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Visual calculus, invented by Mamikon Mnatsakanian (known as Mamikon), is an approach to solving a variety of integral calculus problems. Many problems that would otherwise seem quite difficult yield to the method with hardly a line of calculation, often reminiscent of what Martin Gardner called "aha! solutions" or Roge...
Visual calculus
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In 2022 he was awarded the FOCS Test of Time Award for his work on error correction in the setting of interactive communication. He was the editor-in-chief of the SIAM Journal on Computing for two terms (2013-2018.) He was elected as a Fellow of the Society for Industrial and Applied Mathematics, in the 2022 Class of S...
Leonard Schulman
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Phosphorus triiodide (PI3) is an inorganic compound with the formula PI3. A red solid, it is too unstable to be stored; it is, nevertheless, commercially available. It is widely used in organic chemistry for converting alcohols to alkyl iodides. It is also a powerful reducing agent. Note that phosphorus also forms a lo...
Phosphorus triiodide
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The traditional basis of constructive quantum field theory is the set of Wightman axioms. Osterwalder and Schrader showed that there is an equivalent problem in mathematical probability theory. The examples with d < 4 satisfy the Wightman axioms as well as the Osterwalder–Schrader axioms. They also fall in the related ...
Constructive quantum field theory
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Source: https://aero.engin.umich.edu/people/bram-van-leer/ 1963 – Candidate Astronomy, Leiden State University 1966 – Doctorandus Astrophysics, Leiden State University 1970 – Ph.D. Astrophysics, Leiden State University, 1970 1970–72 – Miller Fellow Astrophysics, University of California Berkeley
Bram van Leer
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Allosteric modulation is used to alter the activity of molecules and enzymes in biochemistry and pharmacology. For comparison, a typical drug is made to bind to the active site of an enzyme which thus prohibits binding of a substrate to that enzyme causing a decrease in enzyme activity. Allosteric modulation occurs whe...
Allosteric inhibition
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His design leveraged the high performance op-amp of his own design, the 535 series (USPTO #3727896) to achieve filtering circuits that were before impossible. Flickinger's patent (USPTO #3752928) from early in 1971 showed the circuit topology that would come to dominate audio equalization until the present day, as well...
Graphic equaliser
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A topological space X is a 3-manifold if every point in X has a neighbourhood that is homeomorphic to Euclidean 3-space. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3...
Low dimensional topology
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{\displaystyle 5=1^{2}+2^{2},\quad 13=2^{2}+3^{2},\quad 17=1^{2}+4^{2},\quad 29=2^{2}+5^{2},\quad 37=1^{2}+6^{2},\quad 41=4^{2}+5^{2}.} On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theor...
Fermat's theorem on sums of two squares
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For a first order system of differential equations d r d t = f ( r , t ) {\displaystyle {\frac {d\mathbf {r} }{dt}}=\mathbf {f} (\mathbf {r} ,t)} where bold indicates vector quantities, a scalar-valued function H(r) is a conserved quantity of the system if, for all time and initial conditions in some specific domain, d...
Conserved quantities
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Michael Dummett introduced the very fundamental idea of logical harmony, building on a suggestion of Nuel Belnap. In brief, a language, which is understood to be associated with certain patterns of inference, has logical harmony if it is always possible to recover analytic proofs from arbitrary demonstrations, as can b...
Proof-theoretic semantics
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For the philosophy of technology the questions arise if a) biotechnology and agriculture should not be an integral part of reflexion, thereby adding new insights to the common focus on the machine and the artifact, and if b) established concepts of technique and technology which stress artificiality should not be modif...
Biofact (philosophy)
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In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively in the whole...
5-simplex honeycomb
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In phylogenetics in general, it is important to keep in mind that the extant and ancestral species that are represented in any phylogeny are only a sparse sample of the species that currently exist or ever have existed. This is why one can safely assume that all transfers that can be detected using phylogenetic methods...
Phylogenetic reconciliation
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In numerical analysis, the Cash–Karp method is a method for solving ordinary differential equations (ODEs). It was proposed by Professor Jeff R. Cash from Imperial College London and Alan H. Karp from IBM Scientific Center. The method is a member of the Runge–Kutta family of ODE solvers.
Cash–Karp method
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SSR operates on a flat address space which is organized as a virtual ring. This is a popular concept in peer-to-peer overlay networks like Chord. The common knowledge about the ring structure enables nodes to route packets without knowing the topology of the underlying physical network. While the physical network can b...
Scalable Source Routing
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N mers form the polymer, whose total unfolded length is: L = N l {\displaystyle L=N\,l} , where N is the number of mers.In this very simple approach where no interactions between mers are considered, the energy of the polymer is taken to be independent of its shape, which means that at thermodynamic equilibrium, all of...
Ideal chain
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Sea urchins are traditional model organisms in developmental biology. This use originated in the 1800s, when their embryonic development became easily viewed by microscopy. The transparency of the urchin's eggs enabled them to be used to observe that sperm cells actually fertilize ova. They continue to be used for embr...
Aristotle's lantern
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There is an on-going debate on whether the wave-function represents the epistemic state of a yet to be discovered ontic variable or, on the contrary, it is a fundamental entity. Under some physical assumptions, the Pusey–Barrett–Rudolph (PBR) theorem demonstrates the inconsistency of quantum states as epistemic states,...
Quantum foundations
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In the field of surface analysis, it is usual to distinguish static SIMS and dynamic SIMS. Static SIMS is the process involved in surface atomic monolayer analysis, or surface molecular analysis, usually with a pulsed ion beam and a time of flight mass spectrometer, while dynamic SIMS is the process involved in bulk an...
Secondary Ion Mass Spectrometry
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This idea was "sharply" criticized by Church.Thus Post in his 1936 paper was also discounting Kurt Gödel's suggestion to Church in 1934–1935 that the thesis might be expressed as an axiom or set of axioms.Turing adds another definition, Rosser equates all three: Within just a short time, Turing's 1936–1937 paper "On Co...
Church–Turing thesis
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The setting of cartesian closed categories is sufficient for the discussion of classical logic; the more general setting of closed monoidal categories is suitable for quantum computation.The difference between these two is that the product for cartesian categories (such as the category of sets, complete partial orders ...
Currying
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In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a co...
Apply
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References to a dividing line between metals and nonmetals appear in the literature as far back as at least 1869. In 1891, Walker published a periodic 'tabulation' with a diagonal straight line drawn between the metals and the nonmetals. In 1906, Alexander Smith published a periodic table with a zigzag line separating ...
Dividing line between metals and nonmetals
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However, these facts are counterintuitive: we do not normally expect open sets, other than connected components, to be compact, and for affine varieties (for example, Euclidean space) we do not even expect the space itself to be compact. This is one instance of the geometric unsuitability of the Zariski topology. Groth...
Closed point
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Fomenko, Anatoly; Fuchs, Dmitry, Homotopical Topology Hatcher, Allen. "Spectral Sequences in Algebraic Topology" (PDF).
Spectral sequences
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The first such theorem was proven by Atle Selberg for co-compact discrete subgroups of the unimodular groups S L n ( R ) {\displaystyle \mathrm {SL} _{n}(\mathbb {R} )} . Shortly afterwards a similar statement was proven by Eugenio Calabi in the setting of fundamental groups of compact hyperbolic manifolds. Finally, th...
Local rigidity
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The open mapping theorem, also known as Banach's homomorphism theorem, gives a sufficient condition for a continuous linear operator between complete metrizable TVSs to be a topological homomorphism.
Topological homomorphism
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After Von Laue's pioneering research, the field developed rapidly, most notably by physicists William Lawrence Bragg and his father William Henry Bragg. In 1912–1913, the younger Bragg developed Bragg's law, which connects the observed scattering with reflections from evenly spaced planes within the crystal. The Braggs...
X-ray crystallographer
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geodesically complete and geometrically close to Minkowski space. Choquet-Bruhat's proof makes use of a clever choice of coordinates, the wave coordinates (which are the Lorentzian equivalent to the harmonic coordinates), in which the Einstein equations become a system of hyperbolic partial differential equations, for ...
Yvonne Choquet-Bruhat
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Bifurcation theory the study of changes in the qualitative or topological structure of a given family. It is a part of dynamical systems theory Biostatistics the development and application of statistical methods to a wide range of topics in biology. Birational geometry a part of algebraic geometry that deals with the ...
Glossary of areas of mathematics
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Testing conducted by the Virginia Department of Transportation and university researchers from 2011 to 2013 showed that some CIPP installations can cause aquatic toxicity. A list of environmental, public health, and infrastructure incidents caused by CIPP installations as of 2013 was published by the Journal of Environ...
Cured-in-place pipe
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Applied Energy is a peer-reviewed academic journal covering research on energy engineering that was established in 1975. The journal covers areas of energy conversion and conservation, the optimal use of energy resources, analysis and optimization of energy processes, mitigation of environmental pollutants, and sustain...
Applied Energy
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Abell 3266 is a galaxy cluster in the southern sky. It is part of the Horologium-Reticulum Supercluster. The galaxy cluster is one of the largest in the southern sky, and one of the largest mass concentrations in the nearby universe. The Department of Physics at the University of Maryland, Baltimore County discovered t...
Abell 3266
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Classically, algebraic functions are defined by an algebraic equation, and transcendental functions (including those discussed above) are defined by some property that holds for them, such as a differential equation. For example, the exponential function is the function which is equal to its own derivative everywhere, ...
Taylor polynomial
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Carbon nanotubes have a wide range of uses, and look set to become crucial to several industries from electronics and computers, to strengthened materials to drug delivery and diagnostics.Nanotechnologies may provide new solutions for the millions of people in developing countries who lack access to basic services, suc...
Impact of nanotechnology
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In geometry, an apeirogonal hosohedron or infinite hosohedron is a tiling of the plane consisting of two vertices at infinity. It may be considered an improper regular tiling of the Euclidean plane, with Schläfli symbol {2,∞}.
Apeirogonal hosohedron
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Nasir al-Din attempted to derive a proof by contradiction of the parallel postulate. He also considered the cases of what are now known as elliptical and hyperbolic geometry, though he ruled out both of them. Nasir al-Din's son, Sadr al-Din (sometimes known as "Pseudo-Tusi"), wrote a book on the subject in 1298, based ...
Parallel axiom
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When studying probability theory the blocks method consists of splitting a sample into blocks (groups) separated by smaller subblocks so that the blocks can be considered almost independent. The blocks method helps proving limit theorems in the case of dependent random variables. The blocks method was introduced by S. ...
Randomized block design
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Triangular patches, introduced by S. Rao, D. Wilton and A. Glisson in 1982, are known as RWG basis functions and are widely used in MoM. Characteristic basis functions were also introduced to accelerate computation and reduce the matrix equation.The testing and basis functions are often chosen to be the same; this is k...
Method of moments (electromagnetics)
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Thus Clairaut demonstrated an implicit understanding of the tangent space of a surface and studied this idea using calculus for the first time. Importantly Clairaut introduced the terminology of curvature and double curvature, essentially the notion of principal curvatures later studied by Gauss and others. Around this...
Analysis on manifolds
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"The Vapor Pressure of Barium". The Journal of Chemical Physics. AIP Publishing.
Vapor pressures of the elements (data page)
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However, after sufficient time has passed, the system reaches a uniform color, a state much easier to describe and explain. Boltzmann formulated a simple relationship between entropy and the number of possible microstates of a system, which is denoted by the symbol Ω. The entropy S is proportional to the natural logari...
Statistical entropy
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The perfusion system chosen might also affect the geometry chosen. For example, in a system that incorporates syringe pumps, channels for perfusion inlet, perfusion outlet, waste, and cell loading would need to be added for the cell culture maintenance. Perfusion in microfluidic cell culture is important to enable long...
Microfluidic cell culture
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State Key Laboratory of Disaster Prevention in Civil Engineering State Key Laboratory of Pollution Control and Resource Reuse State Key Laboratory of Modern Technology of Urban Planning and Design State Key Laboratory of Marine Geology
Tongji University
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Veterinary education is the tertiary education of veterinarians. To become a veterinarian, one must first complete a degree in veterinary medicine Doctor of Veterinary Medicine (DVM, V.M.D., BVS, BVSc, BVMS, BVM etc.). In the United States and Canada, almost all veterinary medical degrees are first entry degrees, and r...
Veterinary education
0.79928
83,146
The Éléments de géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiqu...
Éléments de géométrie algébrique
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The modern concept of polymers as covalently bonded macromolecular structures was proposed in 1920 by Hermann Staudinger, who spent the next decade finding experimental evidence for this hypothesis.Polymers are studied in the fields of polymer science (which includes polymer chemistry and polymer physics), biophysics a...
Organic polymer
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Modern scientific consensus rejects this view as being irreconcilable with modern genetic research. : 360 Scientific racism misapplies, misconstrues, or distorts anthropology (notably physical anthropology), anthropometry, craniometry, evolutionary biology, and other disciplines or pseudo-disciplines, in proposing anth...
Race science
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Textile mills have moved from Western Europe to, more recently, lower-wage areas. Industrial production is currently mostly located in countries like India, Bangladesh, China, and in Latin America. In these regions labour is much less expensive than in the first world, and attracts poor workers. Biotechnology plays an ...
History of cotton
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Daphnia magna has become a model system to study the evolution and ecology of host-parasite interaction. Animals collected from natural habitats are frequently infected. Many parasites that infect D. magna have been identified and studied (Table 1), D. magna shows parasite-induced behavioural characteristics that can d...
Daphnia magna
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Cell-based models are mathematical models that represent biological cells as discrete entities. Within the field of computational biology they are often simply called agent-based models of which they are a specific application and they are used for simulating the biomechanics of multicellular structures such as tissues...
Cell-based models
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In most logics, weakening is either an inference rule or a metatheorem if the logic doesn't have an explicit rule. Notable exceptions are: Relevance logic, where every premise is necessary for the conclusion. Linear logic, which lacks monotonicity and idempotency of entailment.
Monotonic logic
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Text, Speech and Dialogue (TSD) is an annual conference involving topics on natural language processing and computational linguistics. The meeting is held every September alternating in Brno and Plzeň, Czech Republic. The first Text, Speech and Dialogue conference took place in Brno in 1998.
Text, Speech and Dialogue
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Quaternion algebra here means something more general than the algebra of Hamilton's quaternions. When the coefficient field F does not have characteristic 2, every quaternion algebra over F can be described as a 4-dimensional F-vector space with basis { 1 , i , j , k } {\displaystyle \{1,i,j,k\}} , with the following m...
Quaternion algebra
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83,155
The institute has two locations: At the nature-oriented Seewiesen Campus, in the municipality of Pöcking near Starnberg, field research is combined with modern methods of behavioral biology. At the Martinsried Campus in the southwest of Munich, neuroscientific research is currently the main focus. Here, laboratory expe...
Max Planck Institute for Biological Intelligence
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83,156
Seda Atay, a biotechnology researcher at Hacettepe University, experimentally observed this specificity and selectivity between a QCM and MDA-MB 231 breast cells, MCF 7 cells, and starved MDA-MB 231 cells in vitro. With other researchers she devised a method of washing these different metastatic leveled cells over the ...
Biosensor
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83,157
Fouling communities were highlighted particularly in the literature of marine ecology as a potential example of alternate stable states through the work of John Sutherland in the 1970s at Duke University, although this was later called into question by Connell and Sousa.
Fouling community
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83,158
Waring proved the fundamental theorem of symmetric polynomials, and specially considered the relation between the roots of a quartic equation and its resolvent cubic.Lagrange's goal (1770, 1771) was to understand why equations of third and fourth degree admit formulas for solutions, and a key object was the group of pe...
History of group theory
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83,159
Computational chemical methods in solid-state physics follow the same approach as they do for molecules, but with two differences. First, the translational symmetry of the solid has to be utilised, and second, it is possible to use completely delocalised basis functions such as plane waves as an alternative to the mole...
Computational chemical methods in solid-state physics
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83,160
He was appointed Professor of Physical Chemistry at Cambridge University in 1965. He was Master of Sidney Sussex College, Cambridge, on the Council of the Royal Society, and was President of the Faraday Society. Throughout his career as a chemist, he was noted for his wide interests, making substantial contributions in...
Jack Linnett
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1887 On July 11, Dedekind proves the theorem (not relying on the axiom of choice) but neither publishes his proof nor tells Cantor about it. Ernst Zermelo discovered Dedekind's proof and in 1908 he publishes his own proof based on the chain theory from Dedekind's paper Was sind und was sollen die Zahlen? 1895 Cantor st...
Cantor–Bernstein–Schroeder theorem
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The result was a volcano-like inflow that the drillers tried in vain to stop.In the same Marine and Petroleum Geology journal, the group of geologists and drilling engineers refuted the allegation showing that the "kick" maximum pressure were too low to fracture the rock formation. The well pressure analysis based on c...
Sidoarjo mud flow
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83,163
In evolutionary developmental biology, Paired box (Pax) genes are a family of genes coding for tissue specific transcription factors containing an N-terminal paired domain and usually a partial, or in the case of four family members (PAX3, PAX4, PAX6 and PAX7), a complete homeodomain to the C-terminus. An octapeptide a...
Pax genes
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83,164
The common power is going from 1 up to 250kw per unit with an efficiency (SOE) around 2 kgO2/kw. Low speed aerator are used mostly for biology plant aeration for water purification. The higher the diameter, the higher the SOE and mixing.
Water aeration
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83,165
Non-abelian anyons have more complicated fusion relations. As a rule, in a system with non-abelian anyons, there is a composite particle whose statistics label is not uniquely determined by the statistics labels of its components, but rather exists as a quantum superposition (this is completely analogous to how two fer...
Fusion of anyons
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83,166
Schäfer et al. achieved high power outputs at a bandwidth of approximately 10 nm. Schäfer also experimented with laser dyes in the vapor phase under optical excitation.In addition to his pioneering work on the dye laser, Schäfer also made important contributions to femtosecond lasers and the application of these lasers...
Fritz Peter Schäfer
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83,167
When more specific types of differentiation are necessary, such as in multivariate calculus or tensor analysis, other notations are common. For a function f of a single independent variable x, we can express the derivative using subscripts of the independent variable: f x = d f d x f x x = d 2 f d x 2 . {\displaystyle ...
Newton's notation for differentiation
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83,168
Within physics, the Hybrid Theory for photon transport in tissue uses the advantages and eliminates the deficiencies of both the Monte Carlo method and the diffusion theory for photon transport to model photons traveling through tissue both accurately and efficiently.
Hybrid theory for photon transport in tissue
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83,169
These discoveries had significant ramifications in biology, medicine, and pharmacology. The first automated DNA synthesizer resulted from a collaboration with Marvin H. Caruthers of the University of Colorado Boulder, and was based on Caruthers' work elucidating the chemistry of phosphoramidite oligonucleotide synthesi...
Leroy Hood
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83,170
The critical virtue of the Daniels escapement is the virtual elimination of the sliding friction component; i.e., the sliding of the pallet stones over the teeth of the escapement gear. What little sliding friction remains is due to the impossibility of maintaining an exact tangential geometry throughout the duration o...
Co-axial escapement
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83,171
Mapping systems generate three kinds of data: geometry of the chamber(s) of the heart based on movement of catheters in space voltage maps based on the amplitude of electrogram recordings timing maps ("local activation time" or LAT) based on the relative timing of electrogram recordings at different positions in the he...
Electroanatomic mapping
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83,172
with Bojan Mohar: Graphs on surfaces, Johns Hopkins University Press 2001 5-choosability of planar graphs (see List coloring) works on Hypohamiltonian graphs Hamilton connectivity of Tournaments (see Tournament (graph theory)) and of 4-connected planar graphs his proof of Grötzsch's theorem
Carsten Thomassen (mathematician)
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The American Medical Association's Council on Ethical and Judicial Affairs stated that "genetic interventions to enhance traits should be considered permissible only in severely restricted situations: (1) clear and meaningful benefits to the fetus or child; (2) no trade-off with other characteristics or traits; and (3)...
Gene therapy treatment
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83,174
In fact, there are infinitely many strong pseudoprimes to any base greater than 1 (see Theorem 1 of ) and infinitely many Carmichael numbers, but they are comparatively rare. There are three pseudoprimes to base 2 below 1000, 245 below one million, and 21853 less than 25·109. There are 4842 strong pseudoprimes base 2 a...
Fermat pseudoprime
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83,175
Statistical literacy is the ability to understand and reason with statistics and data. The abilities to understand and reason with data, or arguments that use data, are necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. However, scientists also need...
Statistical literacy
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83,176
Samuel Eilenberg announced the theorem without proof in his book; he says "The proof is correct, long, and hard. It is a challenge to find a more reasonable proof of this fine theorem." Georges Hansel proposed a more simple proof, published in the not-easily accessible proceedings of a conference. The proof of Dominiqu...
Cobham's theorem
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83,177
Showing that these subsets of arithmetic skills are supported by different brain mechanisms offers the opportunity for a deeper understanding of the learning processes required to acquire arithmetic proficiency. Neuroimaging studies of mathematical learning disabilities are still rare but dyscalculia is an area of incr...
Educational neuroscience
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83,178
The theorem was proved by Prigogine in 1947 from the Onsager relations. Prigogine's theorem is valid if the kinetic coefficients in the Onsager relations are constant (do not depend on driving forces and flows); for real systems, it is valid only approximately, so the minimum entropy production for a stationary state i...
Prigogine's theorem
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83,179
The biology supplementary textbook for schools Of Pandas and People was drafted presenting creation science arguments, but shortly after the Edwards v. Aguillard ruling, that it was unconstitutional to teach creationism in public school science classes, the authors changed the wording to "intelligent design", introduci...
Irreducibly complex
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Ph.D. Systems Neuroscience Thesis, Centre for Neuroscience Studies, Queen's University, advisor: Stephen H. Scott Timothy Lillicrap, Jonathan J. Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, Daan Wierstra (2015). Continuous Control with Deep Reinforcement Learning.
Timothy Lillicrap
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83,181
The excitation wavelength is blinded by the pump laser and cut out. The rest of the spectra usually have a few bands such as ground-state absorption, excited-state absorption, and stimulated emission. Under normal conditions, the angles of the emission are randomly orientated and not detected in the absorption geometry...
Ultrafast laser spectroscopy
0.79927
83,182
Technology management can also be defined as the integrated planning, design, optimization, operation and control of technological products, processes and services, a better definition would be the management of the use of technology for human advantage. Technology Management was deemed an emerging field of study by th...
Technology management
0.79927
83,183
Brian G. Wowk is a Canadian medical physicist and cryobiologist known for the discovery and development of synthetic molecules that mimic the activity of natural antifreeze proteins in cryopreservation applications, sometimes called "ice blockers". As a senior scientist at 21st Century Medicine, Inc., he was a co-devel...
Brian Wowk
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83,184
In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the x-axis. (Some authors define the angle as the deviation from the direction of the curve at some fixed starting point. This is equivalent to the definiti...
Tangential angle
0.79927
83,185
If histones are subject of interest, it is believed that the distribution of modifications and their localizations may offer new insights into the mechanisms of regulation. One of the long-term goals ChIP-on-chip was designed for is to establish a catalogue of (selected) organisms that lists all protein-DNA interaction...
ChIP-on-chip
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83,186
As of June 2021, Sputnik V is under rolling review process by EMA, but the marketing authorisation application was not submitted yet.Emergency use has also been authorized in Algeria, Bolivia, Serbia, the Palestinian territories, and Mexico.On 25 January 2021, Iran approved the vaccine, with Foreign Minister Mohammad J...
Sputnik V
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83,187
In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of an ample line bundle, although there are several related classes of line b...
Ample line bundle
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83,188
"Forensic Chemistry and Ambient Mass Spectrometry: A Perfect Couple Destined for a Happy Marriage?". Analytical Chemistry. American Chemical Society (ACS).
Livia S. Eberlin
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83,189
Astronomy & Geophysics (A&G) is a scientific journal and trade magazine published on behalf of the Royal Astronomical Society (RAS) by Oxford University Press. It is distributed bimonthly to members of the RAS. A&G publishes content of interest to professional astronomers and geophysicists, including: news reports, int...
Astronomy & Geophysics
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83,190
The use of split-complex numbers dates back to 1848 when James Cockle revealed his tessarines. William Kingdon Clifford used split-complex numbers to represent sums of spins. Clifford introduced the use of split-complex numbers as coefficients in a quaternion algebra now called split-biquaternions. He called its elemen...
Split-complex number
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83,191
See (Street 2003). Furthermore, if M is an R-S-bimodule and L is an T-S-bimodule, then the set HomS(M, L) of all S-module homomorphisms from M to L becomes a T-R-module in a natural fashion. These statements extend to the derived functors Ext and Tor. Profunctors can be seen as a categorical generalization of bimodules...
Bimodule
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83,192
Additionally, assuming a type of all types that includes itself as type leads into a paradox, as in the set of all sets, so one must proceed in steps of levels of abstraction. Research in second order lambda calculus, one step upwards, showed that type inference is undecidable in this generality. Parts of one extra lev...
Hindley–Milner type system
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83,193
A reflexive module is one for which the canonical homomorphism is an isomorphism. A torsionless module is one for which the canonical homomorphism is injective. Example: If G = Spec ⁡ ( A ) {\displaystyle G=\operatorname {Spec} (A)} is a finite commutative group scheme represented by a Hopf algebra A over a commutative...
Dual module
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In mathematics, the Birman–Murakami–Wenzl (BMW) algebra, introduced by Joan Birman and Hans Wenzl (1989) and Jun Murakami (1987), is a two-parameter family of algebras C n ( ℓ , m ) {\displaystyle \mathrm {C} _{n}(\ell ,m)} of dimension 1 ⋅ 3 ⋅ 5 ⋯ ( 2 n − 1 ) {\displaystyle 1\cdot 3\cdot 5\cdots (2n-1)} having the Hec...
Birman–Wenzl algebra
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The Emeritus Group at MPI-Marburg is headed by renowned biochemist and Gottfried Wilhelm Leibniz Prize recipient, Rudolf K. Thauer, who was also the founding director of the institute when it was established in 1991. The scientific focus of the group is on the biochemistry of methanogenic archaea, methanotrophic archae...
Max Planck Institute for Terrestrial Microbiology
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Maxwell–Boltzmann statistics can be derived in various statistical mechanical thermodynamic ensembles: The grand canonical ensemble, exactly. The canonical ensemble, exactly. The microcanonical ensemble, but only in the thermodynamic limit.In each case it is necessary to assume that the particles are non-interacting, a...
Boltzmann statistics
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Only the time difference matters. Noise is due to a very large number of fluctuating charge so that the central limit theorem applie, i.e., the noise is Gaussian or normally distributed. G v v {\displaystyle G_{vv}} decays to zero rapidly over some time τ c {\displaystyle \tau _{c}} .
Quantum noise
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In algebra, given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a quotient vector space. It differs from analogous quotient constructions of rings and groups by the fact that in these cases, the subspace that is used for defining the qu...
Factor module
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Daraio's research develops new materials that combine intriguing chemical composition with a designed architecture at the micro- and macro-scales. Some of her contributions include a version of Newton's cradle that can generate "sound bullets"—sound waves focused tightly enough to disrupt matter; walls filled with ball...
Chiara Daraio
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