id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
83,800 | Euler replied in a letter dated 30 June 1742 and reminded Goldbach of an earlier conversation they had had ("... so Ew vormals mit mir communicirt haben ..."), in which Goldbach had remarked that the first of those two conjectures would follow from the statement This is in fact equivalent to his second, marginal conjec... | Goldbach conjecture | 0.78362 |
83,801 | A direct application is choosing probabilities to maximize transmission rate through a constrained channel, analogously to Fibonacci coding. Its properties also made it useful for example in analysis of complex networks, like link prediction, community detection, robust transport over networks and centrality measures. ... | Maximal Entropy Random Walk | 0.783619 |
83,802 | The formula inside the bracket is discrete Laplace operator, making this equation a discrete analogue of stationary Schrodinger equation. As in quantum mechanics, MERW predicts that the probability distribution should lead exactly to the one of quantum ground state: ρ x ∝ ψ x 2 {\displaystyle \rho _{x}\propto \psi _{x}... | Maximal Entropy Random Walk | 0.783619 |
83,803 | Teleportation is the hypothetical transfer of matter or energy from one point to another without traversing the physical space between them. It is a common subject in science fiction literature and in other popular culture. Teleportation is often paired with time travel, being that the travelling between the two points... | Teleportation | 0.783618 |
83,804 | Researchers believe that quantum teleportation is the foundation of quantum calculation and quantum communication.In 2008, M. Hotta proposed that it may be possible to teleport energy by exploiting quantum energy fluctuations of an entangled vacuum state of a quantum field. There are some papers published but no experi... | Teleportation | 0.783618 |
83,805 | Similarly over a semiperfect ring, every indecomposable projective module is a PIM, and every finitely generated projective module is a direct sum of PIMs. In the context of group algebras of finite groups over fields (which are semiperfect rings), the representation ring describes the indecomposable modules, and the m... | Principal indecomposable module | 0.783617 |
83,806 | In mathematics, especially in the area of abstract algebra known as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective modules, and indecomposable modules. | Principal indecomposable module | 0.783617 |
83,807 | Instead, if A and B are operated on first, and provided D and A − BD−1C are nonsingular, the result is Equating Equations (1) and (2) leads to where Equation (3) is the Woodbury matrix identity, which is equivalent to the binomial inverse theorem. If A and D are both invertible, then the above two block matrix inverses... | Non-singular matrix | 0.783616 |
83,808 | This technique was reinvented several times and is due to Hans Boltz (1923), who used it for the inversion of geodetic matrices, and Tadeusz Banachiewicz (1937), who generalized it and proved its correctness. The nullity theorem says that the nullity of A equals the nullity of the sub-block in the lower right of the in... | Non-singular matrix | 0.783616 |
83,809 | The Arcminute Microkelvin Imager (AMI) consists of a pair of interferometric radio telescopes - the Small and Large Arrays - located at the Mullard Radio Astronomy Observatory near Cambridge. AMI was designed, built and is operated by the Cavendish Astrophysics Group. AMI was designed, primarily, for the study of galax... | Arcminute Microkelvin Imager Large Array | 0.783616 |
83,810 | There is also a Weiertrass preparation theorem for Tate algebras T n ( k ) = { ∑ ν 1 , … , ν n ≥ 0 a ν 1 , … , ν n X 1 ν 1 ⋯ X n ν n , | a ν 1 , … , ν n | → 0 for ν 1 + ⋯ + ν n → ∞ } {\displaystyle T_{n}(k)=\left\{\sum _{\nu _{1},\dots ,\nu _{n}\geq 0}a_{\nu _{1},\dots ,\nu _{n}}X_{1}^{\nu _{1}}\cdots X_{n}^{\nu _{n}},... | Weierstrass preparation theorem | 0.783615 |
83,811 | There is a deeper preparation theorem for smooth functions, due to Bernard Malgrange, called the Malgrange preparation theorem. It also has an associated division theorem, named after John Mather. | Weierstrass preparation theorem | 0.783615 |
83,812 | For one variable, the local form of an analytic function f(z) near 0 is zkh(z) where h(0) is not 0, and k is the order of the zero of f at 0. This is the result that the preparation theorem generalises. We pick out one variable z, which we may assume is first, and write our complex variables as (z, z2, ..., zn). A Weie... | Weierstrass preparation theorem | 0.783615 |
83,813 | In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients of lower d... | Weierstrass preparation theorem | 0.783615 |
83,814 | Then the theorem states that for analytic functions f, if f(0, ...,0) = 0,and f(z, z2, ..., zn)as a power series has some term only involving z, we can write (locally near (0, ..., 0)) f(z, z2, ..., zn) = W(z)h(z, z2, ..., zn)with h analytic and h(0, ..., 0) not 0, and W a Weierstrass polynomial. This has the immediate... | Weierstrass preparation theorem | 0.783615 |
83,815 | More than 780 leukemias and hundreds of solid tumors (lung, prostate, kidney, etc.) are now characterized by an acquired chromosomal abnormality, whose prognostic value is crucial. The identification of these chromosomal abnormalities has led to the discovery of a very large number of "cancer genes" (or oncogenes). The... | Cytological map | 0.783611 |
83,816 | This abnormal chromosome was dubbed the Philadelphia chromosome - as both scientists were doing their research in Philadelphia, Pennsylvania. Thirteen years later, with the development of more advanced techniques, the abnormal chromosome was shown by Janet Rowley to be the result of a translocation of chromosomes 9 and... | Cytological map | 0.783611 |
83,817 | The routine chromosome analysis (Karyotyping) refers to analysis of metaphase chromosomes which have been banded using trypsin followed by Giemsa, Leishmanns, or a mixture of the two. This creates unique banding patterns on the chromosomes. The molecular mechanism and reason for these patterns are unknown, although it ... | Cytological map | 0.783611 |
83,818 | Not all genes on the X chromosome are inactivated, which is why there is a phenotypic effect seen in individuals with extra X chromosomes. Trisomy 13 was associated with Patau syndrome and trisomy 18 with Edwards syndrome. Acquired cytogenetics: In 1960, Peter Nowell and David Hungerford discovered a small chromosome i... | Cytological map | 0.783611 |
83,819 | Following the advent of procedures that allowed easy enumeration of chromosomes, discoveries were quickly made related to aberrant chromosomes or chromosome number. Constitutional cytogenetics: In some congenital disorders, such as Down syndrome, cytogenetics revealed the nature of the chromosomal defect: a "simple" tr... | Cytological map | 0.783611 |
83,820 | Cytogenetics is essentially a branch of genetics, but is also a part of cell biology/cytology (a subdivision of human anatomy), that is concerned with how the chromosomes relate to cell behaviour, particularly to their behaviour during mitosis and meiosis. Techniques used include karyotyping, analysis of G-banded chrom... | Cytological map | 0.783611 |
83,821 | In the 1980s, advances were made in molecular cytogenetics. While radioisotope-labeled probes had been hybridized with DNA since 1969, movement was now made in using fluorescent-labeled probes. Hybridizing them to chromosomal preparations using existing techniques came to be known as fluorescence in situ hybridization ... | Cytological map | 0.783611 |
83,822 | Analysis of FISH specimens is done by fluorescence microscopy by a clinical laboratory specialist in cytogenetics. For oncology, generally, a large number of interphase cells are scored in order to rule out low-level residual disease, generally between 200 and 1,000 cells are counted and scored. For congenital problems... | Cytological map | 0.783611 |
83,823 | This is a list of scientific journals published by the Royal Society of Chemistry. | Contemporary Organic Synthesis | 0.78361 |
83,824 | Green Chemistry (1999–present) | Contemporary Organic Synthesis | 0.78361 |
83,825 | Biomaterials Science (2013–present) | Contemporary Organic Synthesis | 0.78361 |
83,826 | Analyst (1876–present) Analytical Communications (1996–1999) Analytical Methods (2009–present) Analytical Proceedings (1980–1993) Analytical Proceedings including Analytical Communications (1994–1995) Annual Reports on Analytical Atomic Spectroscopy (1971–1984) Annual Reports on the Progress of Chemistry Annual Reports... | Contemporary Organic Synthesis | 0.78361 |
83,827 | Journal of Analytical Atomic Spectrometry (1986 - Present) Journal of the Chemical Society (1849 - 1996) Journal of the Chemical Society, Abstracts (1878 - 1925) Journal of the Chemical Society, Transactions (1878 - 1925) Journal of the Chemical Society A: Inorganic, Physical, Theoretical (1966 - 1971) Journal of the C... | Contemporary Organic Synthesis | 0.78361 |
83,828 | Industrial Chemistry & Materials (2022-present) Integrative Biology (2008–2018) (Now published by Oxford University Press) Inorganic Chemistry Frontiers (2014–present) | Contemporary Organic Synthesis | 0.78361 |
83,829 | Reaction Chemistry & Engineering (2016-Present) RSC Advances (2011-Present) RSC Applied Interfaces (2023-Present) RSC Applied Polymers (2023-Present) RSC Chemical Biology (2020-Present) RSC Medicinal Chemistry (2020-Present) RSC Sustainability (2022-Present) | Contemporary Organic Synthesis | 0.78361 |
83,830 | Perkin Transactions (1997-2002) Photochemical and Photobiological Sciences (2002-present) PhysChemComm (1998-2003) Physical Chemistry Chemical Physics (1999-Present) Polymer Chemistry (2010-Present) Proceedings of the Chemical Society (1841-1964) | Contemporary Organic Synthesis | 0.78361 |
83,831 | Organic and Biomolecular Chemistry (2003-Present) Organic Chemistry Frontiers (2014-Present) | Contemporary Organic Synthesis | 0.78361 |
83,832 | Nanoscale (2009-Present) Nanoscale Advances (2018-Present) Nanoscale Horizons (2016-Present) Natural Product Reports (1984-Present) Natural Product Updates (2002-present) New Journal of Chemistry (1998-Present) | Contemporary Organic Synthesis | 0.78361 |
83,833 | Materials Advances (2020–present) Materials Chemistry Frontiers (2017–present) Materials Horizons (2014–present) MedChemComm (2010–present) Molecular Omics (2018–present) Molecular Systems Design & Engineering (2015–present) | Contemporary Organic Synthesis | 0.78361 |
83,834 | It constitutes the largest expansion of Harvard Medical school witnessed in the last 100 years. It houses the Department of Genetics of the Harvard Medical School, among many other centers and institutes it houses. | New Research Building | 0.78361 |
83,835 | In molecular biology, an oscillating gene is a gene that is expressed in a rhythmic pattern or in periodic cycles. Oscillating genes are usually circadian and can be identified by periodic changes in the state of an organism. Circadian rhythms, controlled by oscillating genes, have a period of approximately 24 hours. F... | Gene oscillations | 0.78361 |
83,836 | On the real line consider the Lebesgue measure and its corresponding 𝜎-algebra Σ . {\displaystyle \Sigma .} Define a function f {\displaystyle f} by the formula The supremum of this function (largest value) is 5, and the infimum (smallest value) is −4. However, the function takes these values only on the sets { 1 } {\... | Essential supremum | 0.783609 |
83,837 | In plane geometry, a lune (from Latin luna 'moon') is the concave-convex region bounded by two circular arcs. It has one boundary portion for which the connecting segment of any two nearby points moves outside the region and another boundary portion for which the connecting segment of any two nearby points lies entirel... | Lune (geometry) | 0.783608 |
83,838 | In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad reduction at some prime is. It is connected to the ramification in the field generated by the torsion points. | Conductor of an abelian variety | 0.783605 |
83,839 | Vacuum arc remelting further removes lingering inclusions to provide superior steel cleanliness and remove gases like oxygen, nitrogen and hydrogen. Controlling the rate at which these droplets form and solidify ensures a consistency of chemistry and microstructure throughout the entire VIM-VAR ingot, making the steel ... | Electric arc furnace | 0.783604 |
83,840 | Temperature sampling and chemical sampling take place via automatic lances. Oxygen and carbon can be automatically measured via special probes that dip into the steel, but for all other elements, a "chill" sample — a small, solidified sample of the steel — is analysed on an arc-emission spectrometer. Once the temperatu... | Electric arc furnace | 0.783604 |
83,841 | Removal of carbon takes place after these elements have burnt out first, as they have a greater affinity for oxygen. Metals that have a poorer affinity for oxygen than iron, such as nickel and copper, cannot be removed through oxidation and must be controlled through scrap chemistry alone, such as introducing the direc... | Electric arc furnace | 0.783604 |
83,842 | The scrap-charging and meltdown process can be repeated as many times as necessary to reach the required heat weight - the number of charges is dependent on the density of scrap; lower-density scrap means more charges. After all scrap charges have completely melted, refining operations take place to check and correct t... | Electric arc furnace | 0.783604 |
83,843 | In materials science, a sandwich-structured composite is a special class of composite materials that is fabricated by attaching two thin-but-stiff skins to a lightweight but thick core. The core material is normally low strength, but its higher thickness provides the sandwich composite with high bending stiffness with ... | Sandwich structured composite | 0.783604 |
83,844 | In population genetics, Ewens's sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample. | Ewens sampling formula | 0.783603 |
83,845 | The biological activity of humic lakes is, however, dominated by bacterial metabolism, which dominates the food web. The chemistry of humic lakes makes it difficult for higher trophic levels such as planktivorous fish to establish themselves, leaving a simplified food web consisting mostly of plants, plankton, and bact... | Dystrophic lake | 0.783602 |
83,846 | Nitrogen is essential in plant biochemistry, being required for chlorophyll and all proteins. In most terrestrial ecosystems nitrogen is in short supply and is sequestered in organic matter that is hard to break down. Fungal symbionts thus offer two advantages to plants: the greater range of their hyphae when compared ... | Ectomycorrhiza | 0.783602 |
83,847 | Reciprocity in evolutionary biology refers to mechanisms whereby the evolution of cooperative or altruistic behaviour may be favoured by the probability of future mutual interactions. A corollary is how a desire for revenge can harm the collective and therefore be naturally deselected. | Reciprocity (evolution) | 0.783601 |
83,848 | Real populations are not well mixed, but have spatial structures or social networks which imply that some individuals interact more often than others. One approach of capturing this effect is evolutionary graph theory, in which individuals occupy the vertices of a graph. The edges determine who interacts with whom. If ... | Reciprocity (evolution) | 0.783601 |
83,849 | Additionally, some connections between the Langlands program and M theory have been posited, as their dualities connect in nontrivial ways, providing potential exact solutions in superstring theory (as was similarly done in group theory through monstrous moonshine). Simply put, the Langlands project implies a deep and ... | Langlands conjecture | 0.783601 |
83,850 | Furthermore, if the reciprocity of such generalized algebras for the posited objects exists, and if their analytical functions can be shown to be well-defined, some very deep results in mathematics could be within reach of proof. Examples include: rational solutions of elliptic curves, topological construction of algeb... | Langlands conjecture | 0.783601 |
83,851 | To a lay reader or even nonspecialist mathematician, abstractions within the Langlands program can be somewhat impenetrable. However, there are some strong and clear implications for proof or disproof of the fundamental Langlands conjectures. As the program posits a powerful connection between analytic number theory an... | Langlands conjecture | 0.783601 |
83,852 | The starting point of the program may be seen as Emil Artin's reciprocity law, which generalizes quadratic reciprocity. The Artin reciprocity law applies to a Galois extension of an algebraic number field whose Galois group is abelian; it assigns L-functions to the one-dimensional representations of this Galois group, ... | Langlands conjecture | 0.783601 |
83,853 | In a very broad context, the program built on existing ideas: the philosophy of cusp forms formulated a few years earlier by Harish-Chandra and Gelfand (1963), the work and approach of Harish-Chandra on semisimple Lie groups, and in technical terms the trace formula of Selberg and others. What initially was very new in... | Langlands conjecture | 0.783601 |
83,854 | Given two reductive groups and a (well behaved) morphism between their corresponding L-groups, this conjecture relates their automorphic representations in a way that is compatible with their L-functions. This functoriality conjecture implies all the other conjectures presented so far. It is of the nature of an induced... | Langlands conjecture | 0.783601 |
83,855 | This in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions. Simply put, the Langlands philosophy allows a general analysis of structuring the abstractions of numbers. Naturally, this description is at once a reduction and over-generalization of the program's proper theore... | Langlands conjecture | 0.783601 |
83,856 | The meaning of such a construction is nuanced, but its specific solutions and generalizations are very powerful. The consequence for proof of existence to such theoretical objects implies an analytical method in constructing the categoric mapping of fundamental structures for virtually any number field. As an analogue ... | Langlands conjecture | 0.783601 |
83,857 | To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integration, by an equivalen... | Langlands conjecture | 0.783601 |
83,858 | In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by Robert Langlands (1967, 1970), it seeks to relate Galois groups in algebraic number theory to automorphic forms and represent... | Langlands conjecture | 0.783601 |
83,859 | Sotrovimab, sold under the brand name Xevudy, is a human neutralizing monoclonal antibody with activity against severe acute respiratory syndrome coronavirus 2, known as SARS-CoV-2. It was developed by GlaxoSmithKline and Vir Biotechnology, Inc. Sotrovimab is designed to attach to the spike protein of SARS-CoV-2.The mo... | Sotrovimab | 0.783601 |
83,860 | Sotrovimab's development began in December 2019, at Vir Biotechnology when Vir scientists first learned of the initial COVID-19 outbreak in China. Vir subsidiary Humabs BioMed had already compiled a library of frozen blood samples from patients infected with viral diseases, including two samples from patients infected ... | Sotrovimab | 0.783601 |
83,861 | A rationally connected variety (or uniruled variety) V is a projective algebraic variety over an algebraically closed field such that through every two points there passes the image of a regular map from the projective line into V. Equivalently, a variety is rationally connected if every two points are connected by a r... | Lüroth’s theorem | 0.783601 |
83,862 | Conversely, such a rational parameterization induces a field homomorphism of the field of functions of V into K ( U 1 , … , U d ) {\displaystyle K(U_{1},\dots ,U_{d})} . But this homomorphism is not necessarily onto. If such a parameterization exists, the variety is said to be unirational. Lüroth's theorem (see below) ... | Lüroth’s theorem | 0.783601 |
83,863 | Let V be an affine algebraic variety of dimension d defined by a prime ideal I = ⟨f1, ..., fk⟩ in K {\displaystyle K} . If V is rational, then there are n + 1 polynomials g0, ..., gn in K ( U 1 , … , U d ) {\displaystyle K(U_{1},\dots ,U_{d})} such that f i ( g 1 / g 0 , … , g n / g 0 ) = 0. {\displaystyle f_{i}(g_{1}... | Lüroth’s theorem | 0.783601 |
83,864 | Suppose that the image of the embedding is a surface S in R3. A local isometry is a diffeomorphism f: U → V between open regions of R3 whose restriction to S ∩ U is an isometry onto its image. Theorema egregium is then stated as follows: For example, the Gaussian curvature of a cylindrical tube is zero, the same as for... | Gaussian curvature | 0.783599 |
83,865 | In particular, the Gaussian curvature is invariant under isometric deformations of the surface. In contemporary differential geometry, a "surface", viewed abstractly, is a two-dimensional differentiable manifold. To connect this point of view with the classical theory of surfaces, such an abstract surface is embedded i... | Gaussian curvature | 0.783599 |
83,866 | Gauss's Theorema egregium (Latin: "remarkable theorem") states that Gaussian curvature of a surface can be determined from the measurements of length on the surface itself. In fact, it can be found given the full knowledge of the first fundamental form and expressed via the first fundamental form and its partial deriva... | Gaussian curvature | 0.783599 |
83,867 | In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r... | Gaussian curvature | 0.783598 |
83,868 | The Gauss–Bonnet theorem links the total curvature of a surface to its Euler characteristic and provides an important link between local geometric properties and global topological properties. | Gaussian curvature | 0.783598 |
83,869 | Since energy in quantum mechanics is defined as the phase factor exp(–iEt) that one gets when one moves forward in time, the way to reverse time while preserving the sign of the energy is to also reverse the sense of "i", so that the sense of phases is reversed. Similarly, any operation that reverses the sense of phase... | Time-reversal symmetry | 0.783597 |
83,870 | Eugene Wigner showed that a symmetry operation S of a Hamiltonian is represented, in quantum mechanics either by a unitary operator, S = U, or an antiunitary one, S = UK where U is unitary, and K denotes complex conjugation. These are the only operations that act on Hilbert space so as to preserve the length of the pro... | Time-reversal symmetry | 0.783597 |
83,871 | This allows one to analyze the conditions under which optical phenomena that locally break time-reversal, such as Faraday isolators and directional dichroism, can occur.) In physics one separates the laws of motion, called kinematics, from the laws of force, called dynamics. Following the classical kinematics of Newton... | Time-reversal symmetry | 0.783597 |
83,872 | Riemann invariants are mathematical transformations made on a system of conservation equations to make them more easily solvable. Riemann invariants are constant along the characteristic curves of the partial differential equations where they obtain the name invariant. They were first obtained by Bernhard Riemann in hi... | Riemann invariant | 0.783596 |
83,873 | Hugh Everett's many-worlds interpretation of quantum physics, "The first and most important of the four strands". Karl Popper's epistemology, especially its anti-inductivism and its requiring a realist (non-instrumental) interpretation of scientific theories, and its emphasis on taking seriously those bold conjectures ... | The Fabric of Reality | 0.783594 |
83,874 | His theory of everything is (weakly) emergentist rather than reductive. It aims not at the reduction of everything to particle physics, but rather at mutual support among multiverse, computational, epistemological, and evolutionary principles. | The Fabric of Reality | 0.783594 |
83,875 | The book expands on his views of quantum mechanics and its implications for understanding reality. This interpretation, which he calls the multiverse hypothesis, is one of a four-strand Theory of Everything (TOE). | The Fabric of Reality | 0.783594 |
83,876 | The foundation is engaged in basic and clinical research in Ayurveda, the clinical trial conducted at The Ayurvedic Trust in collaboration with UCLA Medical School on rheumatoid arthritis to see which works better for rheumatoid arthritis, Ayurveda or the Western drug methotrexate was pronounced as a blue print on how ... | AVP Research Foundation | 0.783593 |
83,877 | Inter-disciplinary research bridging Ayurveda with modern sciences to elucidate the biochemistry behind the inherent theories in Ayurveda is also attempted at AVP Research Foundation. | AVP Research Foundation | 0.783593 |
83,878 | Pyrethroids were introduced by a team of Rothamsted Research scientists in the 1960s and 1970s following the elucidation of the structures of pyrethrin I and II by Hermann Staudinger and Leopold Ružička in the 1920s. The pyrethroids represented a major advancement in the chemistry that would synthesize the analog of th... | Synthetic pyrethroid | 0.783592 |
83,879 | In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyper... | Pure shear | 0.783592 |
83,880 | The CCRU's work is characterized by loose, abstract theoretical writing combining elements of cyberpunk and Gothic horror with critical theory, esotericism, numerology and demonology, which often interplay in their deployment of occult systems and surreal narratives. One of the CCRU's predominant ideas is hyperstition,... | Cybernetic Culture Research Unit | 0.78359 |
83,881 | In mathematics, Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds. Verdier duality was introduced in 1965 by Jean-Louis Verdier (1995) as an analog for locally compact topological spaces of Alexander Grothendieck's theory of Poincaré duality in étale cohomo... | Verdier duality | 0.78359 |
83,882 | AKR II – Ausbildungskernreaktor II, Technische Universität Dresden; rating: 2 W, commissioned 2005 AVR – Arbeitsgemeinschaft Versuchsreaktor, Forschungszentrum Jülich; rating: 15 MW, commissioned 1969; closed 1988 BER II – Berliner-Experimentier-Reaktor II, Helmholtz-Zentrum Berlin für Materialien und Energie; rating: ... | List of nuclear research reactors | 0.783589 |
83,883 | A total of 98 nuclear research facilities, including: T-15 fusion reactor at Kurchatov Institute VVR-M 18 MW reactor at St. Petersburg Institute of Nuclear Physics IBR-2 2 MW pulsed reactor at Joint Institute for Nuclear Research SM, Arbus (ACT-1), MIR.M1, RBT-6, RBT-10 / 1, RBT-10 / 2, BOR-60 and VK-50 Research Instit... | List of nuclear research reactors | 0.783589 |
83,884 | Institute for Nuclear Research, Mioveni, 110 km northwest of Bucharest - TRIGA reactor (capable consisting of either a 500 kW pulse ACPR core, or a 14 MW steady state core) National Institute for Research and Isotopic Separation, Govora, 170 km west of Bucharest - no research reactors, but instead devoted to heavy wate... | List of nuclear research reactors | 0.783589 |
83,885 | Notes: The main uses of the current OPAL reactor are: Irradiation of target materials to produce radioisotopes for medical and industrial applications Research in the fields of materials science and structural biology using neutron beams and its sophisticated suite of experimental equipment Analysis of minerals and sam... | List of nuclear research reactors | 0.783589 |
83,886 | The Hopf theorem (named after Heinz Hopf) is a statement in differential topology, saying that the topological degree is the only homotopy invariant of continuous maps to spheres. | Hopf theorem | 0.783589 |
83,887 | RDRAND (for "read random"; known as Intel Secure Key Technology, codename Bull Mountain) is an instruction for returning random numbers from an Intel on-chip hardware random number generator which has been seeded by an on-chip entropy source. Intel introduced the feature around 2012, and AMD added support for the instr... | RDRAND | 0.783587 |
83,888 | In organic chemistry, a nitrone is a functional group consisting of an N-oxide of an imine. The general structure is R2C=N+O−R’, where R’ is not a hydrogen. A nitrone is a 1,3-dipole, and is used in 1,3-dipolar cycloadditions. Other reactions of nitrones are known, including formal cycloadditions to form 6-membered ri... | Nitrone | 0.783585 |
83,889 | for short). When the measure space is furthermore sigma-finite then L∞(μ) is in turn dual to L1(μ), which by the Radon–Nikodym theorem is identified with the set of all countably additive μ-a.c. measures. | Ca space | 0.783581 |
83,890 | If Σ is a sigma-algebra and μ is a sigma-additive positive measure on Σ then the Lp space L∞(μ) endowed with the essential supremum norm is by definition the quotient space of B(Σ) by the closed subspace of bounded μ-null functions: N μ := { f ∈ B ( Σ ): f = 0 μ -almost everywhere } . {\displaystyle N_{\mu }:=\{f\in B(... | Ca space | 0.783581 |
83,891 | If Σ is a sigma-algebra, then the space c a ( Σ ) {\displaystyle ca(\Sigma )} is defined as the subset of b a ( Σ ) {\displaystyle ba(\Sigma )} consisting of countably additive measures. The notation ba is a mnemonic for bounded additive and ca is short for countably additive. If X is a topological space, and Σ is the ... | Ca space | 0.783581 |
83,892 | All three spaces are complete (they are Banach spaces) with respect to the same norm defined by the total variation, and thus c a ( Σ ) {\displaystyle ca(\Sigma )} is a closed subset of b a ( Σ ) {\displaystyle ba(\Sigma )} , and r c a ( X ) {\displaystyle rca(X)} is a closed set of c a ( Σ ) {\displaystyle ca(\Sigma )... | Ca space | 0.783581 |
83,893 | In particular, this isomorphism allows one to define the integral with respect to a finitely additive measure (note that the usual Lebesgue integral requires countable additivity). This is due to Dunford & Schwartz, and is often used to define the integral with respect to vector measures, and especially vector-valued R... | Ca space | 0.783581 |
83,894 | Let B(Σ) be the space of bounded Σ-measurable functions, equipped with the uniform norm. Then ba(Σ) = B(Σ)* is the continuous dual space of B(Σ). This is due to Hildebrandt and Fichtenholtz & Kantorovich. This is a kind of Riesz representation theorem which allows for a measure to be represented as a linear functional ... | Ca space | 0.783581 |
83,895 | In mathematics, the ba space b a ( Σ ) {\displaystyle ba(\Sigma )} of an algebra of sets Σ {\displaystyle \Sigma } is the Banach space consisting of all bounded and finitely additive signed measures on Σ {\displaystyle \Sigma } . The norm is defined as the variation, that is ‖ ν ‖ = | ν | ( X ) . {\displaystyle \|\nu \... | Ca space | 0.783581 |
83,896 | The Chou–Fasman method is an empirical technique for the prediction of secondary structures in proteins, originally developed in the 1970s by Peter Y. Chou and Gerald D. Fasman. The method is based on analyses of the relative frequencies of each amino acid in alpha helices, beta sheets, and turns based on known protein... | Chou-Fasman method | 0.78358 |
83,897 | In chemistry, catalytic resonance theory was developed to describe the kinetics of reaction acceleration using dynamic catalyst surfaces. Catalytic reactions occurring on surfaces that undergo variation in surface binding energy and/or entropy exhibit overall increase in reaction rate when the surface binding energy fr... | Catalytic resonance theory | 0.783578 |
83,898 | The surface reaction rate constant of species i converting to surface species j includes the dynamic activation energy: k i − j ( t , T ) = A e − E a , i − j ( t ) R T , {\displaystyle k_{i-j}(t,T)=Ae^{\frac {-E_{\rm {a,i-j}}(t)}{RT}},} The resulting surface chemistry kinetics are then described via a surface reaction ... | Catalytic resonance theory | 0.783578 |
83,899 | Similar to the controlled directionality of molecular machines, the resulting ratchet (device) energy mechanism selectively moves molecules through a catalytic reaction against a free energy gradient.Application of dynamic binding energy to a surface with multiple catalytic reactions exhibits complex behavior derived f... | Catalytic resonance theory | 0.783578 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.