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The Annales Henri Poincaré (A Journal of Theoretical and Mathematical Physics) is a peer-reviewed scientific journal which collects and publishes original research papers in the field of theoretical and mathematical physics. The emphasis is on "analytical theoretical and mathematical physics" in a broad sense. The jour...
Annales Henri Poincaré
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If Y {\displaystyle Y} is a Hausdorff space and S {\displaystyle S} is a dense subset of X {\displaystyle X} then a continuous extension of f: S → Y {\displaystyle f:S\to Y} to X , {\displaystyle X,} if one exists, will be unique. The Blumberg theorem states that if f: R → R {\displaystyle f:\mathbb {R} \to \mathbb {R}...
Discontinuity set
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Hash trees can be used to verify any kind of data stored, handled and transferred in and between computers. They can help ensure that data blocks received from other peers in a peer-to-peer network are received undamaged and unaltered, and even to check that the other peers do not lie and send fake blocks. Hash trees a...
Merkle tree
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The harmonic magnitude image in (c) extracted from a using the filter in (b) shows the geometry of the heart. And the harmonic phase image in (d) contains the motion of the myocardium in horizontal direction. In practice, tagged images from two directions (both horizontal and vertical, i.e., k {\displaystyle k} is 1 an...
HARP (algorithm)
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The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and Rainer K. Sachs, shows that if, in a given universe, all freely falling observers measure the cosmic background radiation to have exactly the same properties in all directions (that is, they measure the background radiation to be isotropic...
Ehlers–Geren–Sachs theorem
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Living in the intersection of cryptography and psychology, password psychology is the study of what makes passwords or cryptographic keys easy to remember or guess. In order for a password to work successfully and provide security to its user, it must be kept secret and un-guessable; this also requires the user to memo...
Password psychology
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95,906
Traditionally it served to prove the structure of a complex biocompound in addition to evidence obtained from spectroscopy. It also demonstrates new concepts in organic chemistry (reagents, reaction types) and opens the way to molecular derivatives not found in nature. And for practical purposes, a synthetic biocompoun...
Aflatoxin total synthesis
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The definition of computational photography has evolved to cover a number of subject areas in computer graphics, computer vision, and applied optics. These areas are given below, organized according to a taxonomy proposed by Shree K. Nayar. Within each area is a list of techniques, and for each technique one or two rep...
Mathematical photography
0.796649
95,908
The notion of a non-measurable set has been a source of great controversy since its introduction. Historically, this led Borel and Kolmogorov to formulate probability theory on sets which are constrained to be measurable. The measurable sets on the line are iterated countable unions and intersections of intervals (call...
Non-measurable set
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95,909
Because the Segre map is to the categorical product of projective spaces, it is a natural mapping for describing non-entangled states in quantum mechanics and quantum information theory. More precisely, the Segre map describes how to take products of projective Hilbert spaces.In algebraic statistics, Segre varieties co...
Segre mapping
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In principal ideal domains and Dedekind domains, the Jacobson radical vanishes if and only if there are infinitely many prime ideals. Any finitely generated algebra over a Jacobson ring is a Jacobson ring. In particular, any finitely generated algebra over a field or the integers, such as the coordinate ring of any aff...
Hilbert ring
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The propositional calculus gives us a very simple Scott information system as follows: T := { ϕ ∣ ϕ is satisfiable } {\displaystyle T:=\{\phi \mid \phi {\mbox{ is satisfiable}}\}} C o n := { X ∈ P f ( T ) ∣ X is consistent } {\displaystyle Con:=\{X\in {\mathcal {P}}_{f}(T)\mid X{\mbox{ is consistent}}\}} X ⊢ a ⟺ X ⊢ a ...
Scott information system
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95,912
Males can affect female reproductive success so strongly because for the 20 days up to egg-laying, females spend up to 80% of their time in the nest. This leaves males with the responsibility of providing food regularly and securing (and maintaining) a high-quality territory for nesting. This phenomenon of the genetics...
Sex-limited trait
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Under standard assumptions, the specific orbital energy ( ϵ {\displaystyle \epsilon } ) of an elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form: v 2 2 − μ r = − μ 2 a = ϵ < 0 {\displaystyle {v^{2} \over {2}}-{\mu \over {r}}=-{\mu \over {2a}}...
Elliptic orbits
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In 2012, Gunda Georg (University of Minnesota) and Shaomeng Wang (University of Michigan) succeeded Portoghese (University of Minnesota). In 2021, Craig W. Lindsley (Vanderbilt University) became editor-in-chief. According to the Journal Citation Reports, the journal has a 2021 impact factor of 8.039, ranking it 1st ou...
Journal of Medicinal Chemistry
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The bacterial sroE RNA gene is a non-coding RNA molecule of 90 nucleotides in length. sroE is found in several Enterobacterial species but its function is unknown.SroD and SroH were identified in the same bioinformatics search.
SroE RNA
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95,916
Before beginning, Forbes states, "The members of Forbes Technology Council have their finger on the pulse of upcoming technology advances, including those in the smartphone market." Forbes outlines that there will be more diverse interfaces that will feel more natural and easy to use. Increased interaction with voice a...
Mobile technologies
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Nozzles for vectored thrust include fixed geometry Bristol Siddeley Pegasus and variable geometry F119 (F-22).
Propulsive nozzle
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Localized surface plasmon resonance (LSPR)characteristically occurs in quantum dots which contain a base metal like cadmium or lead. This interaction of nano-scale metals with light is characterized by surface-bound charge density oscillations of the free electrons in resonance with the driving electromagnetic field an...
Cadmium-free quantum dot
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In number theory, Proth's theorem is a primality test for Proth numbers. It states that if p is a Proth number, of the form k2n + 1 with k odd and k < 2n, and if there exists an integer a for which a p − 1 2 ≡ − 1 ( mod p ) , {\displaystyle a^{\frac {p-1}{2}}\equiv -1{\pmod {p}},} then p is prime. In this case p is cal...
Proth's theorem
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Hadamard matrices Complex Hadamard matrices Butson-type Hadamard matrices Generalized Hadamard matrices Regular Hadamard matrices Hall's marriage theorem Perfect matching Hamming distance Hash function Hash collision Perfect hash function Heilbronn triangle problem Helly family Hypergeometric function identities Hyperg...
Index of combinatorics articles
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Groundwater refers to water located beneath the ground surface, as opposed to surface water that forms lakes and rivers. This is called hydrogeology. The nature and location of the groundwater is defined by the geological nature of the soils. In the mid-twentieth century, knowledge of groundwater in Switzerland suffere...
Hydrology of Switzerland
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CurrentRSA Lab's 72-bit RC5 Encryption Challenge — In progress, 10.413% complete as of 28 July 2023 (although RSA Labs has discontinued sponsorship)CryptographyRSA Lab's 56-bit RC5 Encryption Challenge — Completed 19 October 1997 (after 250 days and 47% of the key space tested). RSA Lab's 56-bit DES-II-1 Encryption Cha...
Distributed.net
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Abū Bakr Muḥammad ibn Yaḥyà ibn aṣ-Ṣā’igh at-Tūjībī ibn Bājja (Arabic: أبو بكر محمد بن يحيى بن الصائغ التجيبي بن باجة), best known by his Latinised name Avempace (; c. 1085 – 1138), was an Andalusi polymath, whose writings include works regarding astronomy, physics, and music, as well as philosophy, medicine, botany, a...
Avempace
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Linux at the time, the number 42 refers to the question about "life, the universe and everything" in the Hitchhiker's Guide to the Galaxy book series. After that, the basis packages are received from the SUSE Linux Enterprise, while applications and desktops come from Tumbleweed.At the openSUSE conference held in Nurem...
OpenSUSE
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W. T. Tutte conjectured that every snark has the Petersen graph as a minor. That is, he conjectured that the smallest snark, the Petersen graph, may be formed from any other snark by contracting some edges and deleting others. Equivalently (because the Petersen graph has maximum degree three) every snark has a subgraph...
Snark (graph theory)
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Derivative pricing now embeds counterparty and other considerations through the CVA and XVA "valuation adjustments". Additional to these, are various forms of stress test and scenario analytics, and related economic capital optimization. These tests are typically linked to the macroeconomics, and provide an indicator o...
Financial risk management
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Journal of Graph Theory. 63 (1): 68–81. arXiv:0805.0394. doi:10.1002/jgt.20406.
Sarah-Marie Belcastro
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In any basis, the cross-product a × b {\displaystyle a\times b} is given by the tensorial formula E i j k a i b j {\displaystyle E_{ijk}a^{i}b^{j}} where E i j k {\displaystyle E_{ijk}} is the covariant Levi-Civita tensor (we note the position of the indices). That corresponds to the intrinsic formula given here. In an...
Vector cross product
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95,929
(For Pontryagin duality the Plancherel measure is some Haar measure on the dual group to G, the only issue therefore being its normalization.) For general locally compact groups, or even countable discrete groups, the von Neumann group algebra need not be of type I and the regular representation of G cannot be written ...
Noncommutative harmonic analysis
0.796644
95,930
Mechanism is the belief that natural wholes (principally living things) are similar to complicated machines or artifacts, composed of parts lacking any intrinsic relationship to each other. The doctrine of mechanism in philosophy comes in two different flavors. They are both doctrines of metaphysics, but they are diffe...
Mechanical philosophy
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95,931
Nanotransfer printing (nTP) (compare with microcontact printing) is a purely additive and high resolution metal printing technique. It mainly relies on the principle of surface chemistry - chemically modified surfaces act as interfacial "release" or "glue" layers to aid in transfer printing nano-structured metal ink fr...
Nanotransfer printing
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95,932
In the late 1920s, Pauling began publishing papers on the nature of the chemical bond. Between 1937 and 1938, he took a position as George Fischer Baker Non-Resident Lecturer in Chemistry at Cornell University. While at Cornell, he delivered a series of nineteen lectures and completed the bulk of his famous textbook Th...
Linus Pauling
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TensorFlow Extended (abbrev. TFX) provides numerous components to perform all the operations needed for end-to-end production. Components include loading, validating, and transforming data, tuning, training, and evaluating the machine learning model, and pushing the model itself into production.
TensorFlow
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The "probability plot correlation coefficient" (PPCC plot) is the correlation coefficient between the paired sample quantiles. The closer the correlation coefficient is to one, the closer the distributions are to being shifted, scaled versions of each other. For distributions with a single shape parameter, the probabil...
Quantile plot
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95,935
The Association for Advancing Automation (A3) is an international trade group that serves the robotics industry. It was founded in 1974 and is headquartered in Ann Arbor, Michigan. The organization is involved in safety standards for robots, and sponsors robotics conferences. On April 14, 2021 the Robotic Industries As...
Association for Advancing Automation
0.796642
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In physics, a pulse is a generic term describing a single disturbance that moves through a transmission medium. This medium may be vacuum (in the case of electromagnetic radiation) or matter, and may be indefinitely large or finite.
Pulse (physics)
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95,937
Some critics believe that both human-level AI and superintelligence are unlikely, and that therefore friendly AI is unlikely. Writing in The Guardian, Alan Winfield compares human-level artificial intelligence with faster-than-light travel in terms of difficulty, and states that while we need to be "cautious and prepar...
Friendly artificial intelligence
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(2010). A linguistic ontology of space for natural language processing. Artificial Intelligence, 174(14), 1027–1071. == References ==
John A. Bateman
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doi:10.1090/S0025-5718-1987-0866113-7. MR 0866113.Peter L. Montgomery (1995), "A block Lanczos algorithm for finding dependencies over GF(2)", Advances in cryptology—EUROCRYPT '95 (Saint-Malo, 1995), Lecture Notes in Computer Science, Springer-Verlag, vol. 921, pp. 106–120, doi:10.1007/3-540-49264-X_9, ISBN 978-3-540-5...
Peter Montgomery (mathematician)
0.796642
95,940
If G {\displaystyle \mathrm {G} } is a semisimple algebraic group over a number field F {\displaystyle F} and A {\displaystyle \mathbb {A} } its adèle ring then the group G = G ( A ) {\displaystyle G=\mathrm {G} (\mathbb {A} )} of adélic points is well-defined (modulo some technicalities) and it is a locally compact gr...
Tree lattice
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95,941
As quantum theories such as Wave–particle duality and the behavior of matter on a subatomic behavior evolves, theories have emerged that life is central to being, reality, and the cosmos. Biocentrism, a theory proposed in 2007 by American scientist Robert Lanza, posits that life creates the universe rather than the oth...
Quantum fiction
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95,942
Durham tubes are used in microbiology to detect production of gas by microorganisms. They are simply smaller test tubes inserted upside down in another test tube so they are freely movable. The culture media to be tested is then added to the larger tube and sterilized, which also eliminates the initial air gap produced...
Durham tube
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95,943
The angles which the circumscribed circle forms with the sides of the triangle coincide with angles at which sides meet each other. The side opposite angle α meets the circle twice: once at each end; in each case at angle α (similarly for the other two angles). This is due to the alternate segment theorem, which states...
Circumcenter
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95,944
Furthermore, the quality of the accurate and timely results must be assessed prior to release. But if errors in the results occur before or after the data revision, they should be directly corrected and information should be disseminated to the users at the earliest possible time. Producers of official statistics have ...
Official statistics
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95,945
There are efficient numerical methods to determine whether an LMI is feasible (e.g., whether there exists a vector y such that LMI(y) ≥ 0), or to solve a convex optimization problem with LMI constraints. Many optimization problems in control theory, system identification and signal processing can be formulated using LM...
Linear Matrix Inequalities
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(1957) under the aegis of pioneering computational chemist S. Francis Boys.Following postdoctoral work with Joseph O. Hirschfelder, a stint as a temporary assistant professor at Brandeis University, and further postdoctoral research with Martin Karplus, he became a professor at his alma mater in 1962. In 1967 he moved ...
Isaiah Shavitt
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He is the author or co-author of over 100 articles in refereed journal and has served on several editorial boards. Gregory Beylkin's research is focused on analysis and development of fast algorithms for solving integral and differential equations. Applications include quantum chemistry, gravity field evaluation and es...
Gregory Beylkin
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Most skin injury types can contribute to scarring. This includes burns, acne scars, chickenpox scars, ear piercing, scratches, surgical incisions, and vaccination sites. According to the (US) National Center for Biotechnology Information, keloid scarring is common in young people between the ages of 10 and 20. Studies ...
Keloid
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Many textbooks describe carbon nanotubes (CNTs) in easily understood terms: carbon nanotubes are tubular structures made entirely of rolled-up layers of graphene. The diameters of CNTs ranges from about one nanometer to tens of nanometers, while their lengths can be up to centimeters, much greater than the diameters. I...
Carbon nanotube supported catalyst
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95,950
The Dedekind zeta-function satisfies a functional equation and can be extended by analytic continuation to the whole complex plane. The resulting function encodes important information about the number field K. The extended Riemann hypothesis asserts that for every number field K and every complex number s with ζK(s) =...
Extended Riemann hypothesis
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(1983), Physical Chemistry, second edition, McGraw-Hill, New York, ISBN 978-0072538625. Lieb, E. H.; Yngvason, J. (1999).
Equilibrium state
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95,952
S-layers have many potential biotechnology applications. The use of the high-resolution MA0829 structure to facilitate such studies is complicated by difficulties in reconstituting archaeal S-layers in vitro. == References ==
Methanosarcinales S-layer Tile Protein
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95,953
The Association Computability in Europe was founded in Athens, Greece in 2008. Its founding president (2008 to 2015) was Professor S. Barry Cooper; its current president is Elvira Mayordomo and its current secretary general is Giuseppe Primiero. The Association is promoting the development, particularly in Europe, of c...
Computability in Europe
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95,954
(SiC, C, Si3N4, BN, B4C, ZrC, etc.). There is very little damage to fibres and to the geometry of the preform due to low infiltration temperature and pressures. This process gives considerable flexibility in selecting fibers and matrices. Very pure and uniform matrix can be obtained by carefully controlling the purity ...
Chemical vapor infiltration
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95,955
Another refinement of the notion of a field is a topological field, in which the set F is a topological space, such that all operations of the field (addition, multiplication, the maps a ↦ −a and a ↦ a−1) are continuous maps with respect to the topology of the space. The topology of all the fields discussed below is in...
Field of characteristic zero
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95,956
Ouendan, and Frets on Fire based on Guitar Hero. The open source nature of these clones also enable new utilities, such as developing artificial intelligence agents that have learned and improved their play in Freeciv which in turn can help advance artificial intelligence research. Such games must be careful not to red...
Video game clone
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95,957
An importer needs to recognize all variants in order to read a STEP file consistently. Most CAD software does not support the full set of STEP entries, and as such, are limited to a specific subset of STEP entities. For example Autodesk Knowledge Base, list of supported STEP entities. As a result, most CAD software hav...
STEP format
0.796638
95,958
Reinforcement learning from human feedback (RLHF) through algorithms, such as proximal policy optimization, is used to furtherly fine-tune a model based on a dataset of human preferences.
Large language models
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95,959
Several competitions have been held in Florence, Italy within the Creativity Festival in December 2006, and another official conference competition took place in Hyderabad, India in January 2007, within the International Conference of Artificial Intelligence, where it ranked second out of 25 participants.
WebCrow
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95,960
Twisted geometries are discrete geometries that play a role in loop quantum gravity and spin foam models, where they appear in the semiclassical limit of spin networks. A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph. Intrinsic and extrinsic curvatures are ...
Twisted geometries
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95,961
The FST is initially created through algorithmic parsing of some word source, such as a dictionary, complete with modifier markups. Another approach is through the use of an indexed lookup method, which uses a constructed radix tree. This is not an often-taken route because it breaks down for morphologically complex la...
Morphological parsing
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95,962
Henry J. Kelley (1926-1988) was Christopher C. Kraft Professor of Aerospace and Ocean Engineering at the Virginia Polytechnic Institute. He produced major contributions to control theory, especially in aeronautical engineering and flight optimization.In 1948, he received a Bachelor of Science from NYU in aeronautical e...
Henry J. Kelley
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95,963
In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document i...
Topic modeling
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95,964
The force of the second explosion and the ratio of xenon radioisotopes released after the accident led Yuri V. Dubasov in 2009 to theorize that the second explosion could have been an extremely fast nuclear power transient resulting from core material melting in the absence of its water coolant and moderator. Dubasov a...
Chernobyl disaster
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95,965
Lithium triethylborohydride is the organoboron compound with the formula LiEt3BH. Commonly referred to as LiTEBH or Superhydride, it is a powerful reducing agent used in organometallic and organic chemistry. It is a colorless or white liquid but is typically marketed and used as a THF solution. The related reducing age...
Super hydride
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95,966
For example, Bluegrass Companies designed and fabricated a diamond wire sawing method to dismantle the Tokamak Fusion Test Reactor for the Princeton plasma physics laboratory,“Based upon the demonstration at PPPL on the TFTR surrogate, the diamond wire cutting technology is superior to the baseline technology for both ...
Wire saw
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95,967
The Laboratório Nacional de Engenharia Civil, National Laboratory for Civil Engineering, (LNEC) is a public institution of scientific and technological research and development in Portugal and is a civil engineering laboratory. LNEC acts in the different fields of civil engineering under the jurisdiction of the Ministr...
Laboratório Nacional de Engenharia Civil
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95,968
The first proof of this theorem used the invariance principle in conjunction with an isoperimetric theorem of Borell in Gaussian space; since then more direct proofs were devised.Majority is Stablest implies that the Goemans–Williamson approximation algorithm for MAX-CUT is optimal, assuming the unique games conjecture...
Analysis of Boolean functions
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95,969
Technoculture Podcast – Episode #9: Sabina Leonelli on the Open Science Movement Oxford Internet Institute Podcast on "Researching Life in the Digital Age: A Philosophical Analysis of Data-Intensive Biology" The Dissenter Podcast on Science in the World of Big Data SCI PHI Podcast
Sabina Leonelli
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95,970
Ecology and evolutionary biology are considered sister disciplines of the life sciences. Natural selection, life history, development, adaptation, populations, and inheritance are examples of concepts that thread equally into ecological and evolutionary theory. Morphological, behavioural, and genetic traits, for exampl...
Ecology
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95,971
det ( C A ) = 1 {\displaystyle \det(C_{A})=1} .If A {\displaystyle A} is Morita equivalent to B {\displaystyle B} and the characteristic of R {\displaystyle R} is not two, then B {\displaystyle B} is also cellular w.r.t. a suitable involution. In particular A {\displaystyle A} is cellular (to some involution) if and on...
Cellular algebra
0.796635
95,972
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference. Important special cases of the order statistics are the minimum and maximum value of a sampl...
Order statistic
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95,973
In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields...
Resonant interaction
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95,974
The Joint Artificial Intelligence Center, a branch of the U.S. military, is a center dedicated to the procurement and implementation of AI software and neuromorphic hardware for combat use. Specific applications include smart headsets/goggles and robots. JAIC intends to rely heavily on neuromorphic technology to connec...
Neuromorphic computing
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95,975
After the war, Fermi's and Segrè's involvement in the development of the atomic bomb may have caused some strain in their relations with Rasetti, who had refused to participate. : 248 It also made it awkward to discuss nuclear physics with their former colleagues when the new discoveries often remained classified. : 28...
Via Panisperna boys
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95,976
Izmerov led the development of risk assessment methods for the cases of the employee's simultaneous exposure to the various types of occupational hazards. The institute was established Museum of Occupational Hygiene in 1987Nikolai Izmerov published over 500 journal papers (and other publications), several textbooks and...
Nikolai Izmerov
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95,977
Oxidative/fermentation glucose test (OF glucose test) is a biological technique. It was developed in 1953 by Hugh and Leifson to be utilized in microbiology to determine the way a microorganism metabolizes a carbohydrate such as glucose (dextrose). OF-glucose deeps contain glucose as a carbohydrate, peptones, bromothym...
Oxidative/fermentation glucose test
0.796634
95,978
In the mathematical field of graph theory, a truncated octahedral graph is the graph of vertices and edges of the truncated octahedron. It has 24 vertices and 36 edges, and is a cubic Archimedean graph. It has book thickness 3 and queue number 2.As a Hamiltonian cubic graph, it can be represented by LCF notation in mul...
Truncated tetratetrahedron
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95,979
The SPIRES High Energy Physics database (SPIRES-HEP), installed at Stanford Linear Accelerator Center (SLAC) in the 1970s, became the first website in North America and the first database accessible through the World Wide Web in 1991. It has since expanded into a joint project of SLAC, Fermilab, and DESY, with mirrors ...
Stanford Physics Information Retrieval System
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95,980
: 236 The purpose of BKS Theory was to disprove Einstein's hypothesis of the light quantum.One aspect, the idea of modelling atomic behaviour under incident electromagnetic radiation using "virtual oscillators" at the absorption and emission frequencies, rather than the (different) apparent frequencies of the Bohr orbi...
BKS theory
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95,981
Schubert's theorem Conway's theorem Alexander's theorem
List of knot theory topics
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95,982
The decomposition process described (below) can be carried through on the product of two pure Lorentz transformations to obtain explicitly the rotation of the coordinate axes resulting from the two successive "boosts". In general, the algebra involved is quite forbidding, more than enough, usually, to discourage any ac...
Wigner rotation
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95,983
Because Fe is inexpensive and nontoxic, much effort has been devoted to the development of Fe-based catalysts and reagents. Iron is however less common as a catalyst in commercial processes than more expensive metals. In biology, Fe-containing enzymes are pervasive.Iron catalysts are traditionally used in the Haber–Bos...
Iron
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95,984
For the modern theory to begin foundational work was needed, and was provided by the work of Armand Borel, André Weil, Jacques Tits and others on algebraic groups. Shortly afterwards the finiteness of covolume was proven in full generality by Borel and Harish-Chandra. Meanwhile, there was progress on the general theory...
S-arithmetic group
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95,985
Doom (1993) is a first-person shooter (FPS) game. Student researchers from Carnegie Mellon University used computer vision techniques to create an agent that could play the game using only image pixel input from the game. The students used convolutional neural network (CNN) layers to interpret incoming image data and o...
Machine learning in video games
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95,986
Mihail Roco, one of the architects of the USA's National Nanotechnology Initiative, has proposed four states of nanotechnology that seem to parallel the technical progress of the Industrial Revolution, of which productive nanosystems is the most advanced.1. Passive nanostructures - nanoparticles and nanotubes that prov...
Productive nanosystems
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95,987
Andrzej Bobola Maria Schinzel (5 April 1937 – 21 August 2021) was a Polish mathematician studying mainly number theory.
Andrzej Schinzel
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95,988
Gail Susan Kohl Wolkowicz is a Canadian researcher in differential equations, dynamical systems, and mathematical biology who works as a professor of mathematics and statistics at McMaster University. She is known, among other contributions, for her proof that the competitive exclusion principle holds for inter-species...
Gail Wolkowicz
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95,989
Yang Hui (simplified Chinese: 杨辉; traditional Chinese: 楊輝; pinyin: Yáng Huī, ca. 1238–1298), courtesy name Qianguang (謙光), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theorem, and is b...
Yang Hui
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95,990
The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n {\displaystyle n} that is 2 or more, there exist positive integers x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} for which In other words, the number 4 / n {\displaystyle 4/n} can be ...
Erdős–Straus conjecture
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95,991
In the local form of the work theorem, equation: ∫ Γ Q t T u ∗ d Γ + ∫ Ω Q b T u ∗ d Ω = ∫ Ω Q σ T ε ∗ d Ω . {\displaystyle \int _{\Gamma _{Q}}\mathbf {t} ^{T}\mathbf {u} ^{*}d\Gamma +\int _{\Omega _{Q}}\mathbf {b} ^{T}\mathbf {u} ^{*}d\Omega =\int _{\Omega _{Q}}{\boldsymbol {\sigma }}^{T}{\boldsymbol {\varepsilon }}^{...
Generalized-strain mesh-free formulation
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95,992
T ( n ) = 2 T ( n 2 ) + n 2 {\displaystyle T(n)=2T\left({\frac {n}{2}}\right)+n^{2}} As we can see in the formula above the variables get the following values: a = 2 , b = 2 , f ( n ) = n 2 {\displaystyle a=2,\,b=2,\,f(n)=n^{2}} f ( n ) = Ω ( n c ) {\displaystyle f(n)=\Omega \left(n^{c}\right)} , where c = 2 {\displays...
Master theorem (analysis of algorithms)
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In his works, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing calculations with infinitesimals by equivalent geometrical arguments which were considered beyond reproach. He used the methods of calculus to solve the problem of planetary motion, the shape of the surface of a rotating flui...
Differential and integral calculus
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The following proof by induction on the size of the partially ordered set P {\displaystyle P} is based on that of Galvin (1994). Let P {\displaystyle P} be a finite partially ordered set. The theorem holds trivially if P {\displaystyle P} is empty. So, assume that P {\displaystyle P} has at least one element, and let a...
Dilworth's theorem
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Tellurium tetrafluoride melts at 130 °C and decomposes to tellurium hexafluoride at 194 °C. In the solid phase, it consists of infinite chains of TeF3F2/2 in an octahedral geometry. A lone pair of electrons occupies the sixth position.
Tellurium tetrafluoride
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The phrase "equation of time" is derived from the medieval Latin aequātiō diērum, meaning "equation of days" or "difference of days". The word aequātiō (and Middle English equation) was used in medieval astronomy to tabulate the difference between an observed value and the expected value (as in the equation of the cent...
Equation of Time
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The meridian distance Δ {\displaystyle {\mathit {\Delta }}} from one end point to a fictitious point at the same latitude as the second end point is then calculated by trigonometry. The surface distance Δ {\displaystyle {\mathit {\Delta }}} is reduced to the corresponding distance at MSL, Δ ′ {\displaystyle {\mathit {\...
Grade measurement
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In quantum computing, the Hadamard gate is a one-qubit rotation, mapping the qubit-basis states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } to two superposition states with equal weight of the computational basis states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } . Us...
Hadamard transform
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In computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of the vertices of the triangle containing p. Alternatively, it is a Delaunay triangulation in which each internal edge crosses its dual Voronoi diagram edge. Pit...
Pitteway triangulation
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