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29,000 | Since it can never more than double in frequency with each generation, a gene drive introduced in a single individual typically requires dozens of generations to affect a substantial fraction of a population. Alternatively, releasing drive-containing organisms in sufficient numbers can affect the rest within a few gene... | Gene drives | 0.805758 |
29,001 | In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V1, …, Vm, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies b... | Rainbow-independent set | 0.805757 |
29,002 | Let J be an independent set in GS of size at most |S| – 1. Since the distance between each two vertices of IS is at least 3, every vertex of J is adjacent to at most one vertex of IS. Therefore, there is at least one vertex of IS which is not adjacent to any vertex of J. Therefore IS is special for S. By the previous t... | Rainbow-independent set | 0.805757 |
29,003 | Let H = (X + Y, E) be a bipartite graph satisfying Hall's condition. For each vertex i of X, assign a unique color Vi to all edges of H adjacent to i. For every subset S of colors, Hall's condition implies that S has at least |S| neighbors in Y, and therefore there are at least |S| edges of H adjacent to distinct verti... | Rainbow-independent set | 0.805757 |
29,004 | To see this, it is useful to state the theorem for the special case in which G is the line graph of some other graph H; this means that every vertex of G is an edge of H, and every independent set of G is a matching in H. The vertex-coloring of G corresponds to an edge-coloring of H, and a rainbow-independent-set in G ... | Rainbow-independent set | 0.805757 |
29,005 | Each point x of the triangulation is labeled with a vertex g(x) of G such that: (a) For each point x on a face S, g(x) is an element of IS – the special independent set of S. (b) If points x and y are adjacent in the 1-skeleton of the triangulation, then g(x) and g(y) are not adjacent in G. By Sperner's lemma, there ex... | Rainbow-independent set | 0.805757 |
29,006 | The theorem is proved using Sperner's lemma. : Thm.4.2 The standard simplex with m endpoints is assigned a triangulation with some special properties. Each endpoint i of the simplex is associated with the color-set Vi, each face {i1, …, ik} of the simplex is associated with a set S = {Vi1, …, Vik} of colors. | Rainbow-independent set | 0.805757 |
29,007 | Below, given a subset S of colors (a subset of {V1, …, Vm} ), an independent set IS of GS is called special for S if for every independent subset J of vertices of GS of size at most |S| − 1, there exists some v in IS such that J ∪ {v} is also independent. Figuratively, IS is a team of "neutral members" for the set S of... | Rainbow-independent set | 0.805757 |
29,008 | Below, given a subset S of colors (a subset of {V1, ..., Vm} ), we denote by US the union of all subsets in S (all vertices whose color is one of the colors in S), and by GS the subgraph of G induced by US. The following theorem describes the structure of graphs that have no ISR but are edge-minimal, in the sense that ... | Rainbow-independent set | 0.805757 |
29,009 | This holds if-and-only-if the complex Ind(G) contains a connection between its two simplices V1 and V2. Such a connection is equivalent to an independent set in which one vertex is from V1 and one is from V2. Thus, in this case, the condition of the theorem is not only sufficient but also necessary. | Rainbow-independent set | 0.805757 |
29,010 | Intuitively, when the departments Vi are larger, and there is less conflict between faculty members, an ISR should be more likely to exist. The "less conflict" condition is represented by the vertex degree of the graph. This is formalized by the following theorem:: Thm.2 If the degree of every vertex in G is at most d,... | Rainbow-independent set | 0.805757 |
29,011 | Two ribbon graph representations are said to be equivalent (and define homeomorphic graph embeddings) if they are related to each other that a homeomorphism of the topological space formed by the union of the vertex disks and edge rectangles that preserves the identification of these features. Ribbon graph representati... | Ribbon graph | 0.805754 |
29,012 | In topological graph theory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems or graph-encoded maps. It is convenient for visualizations of embeddings, because it can represent unoriented surfaces without self-intersections (unlike embeddings of the whole surface int... | Ribbon graph | 0.805754 |
29,013 | There are only very few studies about the structure of dispersions (emulsions), although they are plentiful in type and in use all over the world in innumerable applications (see below). In the following, only such dispersions with a dispersed phase diameter of less than 1 µm will be discussed. To understand the format... | Dispersion (chemistry) | 0.805753 |
29,014 | Although suspensions are relatively simple to distinguish from solutions and colloids, it may be difficult to distinguish solutions from colloids since the particles dispersed in the medium may be too small to distinguish by the human eye. Instead, the Tyndall effect is used to distinguish solutions and colloids. Due t... | Dispersion (chemistry) | 0.805753 |
29,015 | Several different solutions to seawater intrusion in coastal aquifers have been proposed, including engineering methods of artificial recharge and implementing physical barriers at the sea boundary.Chemical dispersants are used in oil spills to mitigate the effects of the spill and promote the degradation of oil partic... | Dispersion (chemistry) | 0.805753 |
29,016 | The term dispersion also refers to the physical property of the degree to which particles clump together into agglomerates or aggregates. While the two terms are often used interchangeably, according to ISO nanotechnology definitions, an agglomerate is a reversible collection of particles weakly bound, for example by v... | Dispersion (chemistry) | 0.805753 |
29,017 | Hopcroft and Ullman tend to consider indexed languages as a "natural" class, since they are generated by several formalisms, such as: Aho's indexed grammars Aho's one-way nested stack automata Fischer's macro grammars Greibach's automata with stacks of stacks Maibaum's algebraic characterizationHayashi generalized the ... | Indexed language | 0.805751 |
29,018 | Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata.Indexed languages are a proper subset of context-sensitive languages. They qualify as an abstract family of languages (furthermore a full AFL) and hence satis... | Indexed language | 0.805751 |
29,019 | The semiring's zero is the empty relation and its unit is the identity relation. These relations correspond to the matrix semiring (indeed, matrix semialgebra) of square matrices indexed by U {\displaystyle U} with entries in the Boolean semiring, and then addition and multiplication are the usual matrix operations, wh... | Semiring | 0.805748 |
29,020 | A Boolean ring is also a semiring (indeed, a ring) but it is not idempotent under addition. A Boolean semiring is a semiring isomorphic to a sub-semiring of a Boolean algebra. The commutative semiring formed by the two-element Boolean algebra and defined by 1 + 1 = 1 {\displaystyle 1+1=1} . | Semiring | 0.805748 |
29,021 | More regarding additively idempotent semirings, The set of all ideals of a given semiring form a semiring under addition and multiplication of ideals. Any bounded, distributive lattice is a commutative, semiring under join and meet. A Boolean algebra is a special case of these. | Semiring | 0.805748 |
29,022 | A related version has R ∪ { ± ∞ } {\displaystyle \mathbb {R} \cup \{\pm \infty \}} as the underlying set. They are an active area of research, linking algebraic varieties with piecewise linear structures. The Łukasiewicz semiring: the closed interval {\displaystyle } with addition given by taking the maximum of the ar... | Semiring | 0.805748 |
29,023 | ∪ F n {\displaystyle F^{c}=F_{1}\cup ...\cup F_{n}} for disjoint F i ∈ S {\displaystyle F_{i}\in S} . Then: and every E ∩ F i ∈ S {\displaystyle E\cap F_{i}\in S} since it is closed under intersection, and disjoint since they are contained in the disjoint F i {\displaystyle F_{i}} 's. Moreover the condition is strictly... | Semiring | 0.805748 |
29,024 | If S {\displaystyle {\mathcal {S}}} is a semialgebra and E , F ∈ S {\displaystyle E,F\in {\mathcal {S}}} , then we can write F c = F 1 ∪ . . . | Semiring | 0.805748 |
29,025 | A semialgebra or elementary family is a collection S {\displaystyle {\mathcal {S}}} of subsets of X {\displaystyle X} satisfying the semiring properties except with (3) replaced with: If E ∈ S {\displaystyle E\in {\mathcal {S}}} then there exists a finite number of mutually disjoint sets C 1 , … , C n ∈ S {\displaystyl... | Semiring | 0.805748 |
29,026 | The ( max , + ) {\displaystyle (\max ,+)} and ( min , + ) {\displaystyle (\min ,+)} tropical semirings on the reals are often used in performance evaluation on discrete event systems. The real numbers then are the "costs" or "arrival time"; the "max" operation corresponds to having to wait for all prerequisites of an e... | Semiring | 0.805748 |
29,027 | One complication is that, because any choice is tentative and may be remade, the system must be able to restore old program states by undoing side-effects caused by partially executing a branch that eventually failed. Another method of choice is reinforcement learning, embodied in systems such as Alisp. In such systems... | Nondeterministic programming | 0.805747 |
29,028 | This family of models, instead of using fully connected layers, employs one or more convolutional layers that convolve the input data applying a low-dimensional filter capable of embedding complex structures with few parameters by learning nonlinear features. ConvE: ConvE is an embedding model that represents a good tr... | Knowledge graph embedding | 0.805743 |
29,029 | This family of models uses capsule neural networks to create a more stable representation that is able to recognize a feature in the input without losing spatial information. The network is composed of convolutional layers, but they are organized in capsules, and the overall result of a capsule is sent to a higher-caps... | Knowledge graph embedding | 0.805743 |
29,030 | This class of models leverages the use of recurrent neural network. The advantage of this architecture is to memorize a sequence of fact, rather than just elaborate single events. RSN: During the embedding procedure is commonly assumed that, similar entities has similar relations. In practice, this type of information ... | Knowledge graph embedding | 0.805743 |
29,031 | The machine learning task for knowledge graph embedding that is more often used to evaluate the embedding accuracy of the models is the link prediction. Rossi et al. produced an extensive benchmark of the models, but also other surveys produces similar results. The benchmark involves five datasets FB15k, WN18, FB15k-23... | Knowledge graph embedding | 0.805743 |
29,032 | Given a collection of triples (or facts) F = { < h e a d , r e l a t i o n , t a i l > } {\displaystyle {\mathcal {F}}=\{ \}} , the knowledge graph embedding model produces, for each entity and relation present in the knowledge graph a continuous vector representation. ( h , r , t ) {\displaystyle (h,r,t)} is the corre... | Knowledge graph embedding | 0.805743 |
29,033 | In a similar way, the entity of a fact inderectly determine which is inference path that has to be choose to predict the object of a related triple. CrossE, to do so, learns an additional interaction matrix C {\displaystyle C} , uses the element-wise product to compute the interaction between h {\displaystyle h} and r ... | Knowledge graph embedding | 0.805743 |
29,034 | In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging ... | Knowledge graph embedding | 0.805743 |
29,035 | This group of embedding models uses deep neural network to learn patterns from the knowledge graph that are the input data. These models have the generality to distinguish the type of entity and relation, temporal information, path information, underlay structured information, and resolve the limitations of distance-ba... | Knowledge graph embedding | 0.805743 |
29,036 | Thus inversive geometry includes the ideas originated by Lobachevsky and Bolyai in their plane geometry. Furthermore, Felix Klein was so overcome by this facility of mappings to identify geometrical phenomena that he delivered a manifesto, the Erlangen program, in 1872. Since then many mathematicians reserve the term g... | Circle inversion | 0.805742 |
29,037 | As mentioned above, zero, the origin, requires special consideration in the circle inversion mapping. The approach is to adjoin a point at infinity designated ∞ or 1/0 . In the complex number approach, where reciprocation is the apparent operation, this procedure leads to the complex projective line, often called the R... | Circle inversion | 0.805742 |
29,038 | One of the first to consider foundations of inversive geometry was Mario Pieri in 1911 and 1912. Edward Kasner wrote his thesis on "Invariant theory of the inversion group".More recently the mathematical structure of inversive geometry has been interpreted as an incidence structure where the generalized circles are cal... | Circle inversion | 0.805742 |
29,039 | In order to have a description of what constitutes intelligent behavior, one must study behavior itself. This type of research is closely tied to that in cognitive psychology and psychophysics. By measuring behavioral responses to different stimuli, one can understand something about how those stimuli are processed. Le... | Cognitive studies | 0.805741 |
29,040 | In mathematical finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem. The uniqueness case covers groups G of characteristic 2 type with e(G) ≥ 3 that have an almost strongly p-embedded maximal 2-local subgroup for all primes p who... | Uniqueness case | 0.805738 |
29,041 | It is emitted by a molecule in vacuum tube, C-arc core with metallic salt. The band spectrum is the combination of many different spectral lines, resulting from molecular vibrational, rotational, and electronic transition. Spectroscopy studies spectral bands for astronomy and other purposes. | Spectral band | 0.805736 |
29,042 | Spectral bands are parts of the electromagnetic spectrum of specific wavelengths, which can be filtered by a standard filter. In nuclear physics, spectral bands are referred to the electromagnetic emission of polyatomic systems, including condensed materials, large molecules, etc. Each spectral line corresponds to one ... | Spectral band | 0.805736 |
29,043 | In physics, a neutral particle is a particle without an electric charge, such as a neutron. The term neutral particles should not be confused with truly neutral particles, the subclass of neutral particles that are also identical to their own antiparticles. | Neutral particle | 0.805734 |
29,044 | Prader–Willi syndrome (PWS) is a paternal structural abnormality involving 15q11-13, while a maternal aberration in the same region causes Angelman syndrome (AS). In both syndromes, the majority of cases (75%) are the result of a 3–5 Mb deletion of the PWS/AS critical region. These small aberrations cannot be detected ... | Array-comparative genomic hybridization | 0.805731 |
29,045 | This map gives an injective algebra homomorphism from H to the set of 2 × 2 complex matrices. It has the property that the absolute value of a quaternion q is equal to the square root of the determinant of the matrix image of q. The set of unit quaternions is then given by matrices of the above form with unit determina... | Three-dimensional sphere | 0.805728 |
29,046 | The four Euclidean coordinates for S3 are redundant since they are subject to the condition that x02 + x12 + x22 + x32 = 1. As a 3-dimensional manifold one should be able to parameterize S3 by three coordinates, just as one can parameterize the 2-sphere using two coordinates (such as latitude and longitude). Due to the... | Three-dimensional sphere | 0.805728 |
29,047 | In Edwin Abbott Abbott's Flatland, published in 1884, and in Sphereland, a 1965 sequel to Flatland by Dionys Burger, the 3-sphere is referred to as an oversphere, and a 4-sphere is referred to as a hypersphere. Writing in the American Journal of Physics, Mark A. Peterson describes three different ways of visualizing 3-... | Three-dimensional sphere | 0.805728 |
29,048 | One can even find three linearly independent and nonvanishing vector fields. These may be taken to be any left-invariant vector fields forming a basis for the Lie algebra of the 3-sphere. This implies that the 3-sphere is parallelizable. | Three-dimensional sphere | 0.805728 |
29,049 | The 3-sphere is naturally a smooth manifold, in fact, a closed embedded submanifold of R4. The Euclidean metric on R4 induces a metric on the 3-sphere giving it the structure of a Riemannian manifold. As with all spheres, the 3-sphere has constant positive sectional curvature equal to 1/r2 where r is the radius. Much o... | Three-dimensional sphere | 0.805728 |
29,050 | The first significant results in this area were Jackson networks, for which an efficient product-form stationary distribution exists and the mean value analysis (which allows average metrics such as throughput and sojourn times) can be computed. If the total number of customers in the network remains constant, the netw... | Queueing network | 0.805727 |
29,051 | This operation is used in tensor algebra and its methods, such as Parafac and HOSVD. == References == | Mode-k flattening | 0.805725 |
29,052 | In multilinear algebra, mode-m flattening, also known as matrixizing, matricizing, or unfolding, is an operation that reshapes a multi-way array A {\displaystyle {\mathcal {A}}} into a matrix denoted by A {\displaystyle A_{}} (a two-way array). Matrixizing may be regarded as a generalization of the mathematical concep... | Mode-k flattening | 0.805725 |
29,053 | Until about 2010, computers were far from energy proportional for two primary reasons. A critical issue is high static power, which means that the computer consumes significant energy even when it is idle. High static power is common in servers owing to their architectural, circuit, and manufacturing optimizations that... | Energy proportional computing | 0.805721 |
29,054 | Researchers have proposed improving the low power idle states of servers, and the wake-up/shutdown latencies between active and idle modes, because this is an easier optimization goal than active performance scaling. If servers could wake up and shutdown at a very fine time granularity, then the server would become ene... | Energy proportional computing | 0.805721 |
29,055 | Some authors have proposed that to make datacenter networks more energy proportional, the routing elements need greater power dynamic range. They proposed the use of the flattened butterfly topology instead of the common folded Clos network in use in datacenters (also known as the fat tree) to improve overall power eff... | Energy proportional computing | 0.805721 |
29,056 | (See the section below). What does the mathematical theory of Actors have to say about this? A closed system is defined to be one which does not communicate with the outside. Actor model theory provides the means to characterize all the possible computations of a closed Actor system using the Representation Theorem as... | Indeterminacy in concurrent computation | 0.805721 |
29,057 | Hewitt and Agha , and other published work argued that mathematical models of concurrency did not determine particular concurrent computations as follows: The Actor model makes use of arbitration (often in the form of notional arbiters) for determining which message is next in the arrival ordering of an Actor who is s... | Indeterminacy in concurrent computation | 0.805721 |
29,058 | In number theory, the Fermat quotient of an integer a with respect to an odd prime p is defined as q p ( a ) = a p − 1 − 1 p , {\displaystyle q_{p}(a)={\frac {a^{p-1}-1}{p}},} or δ p ( a ) = a − a p p {\displaystyle \delta _{p}(a)={\frac {a-a^{p}}{p}}} .This article is about the former; for the latter see p-derivation.... | Fermat quotient | 0.805719 |
29,059 | It can occur in electronic-counter-counter-measures (electronic warfare) when computing the location of enemy emitters (radar jammers and radio communications devices). Using such an interferometry technique can provide certain geometric layout where there are degrees of freedom that cannot be accounted for due to inad... | Dilution of precision (GPS) | 0.805719 |
29,060 | The precision of multiple satellites in view of a receiver combine according to the relative position of the satellites to determine the level of precision in each dimension of the receiver measurement. When visible navigation satellites are close together in the sky, the geometry is said to be weak and the DOP value i... | Dilution of precision (GPS) | 0.805719 |
29,061 | Neglecting ionospheric and tropospheric effects, the signal from navigation satellites has a fixed precision. Therefore, the relative satellite-receiver geometry plays a major role in determining the precision of estimated positions and times. Due to the relative geometry of any given satellite to a receiver, the preci... | Dilution of precision (GPS) | 0.805719 |
29,062 | Carl Berry, a lecturer of robotics engineering, described the 2021 AI Day presentation as "the usual overblown hype." Following the Tesla Bot display at the Cyber Rodeo event, researcher Gary Marcus stated he would "bet that no robot will be able to do all human tasks by the end of 2023. "After the second AI Day presen... | Tesla Bot | 0.805718 |
29,063 | Soon after the first AI Day event, many publications reacted with skepticism about the proposed product. Bloomberg News claimed that such a product constituted "mission creep" and stood outside "the company’s clean-energy initiatives." The Washington Post argued that "Tesla has a history of exaggerating timelines and o... | Tesla Bot | 0.805718 |
29,064 | Optimus, also known as Tesla Bot, is a conceptual general-purpose robotic humanoid under development by Tesla, Inc. It was announced at the company's Artificial Intelligence (AI) Day event on August 19, 2021. CEO Elon Musk claimed during the event that Tesla would likely build a prototype by 2022. Musk is on record hav... | Tesla Bot | 0.805718 |
29,065 | Its distorted octahedral structure reflects geometric distortions due to the Jahn–Teller effect. The two most common structures for this complex include one with tetragonal elongation and one with tetragonal compression. For the elongation, two Mn–O bonds are 2.12 Å while the other four are 1.93 Å. For the compression,... | Acetylacetonate complex | 0.805714 |
29,066 | Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as is now known) a fundamental change in the understanding of the world. In other words, Planck then contemplated virtual oscillators. In 1905, Albert Einstein adapted t... | Planck postulate | 0.805711 |
29,067 | The Planck postulate (or Planck's postulate), one of the fundamental principles of quantum mechanics, is the postulate that the energy of oscillators in a black body is quantized, and is given by E = n h ν {\displaystyle E=nh\nu \,} ,where n {\displaystyle n} is an integer (1, 2, 3, ...), h {\displaystyle h} is Planck'... | Planck postulate | 0.805711 |
29,068 | By the fundamental theorems of welfare economics, any CE allocation is Pareto efficient, and any efficient allocation can be sustainable by a competitive equilibrium. Furthermore, by Varian's theorems, a CE allocation in which all agents have the same income is also envy-free. At the competitive equilibrium, the value ... | Competitive Equilibrium | 0.805705 |
29,069 | In the case of indivisible items, we have the following strong versions of the two welfare theorems: Any competitive equilibrium maximizes the social welfare (the sum of utilities), not only over all realistic assignments of items, but also over all fractional assignments of items. I.e., even if we could assign fractio... | Competitive Equilibrium | 0.805705 |
29,070 | Site-directed mutagenesis is a molecular biology method that is used to make specific and intentional changes to the DNA sequence of a gene and any gene products. The technique was developed at a time when the highest quality commercially available DNA polymerase for converting an oligonucleotide into a complete comple... | T7 DNA polymerase | 0.805703 |
29,071 | Where traditional techniques focus on segmenting individual characters for recognition, modern techniques focus on recognizing all the characters in a segmented line of text. Particularly they focus on machine learning techniques that are able to learn visual features, avoiding the limiting feature engineering previous... | Handwritten text recognition | 0.805701 |
29,072 | Since 2009, the recurrent neural networks and deep feedforward neural networks developed in the research group of Jürgen Schmidhuber at the Swiss AI Lab IDSIA have won several international handwriting competitions. In particular, the bi-directional and multi-dimensional Long short-term memory (LSTM) of Alex Graves et ... | Handwritten text recognition | 0.805701 |
29,073 | Outline of artificial intelligence List of emerging technologies | Handwritten text recognition | 0.805701 |
29,074 | The Smith normal form is useful for computing the homology of a chain complex when the chain modules of the chain complex are finitely generated. For instance, in topology, it can be used to compute the homology of a finite simplicial complex or CW complex over the integers, because the boundary maps in such a complex ... | Smith normal form | 0.805696 |
29,075 | He suggested that the potentialities of individual cells via tissue culture as well as that the reciprocal influences of tissues on one another could be determined by this method. Since Haberlandt's original assertions, methods for tissue and cell culture have been realized, leading to significant discoveries in biolog... | Tissue culture | 0.805691 |
29,076 | On the other hand, the strict meaning of "tissue culture" refers to the culturing of tissue pieces, i.e. explant culture. Tissue culture is an important tool for the study of the biology of cells from multicellular organisms. It provides an in vitro model of the tissue in a well defined environment which can be easily ... | Tissue culture | 0.805691 |
29,077 | If an exact functor F: D → T {\displaystyle F\colon D\to T} sends coproducts to coproducts, then F has a right adjoint. The Brown representability theorem can be used to define various functors between triangulated categories. | Exact triangle | 0.805689 |
29,078 | The stable homotopy category is compactly generated by one object, the sphere spectrum S 0 {\displaystyle S^{0}} .Amnon Neeman generalized the Brown representability theorem to any compactly generated triangulated category, as follows. Let D be a compactly generated triangulated category, H: D op → Ab {\displaystyle H\... | Exact triangle | 0.805689 |
29,079 | In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abe... | Exact triangle | 0.805689 |
29,080 | In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. ... | Error curve | 0.805688 |
29,081 | The solutions of homogeneous linear differential equations with polynomial coefficients are called holonomic functions. This class of functions is stable under sums, products, differentiation, integration, and contains many usual functions and special functions such as exponential function, logarithm, sine, cosine, inv... | First-order linear differential equation | 0.805687 |
29,082 | Recent efforts have focused on eliminating membrane fouling by altering the surface chemistry of the membrane material to reduce the likelihood that foulants will adhere to the membrane surface. The exact chemical strategy used is dependent on the chemistry of the solution that is being filtered. For example, membranes... | Membrane (selective barrier) | 0.805687 |
29,083 | He clearly demonstrates that knees have many practical advantages for walking systems. Knees, according to McGeer, solve the problem of feet colliding with the ground when the leg swings forward, and also offers more stability in some settings. Passive dynamics is a valuable addition to the field of controls because it... | Passive dynamics | 0.805685 |
29,084 | In some fields of robotics (legged robotics in particular), design and more relaxed control of passive dynamics has become a complementary (or even alternative) approach to joint-positioning control methods developed through the 20th century. Additionally, the passive dynamics of animals have been of interest to biomec... | Passive dynamics | 0.805685 |
29,085 | The classifying topos for objects of a topos is the topos of presheaves over the opposite of the category of finite sets. The classifying topos for rings of a topos is the topos of presheaves over the opposite of the category of finitely presented rings. The classifying topos for local rings of a topos is the topos of ... | Classifying topos | 0.805684 |
29,086 | The dropping mercury electrode (DME) is a working electrode made of mercury and used in polarography. Experiments run with mercury electrodes are referred to as forms of polarography even if the experiments are identical or very similar to a corresponding voltammetry experiment which uses solid working electrodes. Like... | Dropping mercury electrode | 0.805683 |
29,087 | Voevodsky defined the h topology to be the topology associated to finite families { p i: U i → X } {\displaystyle \{p_{i}:U_{i}\to X\}} of morphisms of finite type such that ⨿ U i → X {\displaystyle \amalg U_{i}\to X} is a universal topological epimorphism (i.e., a set of points in the target is an open subset if and o... | Cdh topology | 0.805683 |
29,088 | However, we could define an h-analogue of the fpqc topology by saying that an hqc-covering is a family { T i → T } i ∈ I {\displaystyle \{T_{i}\to T\}_{i\in I}} such that for each affine open U ⊆ T {\displaystyle U\subseteq T} there exists a finite set K, a map i: K → I {\displaystyle i:K\to I} and affine opens U i ( k... | Cdh topology | 0.805683 |
29,089 | The v-topology (or universally subtrusive topology) is equivalent to the h-topology on the category S c h S f t {\displaystyle Sch_{S}^{ft}} of schemes of finite type over a Noetherian base scheme S. Indeed, a morphism in S c h S f t {\displaystyle Sch_{S}^{ft}} is universally subtrusive if and only if it is universall... | Cdh topology | 0.805683 |
29,090 | In algebraic geometry, the h topology is a Grothendieck topology introduced by Vladimir Voevodsky to study the homology of schemes. It combines several good properties possessed by its related "sub"topologies, such as the qfh and cdh topologies. It has subsequently been used by Beilinson to study p-adic Hodge theory, i... | Cdh topology | 0.805683 |
29,091 | Using abstract blowups and Noetherian induction, if k {\displaystyle k} is a field admitting resolution of singularities (e.g., a characteristic zero field) then any scheme of finite type over k {\displaystyle k} admits an h-covering by smooth k {\displaystyle k} -schemes. More generally, in any situation where de Jong... | Cdh topology | 0.805683 |
29,092 | As mentioned above, in positive characteristic, any h-sheaf satisfies F ( X ) = F ( X p e r f ) {\displaystyle F(X)=F(X^{perf})} . In characteristic zero, we have F ( X ) = F ( X s n ) {\displaystyle F(X)=F(X^{sn})} where X s n {\displaystyle X^{sn}} is the semi-normalisation (the scheme with the same underlying topolo... | Cdh topology | 0.805683 |
29,093 | Since the Frobenius is an h-covering, in positive characteristic we get Ω h n = 0 {\displaystyle \Omega _{h}^{n}=0} for n > 0 {\displaystyle n>0} , but analogous results are true if we replace the h-topology with the cdh-topology. By the Nullstellensatz, a morphism of finite presentation X → Spec ( k ) {\displaystyle... | Cdh topology | 0.805683 |
29,094 | The h-topology is not subcanonical, so representable presheaves are almost never h-sheaves. However, the h-sheafification of representable sheaves are interesting and useful objects; while presheaves of relative cycles are not representable, their associated h-sheaves are representable in the sense that there exists a ... | Cdh topology | 0.805683 |
29,095 | The cdh topology on the category S c h / S f p {\displaystyle Sch_{/S}^{fp}} of schemes of finite presentation over a qcqs base scheme S {\displaystyle S} is generated by: Nisnevich coverings, and families of the form { X ′ → X , Z → X } {\displaystyle \{X'\to X,Z\to X\}} where X ′ → X {\displaystyle X'\to X} is a prop... | Cdh topology | 0.805683 |
29,096 | This agrees with the expression for a half-wave plate in the table above. These rotations are identical to beam unitary splitter transformation in optical physics given by R ( θ ) = ( r t ′ t r ′ ) {\displaystyle R(\theta )={\begin{pmatrix}r&t'\\t&r'\end{pmatrix}}} where the primed and unprimed coefficients represent b... | Jones vectors | 0.805679 |
29,097 | In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by tak... | Jones vectors | 0.805679 |
29,098 | In organic chemistry, the Graham reaction is an oxidation reaction that converts an amidine into a diazirine using a hypohalite reagent. The halide of the hypohalite oxidant, or another similar anionic additive to the reaction, is retained as a substituent on the diazirine product. The reaction was first reported in 19... | Graham reaction | 0.805679 |
29,099 | Organocobalt chemistry is the chemistry of organometallic compounds containing a carbon to cobalt chemical bond. Organocobalt compounds are involved in several organic reactions and the important biomolecule vitamin B12 has a cobalt-carbon bond. Many organocobalt compounds exhibit useful catalytic properties, the preem... | Organocobalt compound | 0.805678 |
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