id
int32
0
100k
text
stringlengths
20
3.54k
source
stringlengths
1
104
similarity
float32
0.8
0.91
90,500
Notable inventions and breakthroughs by CSIRO include: A4 DSP chip Aerogard, insect repellent Atomic absorption spectroscopy Biological control of Salvinia Development of Linola (a flax variety with low alpha-linolenic acid content) with a longer life used as a stockfeed Distance measuring equipment (DME) used for avia...
CSIRO
0.797735
90,501
Webbed spaces are a class of topological vector spaces for which the open mapping theorem and the closed graph theorem hold.
Open mapping theorem (functional analysis)
0.797735
90,502
Most of these axioms were carried over from his Begriffsschrift; the one truly new principle was one he called the Basic Law V (now known as the axiom schema of unrestricted comprehension): the "value-range" of the function f(x) is the same as the "value-range" of the function g(x) if and only if ∀x. However, not only ...
Frege's Theorem
0.797734
90,503
The function field of an algebraic variety of dimension n over k is an algebraic function field of n variables over k. Two varieties are birationally equivalent if and only if their function fields are isomorphic. (But note that non-isomorphic varieties may have the same function field!) Assigning to each variety its f...
Algebraic function field
0.797734
90,504
1971 – Stephen W. Hawking proves the area theorem for black holes. 1971 – Peter C. Aichelburg and Roman U. Sexl introduce the Aichelburg–Sexl ultraboost. 1971 – Introduction of the Khan–Penrose vacuum, a simple explicit colliding plane wave spacetime.
Timeline of gravitational physics and relativity
0.797734
90,505
That is, in the Cantor normal form there is no finite number as last term, and the ordinal is nonzero. It is a limit point of the class of ordinal numbers, with respect to the order topology. (The other ordinals are isolated points. )Some contention exists on whether or not 0 should be classified as a limit ordinal, as...
Limit ordinals
0.797734
90,506
Systems medicine is an interdisciplinary field of study that looks at the systems of the human body as part of an integrated whole, incorporating biochemical, physiological, and environment interactions. Systems medicine draws on systems science and systems biology, and considers complex interactions within the human b...
Systems medicine
0.797733
90,507
As this is an analytical chemistry technique quality control is an important factor to maintain. A laboratory must produce trustworthy results. This can be accomplished by a laboratories continual effort to maintain instrument calibration, measurement reproducibility, and applicability of analytical methods. In all lab...
Radioanalytical chemistry
0.797733
90,508
It was Richard Synge, who in 1952 won the Nobel Prize in Chemistry for his work with partition chromatography, who applied the theoretical knowledge gained from his work in GC to LC. From this revolution, the 1950s also saw the advent of paper chromatography, reversed-phase partition chromatography (RPC), and hydrophob...
Monolithic HPLC column
0.797733
90,509
Creationists point to experiments they have performed, which they claim demonstrate that 1.5 billion years of nuclear decay took place over a short period, from which they infer that "billion-fold speed-ups of nuclear decay" have occurred, a massive violation of the principle that radioisotope decay rates are constant,...
Creation evolution controversy
0.797733
90,510
M. J. Neely. Stochastic Network Optimization with Application to Communication and Queueing Systems, Morgan & Claypool, 2010.
Lyapunov optimization
0.797732
90,511
GENI's goal is to educate world leaders and policy makers on the benefits of this global strategy. The concept of an interconnected global grid linked to renewable resources was first suggested by Buckminster Fuller in the World Game simulation in the 1970s. Fuller concluded that this strategy is the highest priority o...
Global Energy Network Institute
0.797732
90,512
We can also define this topology using the same pretopology we used above. Notice that to satisfy (PT 0), we need to check that for any continuous map of manifolds X → Y and any open subset U of Y, the fibered product U ×Y X is in Mfd/M. This is just the statement that the preimage of an open set is open. Notice, howev...
Grothendieck topologies
0.797732
90,513
Furthermore, IF asserts that theories explaining gravity are not internally consistent nor mathematically reconcilable with quantum mechanics, making gravity a "theory in crisis". IF also makes the claim that gravity is "only a theory", parodying the claims made by creationists regarding the theoretical status of evolu...
Intelligent falling
0.797732
90,514
Leibniz's relationism, in contrast, describes space and time as systems of relations that exist between objects. The rise of general relativity and subsequent work in the history of physics has put Leibniz's stance in a more favorable light. One of Leibniz's projects was to recast Newton's theory as a vortex theory. Ho...
Algebra of concepts
0.797732
90,515
In computer science, a longest common substring of two or more strings is a longest string that is a substring of all of them. There may be more than one longest common substring. Applications include data deduplication and plagiarism detection.
Longest common substring
0.797732
90,516
Systems programming requiring pointer manipulation was typically done in assembly language, though JOVIAL was used for some military applications.IBM's System/360, announced in 1964, was designed as a unified hardware architecture supporting both scientific and commercial applications, and IBM developed PL/I for it as ...
General-purpose programming language
0.797732
90,517
The mathematical concept of a function emerged in the 17th century in connection with the development of the calculus; for example, the slope d y / d x {\displaystyle \operatorname {d} \!y/\operatorname {d} \!x} of a graph at a point was regarded as a function of the x-coordinate of the point. Functions were not explic...
History of the function concept
0.797732
90,518
Their difficulty was one of materials science and the lack of a suitable friction material, before asbestos clutch linings, that could handle the specific power / area at an elevated operating temperature. As the Hele-Shaw clutch did not rely on friction, it generated only a fraction of the heat of other designs and it...
Hele-Shaw clutch
0.797731
90,519
Industrial microbiology can be used to produce antibiotics via the process of fermentation, where the source microorganism is grown in large containers (100,000–150,000 liters or more) containing a liquid growth medium. Oxygen concentration, temperature, pH and nutrient are closely controlled. As antibiotics are second...
Production of antibiotics
0.797731
90,520
If a relation is transitive then its transitive extension is itself, that is, if R is a transitive relation then R1 = R. The transitive extension of R1 would be denoted by R2, and continuing in this way, in general, the transitive extension of Ri would be Ri + 1. The transitive closure of R, denoted by R* or R∞ is the ...
Transitive property
0.797731
90,521
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization...
Quantum annealing
0.797731
90,522
One of the pioneer experiments was that of Bach in 1893, who observed the formation of lower uranium oxides upon irradiation of a solution of uranium acetate and carbon dioxide, implying the formation of formaldehyde. Some experiments included reducing agents such as hydrogen gas, and others detected formaldeyhde or ot...
Photogeochemistry
0.797731
90,523
The physics of energy straggling and multiple scattering was developed by Williams in 1929–1945. Williams devised a theory, which consists of fitting the multiple scattering distribution as a Gaussian-like portion due to small scattering angles and the single collision tail due to the large angles. William, E.J., studi...
Elastic recoil detection
0.797731
90,524
In philosophy, specifically in the area of metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the Kripkean view. The form of the t...
Counterpart theory
0.797731
90,525
The era of Big Science has provoked criticism that it undermines the basic principles of the scientific method. Increased government funding has often meant increased military funding, which some claim subverts the Enlightenment-era ideal of science as a pure quest for knowledge. For example, historian Paul Forman has ...
Big Science
0.79773
90,526
Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as the Drude model, the band structure and the density functional theory. Theoretical models have also been developed to study...
Condensed Matter
0.79773
90,527
Goodstein sequences are defined in terms of a concept called "hereditary base-n notation". This notation is very similar to usual base-n positional notation, but the usual notation does not suffice for the purposes of Goodstein's theorem. In ordinary base-n notation, where n is a natural number greater than 1, an arbit...
Goodstein function
0.79773
90,528
In molecular biology, the HAND domain is a protein domain which adopts a secondary structure consisting of four alpha helices, three of which (H2, H3, H4) form an L-like configuration. Helix H2 runs antiparallel to helices H3 and H4, packing closely against helix H4, whilst helix H1 reposes in the concave surface forme...
HAND domain
0.79773
90,529
Aeromicrobiology (or air microbiology): The study of airborne microorganisms. Biotechnology: related to recombinant DNA technology or genetic engineering. == References ==
Branches of microbiology
0.79773
90,530
(1996a), Partial Differential Equations I: Basic Theory, Springer, pp. 376–378, ISBN 978-0-387-94654-2 Taylor, Michael E. (1996b), Partial Differential Equations II:Qualitative studies of linear equations, Springer, ISBN 978-0-387-94651-1 Bers, Lipman; John, Fritz; Schechter, Martin (1979), Partial differential equatio...
Uniformisation Theorem
0.797729
90,531
Thus, the proximal mechanisms of bioelectric signaling within single cells are becoming well-understood, and advances in optogenetics and magnetogenetics continue to facilitate this research program. More challenging however is the integrative program of understanding how specific patterns of bioelectric dynamics help ...
Bioelectricity
0.797729
90,532
As of 2022, the department consists of the following chairs and professorships: Architecture of Parallel and Distributed Systems Audio Information Processing Automatic Control Engineering Bio-inspired Information Processing Coding and Cryptography Communications Engineering Communication Networks Computer Architecture ...
TUM School of Computation, Information and Technology
0.797729
90,533
Wilde graduated from Jesuit High School in New Orleans, Louisiana in 1998. He received his bachelor's degree in computer engineering from Texas A&M University in 2002, with support from the Thomas Barton Scholarship. He received his Master's degree in electrical engineering from Tulane University in 2004. He received h...
Mark Wilde
0.797729
90,534
Plasma medicine is an emerging field that combines plasma physics, life sciences and clinical medicine. It is being studied in disinfection, healing, and cancer. Most of the research is in vitro and in animal models. It uses ionized gas (physical plasma) for medical uses or dental applications.
Plasma medicine
0.797729
90,535
CAESAR (Comet Astrobiology Exploration Sample Return) is a sample-return mission concept to comet 67P/Churyumov–Gerasimenko. The mission was proposed in 2017 to NASA's New Frontiers program mission 4, and on 20 December 2017 it was one of two finalists selected for further concept development. On 27 June 2019, the othe...
CAESAR (spacecraft)
0.797728
90,536
Weierstrass M-test. Suppose that (fn) is a sequence of real- or complex-valued functions defined on a set A, and that there is a sequence of non-negative numbers (Mn) satisfying the conditions | f n ( x ) | ≤ M n {\displaystyle |f_{n}(x)|\leq M_{n}} for all n ≥ 1 {\displaystyle n\geq 1} and all x ∈ A {\displaystyle x\i...
Weierstrass M-test
0.797728
90,537
In the novel "Prey" by Michael Crichton, self replicating nanobots create autonomous nano-swarms with predatory behaviors. The protagonist must stop the swarm before it evolves into a grey goo plague. In the films Avengers Infinity War and Avengers Endgame Tony Stark's Iron Man suit was constructed using nanotechnology...
Molecular Nanotechnology
0.797728
90,538
Particle physicsParticle physics (also known as high energy physics) is a branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word particle can refer to various types of very small objects (e.g. protons, gas particles, or even household dust), particle physics u...
Glossary of engineering: M–Z
0.797728
90,539
In another application of homological methods to graph theory, Lovász proved both the undirected and directed versions of a conjecture of András Frank: Given a k-connected graph G, k points v 1 , … , v k ∈ V ( G ) {\displaystyle v_{1},\ldots ,v_{k}\in V(G)} , and k positive integers n 1 , n 2 , … , n k {\displaystyle n...
Topological combinatorics
0.797728
90,540
Eulerian matroids were defined by Welsh (1969) as a generalization of the Eulerian graphs, graphs in which every vertex has even degree. By Veblen's theorem the edges of every such graph may be partitioned into simple cycles, from which it follows that the graphic matroids of Eulerian graphs are examples of Eulerian ma...
Eulerian matroid
0.797728
90,541
The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation approaches 0. This can be expressed mathematically as follows: lim T → 0 Δ S = 0 {\displaystyle \lim _{T\to 0}\Delta S=0} The above equation is a modern statement of the theorem. Nernst ofte...
Nernst heat theorem
0.797727
90,542
Also the program MACSYMA deserves to be mentioned explicitly, since it triggered important development with regard to algorithms. In the 1980s new computer algebra systems started to be written in C. This enabled the better exploitation of the resources of the computer (compared to the interpreted language LISP) and at...
Computational particle physics
0.797726
90,543
If R {\displaystyle \mathbb {R} } has its usual Euclidean topology then the open set S = ( 0 , 1 ) ∪ ( 1 , 2 ) {\displaystyle S=(0,1)\cup (1,2)} is not a regular open set, since Int ⁡ ( S ¯ ) = ( 0 , 2 ) ≠ S . {\displaystyle \operatorname {Int} ({\overline {S}})=(0,2)\neq S.} Every open interval in R {\displaystyle \ma...
Regular open set
0.797726
90,544
A spot assay or spot test can also refer to a specific test in microbiology. This test is often used to check the growth rate of bacterial or yeast cells on different media or to perform serial dilution tests of micro-organisms. Usually a 96-pinner (often called frogger) is used to perform these spot assay.
Spot analysis
0.797726
90,545
In June 2021, NASA announced the selection of three payloads from its Payloads and Research Investigations on the Surface of the Moon (PRISM) call for proposals. These payloads will be sent to Reiner Gamma and Schrödinger Basin in the 2023–2024 timeframe. Lunar Vertex: a joint lander and rover payload suite slated for ...
Commercial Lunar Payload Services
0.797726
90,546
Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching. The Tutte theorem provides a characterization for arbitrary graphs. A perfect matching is a spanning 1-regular subgraph, a.k.a.
Perfect matching
0.797726
90,547
Indeed, a character on T {\displaystyle \mathbb {T} } is of the form z ↦ z n {\displaystyle z\mapsto z^{n}} for n {\displaystyle n} an integer. Since T {\displaystyle \mathbb {T} } is compact, the topology on the dual group is that of uniform convergence, which turns out to be the discrete topology. The group of real n...
Locally compact abelian group
0.797726
90,548
The America Rocketry Challenge (TARC) is an annual American model rocketry competition for students in grades seven to 12 sponsored by the Aerospace Industries Association and the National Association of Rocketry. Co-sponsors include NASA, United States Department of Defense, the American Association of Physics Teacher...
Aerospace Industries Association
0.797725
90,549
Yet Kurt Gödel's incompleteness theorem showed this impossible except in trivial cases, and Alfred Tarski's undefinability theorem shattered all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap's 1934 work Logische Syntax der Sprache (Logical Syntax of Language). Still, some...
Observational statement
0.797725
90,550
In diatonic set theory the common tone theorem explains that scales possessing the deep scale property share a different number of common tones, not counting enharmonic equivalents (for example, C♯ and C♭ have no common tones with C major), for every different transposition of the scale. However many times an interval ...
Common tone (scale)
0.797725
90,551
In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same answer. This allows...
Origin (mathematics)
0.797725
90,552
Their added value lies in the ability to bring together and connect three forms of intelligence: human intelligence of the city's population, collective intelligence of institutions supporting learning and innovation, and artificial intelligence of smart environments, digital networks and online services. Main fields o...
URENIO
0.797725
90,553
For AMC clinical exam, a candidate is required to pass 12 out of 16 cases: including one compulsory case in both gynecology and pediatrics. IMGs who have passed the necessary exams and obtained AMC certification can then apply to Australian specialty training positions.Australia is in the process of establishing a nati...
International medical graduate
0.797725
90,554
Let V , W {\displaystyle V,W} be vector spaces over some field F , {\displaystyle F,} and T {\displaystyle T} defined as in the statement of the theorem with dim ⁡ V = n {\displaystyle \dim V=n} . As Ker ⁡ T ⊂ V {\displaystyle \operatorname {Ker} T\subset V} is a subspace, there exists a basis for it. Suppose dim ⁡ Ker...
Fundamental theorem of linear algebra
0.797724
90,555
This initiative was an opportunity for the citizens of Earth to gain a deeper insight into astronomy's role in enriching all human cultures. Moreover, served as a platform for informing the public about the latest astronomical discoveries while emphasizing the essential role of astronomy in science education. IYA2009 w...
International Year of Astronomy
0.797724
90,556
Epistasis is a phenomenon in genetics in which the effect of a gene mutation is dependent on the presence or absence of mutations in one or more other genes, respectively termed modifier genes. In other words, the effect of the mutation is dependent on the genetic background in which it appears. Epistatic mutations the...
Modifier gene
0.797724
90,557
Tuzhilin received his B.A. in Mathematics from the New York University in 1980, M.S. in Engineering Economics from the Department of Management Science and Engineering at Stanford University in 1981, and Ph.D. in computer science from NYU's Courant Institute of Mathematical Sciences in 1989, his doctoral advisor being ...
Alexander Tuzhilin
0.797724
90,558
The treatise purports to quote Paracelsus on the point that "The light of the soul, by the will of the Triune God, made all earthly things appear from the primal Chaos." Martin Ruland the Younger, in his 1612 Lexicon Alchemiae, states, "A crude mixture of matter or another name for Materia Prima is Chaos, as it is in t...
Primordial chaos
0.797724
90,559
In molecular biology, the protein domain named the Shugoshin N-terminal coiled-coil region is a domain found on the N-terminal region of the Shugoshin protein in eukaryotes. It has a role in attaching to the kinetochores, structures on the chromatids where microtubules attach. Shugoshin has a conserved coiled-coil N-te...
Shugoshin N terminal protein domain
0.797724
90,560
Improved DOS functionality. New unified graphics library with RTG support which allows for (current and future) very substantial general and platform specific performance optimizations e.g. through the use of on-chip DMA engines (present on recently released hardware going back to the Sam440).
AmigaOS 4 version history
0.797723
90,561
In this research, Haddad has brought a longstanding research theme to fruition by his work on vector dissipative systems approaches to large-scale nonlinear dynamical systems. This work has broad application to large-scale aerospace systems, air traffic control systems, power and energy grid systems, manufacturing and ...
Wassim Michael Haddad
0.797723
90,562
In medicine, public health, and biology, transmission is the passing of a pathogen causing communicable disease from an infected host individual or group to a particular individual or group, regardless of whether the other individual was previously infected. The term strictly refers to the transmission of microorganism...
Disease spread
0.797723
90,563
It results in an inability to flex the stifle, so the horse must walk with an extended hind leg. It is associated with straight hind limb conformation (post leg), poor muscling of the hind limb, stifle trauma, and genetics. Fibrotic myopathy is caused by damage to the hamstring muscles, usually from trauma or intramusc...
Equine lameness
0.797723
90,564
Therefore, this integral defines the critical temperature and particle number corresponding to the conditions of negligible chemical potential μ {\displaystyle \mu } . In Bose–Einstein statistics distribution, μ {\displaystyle \mu } is actually still nonzero for BECs; however, μ {\displaystyle \mu } is less than the gr...
Bose condensate
0.797723
90,565
Non-linear inequalities of Korn on a surface: Philippe Ciarlet gave several new proofs of the fundamental theorem of surface theory, concerning the reconstruction of a surface according to its first and second fundamental forms. He was the first to show that a surface continuously varies according to its two fundamenta...
Philippe G. Ciarlet
0.797722
90,566
Acoustics emerged as a mathematical field of music theory and later an independent branch of physics. In the experimental investigation of sound phenomena, numbers had no symbolic meaning and were merely used to measure physical phenomena and relationships such as frequency and vibration of a string.Many of the most em...
Pythagorean school
0.797722
90,567
The L-groups of a group π {\displaystyle \pi } are the L-groups L ∗ ( Z ) {\displaystyle L_{*}(\mathbf {Z} )} of the group ring Z {\displaystyle \mathbf {Z} } . In the applications to topology π {\displaystyle \pi } is the fundamental group π 1 ( X ) {\displaystyle \pi _{1}(X)} of a space X {\displaystyle X} . The qu...
L-theory
0.797722
90,568
In this variant, U is an m × r {\displaystyle m\times r} semi-unitary matrix and V {\displaystyle \ \mathbf {V} \ } is an n × r {\displaystyle n\times r} semi-unitary matrix, such that U ∗ U = V ∗ V = I r . {\displaystyle \ \mathbf {U^{*}U} =\mathbf {V^{*}V} =\mathbf {I} _{r}\ .} Mathematical applications of the SVD in...
Matrix approximation
0.797722
90,569
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the p...
Complex-valued amplitude
0.797722
90,570
In algebraic geometry, a branch of mathematics, the étale spectrum of a commutative ring or an E∞-ring, denoted by Specét or Spét, is an analog of the prime spectrum Spec of a commutative ring that is obtained by replacing Zariski topology with étale topology. The precise definition depends on one's formalism. But the ...
Étale spectrum
0.797721
90,571
Analogue to differential geometry, where differentiable functions are replaced with analytic functions. It is a subarea of both complex analysis and algebraic geometry. Analytic number theory An area of number theory that applies methods from mathematical analysis to solve problems about integers.
Glossary of areas of mathematics
0.797721
90,572
Finally, a graph is Hamiltonian if there exists a cycle that passes through each of its vertices exactly once. Barnette's conjecture states that every cubic bipartite polyhedral graph is Hamiltonian. By Steinitz's theorem, a planar graph represents the edges and vertices of a convex polyhedron if and only if it is poly...
Barnette's conjecture
0.797721
90,573
La Niña The counterpart to El Niño. lake An inland body of water localized in a basin and often fed by a river. lake ecosystem lake stratification landscape ecology An interdisciplinary branch of ecology combining aspects of ecology, botany, biogeography, physical geography and environmental planning. large marine ecos...
Glossary of ecology
0.797721
90,574
Other publications by Campbell include Modern Electrical Theory (1907 with supplementary chapters 1921-23), The Principles of Electricity (1912) and An Account of the Principles of Measurement and Calculation (1928). His most important work on the philosophy of science was his Physics: The Elements, published in 1919 (...
Norman Robert Campbell
0.79772
90,575
An X-ray astronomy instrument was carried aboard a Thor missile launched from the same atoll on September 24, 1970, at 12:54 UTC and altitudes above 300 km (190 mi), to search for the Small Magellanic Cloud and to extend observation of the LMC. The source in the LMC appeared extended and contained star ε Dor. The X-ray...
Large Magellanic Cloud
0.79772
90,576
In cryptography, a verifiable random function (VRF) is a public-key pseudorandom function that provides proofs that its outputs were calculated correctly. The owner of the secret key can compute the function value as well as an associated proof for any input value. Everyone else, using the proof and the associated publ...
Verifiable random function
0.79772
90,577
The first model of quantum mechanics (Heisenberg, 1925) represented the theory's operators by infinite-dimensional matrices acting on quantum states. This is also referred to as matrix mechanics. One particular example is the density matrix that characterizes the "mixed" state of a quantum system as a linear combinatio...
Matrix (mathematics)
0.79772
90,578
Matjaž Perc is Professor of Physics at the University of Maribor in Slovenia, and director of the Complex Systems Center Maribor. He is member of Academia Europaea and among top 1% most cited physicists according to Thomson Reuters Highly Cited Researchers. He is Outstanding Referee of the Physical Review and Physical ...
Matjaž Perc
0.79772
90,579
In geometry, the hendecagonal prism is one in an infinite set of convex prisms formed by square sides and two regular polygon caps, in this case two hendecagons. So, it has 2 hendecagons and 11 squares as its faces.
Hendecagonal prism
0.79772
90,580
Since its discovery in 1994, A. caldus has been found to have a significant practical application in the industrial field of biomining and mineral biotechnology, contributing to the enhanced recovery of desired minerals from rocks known as ores. Metals such as gold have been recovered from ores which contain pyrite (al...
Acidithiobacillus caldus
0.79772
90,581
Phosphorus tribromide is used in organic chemistry to convert alcohols to alkyl bromides and carboxylic acids to acyl bromides (e.g. in the Hell-Volhard-Zelinsky reaction). Phosphorus triiodide also finds use in organic chemistry, as a mild oxygen acceptor. The trihalides are fairly readily oxidized by chalcogens to gi...
Phosphorus chlorides
0.79772
90,582
In order to obtain a basis of simple roots for the affine algebra, an extra simple root must be appended, and is given by where θ {\displaystyle \theta } is the highest root of g {\displaystyle {\mathfrak {g}}} , using the usual notion of height of a root. This allows definition of the extended Cartan matrix and extend...
Affine Lie algebra
0.79772
90,583
In biology, autolysis, more commonly known as self-digestion, refers to the destruction of a cell through the action of its own enzymes. It may also refer to the digestion of an enzyme by another molecule of the same enzyme. The term derives from the Greek αὐτο- ("self") and λύσις ("splitting").
Autolysis (biology)
0.79772
90,584
One can generalize Vandermonde's identity as follows: ∑ k 1 + ⋯ + k p = m ( n 1 k 1 ) ( n 2 k 2 ) ⋯ ( n p k p ) = ( n 1 + ⋯ + n p m ) . {\displaystyle \sum _{k_{1}+\cdots +k_{p}=m}{n_{1} \choose k_{1}}{n_{2} \choose k_{2}}\cdots {n_{p} \choose k_{p}}={n_{1}+\dots +n_{p} \choose m}.} This identity can be obtained throug...
Vandermonde's identity
0.79772
90,585
Black-Body Theory and the Quantum Discontinuity, 1894–1912 (1978; second edition 1987) is a book by the philosopher Thomas Kuhn, in which the author surveys the development of quantum mechanics. The second edition has a new afterword.
Black-Body Theory and the Quantum Discontinuity, 1894–1912
0.79772
90,586
Collected methods in fluxomics have been described as "COBRA" methods, for constraint based reconstruction and analysis. A number of software tools and environments have been created for this purpose.Although it can only be measured indirectly, metabolic flux is the critical link between genes, proteins and the observa...
Fluxomics
0.797719
90,587
In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. A...
Normal variety
0.797719
90,588
Mathematical anxiety, also known as math phobia, is a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in daily life and academic situations. This is, arguably, distinct from statistics anxiety where the negative state is the result of encountering...
Math phobia
0.797719
90,589
The state-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation given by d x ( t ) d t = A x ( t ) + B u ( t ) + E w ( t ) , {\displaystyle {\frac {dx(t)}{dt}}=Ax(t)+Bu(t)+Ew(t),} with state vector x, control vector u, vector w of additive dist...
State-transition equation
0.797719
90,590
When the “Atlas” is being controlled, the control software doesn’t explicitly tell the robot how to move its joints, but rather it employs mathematical models of the underlying physics of the robot’s body and how it interacts with the environment”. Instead of inputting data into every single joint of the robot, the eng...
Robot control
0.797719
90,591
Available pesticides are not sufficient and new developments are needed. Continued research into the basic biology of pests may identify new vulnerabilities and produce new pesticides; it may also yield pesticides with better financial and environmental characteristics than those presently used. Plant-derived pesticide...
Crop spraying
0.797718
90,592
)Twenty-eight studies were proposed, of which eight were selected for peer review by the Biotechnology and Biological Sciences Research Council. From these eight the Rowett Research Institute's proposal was chosen and a combined team of academics from the Scottish Crop Research Institute, the Durham University Departme...
Pusztai affair
0.797718
90,593
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulat...
Clique problem
0.797717
90,594
The discovery of PFGE can be traced back to the late 1970s and early 1980s.One of the earliest references to the use of PFGE for DNA analysis is a 1977 paper by Dr. David Burke and colleagues at the University of Colorado, where they described a method of separating DNA molecules based on their size using conventional ...
Pulsed field gel electrophoresis
0.797717
90,595
The disadvantages of model-based design are fairly well understood this late in development lifecycle of the product and development. One major disadvantage is that the approach taken is a blanket or coverall approach to standard embedded and systems development. Often the time it takes to port between processors and e...
Model Based Design
0.797717
90,596
Green Chemistry (RSC) Green Chemistry Letters and Reviews (Open Access) (Taylor & Francis) ChemSusChem (Wiley) ACS Sustainable Chemistry & Engineering (ACS)
Sustainable chemistry
0.797717
90,597
Pre-molded joints are injection molded bodies created in two or more stages. Due to automation, the faraday cage will have a precise geometry and placement not achievable in taped joints. Pre-molded joints come in many different body sizes that much be matched up to the cable Semicon's outside diameter. A tight joint i...
High-voltage cable
0.797717
90,598
The odds strategy is the rule to observe the events one after the other and to stop on the first interesting event from index s onwards (if any), where s is the stopping threshold of output a. The importance of the odds strategy, and hence of the odds algorithm, lies in the following odds theorem.
Bruss algorithm
0.797717
90,599
In inorganic chemistry, a homoleptic chemical compound is a metal compound with all ligands identical. The term uses the "homo-" prefix to indicate that something is the same for all. Any metal species which has more than one type of ligand is heteroleptic.
Homoleptic
0.797717