n over an algebraically closed field, which are defined by n homogeneous polynomials in n + 1 variables, of degrees d 1 , … , d n . {\displaystyle d_{1},\ldots ,d_{n}.} Then either the num... | Bézout's theorem | 0.78445 |
81,768 | Moreover, the finite case occurs almost always. In the case of two variables and in the case of affine hypersurfaces, if multiplicities and points at infinity are not counted, this theorem provides only an upper bound of the number of points, which is almost always reached. This bound is often referred to as the Bézout... | Bezout's theorem | 0.78445 |
81,769 | Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. It is named after Étienne Bézout. In some elementary ... | Bezout's theorem | 0.78445 |
81,770 | Bézout's theorem can be proved by recurrence on the number of polynomials by using the following theorem. Let V be a projective algebraic set of dimension δ {\displaystyle \delta } and degree d 1 {\displaystyle d_{1}} , and H be a hypersurface (defined by a single polynomial) of degree d 2 {\displaystyle d_{2}} , that ... | Bezout's theorem | 0.78445 |
81,771 | Writing the circle in homogeneous coordinates, we get from which it is clear that the two points (1: i: 0) and (1: –i: 0) lie on every circle. When two circles do not meet at all in the real plane, the two other intersections have non-real coordinates, or if the circles are concentric then they meet at exactly the two ... | Bezout's theorem | 0.78445 |
81,772 | Two conic sections generally intersect in four points, some of which may coincide. To properly account for all intersection points, it may be necessary to allow complex coordinates and include the points on the infinite line in the projective plane. For example: Two circles never intersect in more than two points in th... | Bezout's theorem | 0.78445 |
81,773 | Moreover, there are cases where a convenient deformation is difficult to define (as in the case of more than two plane curves having a common intersection point), and even cases where no deformation is possible.Currently, following Jean-Pierre Serre, a multiplicity is generally defined as the length of a local ring ass... | Bezout's theorem | 0.78445 |
81,774 | The concept of multiplicity is fundamental for Bézout's theorem, as it allows having an equality instead of a much weaker inequality. Intuitively, the multiplicity of a common zero of several polynomials is the number of zeros into which the common zero can split when the coefficients are slightly changed. For example,... | Bezout's theorem | 0.78445 |
81,775 | This and the fact that the concept of intersection multiplicity was outside the knowledge of his time led to a sentiment expressed by some authors that his proof was neither correct nor the first proof to be given.The proof of the statement that includes multiplicities requires an accurate definition of the intersectio... | Bézout's theorem | 0.78445 |
81,776 | In the case of plane curves, Bézout's theorem was essentially stated by Isaac Newton in his proof of lemma 28 of volume 1 of his Principia in 1687, where he claims that two curves have a number of intersection points given by the product of their degrees.The general theorem was later published in 1779 in Étienne Bézout... | Bézout's theorem | 0.78445 |
81,777 | The Common Interface allows them to communicate with each other. All Common Interface equipment must comply with the EN 50221-1997 standard. This is a defined standard that enables the addition of a CAM in a DTV receiver to adapt it to different kinds of cryptography. | Common Interface | 0.784449 |
81,778 | In such a case, only the smart card reader normally in the CAM is fitted and not the PCMCIA type CI slots. Even if the Common Interface has been created to resolve cryptography issues, it can have other functions using other types of modules such as Web Browser, iDTV (Interactive Television), and so forth. In Europe, D... | Common Interface | 0.784449 |
81,779 | Schwartz's Paley–Wiener theorem asserts that the Fourier transform of a distribution of compact support on R n {\displaystyle \mathbb {R} ^{n}} is an entire function on C n {\displaystyle \mathbb {C} ^{n}} and gives estimates on its growth at infinity. It was proven by Laurent Schwartz (1952). The formulation presented... | Paley-Wiener criterion | 0.784449 |
81,780 | Nodes are distributed along a DeviceNet network by the means of a trunkline-dropline topology. This topology allows for ease in wiring and access to the network from multiple taps. In addition, nodes can be easily removed and added to reduce production downtime, increase network flexibility, and decrease troubleshootin... | DeviceNet | 0.784448 |
81,781 | There exists a close analogy of geometry of spacetime with the structure of defects in crystal. Dislocations are represented by torsion, disclinations by curvature. These defects are not independent of each other. A dislocation is equivalent to a disclination-antidisclination pair, a disclination is equivalent to a str... | Teleparallelism | 0.784447 |
81,782 | This is identified with the translational (co-)tetrad which is a one-form which takes on values in the Lie algebra of the translational Abelian group R4, whence it is gauge invariant. But what does this mean? xa = ξa(p) is a local section of the (pure translational) affine internal bundle M → M, another important struc... | Teleparallelism | 0.784447 |
81,783 | In any particular gauge, the value of xa at the point p is given by the section The covariant derivative is defined with respect to the connection form B, a 1-form assuming values in the Lie algebra of the translational abelian group R4. Here, d is the exterior derivative of the ath component of x, which is a scalar fi... | Teleparallelism | 0.784447 |
81,784 | Over the last century, they have been the focus of extensive research, particularly in trophic ecology, and continue to provoke important ideas that are relevant beyond this unique ecosystem. For example, kelp forests can influence coastal oceanographic patterns and provide many ecosystem services.However, the influenc... | Kelp bed | 0.784446 |
81,785 | In physics, the stochastic vacuum model is a nonperturbative, phenomenological approach to derive cross section in quantum chromodynamics. It is deemed impossible to calculate the vacuum averages of gauge-invariant quantities in QCD in a closed form, e.g. using the path integrals. But standard perturbation theory techn... | Stochastic vacuum model | 0.784444 |
81,786 | H. Schwartz observed in 1955 that the decay of the tritium molecule T2 = 3H2 should generate the helium hydride ion + with high probability. In 1963, F. Cacace at the Sapienza University of Rome conceived the decay technique for preparing and studying organic radicals and carbenium ions. In a variant of that technique,... | Helium hydride ion | 0.784443 |
81,787 | It is believed to be the first compound to have formed in the universe, and is of fundamental importance in understanding the chemistry of the early universe. This is because hydrogen and helium were almost the only types of atoms formed in Big Bang nucleosynthesis. Stars formed from the primordial material should cont... | Helium hydride ion | 0.784443 |
81,788 | Iron tetracarbonyl dihydride undergoes rapid ligand substitutions by phosphorus ligands: H2Fe(CO)4 + PPh3 → H2Fe(CO)3PPh3The substitution mechanism is proposed to entail transient formation of a 16e− formyl intermediate.H2Fe(CO)4 has pK1 of 6.8 and pK2 of 15. The monoanion − has more extensive reaction chemistry becaus... | Iron carbonyl hydride | 0.784442 |
81,789 | The descriptor "surround suppression" suffers from a similar problem, as the activities of neurons in the "surround" of the "classical receptive field are similarly determined by connectivities and processes involving neurons beyond it.) This nonlinear effect is one of many that reveals the complexity of biological sen... | Surround suppression | 0.78444 |
81,790 | The goal of computer vision is to perform automated tasks similar to those of the human visual system, quickly and accurately interpreting the world and making decisions based on visual information. Because surround suppression seems to play a role in efficient and accurate perception, there have been a few computer vi... | Surround suppression | 0.78444 |
81,791 | If many cells respond to parts of the same stimulus, for instance, a lot of redundant information is encoded. The cell needs metabolic energy for each action potential it produces. Therefore, surround suppression likely helps to produce a neural code that is more metabolically efficient. There are additional theoretica... | Surround suppression | 0.78444 |
81,792 | The concept of synapomorphy depends on a given clade in the tree of life. Cladograms are diagrams that depict evolutionary relationships within groups of taxa. These illustrations are accurate predictive device in modern genetics. They are usually depicted in either tree or ladder form. | Apomorphy and synapomorphy | 0.784439 |
81,793 | In phylogenetics, an apomorphy (or derived trait) is a novel character or character state that has evolved from its ancestral form (or plesiomorphy). A synapomorphy is an apomorphy shared by two or more taxa and is therefore hypothesized to have evolved in their most recent common ancestor. In cladistics, synapomorphy ... | Apomorphy and synapomorphy | 0.784439 |
81,794 | Years after the exposition of Einstein via his EPR experiment, many physicists started performing experiments to show that Einstein's view of a spooky action in a distance is indeed consistent with the laws of physics. The first experiment to definitively prove that this was the case was in 1949, when physicists Chien-... | Quantum revolution | 0.784439 |
81,795 | These properties are incompatible according to the formalism. 6) Since natural and obvious requirements have forced the conclusion that photon 2 simultaneously possesses incompatible properties, this means that, even if it is not possible to determine these properties simultaneously and with arbitrary precision, they a... | Quantum revolution | 0.784439 |
81,796 | The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science, insofar as the disagreements—and the outcome of Bohr's version of quantum mechanics becoming the prevalent vie... | Quantum revolution | 0.784439 |
81,797 | Maxima does not include many of the numerous features added during the period of commercial development between 1982–1999, but is a current, free, open codebase that includes numerous additional features, several alternative front ends, and works with a number of Common Lisp engines. While this has resulted in some inc... | Macsyma | 0.784438 |
81,798 | Later major contributors to the core mathematics engine were: Yannis Avgoustis (special functions), David Barton (solving algebraic systems of equations), Richard Bogen (special functions), Bill Dubuque (indefinite integration, limits, power series, number theory, special functions, functional equations, pattern matchi... | Macsyma | 0.784438 |
81,799 | Also Macsyma's matrices were implemented as lists of lists, which cost another factor of perhaps 5–10 in speed for key algorithms. Macsyma did not have many of the basic algorithms of numerical linear algebra, such as LU decomposition. In 1987-88, the Macsyma group tried to build a PC Macsyma with Gold Hill Lisp. | Macsyma | 0.784438 |
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