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30,000 | Many texts prove the theorem with the use of strong induction and the class equation, though considerably less machinery is required to prove the theorem in the abelian case. One can also invoke group actions for the proof. | Cauchy's theorem (group theory) | 0.805163 |
30,001 | In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p. That is, there is x in G such that p is the smallest positive integer with xp = e, where e is the identity ... | Cauchy's theorem (group theory) | 0.805163 |
30,002 | A practically immediate consequence of Cauchy's theorem is a useful characterization of finite p-groups, where p is a prime. In particular, a finite group G is a p-group (i.e. all of its elements have order pk for some natural number k) if and only if G has order pn for some natural number n. One may use the abelian ca... | Cauchy's theorem (group theory) | 0.805163 |
30,003 | Let G be a finite group where x2 = e for all elements x of G. Then G has the order 2n for some non negative integer n. Let |G| equal m. In the case of m is 1, then G = {e}. In the case of m ≥ 2, if m has the odd prime factor p, G has the element x where xp = e from Cauchy's theorem. It conflicts with the assumption. | Cauchy's theorem (group theory) | 0.805163 |
30,004 | The result is a rotation around their intersection line a ∧ b {\displaystyle a\wedge b} , which could also lie on the plane at infinity when the two reflections are parallel, in which case the bireflection a b {\displaystyle ab} is a translation. A screw motion S {\displaystyle S} is the product of four non-collinear r... | Chasles' theorem (kinematics) | 0.805163 |
30,005 | The calculation of the commuting translation and rotation from a screw motion can be performed using 3DPGA ( R 3 , 0 , 1 {\displaystyle \mathbb {R} _{3,0,1}} ), the geometric algebra of 3D Euclidean space. It has three Euclidean basis vectors e i {\displaystyle \mathbf {e} _{i}} satisfying e i 2 = 1 {\displaystyle \mat... | Chasles' theorem (kinematics) | 0.805163 |
30,006 | These points lie on the Mozzi axis through which the rigid motion can be accomplished through a screw motion. Another elementary proof of Mozzi–Chasles' theorem was given by E. T. Whittaker in 1904. Suppose A is to be transformed into B. Whittaker suggests that line AK be selected parallel to the axis of the given rota... | Chasles' theorem (kinematics) | 0.805163 |
30,007 | Mozzi considers a rigid body undergoing first a rotation about an axis passing through the center of mass and then a translation of displacement D in an arbitrary direction. Any rigid motion can be accomplished in this way due to a theorem by Euler on the existence of an axis of rotation. The displacement D of the cent... | Chasles' theorem (kinematics) | 0.805163 |
30,008 | In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a translation along a line (called its screw axis or Mozzi axis) followed (or preceded) by a rotation about an axis parallel to that line. | Chasles' theorem (kinematics) | 0.805163 |
30,009 | Other concepts that have been proposed are speculative, using "frontier physics" and concepts from modern physics. So far none of these methods have been unambiguously demonstrated, much less proven practical. The Woodward effect is based on a controversial concept of inertia and certain solutions to the equations for ... | Field propulsion | 0.805162 |
30,010 | Conservation of momentum is a fundamental requirement of propulsion systems because in experiments momentum is always conserved,. This conservation law is implicit in the published work of Newton and Galileo, but arises on a fundamental level from the spatial translation symmetry of the laws of physics, as given by Noe... | Field propulsion | 0.805162 |
30,011 | The following characterization describes tropical varieties intrinsically without reference to algebraic varieties and tropicalization. A set V in R n {\displaystyle \mathbb {R} ^{n}} is an irreducible tropical variety if it is the support of a weighted polyhedral complex of pure dimension d that satisfies the zero-ten... | Tropical mathematics | 0.805161 |
30,012 | Tropical geometry has also been used for analyzing the complexity of feedforward neural networks with ReLU activation.Moreover, several optimization problems arising for instance in job scheduling, location analysis, transportation networks, decision making and discrete event dynamical systems can be formulated and sol... | Tropical mathematics | 0.805161 |
30,013 | A tropical line appeared in Paul Klemperer's design of auctions used by the Bank of England during the financial crisis in 2007. Yoshinori Shiozawa defined subtropical algebra as max-times or min-times semiring (instead of max-plus and min-plus). He found that Ricardian trade theory (international trade without input t... | Tropical mathematics | 0.805161 |
30,014 | However, only since the late 1990s has an effort been made to consolidate the basic definitions of the theory. This was motivated by its application to enumerative algebraic geometry, with ideas from Maxim Kontsevich and works by Grigory Mikhalkin among others. The adjective tropical was coined by French mathematicians... | Tropical mathematics | 0.805161 |
30,015 | The basic ideas of tropical analysis were developed independently using the same notation by mathematicians working in various fields. The central ideas of tropical geometry appeared in different forms in a number of earlier works. For example, Victor Pavlovich Maslov introduced a tropical version of the process of int... | Tropical mathematics | 0.805161 |
30,016 | In theoretical physics, it is often important to study theories with the diffeomorphism symmetry such as general relativity. These theories are invariant under arbitrary coordinate transformations. Equations of motion are generally derived from the requirement that the action is stationary. There are special variations... | Diffeomorphism constraint | 0.80516 |
30,017 | In computer programming, apply applies a function to a list of arguments. Eval and apply are the two interdependent components of the eval-apply cycle, which is the essence of evaluating Lisp, described in SICP. Function application corresponds to beta reduction in lambda calculus. | Apply | 0.80516 |
30,018 | This notation is in conflict with the use of λ {\displaystyle \lambda } in lambda calculus, where lambda is used to denote bound variables. With all of these notational changes accounted for, the adjointness of Apply and curry is then expressed in the commuting diagram The articles on exponential object and Cartesian c... | Apply | 0.80516 |
30,019 | In category theory, however, {\displaystyle } is known as the exponential object, and is written as B A {\displaystyle B^{A}} . There are other common notational differences as well; for example Apply is often called Eval, even though in computer science, these are not the same thing, with eval distinguished from Appl... | Apply | 0.80516 |
30,020 | Consider a function g: ( X × Y ) → Z {\displaystyle g:(X\times Y)\to Z} , that is, g ∈ {\displaystyle g\in } where the bracket notation {\displaystyle } denotes the space of functions from A to B. By means of currying, there is a unique function curry ( g ): X → {\displaystyle {\mbox{curry}}(g):X\to } . Then Apply p... | Apply | 0.80516 |
30,021 | In order theory, in the category of complete partial orders endowed with the Scott topology, both curry and apply are continuous functions (that is, they are Scott continuous). This property helps establish the foundational validity of the study of the denotational semantics of computer programs. In algebraic geometry ... | Apply | 0.80516 |
30,022 | Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology. T... | Apply | 0.80516 |
30,023 | 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 | 0.80516 |
30,024 | Then, linearization gives ω ( k ) ≈ ω 0 + ( k − k 0 ) ω 0 ′ {\displaystyle \omega (k)\approx \omega _{0}+\left(k-k_{0}\right)\omega '_{0}} where ω 0 = ω ( k 0 ) {\displaystyle \omega _{0}=\omega (k_{0})} and ω 0 ′ = ∂ ω ( k ) ∂ k | k = k 0 {\displaystyle \omega '_{0}=\left. {\frac {\partial \omega (k)}{\partial k}}\rig... | Group velocities | 0.805159 |
30,025 | If an unknown weight W is balanced with 3 (31) on its pan and 1 and 27 (30 and 33) on the other, then its weight in decimal is 25 or 1011 in balanced base-3. 10113 = 1 × 33 + 0 × 32 − 1 × 31 + 1 × 30 = 25.The factorial number system uses a varying radix, giving factorials as place values; they are related to Chinese re... | Place-value notation | 0.805157 |
30,026 | m a x z − v p . m i n z ) ) {\displaystyle {\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}{vp}.X+(1.0+v.X)*{vp}.{width}/2.0\\{vp}.Y+(1.0-v.Y)*{vp}.{height}/2.0\\{vp}.{minz}+v.Z*({vp}.{maxz}-{vp}. {minz})\end{pmatrix}}} With vp=Viewport; v=Point after projectionOn modern hardware, most of the geometry computation... | Viewing transformation | 0.805153 |
30,027 | Instead, they propose to assess the performance with a new finite sample criterion. They presented three new calibration techniques for scan statistics that perform well across a range of relevant signal lengths to optimally increase performance of short signals. The scan-statistic-based methods have been specifically ... | Scan statistics | 0.805149 |
30,028 | Recent results have shown that using scale-dependent critical values for the scan statistic allows to attain asymptotically optimal detection simultaneously for all signal lengths, thereby improving on the traditional scan, but this procedure has been criticized for losing too much power for short signals. Walther and ... | Scan statistics | 0.805149 |
30,029 | In statistics, a scan statistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem is the maximum size of a cluster of points on a line or the longest series of successes recorded by a moving window of fixed length.Joseph Naus first published on th... | Scan statistics | 0.805149 |
30,030 | The Poisson–Boltzmann equation describes the electrochemical potential of ions in the diffuse layer. The three-dimensional potential distribution can be described by the Poisson equation where ρ e {\displaystyle \rho _{e}} is the local electric charge density in C/m3, ε r {\displaystyle \varepsilon _{r}} is the dielect... | Poisson-Boltzmann equation | 0.805148 |
30,031 | The journal publishes research articles on: theoretical and experimental topics in the physics of elementary particles and fields; intermediate-energy physics and nuclear physics; experimental and theoretical research in particle, neutrino, and nuclear astrophysics; research arising from all interface areas among these... | Journal of Physics G | 0.805146 |
30,032 | Journal of Physics G: Nuclear and Particle Physics is a peer-reviewed journal that publishes theoretical and experimental research into nuclear physics, particle physics and particle astrophysics, including all interface areas between these fields. The editor-in-chief is Jacek Dobaczewski, University of York, UK. | Journal of Physics G | 0.805146 |
30,033 | Robins experimented with musket balls of around one ounce in mass (28 g), while other contemporaries used his methods with cannon shot of one to three pounds (0.5 to 1.4 kg).Robins' original work used a heavy iron pendulum, faced with wood, to catch the bullet. Modern reproductions, used as demonstrations in physics cl... | Ballistic pendulum | 0.805143 |
30,034 | Most physics textbooks provide a simplified method of calculation of the bullet's velocity that uses the mass of the bullet and pendulum and the height of the pendulum's travel to calculate the amount of energy and momentum in the pendulum and bullet system. Robins' calculations were significantly more involved, and us... | Ballistic pendulum | 0.805143 |
30,035 | The ballistic pendulum is still found in physics classrooms today, because of its simplicity and usefulness in demonstrating properties of momentum and energy. Unlike other methods of measuring the speed of a bullet, the basic calculations for a ballistic pendulum do not require any measurement of time, but rely only o... | Ballistic pendulum | 0.805143 |
30,036 | More recently, similarity scores have been used to determine career paths and projected statistics for players. The logic behind this line of thought is simple: players often follow similar career trajectories to their most similar players, so the historical similar players' performance in years after the active player... | Similarity score | 0.80514 |
30,037 | JChemPaint is computer software, a molecule editor and file viewer for chemical structures using 2D computer graphics. It is free and open-source software, released under a GNU Lesser General Public License (LGPL). It is written in Java and so can run on the operating systems Windows, macOS, Linux, and Unix. There is a... | JChemPaint | 0.805139 |
30,038 | Construct a KKMS covering C J ′ {\displaystyle C'_{J}} as follows: C J ′ = C i {\displaystyle C'_{J}=C_{i}} whenever J = { i } {\displaystyle J=\{i\}} ( J {\displaystyle J} is a singleton that contains only element i {\displaystyle i} ). C J ′ = ∅ {\displaystyle C'_{J}=\emptyset } otherwise.The KKM condition on the ori... | KKMS lemma | 0.805138 |
30,039 | The collection {{1,2}, {2,3}, {1}} is balanced: choose w 1 , 2 = 0 , w 2 , 3 = 1 , w 1 = 1 {\displaystyle w_{1,2}=0,w_{2,3}=1,w_{1}=1} .In hypergraph terminology, a collection B is balanced with respect to its ground-set V, iff the hypergraph with vertex-set V and edge-set B admits a perfect fractional matching. The KK... | KKMS lemma | 0.805138 |
30,040 | in general, it is not true that the common intersection of all 2 n − 1 {\displaystyle 2^{n}-1} sets in a KKMS covering is nonempty; this is illustrated by the special case of a KKM covering, in which most sets are empty. The KKMS theorem says that, in every KKMS covering, there is a balanced collection B {\displaystyle... | KKMS lemma | 0.805138 |
30,041 | The KKMS theorem is a generalization of the KKM lemma by Lloyd Shapley. It is useful in economics, especially in cooperative game theory. While a KKM covering contains n closed sets, a KKMS covering contains 2 n − 1 {\displaystyle 2^{n}-1} closed sets - indexed by the nonempty subsets of {\displaystyle } (equivalently... | KKMS lemma | 0.805138 |
30,042 | While the diagrams in these first articles were hand-drawn, the advent of typesetting software such as LaTeX and PGF/TikZ made the publication of string diagrams more wide-spread.The existential graphs and diagrammatic reasoning of Charles Sanders Peirce are arguably the oldest form of string diagrams, they are interpr... | String diagrams | 0.805138 |
30,043 | In the context of categorical quantum mechanics, this is known as the snake equation. The category of Hilbert spaces is rigid, this fact underlies the proof of correctness for the quantum teleportation protocol. The unit and counit of the adjunction are an abstraction of the Bell state and the Bell measurement respecti... | String diagrams | 0.805138 |
30,044 | String diagrams are a formal graphical language for representing morphisms in monoidal categories, or more generally 2-cells in 2-categories. They are a prominent tool in applied category theory. When interpreted in the monoidal category of vector spaces and linear maps with the tensor product, string diagrams are call... | String diagrams | 0.805138 |
30,045 | Unparticle physics and the unhiggs models posit that the Higgs sector and Higgs boson are scaling invariant, also known as unparticle physics. UV-Completion by Classicalization, in which the unitarization of the WW scattering happens by creation of classical configurations. Symmetry breaking driven by non-equilibrium d... | Mass generation mechanism | 0.805136 |
30,046 | In theoretical physics, a mass generation mechanism is a theory that describes the origin of mass from the most fundamental laws of physics. Physicists have proposed a number of models that advocate different views of the origin of mass. The problem is complicated because the primary role of mass is to mediate gravitat... | Mass generation mechanism | 0.805136 |
30,047 | In organic chemistry, organic anions are chemically heterogeneous substances possessing a carbon backbone and a net negative charge. Organic anions are conjugate bases of organic acids. The following table lists some of the organic anions and their conjugate acids which are substrates of the organic acid transporter (O... | Organic anion | 0.805135 |
30,048 | As of June 2023, SCSP's president and CEO is Ylli Bajraktari, former executive director of the National Security Commission on Artificial Intelligence. Former Chief of Staff for the National Security Commission on Artificial Intelligence (NSCAI) Michael Gable serves as Executive Vice President, and former Director of O... | Special Competitive Studies Project | 0.805135 |
30,049 | The Special Competitive Studies Project (SCSP) is a non-partisan U.S. think tank and private foundation focused on technology and security. Founded by former Google CEO Eric Schmidt in October 2021, SCSP's stated mission is to "make recommendations to strengthen America’s long-term competitiveness as artificial intelli... | Special Competitive Studies Project | 0.805135 |
30,050 | Inspired by the Rockefeller Special Studies Project launched in the 1950s and led by Henry Kissinger, SCSP seeks to expand on the work of the National Security Commission on Artificial Intelligence by including other emerging technologies and issues of concern in its analyses. | Special Competitive Studies Project | 0.805135 |
30,051 | Polyacetylene itself did not find practical applications, but organic light-emitting diodes (OLEDs) emerged as one application of conducting polymers.Teaching and research programs in polymer chemistry were introduced in the 1940s. An Institute for Macromolecular Chemistry was founded in 1940 in Freiburg, Germany under... | Polymer Chemistry | 0.805134 |
30,052 | Stephanie Kwolek developed an aramid, or aromatic nylon named Kevlar, patented in 1966. Karl Ziegler and Giulio Natta received a Nobel Prize for their discovery of catalysts for the polymerization of alkenes. Alan J. Heeger, Alan MacDiarmid, and Hideki Shirakawa were awarded the 2000 Nobel Prize in Chemistry for the de... | Polymer Chemistry | 0.805134 |
30,053 | Staudinger received the Nobel Prize in Chemistry in 1953. Wallace Carothers invented the first synthetic rubber called neoprene in 1931, the first polyester, and went on to invent nylon, a true silk replacement, in 1935. Paul Flory was awarded the Nobel Prize in Chemistry in 1974 for his work on polymer random coil con... | Polymer Chemistry | 0.805134 |
30,054 | Illustrative of the quantitative aspects of polymer chemistry, particular attention is paid to the number-average and weight-average molecular weights M n {\displaystyle M_{n}} and M w {\displaystyle M_{w}} , respectively. M n = ∑ M i N i ∑ N i , M w = ∑ M i 2 N i ∑ M i N i , {\displaystyle M_{n}={\frac {\sum M_{i}N_{i... | Polymer Chemistry | 0.805134 |
30,055 | Leading figures in polymer chemistry The chemist Hermann Staudinger first proposed that polymers consisted of long chains of atoms held together by covalent bonds, which he called macromolecules. His work expanded the chemical understanding of polymers and was followed by an expansion of the field of polymer chemistry ... | Polymer Chemistry | 0.805134 |
30,056 | However, polymer chemistry is typically related to synthetic and organic compositions. Synthetic polymers are ubiquitous in commercial materials and products in everyday use, such as plastics, and rubbers, and are major components of composite materials. Polymer chemistry can also be included in the broader fields of p... | Polymer Chemistry | 0.805134 |
30,057 | Polymer chemistry is a sub-discipline of chemistry that focuses on the structures of chemicals, chemical synthesis, and chemical and physical properties of polymers and macromolecules. The principles and methods used within polymer chemistry are also applicable through a wide range of other chemistry sub-disciplines li... | Polymer Chemistry | 0.805134 |
30,058 | Alternatively, z {\displaystyle z} and w {\displaystyle w} can be removed, yielding x y {\displaystyle xy} . Finally, x {\displaystyle x} and w {\displaystyle w} can be removed, yielding y z {\displaystyle yz} .The process of removing literals from a Boolean term is called expanding the term. Expanding by one literal d... | Prime implicant | 0.805134 |
30,059 | Further developments are reflected by the references below, and by their contents. For some purposes, like dynamical systems, more sophisticated invariants were developed under the name strong shape. Generalizations to noncommutative geometry, e.g. the shape theory for operator algebras have been found. | Shape theory (mathematics) | 0.805133 |
30,060 | Borsuk's shape theory was generalized onto arbitrary (non-metric) compact spaces, and even onto general categories, by Włodzimierz Holsztyński in year 1968/1969, and published in Fund. Math. 70 , 157–168, y.1971 (see Jean-Marc Cordier, Tim Porter, (1989) below). This was done in a continuous style, characteristic for t... | Shape theory (mathematics) | 0.805133 |
30,061 | Borsuk lived and worked in Warsaw, hence the name of one of the fundamental examples of the area, the Warsaw circle. It is a compact subset of the plane produced by "closing up" a topologist's sine curve with an arc. The homotopy groups of the Warsaw circle are all trivial, just like those of a point, and so any map be... | Shape theory (mathematics) | 0.805133 |
30,062 | Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory. | Shape theory (mathematics) | 0.805133 |
30,063 | Since in natural language processing, one should evaluate a large set of candidate strings, one must generalize the BLEU score to the case where one has a list of M candidate strings (called a "corpus") ( y ^ ( 1 ) , ⋯ , y ^ ( M ) ) {\displaystyle ({\hat {y}}^{(1)},\cdots ,{\hat {y}}^{(M)})} , and for each candidate st... | Bilingual evaluation understudy | 0.805132 |
30,064 | Applications of nanotechnology often depend on the lateral assembly and spatial arrangement of nanoparticles at interfaces. Chemical reactions can be induced at solid/liquid interfaces by manipulating the location and orientation of functional groups of nanoparticles. This can be achieved through external stimuli or di... | Self-assembly of nanoparticles | 0.805132 |
30,065 | Nanoparticles have the ability to assemble chemically through covalent or noncovalent interactions with their capping ligand. The terminal functional group(s) on the particle are known as capping ligands. As these ligands tend to be complex and sophisticated, self-assembly can provide a simpler pathway for nanoparticle... | Self-assembly of nanoparticles | 0.805132 |
30,066 | By size Among the more sophisticated and structurally complex nanostructures currently available are organic macromolecules, wherein their assembly relies on the placement of atoms into molecular or extended structures with atomic-level precision. It is now known that organic compounds can be conductors, semiconductors... | Self-assembly of nanoparticles | 0.805132 |
30,067 | To learn from nature and build the nanoworld with noncovalent bonds, more research is needed in this area. Self assembly of nanomaterials is currently considered broadly for nano-structuring and nano-fabrication because of its simplicity, versatility and spontaneity. Exploiting the properties of the nano assembly holds... | Self-assembly of nanoparticles | 0.805132 |
30,068 | According to George M. Whitesides, "Self-assembly is the autonomous organization of components into patterns or structures without human intervention." Another definition by Serge Palacin & Renaud Demadrill is "Self-assembly is a spontaneous and reversible process that brings together in a defined geometry randomly mov... | Self-assembly of nanoparticles | 0.805132 |
30,069 | For hard particles, Pauling's rules are useful in understanding the structure of ionic compounds in the early days, and the later entropy maximization principle shows favor of dense packing in the system. Therefore, finding the densest packing for a given shape is a starting point for predicting the structure of hard n... | Self-assembly of nanoparticles | 0.805132 |
30,070 | The research groups of Edward Boyden at MIT and Fei Chen at Harvard, both in Cambridge, Massachusetts, U.S.A, developed RNA timestamps, a new (2020) method that allows the age chosen transcripts in a cell to be inferred. This technology provides the means to understand cellular biology at a new level and deepen our und... | RNA timestamp | 0.805127 |
30,071 | The advent of RNA-sequencing (RNA-seq) in 2009 allowed for a deeper look into the biology of unique cell types by allowing researchers to examine the presence and quantity of RNA in a sample at any given time. The ability for analysis of the transcriptome has revealed valuable information about cellular differences and... | RNA timestamp | 0.805127 |
30,072 | The Minkowski functional of a convex, absorbing, and solid set is a called a lattice semi-norm. Equivalently, it is a semi-norm p {\displaystyle p} such that | y | ≤ | x | {\displaystyle |y|\leq |x|} implies p ( y ) ≤ p ( x ) . {\displaystyle p(y)\leq p(x).} The topology of a locally convex vector lattice is generated ... | Locally convex vector lattice | 0.805126 |
30,073 | Therefore geometric spanners are graph spanners of complete graphs embedded in the plane with edge weights equal to the distances between the embedded vertices in the corresponding metric. Spanners may be used in computational geometry for solving some proximity problems. They have also found applications in other area... | Geometric spanner | 0.805125 |
30,074 | A geometric spanner or a t-spanner graph or a t-spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a t-path between any pair of vertices for a fixed parameter t. A t-path is defined as a path through the graph with weight at most t times the spatial distance bet... | Geometric spanner | 0.805125 |
30,075 | Bhatt & Mathew (2018) have introduced the arc-topology, which is similar in its definition, except that only valuation rings of rank ≤ 1 are considered in the definition. A variant of this topology, with an analogous relationship that the h-topology has with the cdh topology, called the cdarc-topology was later introdu... | V-topology | 0.805124 |
30,076 | In mathematics, especially in algebraic geometry, the v-topology (also known as the universally subtrusive topology) is a Grothendieck topology whose covers are characterized by lifting maps from valuation rings. This topology was introduced by Rydh (2010) and studied further by Bhatt & Scholze (2017), who introduced t... | V-topology | 0.805124 |
30,077 | A Southern blot is a method routinely used in molecular biology for detection of a specific DNA sequence in DNA samples. Southern blotting combines transfer of electrophoresis-separated DNA fragments to a filter membrane and subsequent fragment detection by probe hybridization. | Blot (biology) | 0.805124 |
30,078 | A blot, in molecular biology and genetics, is a method of transferring proteins, DNA or RNA onto a carrier (for example, a nitrocellulose, polyvinylidene fluoride or nylon membrane). In many instances, this is done after a gel electrophoresis, transferring the molecules from the gel onto the blotting membrane, and othe... | Blot (biology) | 0.805124 |
30,079 | A maternal effect is a situation where the phenotype of an organism is determined not only by the environment it experiences and its genotype, but also by the environment and genotype of its mother. In genetics, maternal effects occur when an organism shows the phenotype expected from the genotype of the mother, irresp... | Maternal effect | 0.805123 |
30,080 | The mechanism by which GHR transcription is regulated is unknown, but it may be due to hormones within the yolk produced by the mother, or just by the yolk quantity itself. This may lead to DNA methylation or histone modifications which control genic transcription levels.Ecologically, this is an example of the mother u... | Maternal effect | 0.805123 |
30,081 | The fact that methylation can be influenced by the maternal environment, makes it similar to adaptive maternal effects. Further similarities are seen by the fact that methylation can often increase the fitness of the offspring. Additionally, epigenetics can refer to histone modifications or non-coding RNAs that create ... | Maternal effect | 0.805123 |
30,082 | Related to adaptive maternal effects are epigenetic effects. Epigenetics is the study of long lasting changes in gene expression that are produced by modifications to chromatin instead of changes in DNA sequence, as is seen in DNA mutation. This "change" refers to DNA methylation, histone acetylation, or the interactio... | Maternal effect | 0.805123 |
30,083 | Given an arbitrary basis of a space of dimension n , { b ^ i } {\displaystyle n,\{{\hat {b}}_{i}\}} , the metric is defined as the inner product of the basis vectors. Where 1 ≤ i , j ≤ n {\displaystyle 1\leq i,j\leq n} and the inner product is with respect to the ambient space (usually its δ i j {\displaystyle \delta _... | Line element | 0.805122 |
30,084 | The coordinate-independent definition of the square of the line element ds in an n-dimensional Riemannian or Pseudo Riemannian manifold (in physics usually a Lorentzian manifold) is the "square of the length" of an infinitesimal displacement d q {\displaystyle d\mathbf {q} } (in pseudo Riemannian manifolds possibly neg... | Line element | 0.805122 |
30,085 | In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc length, is a function of the metric tensor and is denoted by d s {\displays... | Line element | 0.805122 |
30,086 | The mechanical properties of carbon nanotubes reveal them as one of the strongest materials in nature. Carbon nanotubes (CNTs) are long hollow cylinders of graphene. Although graphene sheets have 2D symmetry, carbon nanotubes by geometry have different properties in axial and radial directions. It has been shown that C... | Mechanical properties of carbon nanotubes | 0.805122 |
30,087 | A complete phase diagram giving the transition to the radially collapsed geometry as function of diameter, pressure and number of tube-walls has been produced from semiempirical grounds.Radial direction elasticity of CNTs is important especially for carbon nanotube composites where the embedded tubes are subjected to l... | Mechanical properties of carbon nanotubes | 0.805122 |
30,088 | Multi-walled nanotubes are multiple concentric nanotubes precisely nested within one another. These exhibit a striking telescoping property whereby an inner nanotube core may slide, almost without friction, within its outer nanotube shell, thus creating an atomically perfect linear or rotational bearing. This is one of... | Mechanical properties of carbon nanotubes | 0.805122 |
30,089 | For example, in (5,5) tubes, a critical tensile strain of ~5% results in defect generation. The defect structure reduces strain because the heptagon geometry is able to stretch more than the original hexagonal rings, while the C-C bond remains about the same length. Bending the tubes beyond a critical curvature has the... | Mechanical properties of carbon nanotubes | 0.805122 |
30,090 | In chemistry, the self-energy or Born energy of an ion is the energy associated with the field of the ion itself.In solid state and condensed-matter physics self-energies and a myriad of related quasiparticle properties are calculated by Green's function methods and Green's function (many-body theory) of interacting lo... | Electron self-energy | 0.805121 |
30,091 | Mathematically, this energy is equal to the so-called on mass shell value of the proper self-energy operator (or proper mass operator) in the momentum-energy representation (more precisely, to ℏ {\displaystyle \hbar } times this value). In this, or other representations (such as the space-time representation), the self... | Electron self-energy | 0.805121 |
30,092 | Tarski's exponential function problem concerns the extension of this theory to another primitive operation, the exponential function. It is an open problem whether this theory is decidable, but if Schanuel's conjecture holds then the decidability of this theory would follow. In contrast, the extension of the theory of ... | Decidability of first-order theories of the real numbers | 0.80512 |
30,093 | The theory of real closed fields is the theory in which the primitive operations are multiplication and addition; this implies that, in this theory, the only numbers that can be defined are the real algebraic numbers. As proven by Tarski, this theory is decidable; see Tarski–Seidenberg theorem and Quantifier eliminatio... | Decidability of first-order theories of the real numbers | 0.80512 |
30,094 | Research grade agar is used extensively in plant biology as it is optionally supplemented with a nutrient and/or vitamin mixture that allows for seedling germination in Petri dishes under sterile conditions (given that the seeds are sterilized as well). Nutrient and/or vitamin supplementation for Arabidopsis thaliana i... | Agar agar | 0.805119 |
30,095 | Losing reaches is when the water flow decreases as it travels downstream and is fracturing deeper than surface water or in karst geology because limestone and dolomite high storage. Gaining reaches is when flow increases as it travels downstream. Gaining reaches are common in humid mountainous regions where the water t... | Baseflow | 0.805118 |
30,096 | Methods for identifying baseflow sources and residence/transit time include using solutes and tracers. Solutes that originate in distinct areas of the watershed can be used to source baseflow-geochemical signatures. Tracers may be inserted into different parts of the watershed to identify flow paths and transit times.M... | Baseflow | 0.805118 |
30,097 | In physics, mechanics and engineering, an adiabatic shear band is one of the many mechanisms of failure that occur in metals and other materials that are deformed at a high rate in processes such as metal forming, machining and ballistic impact. Adiabatic shear bands are usually very narrow bands, typically 5-500 μm wi... | Adiabatic shear band | 0.805117 |
30,098 | The gauge was introduced to particle physics by Steven Weinberg in the context of the electroweak theory. In electroweak theory, the degrees of freedom in a unitarity gauge are the massive spin-1 W+, W− and Z bosons with three polarizations each, the photon with two polarizations, and the scalar Higgs boson. The unitar... | Unitarity gauge | 0.805116 |
30,099 | In theoretical physics, the unitarity gauge or unitary gauge is a particular choice of a gauge fixing in a gauge theory with a spontaneous symmetry breaking. In this gauge, the scalar fields responsible for the Higgs mechanism are transformed into a basis in which their Goldstone boson components are set to zero. In ot... | Unitarity gauge | 0.805116 |
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