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This by itself doesn't prove the 105th polynomial has another coefficient, but does show it is the first one which even has a chance of working (and then a computation of the coefficients shows it does). A theorem of Schur says that there are cyclotomic polynomials with coefficients arbitrarily large in absolute value....
Primitive nth root of unity
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The process is cost effective because it relies on computers rather than human effort, and is equally suitable for low-budget colorization and broadcast-quality or theatrical projection. A team at the Hebrew University of Jerusalem's Benin School of Computer Science and Engineering describe their method as an interacti...
Film colorization
0.795865
99,802
The role of bioturbators in sediment biogeochemistry makes bioturbation a common parameter in sediment biogeochemical models, which are often numerical models built using ordinary and partial differential equations. Bioturbation is typically represented as DB, or the biodiffusion coefficient, and is described by a diff...
Bioturbation
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Some examples of statistics are: "In a recent survey of Americans, 52% of Republicans say global warming is happening. "In this case, "52%" is a statistic, namely the percentage of Republicans in the survey sample who believe in global warming. The population is the set of all Republicans in the United States, and the ...
Sample statistic
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99,804
Thomas Hunt Morgan began his career in genetics as a saltationist and started out trying to demonstrate that mutations could produce new species in fruit flies. However, the experimental work at his lab with the fruit fly, Drosophila melanogaster showed that rather than creating new species in a single step, mutations ...
Neo-darwinian synthesis
0.795865
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Aquametry in analytical chemistry refer to analytical processes to measure the water present in materials.The methods widely used in aquametry encompasses Karl Fischer titration, distillation, chromatography etc.
Aquametry
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99,806
Indeed, if g were a total computable function extending f then g would be computable by some Turing machine; fix e as the index of such a machine. Build a Turing machine M, using Kleene's recursion theorem, which on input 0 simulates the machine with index e running on an index nM for M (thus the machine M can produce ...
Total Turing machine
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99,807
Instead of constructing flow by function composition, another approach is to formulate the flow as a continuous-time dynamic. Let z 0 {\displaystyle z_{0}} be the latent variable with distribution p ( z 0 ) {\displaystyle p(z_{0})} . Map this latent variable to data space with the following flow function: x = F ( z 0 )...
Flow-based generative model
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99,808
The tetrachloroferrate anion, with iron(III) in the center, has tetrahedral geometry. It is useful as a non-coordinating anion comparable to perchlorate. Several organoammonium salts have been studied for their novel material properties. 1-Butyl-3-methylimidazolium tetrachloroferrate is one of several ionic liquids tha...
Tetrachloroferrate
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99,809
The idea was presented in a 2018 paper by Adam Frank, an astrophysicist at the University of Rochester, and Gavin Schmidt, director of the Goddard Institute for Space Studies. Frank and Schmidt imagined an advanced civilization before humans and pondered whether it would "be possible to detect an industrial civilizatio...
Silurian hypothesis
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99,810
After a talk by Lage-Castellanos at the First Workshop on Complex Matter Physics in Havana (MarchCOMeeting'2012), professor Troy Shinbrot of Rutgers University became interested in the subject. Together with student Theo Siu, Cuban results were confirmed and expanded with new experiments and numerical simulations at Ru...
Upstream contamination
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99,811
Dingler claims that this operational analysis leads one to Euclidean geometry and Newtonian mechanics, which are the only possible results. Dingler opposed Albert Einstein's relativity theory and was therefore opposed and snubbed by most of the leaders of the German physics and mathematics community. This opposition, a...
Hugo Dingler
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99,812
Content-based image retrieval, also known as query by image content (QBIC) and content-based visual information retrieval (CBVIR), is the application of computer vision techniques to the image retrieval problem, that is, the problem of searching for digital images in large databases (see this survey for a scientific ov...
Content-based image retrieval
0.795862
99,813
Eötvös is remembered today for his experimental work on gravity, in particular his study of the equivalence of gravitational and inertial mass (the so-called weak equivalence principle) and his study of the gravitational gradient on the Earth's surface. The weak equivalence principle plays a prominent role in relativit...
Loránd Eötvös
0.795862
99,814
The proton spin crisis (or proton spin puzzle) is a theoretical crisis precipitated by a 1987 experiment by the European Muon Collaboration (EMC), which tried to determine the distribution of spin within the proton.Physicists expected that the quarks carry all a proton's spin. However, not only was the total proton spi...
Proton spin crisis
0.795861
99,815
Tenma was the second Japanese X-ray astronomy satellite launched on Feb 20 1983. Tenma carried GSFC detectors which had an improved energy resolution (by a factor of 2) compared to proportional counters and performed the first sensitive measurements of the iron spectral region for many astronomical objects. Energy Rang...
X-ray transient
0.795861
99,816
The type 2 copper center of a copper nitrite reductase is the active site of the enzyme. The Cu is bound by nitrogens of two Histidines from one monomer, and bound by one Histidine from another monomer; the Cys-His bridge to the type 1 Cu. This gives the molecule a distorted tetrahedral geometry.
Nitrite reductase
0.79586
99,817
The traditional Copenhagen interpretation of quantum mechanics rejects counterfactual definiteness as it does not ascribe any value at all to a measurement that was not performed. When measurements are performed, values result, but these are not considered to be revelations of pre-existing values. In the words of Asher...
Counterfactual definiteness
0.79586
99,818
In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped-geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-d...
Warp factor
0.79586
99,819
YugabyteDB is a distributed SQL database that aims to be strongly transactionally consistent across failure zones (i.e. ACID compliance]. Jepsen testing, the de facto industry standard for verifying correctness, has never fully passed, mainly due to race conditions during schema changes. In CAP Theorem terms YugabyteDB...
YugabyteDB
0.795859
99,820
By Steinitz's theorem, the Goldner–Harary graph is a polyhedral graph: it is planar and 3-connected, so there exists a convex polyhedron having the Goldner–Harary graph as its skeleton. Geometrically, a polyhedron representing the Goldner–Harary graph may be formed by gluing a tetrahedron onto each face of a triangular...
Goldner–Harary graph
0.795859
99,821
Lithium, sodium, and potassium bis(trimethylsilyl)amides are commercially available. When free of solvent, the lithium and sodium complexes are trimeric, and the potassium complex is dimeric in solid state. The lithium reagent may be prepared from n-butyllithium and bis(trimethylsilyl)amine: nBuLi + HN(SiMe3)2 → Li(hmd...
Metal bis(trimethylsilyl)amides
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99,822
Princeton University sponsors a fellowship honoring Robert A. Ellis that is awarded at the Princeton Plasma Physics Laboratory. == References ==
Robert Ellis (physicist)
0.795859
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The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics ...
Newtons second law
0.795859
99,824
His doctorate in biophysics was finally awarded by Harvard University in 1966. Alberts credits his initial failure with teaching him much more than his successes. "That was a very important learning experience for me. I had decided that experimental strategy was everything in science, and nobody had ever told me anythi...
Bruce Alberts
0.795859
99,825
Walter Daelemans (born June 3, 1960) is professor in computational linguistics at the University of Antwerp. He is also a research director of the Computational Linguistics and Psycholinguistics Research Center (CLiPS). Daelemans holds a Ph.D. from the Katholieke Universiteit Leuven.Daelemans pioneered the use of machi...
Walter Daelemans
0.795859
99,826
van Schuppen, Primes in several classes of the positive matrices, Linear Algebra and its Applications 277 (1998), 149–185. J.H. van Schuppen, Stochastic realization of a Gaussian stochastic control system, Acta Applicandae Mathematicae 35(1994), 193–212.
Jan H. van Schuppen
0.795859
99,827
Its use in military engineering for both airplanes and tank engines advanced.Aluminium obtained from recycling was considered inferior to primary aluminium because of poorer chemistry control as well as poor removal of dross and slags. Recycling grew overall but depended largely on the output of primary production: for...
History of aluminium
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99,828
4 (1970), 337-352.1979 Alberto Calderón for "his fundamental work on the theory of singular integrals and partial differential equations" and in particularCauchy integrals on Lipschitz curves and related operators. Proc. Natl.
Bôcher Memorial Prize
0.795858
99,829
In the geometry of hyperbolic 3-space, the order-6-3 square honeycomb or 4,6,3 honeycomb is a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.
Order-6-3 pentagonal honeycomb
0.795858
99,830
In molecular biology, the catalase-related immune-responsive domain is a protein domain found in catalases. This domain carries the immune-responsive amphipathic octa-peptide that is recognised by T cells. == References ==
Catalase-related immune-responsive domain
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99,831
Higher-order functions are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the differential operator d / d x {\displaystyle d/dx} , which returns the derivative of a function f {\displaystyle f} . Higher-order functions are clo...
Functional language
0.795858
99,832
Antibody-treated mice showed significantly less cancer growth than the controls.Bluestone and Linsley separately studied the similarities between CD28 and CTLA-4. Bluestone's lab published studies, one together with Krummel and Allison, for in vitro studies of CTLA-4 function. In collaboration with Mark Jenkins, they w...
Ipilimumab
0.795858
99,833
Thomas A. Moore "Least-Action Principle" in Macmillan Encyclopedia of Physics (Simon & Schuster Macmillan, 1996), Volume 2, ISBN 0-02-897359-3, OCLC 35269891, pages 840–842. Gerald Jay Sussman and Jack Wisdom, Structure and Interpretation of Classical Mechanics (MIT Press, 2001). Begins with the principle of least acti...
Action Integral
0.795858
99,834
Firstly, there are non-isomorphic quadratic forms of a given degree, classified by signature. Every nondegenerate quadratic form on a real vector space is equivalent to the standard diagonal form: Q ( u ) = u 1 2 + ⋯ + u p 2 − u p + 1 2 − ⋯ − u p + q 2 {\displaystyle Q(u)=u_{1}^{2}+\cdots +u_{p}^{2}-u_{p+1}^{2}-\cdots ...
Pseudoscalar (Clifford algebra)
0.795858
99,835
Phenyl azide ("diazoamidobenzol"), was prepared in 1864 by Peter Griess by the reaction of ammonia and phenyldiazonium. In the 1890s, Theodor Curtius, who had discovered hydrazoic acid (HN3), described the rearrangement of acyl azides to isocyanates subsequently named the Curtius rearrangement. Rolf Huisgen described t...
Organic azide
0.795858
99,836
The next steps for the next phase of gridSMART were identified to be upgrading current technologies in order to better manage supply, reduce costs, and minimize the number of customers affected by outages. This has been proposed through the installation of smart meter technology, distribution automation circuit reconfi...
Transactive energy
0.795858
99,837
Gernot Frenking (born January 23, 1946, in Körbecke) is a German chemist known for his contribution in theoretical chemistry.
Gernot Frenking
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99,838
The components of the fields are required to have the right spin-statistic. The equations need to be slightly modified.There also exist Vasiliev's equations in other dimensions: in three dimensions there is the minimal higher-spin theory and its development, known as Prokushkin–Vasiliev theory, that is based on a one-p...
Vasiliev equations
0.795857
99,839
Polyspermy is very rare in human reproduction. The decline in the numbers of sperm that swim to the oviduct is one of two ways that prevents polyspermy in humans. The other mechanism is the blocking of sperm in the fertilized egg. According to Developmental Biology Interactive, if an egg becomes fertilized by multiple ...
Polyspermy
0.795857
99,840
If G {\displaystyle G} is a graph that contains a subgraph H {\displaystyle H} that is a subdivision of K 5 {\displaystyle K_{5}} or K 3 , 3 {\displaystyle K_{3,3}} , then H {\displaystyle H} is known as a Kuratowski subgraph of G {\displaystyle G} . With this notation, Kuratowski's theorem can be expressed succinctly:...
Kuratowski's theorem
0.795857
99,841
On the contrary, acronym SPASER (Surface Plasmon Amplification by Stimulated Emission of Radiation) is capitalized. Many scientific acronyms or abbreviations reflect the artistic sense of their creators, e.g., AMANDA – Antarctic Muon And Neutrino Detector Array, a neutrino telescope BLAST – Balloon-borne Large Aperture...
Scientific terminology
0.795857
99,842
Furthermore, studying bipedal and insect-like robots may beneficially impact on biomechanics. A major goal in this field is in developing capabilities for robots to autonomously decide how, when, and where to move. However, coordinating numerous robot joints for even simple matters, like negotiating stairs, is difficul...
Robot locomotion
0.795856
99,843
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations are strongly conti...
Unitary representation
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99,844
In Algebraic Multigrid Methods and in iterative aggregation methods in mathematical economics and Markov chains, the coarse problem is generally obtained by the Galerkin approximation on a subspace. In mathematical economics, the coarse problem may be obtained by the aggregation of products or industries into a coarse ...
Coarse space (numerical analysis)
0.795856
99,845
Psychopharmacology is the study of the use of drugs that affect the psyche, mind and behavior (e.g. antidepressants) in treating mental disorders (e.g. depression). It incorporates approaches and techniques from neuropharmacology, animal behavior and behavioral neuroscience, and is interested in the behavioral and neur...
Pharmacology
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99,846
": 639 Other fields or branches related to the historical development of human ecology as a discipline include cultural ecology, urban ecology, environmental sociology, and anthropological ecology. Even though the term ‘human ecology' was popularized in the 1920s and 1930s, studies in this field had been conducted sinc...
Human ecology
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99,847
(1974). "The DAD theorem for arbitrary row sums". Proc.
Richard A. Brualdi
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99,848
Anatoly Kondratenko (Russian: Анатолий Кондратенко, Ukrainian: Анатолій Кіндратенко; 6 December 1935, Leningrad, Soviet Union) is a Professor of Physics at University of Kharkiv. A theoretical physicist who has been working in the field of plasma and plasma electronics for over 50 years, Kondratenko has written over 27...
Anatoly Kondratenko
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99,849
Later, as Professor Emeritus of Chemistry of the University of Wisconsin–Madison, he led a group of solar scientists who proposed that AFASE be reorganized, that its directors and officers be elected by the membership, and that the name be changed to The Solar Energy Society – all of which was done. He supported solar ...
Farrington Daniels
0.795854
99,850
According to one of the researchers, "If life arose relatively quickly on Earth … then it could be common in the universe. "All organisms on Earth are descended from a common ancestor or ancestral gene pool. Highly energetic chemistry is thought to have produced a self-replicating molecule around 4 billion years ago, a...
Basal animal
0.795854
99,851
In 1967, a radio signal was detected using the Interplanetary Scintillation Array of the Mullard Radio Astronomy Observatory in Cambridge, UK, by Jocelyn Bell Burnell. The signal had a 1.337302088331-second period (not in 1967, but in 1991) and 0.04-second pulsewidth. It originated at celestial coordinates 19h 19m righ...
PSR B1919+21
0.795854
99,852
These concessions preserve the spirit of empiricism insofar as the restriction to experience still applies to knowledge about the external world. In some fields, like metaphysics or ethics, the choice between empiricism and rationalism makes a difference not just for how a given claim is justified but for whether it is...
Empirical validation
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99,853
In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness theorem when the two varieties are birational. Zaris...
Zariski's main theorem
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99,854
This naturally sets the low energy scale of the dark energy.In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w = −1) from above to below. A no-go theorem has been proved that this scenario...
Dark Energy
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99,855
These results are in accord with computational chemistry results, which further assert that the transition state is under kinetic control. Significantly, these stereochemical experiments imply that the cationic 2-aza-Cope rearrangement (as well as Mannich cyclization) occur faster than enol or iminium tautomerization. ...
Aza-Cope rearrangement
0.795853
99,856
The concepts that seeded nanotechnology were first discussed in 1959 by renowned physicist Richard Feynman in his talk There's Plenty of Room at the Bottom, in which he described the possibility of synthesis via direct manipulation of atoms. The term "nano-technology" was first used by Norio Taniguchi in 1974, though i...
Nano sciences
0.795853
99,857
The mechanotransduction of these physical cues to endothelial and smooth muscle cells in the vascular wall can also trigger the promotion or repression of certain genes which are responsible for vasodilation, cell alignment, and other shear stress-mitigating factors. This relationship between genetics and environment i...
Vascular remodelling in the embryo
0.795853
99,858
The encoder calculates a log mel spectrogram and performs vector quantization to store the spectrogram in a data stream. The decoder is a WaveNet neural network that takes the spectrogram and reconstructs the input audio.A second version (v2/1.2.0), released in September 2022, improved sound quality, latency, and perfo...
Lyra (codec)
0.795853
99,859
Additionally, low-temperature isothermal mechanical cycling is typically modeled with a combination of LCF and HCF strain range or strain energy models. The solder alloy, assembly geometry and materials, boundary conditions, and loading conditions will affect whether fatigue damage is dominated by elastic (HCF) or plas...
Solder Fatigue
0.795853
99,860
Neither Lefschetz's proof nor Andreotti and Frankel's proof directly imply the Lefschetz hyperplane theorem for homotopy groups. An approach that does was found by René Thom no later than 1957 and was simplified and published by Raoul Bott in 1959. Thom and Bott interpret Y as the vanishing locus in X of a section of a...
Hard Lefschetz theorem
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99,861
Critical in the history of molecular anthropology: That molecular phylogenetics could compete with comparative anthropology for determining the proximity of species to humans. Wilson and King realized in 1975, that while there was equity between the level of molecular evolution branching from chimp to human to putative...
Molecular anthropology
0.795852
99,862
The origins of Sunspot as a Solar Observatory date back to the sudden increased interest of solar physics to the US military during the Second World War. In 1940, the High Altitude Observatory (HAO) was established in 1940 in Climax, Colorado, by Walter Orr Roberts and Donald Menzel. It was associated with both Harvard...
Sunspot Solar Observatory
0.795852
99,863
In some cases, differential equations can be represented in a format that looks like delay differential equations. Example 1 Consider an equation Introduce y ( t ) = ∫ − ∞ 0 x ( t + τ ) e λ τ d τ {\displaystyle y(t)=\int _{-\infty }^{0}x(t+\tau )e^{\lambda \tau }\,d\tau } to get a system of ODEs Example 2 An equation i...
Delay differential equation
0.795852
99,864
In linear algebra and the theory of matrices, the Schur complement of a block matrix is defined as follows. Suppose p, q are nonnegative integers, and suppose A, B, C, D are respectively p × p, p × q, q × p, and q × q matrices of complex numbers. Let so that M is a (p + q) × (p + q) matrix.
Schur complement
0.795852
99,865
According to the uncertainty principle, a particle's momentum and its position cannot simultaneously be determined with arbitrarily high precision.In 1935, Einstein, Boris Podolsky, and Nathan Rosen published a claim that quantum mechanics predicts that more information about a pair of entangled particles could be obse...
Loopholes in Bell tests
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99,866
Publicly available information from biomedical documents is readily accessible through the internet and is becoming a powerful resource for collecting known protein–protein interactions (PPIs), PPI prediction and protein docking. Text mining is much less costly and time-consuming compared to other high-throughput techn...
Protein interaction
0.795851
99,867
In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they...
Tridiminished rhombicosidodecahedron
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99,868
The sbcD RNA motif is a conserved RNA structure identified using bioinformatics. sbc RNAs are found some species of bacteria classified under the family Burkholderiaceae, and usually reside in plasmids. They are always located in what might be the 5' untranslated regions of operons that include sbcD genes. sbcD genes a...
SbcD RNA motif
0.795851
99,869
Ester pyrolysis in organic chemistry is a vacuum pyrolysis reaction converting esters containing a β-hydrogen atom into the corresponding carboxylic acid and the alkene. The reaction is an Ei elimination and operates in a syn fashion. Examples include the synthesis of acrylic acid from ethyl acrylate at 590 °C, the syn...
Ester pyrolysis
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99,870
Either this number is prime, or all of its prime factors are greater than n. Without establishing a specific prime number, this proves that one exists that is greater than n, contrary to the original postulate. Now consider the theorem "there exist irrational numbers a {\displaystyle a} and b {\displaystyle b} such tha...
Constructive proof
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99,871
The AA units included the SCR-584 radar unit produced by the Radiation Lab at MIT and the proximity fuse mechanism, developed by Merle Tuve and his special Division T at NDRC, that detonated near the target using a microwave controlled fuse called the VT or variable time fuse, enabling a larger detonation reach envelop...
Hendrik Wade Bode
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99,872
Most auroras occur in a band known as the "auroral zone", which is typically 3° to 6° wide in latitude and between 10° and 20° from the geomagnetic poles at all local times (or longitudes), most clearly seen at night against a dark sky. A region that currently displays an aurora is called the "auroral oval", a band dis...
Aurora Borealis
0.79585
99,873
To date, there is no DNA extraction method applicable to any sample.Another method against olive oil adulteration, making use of artificial, sub-micrometer-sized DNA barcodes, has recently been developed. The barcodes consist of magnetically recoverable silica particles containing synthetic DNA sequences, which are add...
Olive oil regulation and adulteration
0.79585
99,874
In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid.It has two distinct forms, which are mirror images (or "enantiomorphs") of each other.
Gyroid (crystallography)
0.79585
99,875
However, as there is no consensus as to the ‘best’ basis for V k , d , n {\displaystyle V_{k,d,n}} , this term can be ambiguous. From a foundational perspective, the above theorem is usually used as the definition of Gr ⁡ ( k , d , n ) {\displaystyle \operatorname {Gr} (k,d,n)} . That is, the Chow variety is usually de...
Chow quotient
0.79585
99,876
Theriogenology is a specialty of veterinary medicine concerned with animal reproduction. This includes the physiology and pathology of male and female reproductive systems of animals and the clinical practice of veterinary obstetrics, gynecology, andrology and assisted reproductive technologies (ART). Theriogenologists...
Theriogenology
0.79585
99,877
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: MAPE = 1 n ∑ t = 1 n | A t − F t A t | {\displaystyle {\mbox{MAPE}}={\frac {...
Mean absolute percentage error
0.79585
99,878
In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands (1979, 1983) in his work on the stable trace formula. Roughly speaking, an endoscopic group H of G is a quasi-split group whose L-group is the connected component of the centralizer of a semisimple element of the L-group...
Endoscopic group
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99,879
Salvinorin A has only been administered to humans in a few studies, one showing that its effects peaked at about 2 minutes, that its subjective effects may overlap with those of serotonergic psychedelics, and that it temporarily impairs recall and recognition memory. Like most other agonists of kappa opioid receptors, ...
Salvinorin A
0.795849
99,880
In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold F {\displaystyle F} of a manifold M {\displaystyle M} is said to be 2-sided in M {\displaystyle M} when there is an embedding h: F × → M {\displaystyle h\colon F\times \to M} with h ( x , 0 ) = x {\displaystyle h(x,0)=x} for e...
2-sided
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99,881
Davidson began conducting research as a teenager at The Marine Biological Laboratory. After graduating from high school, he matriculated to the University of Pennsylvania and graduated with a B.A. in biology in 1958. Davidson's Ph.D. work entailed studying RNA synthesis and gene expression in early development of the a...
Eric H. Davidson
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99,882
The above technical condition ensures that β {\displaystyle \beta } is unique. The first above technical condition means that the degrees used in the definition of the resultant are p and q; this implies that the degree of R is pq (see Resultant § Homogeneity). As R is a homogeneous polynomial in two indeterminates, th...
Bezouts theorem
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99,883
Volume IX contains chapter XXIV on elementary differential topology. Unlike the earlier volumes there is no English translation of it. Dieudonné, J. (1982), Éléments d'analyse.
Treatise on Analysis
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Every topological vector space (and more generally, a topological group) has a canonical uniform structure, induced by its topology, which allows the notions of completeness and uniform continuity to be applied to it. If X {\displaystyle X} is a metrizable TVS and d {\displaystyle d} is a metric that defines X {\displa...
Fréchet combination
0.795848
99,885
Sarkar attended secondary school at South Point High School in his hometown, Calcutta, India. In the International Mathematical Olympiads in 2001 and 2002, he received gold and silver medals respectively. He completed his Bachelor of Mathematics degree from the Indian Statistical Institute, Bangalore in 2005.Sarkar rec...
Sucharit Sarkar
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99,886
Microfluorimetry has uses for many different fields including cell biology, microbiology, immunology, cell cycle analysis and "flow karyotyping" of cells. In flow karotyping, isolated metaphase chromosomes are stained and measured in a flow microfluorometer. Fluorescent staining of chromosomes can also give distributio...
Microfluorimetry
0.795848
99,887
V(CO)6 adopts an octahedral coordination geometry and is isostructural with chromium hexacarbonyl, even though they have differing valence electron counts. High resolution X-ray crystallography indicates that the molecule is slightly distorted with two (axial) shorter V–C distances of 1.993(2) Å vs. four (equatorial) 2...
Vanadium hexacarbonyl
0.795848
99,888
The noise levels on a trace/network is highly dependent on the routing topology selected. In a point-to-point topology, the signal is routed from the transmitter directly to the receiver (this is applied in PCIe, RapidIO, Gigabit Ethernet, DDR2/DDR3/DDR4 DQ/DQS etc.). A point-to-point topology has the least SI-problems...
Signal integrity
0.795847
99,889
The journal publishes 4 issues per year in simultaneous print and online editions and is available on a subscription basis and as individual articles All back-issues of the journal are available online on the publisher's website. Subscribers to the electronic edition of Critical Reviews in Biotechnology receive access ...
Critical Reviews in Biotechnology
0.795847
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It accounts for the user's capabilities and limitations in seeking to ensure that tasks, functions, information, and the environment suit that user. To assess the fit between a person and the used technology, human factors specialists or ergonomists consider the job (activity) being done and the demands on the user; th...
Physical ergonomics
0.795847
99,891
Serum produced for use in the biotechnology industry and research sectors is highly regulated. The collection and movement of all animal derived products globally is strictly controlled. Veterinary control of animal derived products largely follows the regulations set by the EU (DG SANCO) and the US (USDA). The current...
Fetal bovine serum
0.795846
99,892
In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube. There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube are located as pairs on the edge of the 7-cube.
Bitruncated 7-cube
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99,893
Polymake version 1.0 first appeared in the proceedings of DMV-Seminar "Polytopes and Optimization" held in Oberwolfach, November 1997. Version 1.0 only contained the polytope application, but the system of "applications" was not yet developed. Version 2.0 was released sometime in 2003, and version 3.0 was released in 2...
Polymake
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99,894
The exponential map exp: g → G {\displaystyle \exp \colon {\mathfrak {g}}\to G} is a smooth map. Its differential at zero, exp ∗: g → g {\displaystyle \exp _{*}\colon {\mathfrak {g}}\to {\mathfrak {g}}} , is the identity map (with the usual identifications). It follows from the inverse function theorem that the exponen...
Exponential map (Lie theory)
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99,895
The quadratic identities can be proved in a finite-dimensional Jordan algebra over R or C following Max Koecher, who used an invertible element. They are also easy to prove in a Jordan algebra defined by a unital associative algebra (a "special" Jordan algebra) since in that case Q(a)b = aba. They are valid in any Jord...
Quadratic Jordan algebra
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Cauer II form expands Z ( s ) {\displaystyle Z(s)} in exactly the same way as Cauer I form except that lowest degree term is extracted first in the continued fraction expansion rather than the highest degree term as is done in Cauer I form. The example used for the Cauer I form and the Foster forms when expanded as a C...
Cauer synthesis
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Beginning in the 1970s, however, inspired by work on the renormalization group and effective field theory, and despite the fact that Dirac and various others—all of whom belonged to the older generation—never withdrew their criticisms, attitudes began to change, especially among younger theorists. Kenneth G. Wilson and...
Renormalization
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99,898
The corona or corona algebra of A is the quotient M(A)/A. For example, the corona algebra of the algebra of compact operators on a Hilbert space is the Calkin algebra. The corona algebra is a noncommutative analogue of the corona set of a topological space.
Corona algebra
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The non-classical description of the 2-norbornyl cation can be seen as the donation of an electron pair from a carbon-carbon sigma bond into an empty p-orbital of carbon 2. Thus this carbocation showed that sigma-bond electron donation is as plausible as pi-bond electron donation.The intense debate that followed Brown’...
2-Norbornyl cation
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