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This technique is much faster than traditional histology (5 minutes vs 16 hours) and is used in conjunction with medical procedures to achieve a quick diagnosis. Cryosections can also be used in immunohistochemistry as freezing tissue stops degradation of tissue faster than using a fixative and does not alter or mask i...
Microtome
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The optimal angle depends upon the knife geometry, the cut speed and many other parameters. If the angle is adjusted to zero, the knife cut can often become erratic, and a new location of the knife must be used to smooth this out. If the angle is too large, the sample can crumple and the knife can induce periodic thick...
Microtome
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Note that Z / Z {\displaystyle \mathbb {Z} /\mathbb {Z} } is also a faithful Z {\displaystyle \mathbb {Z} } module. So, this also provides an example of a faithful Artinian module over a non-artinian ring. This does not happen for Noetherian case; If M is a faithful Noetherian module over A then A is Noetherian as wel...
Artinian module
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In mathematics, specifically abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over itself (with left or right multiplication). ...
Artinian module
0.779761
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In mathematics, the Milman–Pettis theorem states that every uniformly convex Banach space is reflexive. The theorem was proved independently by D. Milman (1938) and B. J. Pettis (1939). S. Kakutani gave a different proof in 1939, and John R. Ringrose published a shorter proof in 1959. Mahlon M. Day (1941) gave examples...
Milman–Pettis theorem
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Nonrenormalization theorems in supersymmetric theories are often consequences of the fact that certain objects must have a holomorphic dependence on the quantum fields and coupling constants. In this case the nonrenormalization theory is said to be a consequence of holomorphy. The more supersymmetry a theory has, the m...
Nonrenormalization theorem
0.779759
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In particle physics, the Glashow resonance is the resonant formation of the W boson in antineutrino-electron collisions: νe + e− → W−.
Glashow resonance
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The Mario Schenberg (Gravitational Wave Detector, or Brazilian Graviton Project or Graviton) is a spherical, resonant-mass, gravitational wave detector formerly run by the Physics Institute of the University of São Paulo, named after Mário Schenberg. Similar to the Dutch-run MiniGrail, the 1.15 ton, 65 cm diameter sphe...
Mario Schenberg (Gravitational Wave Detector)
0.779755
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Trends in Ecology & Evolution. 15 (4): 137–139. doi:10.1016/s0169-5347(99)01807-8.
Biological pest control
0.779754
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Greenhouse gases can be removed from the atmosphere by various processes, as a consequence of: a physical change (condensation and precipitation remove water vapor from the atmosphere). a chemical reaction within the atmosphere. For example, methane is oxidized by reaction with naturally occurring hydroxyl radical, OH·...
Green house gasses
0.779754
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Since the beginning of the Industrial Revolution, the concentrations of many of the greenhouse gases have increased. For example, the mole fraction of carbon dioxide has increased from 280 ppm to 421 ppm, or 140 ppm over modern pre-industrial levels. The first 30 ppm increase took place in about 200 years, from the sta...
Green house gasses
0.779754
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In the field of topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy).
List of specially named circles
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Squaring the circle is the problem, proposed by ancient geometers, of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that p...
List of specially named circles
0.779753
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SPOCs support blended learning and flipped classroom learning, which variously combine online resources and technology with personal engagement between faculty and students. Early research results point to improved learning and student outcomes using such approaches.In spring 2013, edX and MITx piloted two blended clas...
Small private online course
0.779752
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The Conscious Mind has been reviewed in journals such as Foundations of Physics, Psychological Medicine, Mind, The Journal of Mind and Behavior, and Australian Review of Books. The book was described by The Sunday Times as "one of the best science books of the year."
The Conscious Mind
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What is it about consciousnesses that says that consciousness must not be "aware" of that tantalising linear combination of both a dead and a live cat? It seems to me that a theory of consciousness would be needed for one to square the many world view with what one actually observes.Chalmers' earlier account of conscio...
The Conscious Mind
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So causation may also play a role. Interestingly, this account of consciousness has predictive power within the realm of quantum theory. Namely, it addresses objections made by the physicist Roger Penrose regarding the many worlds interpretation of quantum mechanics:I do not see why a conscious being need be aware of o...
The Conscious Mind
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Branch activities including technical, social and networking meetings. Special interest groups including Cook Chill, Microbiology, Nutrition, Product Development and Sensory Evaluation.
Australian Institute of Food Science and Technology
0.779751
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The Finnish Meteorological Institute has investigated air quality processes and air pollution prevention techniques since the early 1970s. Their staff members have comprehensive competence within the areas of meteorology, physics, chemistry, biology and engineering. Integrated work is done in cooperation with many othe...
Finnish Meteorological Institute
0.77975
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Inverse and hyperbolic trigonometry functions cannot be used with complex numbers. Base-e (natural) logarithms and exponentiation can be used, but not base-10. However, workarounds exist for many of those limitations.
HP 35s
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As well as variables and programs, the user can store any number of equations in the calculator. "Equations" in this context means expressions ( f(x,...) ), equalities ( f1(x,...) = f2(x,...) ), and assignments (y = f(x,...)), which are each handled in different ways. Equations typically include named variables whose v...
HP 35s
0.779748
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The calculator can be set to display values in binary, octal, or hexadecimal form, as well as the default decimal. When a non-decimal base is selected, calculation results are truncated to integers. Regardless of which display base is set, non-decimal numbers must be entered with a suffix indicating their base, which i...
HP 35s
0.779748
93,222
Indirect branching, which allows the contents of a memory register to be used as the target of a branching instruction (GTO or XEQ) is omitted from the HP 35s. No arbitrary limit to length of equations (the 33s had a limit of 255 characters). Algebraic mode uses typical infix notation (algebraic mode in the 33s used a ...
HP 35s
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The HP 35s uses either Reverse Polish Notation (RPN) or algebraic infix notation as input. Other features of the HP 35s include: Two-line alphanumeric LCD Over 800 memory registers (26 directly labelled) Scientific and statistical functions Operation in decimal, binary, octal, hexadecimal Equation solver with arbitrary...
HP 35s
0.779748
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The RPN version is significantly shorter. Algebraic version: RPN version: Equations may be embedded in programs, as a single program step.
HP 35s
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As in normal operation, programming can be done in either RPN or algebraic (infix) mode. RPN-mode programs are usually smaller and faster.Here is a sample program that computes the factorial of an integer number from 2 to 69 (ignoring the calculator's built-in factorial/gamma function). There are two versions of the ex...
HP 35s
0.779748
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The 35s's statistics capabilities are fairly standard. It can process a set of one-variable or two-variable statistics. Calculated results include means, weighted mean, standard deviation, and linear regression figures. The summation registers are also accessible for further calculations. Probability functions (combina...
HP 35s
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Algebraic mode works by the user entering an expression, then pressing ↵ Enter to have it evaluated. The expression appears on the upper line of the display, the result on the lower line. The expression can be edited using the arrow and backspace keys, and re-evaluated as desired.
HP 35s
0.779748
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The 35s supports both RPN and algebraic entry modes. Like most HP calculators, it defaults to RPN. The entry mode can be easily changed by the user. An annunciator on the display indicates the current entry mode.
HP 35s
0.779748
93,229
The permanently allocated variables and the statistics registers may also be accessed indirectly, using negative sequence numbers of -1 to -32. The calculator provides a set of 41 mathematical and physical constants, which may be scrolled through and selected using the CONST key. A set of 12 binary flags are available;...
HP 35s
0.779748
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The 35s provides 30k bytes of user memory, which is shared among data, stored equations, and programs. Since complex numbers and vectors of up to three elements can be stored as a single value, each data variable occupies 37 bytes, enough for a type indicator and three floating-point numbers.The 26 alpha-labelled varia...
HP 35s
0.779748
93,231
The Perko pair gives a counterexample to a "theorem" claimed by Little in 1900 that the writhe of a reduced diagram of a knot is an invariant (see Tait conjectures), as the two diagrams for the pair have different writhes. In some later knot tables, the knots have been renumbered slightly (knots 10163 to 10166 are renu...
Perko pair
0.779748
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In mathematics, Waldspurger's theorem, introduced by Jean-Loup Waldspurger (1981), is a result that identifies Fourier coefficients of modular forms of half-integral weight k+1/2 with the value of an L-series at s=k/2.
Waldspurger's theorem
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In other words, every point admits a foliation chart, i.e. the distribution Δ {\displaystyle \Delta } is tangent to the leaves of a foliation. Moreover, this local characterisation coincides with the definition of integrability for a G {\displaystyle G} -structures, when G {\displaystyle G} is the group of real inverti...
Distribution (differential geometry)
0.779745
93,234
The definitions of integral manifolds and of integrability given above applies also to the singular case (removing the requirement of the fixed dimension). However, Frobenius theorem does not hold in this context, and involutivity is in general not sufficient for integrability (counterexamples in low dimensions exist)....
Distribution (differential geometry)
0.779745
93,235
Convolutional neural networks running on GPUs. Hyperparameter grid search in machine learning. Parallel search in constraint programming
Embarrassingly parallel
0.779744
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Sieving step of the quadratic sieve and the number field sieve. Tree growth step of the random forest machine learning technique. Discrete Fourier transform where each harmonic is independently calculated.
Embarrassingly parallel
0.779744
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Ensemble calculations of numerical weather prediction. Event simulation and reconstruction in particle physics. The marching squares algorithm.
Embarrassingly parallel
0.779744
93,238
Notable real-world examples include distributed.net and proof-of-work systems used in cryptocurrency. BLAST searches in bioinformatics with split databases. Large scale facial recognition systems that compare thousands of arbitrary acquired faces (e.g., a security or surveillance video via closed-circuit television) wi...
Embarrassingly parallel
0.779744
93,239
Rendering of computer graphics. In computer animation, each frame or pixel may be rendered independently (see parallel rendering). Some brute-force searches in cryptography.
Embarrassingly parallel
0.779744
93,240
Users can select their own type of participation based on the system capability. In projector-based virtual reality, modeling of the real environment plays a vital role in various virtual reality applications, including robot navigation, construction modeling, and airplane simulation. Image-based virtual reality system...
Virtual reality simulator
0.779743
93,241
Tamper resistance finds application in smart cards, set-top boxes and other devices that use digital rights management (DRM). In this case, the issue is not about stopping the user from breaking the equipment or hurting themselves, but about either stopping them from extracting codes, or acquiring and saving the decode...
Tamper resistance
0.779743
93,242
Mandiant is an American cybersecurity firm and a subsidiary of Google. It rose to prominence in February 2013 when it released a report directly implicating China in cyber espionage. In December 2013, Mandiant was acquired by FireEye for $1 billion, who eventually sold the FireEye product line, name, and its employees ...
Mandiant
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One application area that has seen significant academic effort and some commercial effort is in the area of particle detection in fluids. Particle detection of small fluid-borne particles down to about 1 μm in diameter is typically done using a Coulter counter, in which electrical signals are generated when a weakly-co...
Microfluidic device
0.779741
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Although these methods have benefits, they currently lack the ability to be produced at large scale that is needed for commercialization. Microfluidics are also used in research as they allow for innovation in food chemistry and food processing. An example in food engineering research is a novel micro-3D-printed device...
Microfluidic device
0.779741
93,245
Excessive profiling or the manipulation of people is forbidden. "In October 2021, an International Network on Digital Self-Determination was created with the intention of "bringing together diverse perspectives from different fields around the world to study and design ways to engage in trustworthy data spaces and ensu...
Digital self-determination
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For example, Japan's government established its "Social Principles of Human-Centric AI", which is closely linked to its "AI strategy 2019: AI for Everyone: People, Industries, Regions and Governments", and a separate set of AI Utilization Guidelines that encourage voluntary adherence and emphasize that AI shall be used...
Digital self-determination
0.779737
93,247
These behaviors are promising for the development of technologies in quantum computing, spin superconductors, and low power electronics. As of 2019, more Kagome materials displaying similar topology were being experimented with, such as in magnetically doped Weyl-Semimetals Co2MnGa and Co3Sn2S2. The new class of Kagome...
Fe3Sn2
0.779737
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By building metal out of a ferromagnetic material, that exterior magnetic field was no longer necessary, and the quantum Hall effect persists into room temperature. The Kagome alloy Fe3Sn2 displayed several exotic quantum electronic behaviors that add to its quantum topology. The lattice harbors massive Dirac fermions,...
Fe3Sn2
0.779737
93,249
Therefore, this is an ideal system to explore the rich interplay between geometry, correlation, and topology. In the Kagome structure, atoms are arranged into layered sets of overlapping triangles so that there exist large empty hexagonal spaces. Electrons in the metal experience a "three-dimensional cousin of the quan...
Fe3Sn2
0.779737
93,250
They generally feature a 3d transition metal based magnetic kagome lattice with an in-plane lattice constant ~5.5 Å. Their 3d electrons dominate the low-energy electronic structure in these quantum materials, thus exhibiting electronic correlation. Crucially, the kagome lattice electrons generally feature Dirac band cr...
Fe3Sn2
0.779737
93,251
Artificial intelligence and digital self-determination The proliferation of artificial intelligence (AI), as not a single technology but rather a set of technologies, is increasingly shaping the technologically-mediated spaces for individuals and communities to conduct their lives. From algorithmic recommendation in e-...
Digital self-determination
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93,252
The DSA is one of two proposals of the Digital Services Act package.The Digital Markets Act, a legislative proposal aimed at regulating the performance of the large online platforms acting as "gatekeepers" in the European Single Market, thus guaranteeing fair competition and "leveling the playing field". The DMA is one...
Digital self-determination
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93,253
the EU Commission Digital Strategy, the European Data Strategy, and the EU's White Paper on Artificial Intelligence. Subsequently, the EU has pursued the abovementioned objectives through the adoption or proposal of several legal instruments including: The General Data Protection Regulation, aimed at laying down "rules...
Digital self-determination
0.779737
93,254
In organic chemistry, organic peroxides are organic compounds containing the peroxide functional group (R−O−O−R′). If the R′ is hydrogen, the compounds are called hydroperoxides, which are discussed in that article. The O−O bond of peroxides easily breaks, producing free radicals of the form RO• (the dot represents an ...
Dialkyl peroxides
0.779736
93,255
In mechanical engineering, an envelope is a solid representing all positions which may be occupied by an object during its normal range of motion. Another (jargon) word for this is a "flop".
Work envelope
0.779736
93,256
The Alexander von Humboldt Biological Resources Research Institute (Spanish: Instituto de Investigación de Recursos Biológicos Alexander von Humboldt), sometimes referred to as IAVH, is an independent non-regulatory research institute of the Executive Branch of the Government of Colombia charged with conducting scienti...
Alexander von Humboldt Biological Resources Research Institute
0.779735
93,257
Skyglobe is an astronomy program for MS-DOS and Microsoft Windows first developed in the late 1980s and early 1990s, and originally sold as Shareware but now available as closed-source freeware. It plots the positions of stars, Messier objects, planets, sun and moon.Skyglobe was designed by Mark A. Haney and his compan...
Skyglobe
0.779735
93,258
Fault fluids are conductive, and can produce telluric currents at depth. The resulting change in the local magnetic field in the fault triggers dissolution of minerals and weakens the rock, while also potentially changing the groundwater chemistry and level. After the seismic event, different minerals may be precipitat...
Earthquake prediction
0.779734
93,259
When the solar data are removed from the time series, the correlation is no longer statistically significant. A subsequent article in Physics of the Earth and Planetary Interiors in 2020 shows that solar weather and ionospheric disturbances are a potential cause to trigger large earthquakes based on this statistical re...
Earthquake prediction
0.779734
93,260
The study of such currents and interactions is known as "Freund physics".Most seismologists reject Freund's suggestion that stress-generated signals can be detected and put to use as precursors, for a number of reasons. First, it is believed that stress does not accumulate rapidly before a major earthquake, and thus th...
Earthquake prediction
0.779734
93,261
In his investigations of crystalline physics, Friedemann Freund found that water molecules embedded in rock can dissociate into ions if the rock is under intense stress. The resulting charge carriers can generate battery currents under certain conditions. Freund suggested that perhaps these currents could be responsibl...
Earthquake prediction
0.779734
93,262
Iben Browning (a scientist with a Ph.D. degree in zoology and training as a biophysicist, but no experience in geology, geophysics, or seismology) was an "independent business consultant" who forecast long-term climate trends for businesses. He supported the idea (scientifically unproven) that volcanoes and earthquakes...
Earthquake prediction
0.779734
93,263
For validation testing, DeVries et al. (2018) reserved 10% of positive training earthquake data samples and an equal quantity of randomly chosen negative samples.Arnaud Mignan and Marco Broccardo have similarly analyzed the application of artificial neural networks to earthquake prediction. They found in a review of li...
Earthquake prediction
0.779734
93,264
Using the Theano and TensorFlow software libraries, DeVries et al. (2018) trained a neural network that achieved higher accuracy in the prediction of spatial distributions of earthquake aftershocks than the previously established methodology of Coulomb failure stress change. Notably, DeVries et al. (2018) reported that...
Earthquake prediction
0.779734
93,265
Due to the rarity of the most catastrophic earthquakes, acquiring representative data remains problematic. In response, Rouet-Leduc et al. (2019) have conjectured that their model would not need to train on data from catastrophic earthquakes, since further research has shown the seismic patterns of interest to be simil...
Earthquake prediction
0.779734
93,266
In southern California about 6% of M≥3.0 earthquakes are "followed by an earthquake of larger magnitude within 5 days and 10 km." In central Italy 9.5% of M≥3.0 earthquakes are followed by a larger event within 48 hours and 30 km. While such statistics are not satisfactory for purposes of prediction (giving ten to twen...
Earthquake prediction
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93,267
On the other hand, the Section "Earthquake Precursors and Prediction" of "Encyclopedia of Solid Earth Geophysics: part of "Encyclopedia of Earth Sciences Series" (Springer 2011) ends as follows (just before its summary): "it has recently been shown that by analyzing time-series in a newly introduced time domain "natura...
Earthquake prediction
0.779734
93,268
More recent work, by employing modern methods of statistical physics, i.e., detrended fluctuation analysis (DFA), multifractal DFA and wavelet transform revealed that SES are clearly distinguished from signals produced by man made sources.The validity of the VAN method, and therefore the predictive significance of SES,...
Earthquake prediction
0.779734
93,269
The most touted, and most criticized, claim of an electromagnetic precursor is the VAN method of physics professors Panayiotis Varotsos, Kessar Alexopoulos and Konstantine Nomicos (VAN) of the University of Athens. In a 1981 paper they claimed that by measuring geoelectric voltages – what they called "seismic electric ...
Earthquake prediction
0.779734
93,270
Extrapolation from the 1966 event led to a prediction of an earthquake around 1988, or before 1993 at the latest (at the 95% confidence interval). The appeal of such a method is that the prediction is derived entirely from the trend, which supposedly accounts for the unknown and possibly unknowable earthquake physics a...
Earthquake prediction
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(335 pp.). ISBN 978-0-691-12807-8". Physics Today.
Earthquake prediction
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93,272
Robbins, Stuart (1 September 2012). "Lunatic Earthquakes: Do Tides Cause Quakes?". Exposing PseudoAstronomy Podcast. – discussing why the claim that earthquakes can be predicted is false.
Earthquake prediction
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93,273
In 2015 it carried out research into the biochemistry of hydration.It conducts research into public health and into children's health, and types of exercise.
School of Sport, Exercise and Health Sciences
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93,274
It teaches sports psychology, sport biomechanics, exercise physiology and exercise biochemistry.
School of Sport, Exercise and Health Sciences
0.779732
93,275
Much of the early work on the chemistry of the firefly luminescence was done in the lab of William D. McElroy at Johns Hopkins University. The luciferin was first isolated and purified in 1949, though it would be several years until a procedure was developed to crystallize the compound in high yield. This, along with t...
Firefly luciferin
0.779731
93,276
G is a connected, reductive algebraic group over an algebraically closed field. B is a Borel subgroup of G W is a Weyl group of G corresponding to a maximal torus of B.The Bruhat decomposition of G is the decomposition G = B W B = ⨆ w ∈ W B w B {\displaystyle G=BWB=\bigsqcup _{w\in W}BwB} of G as a disjoint union of do...
Bruhat decomposition
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93,277
The cells in the Bruhat decomposition correspond to the Schubert cell decomposition of flag varieties. The dimension of the cells corresponds to the length of the word w in the Weyl group. Poincaré duality constrains the topology of the cell decomposition, and thus the algebra of the Weyl group; for instance, the top d...
Bruhat decomposition
0.779729
93,278
Let G be the general linear group GLn of invertible n × n {\displaystyle n\times n} matrices with entries in some algebraically closed field, which is a reductive group. Then the Weyl group W is isomorphic to the symmetric group Sn on n letters, with permutation matrices as representatives. In this case, we can take B ...
Bruhat decomposition
0.779729
93,279
In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upp...
Bruhat decomposition
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93,280
Kevin H. Knuth is an associate professor of physics at the University at Albany (SUNY). Knuth conducts research in information physics, foundations of quantum mechanics, and Bayesian analysis with applications towards various problems in physics. He also conducts research into UFOs.
Kevin Knuth
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After receiving his doctorate, Knuth taught in the Department of Speech and Hearing Sciences of the Graduate Center, CUNY, the Departments of Otolaryngology and Neuroscience of the Albert Einstein College of Medicine, and the Department of Physiology and Biophysics of the Cornell University Medical Center from 1997 to ...
Kevin Knuth
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93,282
Knuth received a Bachelor of Science in physics and mathematics from the University of Wisconsin–Oshkosh in 1988, a Master of Science in physics from Montana State University in 1990, and a PhD in physics (with a minor in mathematics) from the University of Minnesota (1995).
Kevin Knuth
0.779728
93,283
ddal is an epidemiological model for sharka providing simulation of dispersal and optimization of control strategies for either epidemiological or economic threshold goals.Sources of resistance exist in Prunus, but are not common. A team of scientists from the United States and France has genetically engineered a plum ...
Plum pox virus
0.779728
93,284
In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X {\displaystyle X} to itself by means of traces of the induced mappings on the homology groups of X {\displaystyle X} . It is named after Solomon Lefschetz, who first sta...
Lefschetz–Hopf theorem
0.779725
93,285
The theory of time series analysis makes use of the idea of decomposing a times series into deterministic and non-deterministic components (or predictable and unpredictable components). See Wold's theorem and Wold decomposition.
Decomposition of time series
0.779724
93,286
Kendall shows an example of a decomposition into smooth, seasonal and irregular factors for a set of data containing values of the monthly aircraft miles flown by UK airlines.In policy analysis, forecasting future production of biofuels is key data for making better decisions, and statistical time series models have re...
Decomposition of time series
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93,287
The recipients of the Hans Schneider Prize in Linear Algebra are: 1993: Miroslav Fiedler 1993: Shmuel Friedland 1993: Israel Gohberg 1996: Mike Boyle 1996: David Handelman 1996: Robert C. Thompson 1999: Ludwig Elsner 2002: Tsuyoshi Ando 2002: Peter Lancaster 2005: Richard A. Brualdi 2005: Richard S. Varga 2010: Cleve M...
Hans Schneider Prize in Linear Algebra
0.779723
93,288
The Hans Schneider Prize in Linear Algebra is awarded every three years by the International Linear Algebra Society. It recognizes research, contributions, and achievements at the highest level of linear algebra and was first awarded in 1993. It may be awarded for an outstanding scientific achievement or for lifetime c...
Hans Schneider Prize in Linear Algebra
0.779723
93,289
A drilling rig is used to create a borehole or well (also called a wellbore) in the earth's sub-surface, for example in order to extract natural resources such as gas or oil. During such drilling, data is acquired from the drilling rig sensors for a range of purposes such as: decision-support to monitor and manage the ...
Mud pulse technology
0.779722
93,290
Twiggs presented the idea to Puig-Suari in the summer of 1999 and then at the Japan–U.S. Science, Technology and Space Applications Program (JUSTSAP) conference in November 1999.: 157–159 The term "CubeSat" was coined to denote nanosatellites that adhere to the standards described in the CubeSat design specification. C...
3U CubeSat
0.779722
93,291
Beyond the restrictions set forth by launch service providers, various technical challenges further reduce the usefulness of CubeSat propulsion. Gimbaled thrust cannot be used in small engines due to the complexity of gimbaling mechanisms, thrust vectoring must instead be achieved by thrusting asymmetrically in multipl...
3U CubeSat
0.779721
93,292
Didron and others have speculated that the description of the Trinity as three equal circles in canto 33 of Dante's Paradiso was inspired by similar images, although Dante does not detail the geometric arrangement of these circles. The psychoanalyst Jacques Lacan found inspiration in the Borromean rings as a model for ...
Borromean rings
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93,293
It is impossible to realize them using circles in three-dimensional space, but it has been conjectured that they may be realized by copies of any non-circular simple closed curve in space. In knot theory, the Borromean rings can be proved to be linked by counting their Fox n-colorings. As links, they are Brunnian, alte...
Borromean rings
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93,294
They are also an algebraic link, a link that can be decomposed by Conway spheres into 2-tangles. They are the simplest alternating algebraic link which does not have a diagram that is simultaneously alternating and algebraic. It follows from the Tait conjectures that the crossing number of the Borromean rings (the fewe...
Borromean rings
0.779721
93,295
In either case, the third circle must pass through this plane or sphere four times, without lying in it, which is impossible. Another argument for the impossibility of circular realizations, by Helge Tverberg, uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to...
Borromean rings
0.779721
93,296
The Borromean rings are typically drawn with their rings projecting to circles in the plane of the drawing, but three-dimensional circular Borromean rings are an impossible object: it is not possible to form the Borromean rings from circles in three-dimensional space. More generally Michael H. Freedman and Richard Skor...
Borromean rings
0.779721
93,297
The Borromean rings are a hyperbolic link: the space surrounding the Borromean rings (their link complement) admits a complete hyperbolic metric of finite volume. Although hyperbolic links are now considered plentiful, the Borromean rings were one of the earliest examples to be proved hyperbolic, in the 1970s, and this...
Borromean rings
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93,298
{\displaystyle \operatorname {cl} _{X}(R)+\operatorname {cl} _{X}(S).} If X {\displaystyle X} is a real TVS and S ⊆ X , {\displaystyle S\subseteq X,} then where the left hand side is independent of the topology on X ; {\displaystyle X;} moreover, if S {\displaystyle S} is a convex neighborhood of the origin then equali...
Linear topological space
0.77972
93,299
{\displaystyle \mathbb {S} .} Defining vector topologies using collections of strings is particularly useful for defining classes of TVSs that are not necessarily locally convex. If S {\displaystyle \mathbb {S} } is the set of all topological strings in a TVS ( X , τ ) {\displaystyle (X,\tau )} then τ S = τ . {\display...
Linear topological space
0.77972