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27,700 | If there is a remainder in a place value decimal rod calculus division, both the remainder and the divisor must be left in place with one on top of another. In Liu Hui's notes to Jiuzhang suanshu (2nd century BCE), the number on top is called "shi" (实), while the one at bottom is called "fa" (法). In Sunzi Suanjing, the... | Rod calculus | 0.806479 |
27,701 | The basic equipment for carrying out rod calculus is a bundle of counting rods and a counting board. The counting rods are usually made of bamboo sticks, about 12 cm- 15 cm in length, 2mm to 4 mm diameter, sometimes from animal bones, or ivory and jade (for well-heeled merchants). A counting board could be a table top,... | Rod calculus | 0.806479 |
27,702 | Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics ... | Rod calculus | 0.806479 |
27,703 | Yuan dynasty mathematician Li Zhi developed rod calculus into Tian yuan shu Example Li Zhi Ceyuan haijing vol II, problem 14 equation of one unknown: − x 2 − 680 x + 96000 = 0 {\displaystyle -x^{2}-680x+96000=0} 元 | Rod calculus | 0.806479 |
27,704 | The key software required for rod calculus was a simple 45 phrase positional decimal multiplication table used in China since antiquity, called the nine-nine table, which were learned by heart by pupils, merchants, government officials and mathematicians alike. | Rod calculus | 0.806479 |
27,705 | In algebra, this problem can be expressed in three system equations with three unknowns. { 3 x + 2 y + z = 39 2 x + 3 y + z = 34 x + 2 y + 3 z = 26 {\displaystyle {\begin{cases}3x+2y+z=39\\2x+3y+z=34\\x+2y+3z=26\end{cases}}} This problem was solved in Jiuzhang suanshu with counting rods laid out on a counting board in ... | Rod calculus | 0.806479 |
27,706 | Algorithm for extraction of square root was described in Jiuzhang suanshu and with minor difference in terminology in Sunzi Suanjing. The animation shows the algorithm for rod calculus extraction of an approximation of the square root 234567 ≈ 484 311 968 {\displaystyle {\sqrt {234567}}\approx 484{\tfrac {311}{968}}} f... | Rod calculus | 0.806479 |
27,707 | Rod calculus works on the principle of addition. Unlike Arabic numerals, digits represented by counting rods have additive properties. The process of addition involves mechanically moving the rods without the need of memorising an addition table. This is the biggest difference with Arabic numerals, as one cannot mechan... | Rod calculus | 0.806479 |
27,708 | Mathematician Zhu Shijie further developed rod calculus to include polynomial equations of 2 to four unknowns. For example, polynomials of three unknowns: Equation 1: − y − z − y 2 ∗ x − x + x y z = 0 {\displaystyle -y-z-y^{2}*x-x+xyz=0} 太 Equation 2: − y − z + x − x 2 + x z = 0 {\displaystyle -y-z+x-x^{2}+xz=0} Equati... | Rod calculus | 0.806479 |
27,709 | Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems. As an example, in the field of artificial intelligence, classical puzzles, games and problems are often used as toy problems. These include sliding-block puzzles, N-Queens problem, missionaries and cann... | Toy problem | 0.806478 |
27,710 | Parse trees are usually constructed based on either the constituency relation of constituency grammars (phrase structure grammars) or the dependency relation of dependency grammars. Parse trees may be generated for sentences in natural languages (see natural language processing), as well as during processing of compute... | Concrete syntax | 0.806477 |
27,711 | A partition of the set N = {1, 2, ..., n} with corresponding equivalence relation ~ is noncrossing if it has the following property: If four elements a, b, c and d of N having a < b < c < d satisfy a ~ c and b ~ d, then a ~ b ~ c ~ d. The name comes from the following equivalent definition: Imagine the elements 1, 2, .... | Partition of a set | 0.806476 |
27,712 | A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold: The family P does not contain the... | Partition of a set | 0.806476 |
27,713 | In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree, spanning trees of a grap... | Random tree | 0.806476 |
27,714 | Photopolymer/light activated polymers (LAP) are another type of SMP that are activated by light stimuli. The LAP actuators can be controlled remotely with instant response and, without any physical contact, only with the variation of light frequency or intensity. A need for soft, lightweight and biocompatible soft actu... | Actuator | 0.806474 |
27,715 | The majority of the existing soft actuators are fabricated using multistep low yield processes such as micro-moulding, solid freeform fabrication, and mask lithography. However, these methods require manual fabrication of devices, post processing/assembly, and lengthy iterations until maturity in the fabrication is ach... | Actuator | 0.806474 |
27,716 | A soft actuator is one that changes its shape in response to stimuli including mechanical, thermal, magnetic, and electrical. Soft actuators mainly deal with the robotics of humans rather than industry which is what most of the actuators are used for. For most actuators they are mechanically durable yet do not have an ... | Actuator | 0.806474 |
27,717 | Applications for the rotary actuators are just about endless but, will more than likely be found dealing with mostly hydraulic pressured devices and industries. Rotary actuators are even used in the robotics field when seeing robotic arms in industry lines. Anything you see that deals with motion control systems to per... | Actuator | 0.806474 |
27,718 | A measure space X is called a standard Borel space if it is Borel-isomorphic to a Borel subset of a Polish space. Kuratowski's theorem then states that two standard Borel spaces X and Y are Borel-isomorphic iff |X| = |Y|. | Borel equivalence relation | 0.806473 |
27,719 | In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology). | Borel equivalence relation | 0.806473 |
27,720 | Fractional calculus on time scales is treated in Bastos, Mozyrska, and Torres. | Dynamic equations on time scales | 0.806473 |
27,721 | The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. Dynamic equations on a time scale have a potential for applications such as in population dynamics. For example, they can model insect populations that evolve continuously while in season, di... | Dynamic equations on time scales | 0.806473 |
27,722 | Many results concerning differential equations carry over quite easily to corresponding results for difference equations, while other results seem to be completely different from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twic... | Dynamic equations on time scales | 0.806473 |
27,723 | Take a function: f: T → R , {\displaystyle f:\mathbb {T} \to \mathbb {R} ,} (where R could be any Banach space, but is set to the real line for simplicity). Definition: The delta derivative (also Hilger derivative) f Δ ( t ) {\displaystyle f^{\Delta }(t)} exists if and only if: For every ε > 0 {\displaystyle \varepsilo... | Dynamic equations on time scales | 0.806473 |
27,724 | Immersed plane curves have a well-defined turning number, which can be defined as the total curvature divided by 2π. This is invariant under regular homotopy, by the Whitney–Graustein theorem – topologically, it is the degree of the Gauss map, or equivalently the winding number of the unit tangent (which does not vanis... | Immersion (mathematics) | 0.806471 |
27,725 | Hassler Whitney initiated the systematic study of immersions and regular homotopies in the 1940s, proving that for 2m < n + 1 every map f: M m → N n of an m-dimensional manifold to an n-dimensional manifold is homotopic to an immersion, and in fact to an embedding for 2m < n; these are the Whitney immersion theorem and... | Immersion (mathematics) | 0.806471 |
27,726 | A mathematical rose with k petals is an immersion of the circle in the plane with a single k-tuple point; k can be any odd number, but if even must be a multiple of 4, so the figure 8, with k = 2, is not a rose. The Klein bottle, and all other non-orientable closed surfaces, can be immersed in 3-space but not embedded.... | Immersion (mathematics) | 0.806471 |
27,727 | A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points. The points in a line are said to be incident with the line. | Linear space (geometry) | 0.806469 |
27,728 | However, an important assumption from the microscopic theory of superconductivity is that the superconducting state of a system is the ground state, and according to a theorem of Bloch's, in such a state the canonical momentum p is zero. This leaves j = − n s e 2 m A s , {\displaystyle \mathbf {j} =-{\frac {n_{\rm {s}}... | London equations | 0.806465 |
27,729 | The realization of Intelligent Environments requires the convergence of different disciplines: Information and Computer Science, Architecture, Material Engineering, Artificial Intelligence, Sociology, and Design. Besides, technical breakthroughs are required in key enabling technology fields, such as microelectronics (... | AI and Environment | 0.806464 |
27,730 | The idea of having an artificial intelligence capable of managing an environment, recollect data, and respond in consequence is older than we would expect. In the novel 2001: A Space Odyssey from 1968, long before the microcomputers revolution, you have the fictional character HAL 9000, a computer capable of controllin... | AI and Environment | 0.806464 |
27,731 | Artistic expression has had a significant influence on this since we have seen new forms of art using Artificial Intelligence and IE. Take for example the work of the artist Chris Milk where you can see the implementation of immersive installations that make the user not only appreciate a work of art but also be part o... | AI and Environment | 0.806463 |
27,732 | Exoplanet detection and classification is a very active sub-discipline in astronomy; the first possible terrestrial planet discovered within a star's habitable zone was found in 2007. New refinements in exoplanet detection methods, and use of existing methods from space (such as the Kepler and TESS missions) are starti... | Fermi's Paradox | 0.806461 |
27,733 | Another possibility is that human theoreticians have underestimated how much alien life might differ from that on Earth. Aliens may be psychologically unwilling to attempt to communicate with human beings. Perhaps human mathematics is parochial to Earth and not shared by other life, though others argue this can only ap... | Fermi's Paradox | 0.806461 |
27,734 | Rather than contending with the long delays a radio dialogue would suffer, a probe housing an artificial intelligence would seek out an alien civilization to carry on a close-range communication with the discovered civilization. The findings of such a probe would still have to be transmitted to the home civilization at... | Fermi's Paradox | 0.806461 |
27,735 | This is the argument that technological civilizations may usually or invariably destroy themselves before or shortly after developing radio or spaceflight technology. The astrophysicist Sebastian von Hoerner stated that the progress of science and technology on Earth was driven by two factors—the struggle for dominatio... | Fermi's Paradox | 0.80646 |
27,736 | There is a covariant and a contravariant functoriality of the group of algebraic cycles. Let f: X → X' be a map of varieties. If f is flat of some constant relative dimension (i.e. all fibers have the same dimension), we can define for any subvariety Y' ⊂ X': f ∗ ( ) = {\displaystyle f^{*}()=\,\!} which by assumption... | Algebraic cycle | 0.806459 |
27,737 | In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of V that is directly accessible by algebraic methods. Understanding the algebraic cycles on a variety can give profound insights into the structure of the varie... | Algebraic cycle | 0.806459 |
27,738 | The Hodge conjecture, one of the Clay Mathematics Institute's Millennium Prize Problems, predicts that the topology of a complex algebraic variety forces the existence of certain algebraic cycles. The Tate conjecture makes a similar prediction for étale cohomology. Alexander Grothendieck's standard conjectures on algeb... | Algebraic cycle | 0.806459 |
27,739 | The hypothesis that the geometric genus is positive essentially means (by the Lefschetz theorem on (1,1)-classes) that the cohomology group H 2 ( S ) {\displaystyle H^{2}(S)} contains transcendental information, and in effect Mumford's theorem implies that, despite CH 2 ( S ) {\displaystyle \operatorname {CH} ^{2}(S)... | Algebraic cycle | 0.806459 |
27,740 | While divisors on higher-dimensional varieties continue to play an important role in determining the structure of the variety, on varieties of dimension two or more there are also higher codimension cycles to consider. The behavior of these cycles is strikingly different from that of divisors. For example, every curve ... | Algebraic cycle | 0.806459 |
27,741 | The earliest work on algebraic cycles focused on the case of divisors, particularly divisors on algebraic curves. Divisors on algebraic curves are formal linear combinations of points on the curve. Classical work on algebraic curves related these to intrinsic data, such as the regular differentials on a compact Riemann... | Algebraic cycle | 0.806459 |
27,742 | Proponents of orthomolecular medicine hold that treatment must be based on each patient's individual biochemistry.The scientific and medical consensus holds that the broad claims of efficacy advanced by advocates of orthomolecular medicine are not adequately tested as drug therapies. It has been described as a form of ... | Orthomolecular medicine | 0.806457 |
27,743 | Orthomolecular medicine is a form of alternative medicine that aims to maintain human health through nutritional supplementation. The concept builds on the idea of an optimal nutritional environment in the body and suggests that diseases reflect deficiencies in this environment. Treatment for disease, according to this... | Orthomolecular medicine | 0.806457 |
27,744 | In the early 20th century, some doctors hypothesised that vitamins could cure disease, and supplements were prescribed in megadoses by the 1930s. Their effects on health were disappointing, though, and in the 1950s and 1960s, nutrition was de-emphasised in standard medical curricula. Riordon's organization cite figures... | Orthomolecular medicine | 0.806457 |
27,745 | In cryptography, polyinstantiation is the existence of a cryptographic key in more than one secure physical location. == References == | Polyinstantiation | 0.806454 |
27,746 | Polyinstantiation in computer science is the concept of type (class, database row or otherwise) being instantiated into multiple independent instances (objects, copies). It may also indicate, such as in the case of database polyinstantiation, that two different instances have the same name (identifier, primary key). | Polyinstantiation | 0.806454 |
27,747 | Let ( Ω , A , P ) {\displaystyle (\Omega ,{\mathcal {A}},P)} be a probability space and let I {\displaystyle I} be an index set with a total order ≤ {\displaystyle \leq } (often N {\displaystyle \mathbb {N} } , R + {\displaystyle \mathbb {R} ^{+}} , or a subset of R + {\displaystyle \mathbb {R} ^{+}} ). For every i ∈ I... | Usual hypotheses | 0.806453 |
27,748 | Let ( X n ) n ∈ N {\displaystyle (X_{n})_{n\in \mathbb {N} }} be a stochastic process on the probability space ( Ω , A , P ) {\displaystyle (\Omega ,{\mathcal {A}},P)} . Then F n := σ ( X k ∣ k ≤ n ) {\displaystyle {\mathcal {F}}_{n}:=\sigma (X_{k}\mid k\leq n)} is a σ-algebra and F = ( F n ) n ∈ N {\displaystyle \math... | Usual hypotheses | 0.806453 |
27,749 | This intricate molecular structure and genetic diversity enable the receptor to carry out a wide range of physiological functions within the nervous system. All the subunits share a common membrane topology that is dominated by a large extracellular N-terminus, a membrane region comprising three transmembrane segments,... | NMDA channel | 0.806448 |
27,750 | The first known body of constant brightness that is not a sphere was constructed by Wilhelm Blaschke in 1915. Its boundary is a surface of revolution of a curved triangle (but not the Reuleaux triangle). It is smooth except on a circle and at one isolated point where it is crossed by the axis of revolution. The circle ... | Body of constant brightness | 0.806446 |
27,751 | In convex geometry, a body of constant brightness is a three-dimensional convex set all of whose two-dimensional projections have equal area. A sphere is a body of constant brightness, but others exist. Bodies of constant brightness are a generalization of curves of constant width, but are not the same as another gener... | Body of constant brightness | 0.806446 |
27,752 | A body has constant brightness if and only if the reciprocal Gaussian curvatures at pairs of opposite points of tangency of parallel supporting planes have almost-everywhere-equal sums.According to an analogue of Barbier's theorem, all bodies of constant brightness that have the same projected area A {\displaystyle A} ... | Body of constant brightness | 0.806446 |
27,753 | Whereas a scalar processor must complete the entire process of fetching, decoding and executing each instruction and value in a set of data, a vector processor can perform a single operation on a comparatively large set of data with one instruction. This is only possible when the application tends to require many steps... | Central Processing Unit | 0.806446 |
27,754 | Global derating considers system-wide stops, slow-downs and set ups as well as machine factors. To calculate the amount of global or system derating, one should take the average of the number of total components placed per hour in a long period (i.e. an entire product shift). Regularly scheduled stops should be include... | Component placement | 0.806446 |
27,755 | There is an intrinsic difference between deep learning layering and neocortical layering: deep learning layering depends on network topology, while neocortical layering depends on intra-layers homogeneity. | Layer (deep learning) | 0.806446 |
27,756 | A layer in a deep learning model is a structure or network topology in the model's architecture, which takes information from the previous layers and then passes it to the next layer. | Layer (deep learning) | 0.806446 |
27,757 | We call such systems "organic". Hence, an "Organic Computing System" is a technical system which adapts dynamically to exogenous and endogenous change. It is characterized by the properties of self-organization, self-configuration, self-optimization, self-healing, self-protection, self-explaining, and context awareness... | Organic computing | 0.806444 |
27,758 | Its lifetime, ranging from hours to days in coastal waters, can be as long as 15 days in Antarctic seawater. H2O2 is important in aquatic environments because it can oxidize dissolved organic matter and affect the redox chemistry of iron, copper, and manganese. Since hydrogen peroxide, as an uncharged molecule, diffuse... | Reactive oxygen species production in marine microalgae | 0.806443 |
27,759 | In sea water, ROS can be generated through abiotic as well as biotic processes, among which are the radiolysis and photolysis of water molecules and cellular respiration. According to a model proposed by Fan for the prediction of ROS in surface waters, the biochemistry mediated by phytoplankton may be just as important... | Reactive oxygen species production in marine microalgae | 0.806443 |
27,760 | Leopold Kronecker first stated Minkowski's theorem in 1882, though the first proof was given by Hermann Minkowski in 1891. In the same year, Minkowski published his bound on the discriminant. Near the end of the nineteenth century, Ludwig Stickelberger obtained his theorem on the residue of the discriminant modulo four... | Relative discriminant | 0.806438 |
27,761 | The definition of the discriminant of a general algebraic number field, K, was given by Dedekind in 1871. At this point, he already knew the relationship between the discriminant and ramification.Hermite's theorem predates the general definition of the discriminant with Charles Hermite publishing a proof of it in 1857.... | Relative discriminant | 0.806438 |
27,762 | In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a weak perturbation. This transition rate is effectively independent of t... | Fermi golden rule | 0.806431 |
27,763 | It has been shown that a randomly generated periodic task system will usually meet all deadlines when the utilization is 88% or less, however this fact depends on knowing the exact task statistics (periods, deadlines) which cannot be guaranteed for all task sets, and in some cases the authors found that the utilization... | Rate-monotonic scheduling | 0.806431 |
27,764 | The following are two of the few results about infinite graph coloring: If all finite subgraphs of an infinite graph G are k-colorable, then so is G, under the assumption of the axiom of choice. This is the de Bruijn–Erdős theorem of de Bruijn & Erdős (1951). If a graph admits a full n-coloring for every n ≥ n0, it adm... | Graph coloring problem | 0.806425 |
27,765 | A graph has a k-coloring if and only if it has an acyclic orientation for which the longest path has length at most k; this is the Gallai–Hasse–Roy–Vitaver theorem (Nešetřil & Ossona de Mendez 2012). For planar graphs, vertex colorings are essentially dual to nowhere-zero flows. About infinite graphs, much less is know... | Graph coloring problem | 0.806425 |
27,766 | For example, the abelian extension Q ( i , 1 + 2 i 4 ) / Q ( i ) {\displaystyle \mathbf {Q} (i,{\sqrt{1+2i}})/\mathbf {Q} (i)} is not generated by singular moduli and roots of unity. One particularly appealing way to state the Kronecker–Weber theorem is by saying that the maximal abelian extension of Q can be obtained ... | Hilbert's twelfth problem | 0.806424 |
27,767 | Kronecker's (and Hilbert's) question addresses the situation of a more general algebraic number field K: what are the algebraic numbers necessary to construct all abelian extensions of K? The complete answer to this question has been completely worked out only when K is an imaginary quadratic field or its generalizatio... | Hilbert's twelfth problem | 0.806424 |
27,768 | Another type of abelian extension of the field Q of rational numbers is given by adjoining the nth roots of unity, resulting in the cyclotomic fields. Already Gauss had shown that, in fact, every quadratic field is contained in a larger cyclotomic field. The Kronecker–Weber theorem shows that any finite abelian extensi... | Hilbert's twelfth problem | 0.806424 |
27,769 | The fundamental problem of algebraic number theory is to describe the fields of algebraic numbers. The work of Galois made it clear that field extensions are controlled by certain groups, the Galois groups. The simplest situation, which is already at the boundary of what is well understood, is when the group in questio... | Hilbert's twelfth problem | 0.806424 |
27,770 | Kronecker's Jugendtraum or Hilbert's twelfth problem, of the 23 mathematical Hilbert problems, is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field. That is, it asks for analogues of the roots of unity, as complex numbers that are particular values of t... | Hilbert's twelfth problem | 0.806424 |
27,771 | Every LP with an optimal solution has a PD-optimal basis, and it is found by the Simplex algorithm. However, its run-time is exponential in the worst case. Nimrod Megiddo proved the following theorems: There exists a strongly polynomial time algorithm that inputs an optimal solution to the primal LP and an optimal solu... | Basis of a linear program | 0.806424 |
27,772 | 1. A BFS is determined only by the constraints of the LP (the matrix A {\displaystyle A} and the vector b {\displaystyle \mathbf {b} } ); it does not depend on the optimization objective. 2. By definition, a BFS has at most m non-zero variables and at least n-m zero variables. | Basis of a linear program | 0.806424 |
27,773 | Molecular oncology is an interdisciplinary medical specialty at the interface of medicinal chemistry and oncology that refers to the investigation of the chemistry of cancer and tumors at the molecular scale. Also the development and application of molecularly targeted therapies. | Molecular oncology | 0.806424 |
27,774 | Molecular oncology has identified genes that are involved in the development of cancer. The research combined diverse techniques ranging from genomics, computational biology, tumour imaging, in vitro and in vivo functional models to study biological and clinical phenotypes. The proteins produced by these genes may serv... | Molecular oncology | 0.806424 |
27,775 | In mathematics, a pseudometric space is a generalization of a metric space in which the distance between two distinct points can be zero. Pseudometric spaces were introduced by Đuro Kurepa in 1934. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this a... | Pseudometrizable space | 0.806423 |
27,776 | In mathematics, and more specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of the ring as its vertices, and pairs of elements whose product is zero as its edges. | Zero-divisor graph | 0.806423 |
27,777 | Power autonomy. Maximize the power autonomy of products and processes so they can function on renewable energy. 4. | The Biosphere Rules | 0.806422 |
27,778 | As energy efficiency increases new options for generation and energy storage open up because less total energy is needed. The renewable energy technologies and energy storage technologies can be adopted that move the business towards a state of autonomous power generation. Power autonomy can be seen from a fractal pers... | The Biosphere Rules | 0.806422 |
27,779 | The power autonomy rule applied to human manufacturing requires that products and production processes run on solar-motivated renewable energy sources as in the biosphere. The power autonomy approach sees this occurring in a two step process. The first step is to increase the energy efficiency products and production p... | The Biosphere Rules | 0.806422 |
27,780 | As green chemistry research results in new polymers that can be recycled at the materials level, greater adoption of deep-loop value cycling approaches can be implemented. Rule #3: Power Autonomy Every transformation of materials in nature - from turtle to tree - requires energy. In nature, the energy source is solar p... | The Biosphere Rules | 0.806422 |
27,781 | Bring's curve is a Riemann surface of genus four, with a domain that is a regular hyperbolic 20-sided icosagon. By the Gauss-Bonnet theorem, the area of this fundamental polygon is equal to 12 π {\displaystyle 12\pi } . The Leech lattice, which holds the solution to the kissing number in twenty-four dimensions, has a d... | 12 (number) | 0.806419 |
27,782 | It is a coupled system of linear ordinary differential equations. The functions q 1 , q 2 {\displaystyle q_{1},q_{2}} represent the envelope of the electromagnetic field as an initial condition. | Manakov equations | 0.806416 |
27,783 | Machinery's Handbook for machine shop and drafting-room; a reference book on machine design and shop practice for the mechanical engineer, draftsman, toolmaker, and machinist (the full title of the 1st edition) is a classic reference work in mechanical engineering and practical workshop mechanics in one volume publishe... | Machinery's Handbook | 0.806416 |
27,784 | Variations in cytoplasmic shape range from stretched to polygonal. Immunochemistry is needed to prove the presence of rhabdomyoblast differentiation. Detection for MyoD1 and myogenin is used frequently. | Rhabdomyoblast | 0.806412 |
27,785 | A rhabdomyoblast is a cell type which is found in some rhabdomyosarcomas. When found histologically, a rhabdomyoblast aids the diagnosis of embryonal, alveolar, spindle cell/sclerosing, and pleomorphic rhabdomyosarcomas; however, in a tumor, expression of the rhabdomyoblast phenotype is not the only factor in diagnosin... | Rhabdomyoblast | 0.806412 |
27,786 | Type 1 pleuropulmonary blastomas have the potential to progress into type 2 and type 3, which consist of a mixture of cystic and solid tumors and purely solid tumors respectively. In the type 1 categorization, the exterior region of the cyst may contain rhabdomyoblastic differentiation in addition to the early stages o... | Rhabdomyoblast | 0.806412 |
27,787 | Natural language processing methods are used to extract and identify language usage patterns common to speakers of an L1-group. This is done using language learner data, usually from a learner corpus. Next, machine learning is applied to train classifiers, like support vector machines, for predicting the L1 of unseen t... | Native-language identification | 0.806409 |
27,788 | In welfare economics, the theory of the second best (also known as the general theory of second best or the second best theorem) concerns the situation when one or more optimality conditions cannot be satisfied. The economists Richard Lipsey and Kelvin Lancaster showed in 1956, that if one optimality condition in an ec... | Theory of the Second Best | 0.806407 |
27,789 | Population balance equations (PBEs) have been introduced in several branches of modern science, mainly in Chemical Engineering, to describe the evolution of a population of particles. This includes topics like crystallization, leaching (metallurgy), liquid–liquid extraction, gas-liquid dispersions like water electrolys... | Population balance equation | 0.806404 |
27,790 | Word play also features prominently in the work. Puns are occasionally used to connect ideas, such as "the Magnificrab, Indeed" with Bach's Magnificat in D; "SHRDLU, Toy of Man's Designing" with Bach's Jesu, Joy of Man's Desiring; and "Typographical Number Theory", or "TNT", which inevitably reacts explosively when it ... | Gödel, Escher, Bach | 0.806403 |
27,791 | Elements of computer science such as call stacks are also discussed in Gödel, Escher, Bach, as one dialogue describes the adventures of Achilles and the Tortoise as they make use of "pushing potion" and "popping tonic" involving entering and leaving different layers of reality. The same dialogue has a genie with a lamp... | Gödel, Escher, Bach | 0.806403 |
27,792 | The book contains many instances of recursion and self-reference, where objects and ideas speak about or refer back to themselves. One is Quining, a term Hofstadter invented in homage to Willard Van Orman Quine, referring to programs that produce their own source code. Another is the presence of a fictional author in t... | Gödel, Escher, Bach | 0.806403 |
27,793 | Current traveled through the plasma and returned along the center rod. This geometry was slightly different than a z-pinch in that the conductor was in the center, not the sides. Cylindrical pinch Orthogonal pinch effect Ware pinch – A pinch that occurs inside a Tokamak plasma, when particles inside the banana orbit co... | Pinch (plasma physics) | 0.806403 |
27,794 | Pinches exist in nature and in laboratories. Pinches differ in their geometry and operating forces. These include: Uncontrolled – Any time an electric current moves in large amounts (e.g., lightning, arcs, sparks, discharges) a magnetic force can pull together plasma. | Pinch (plasma physics) | 0.806403 |
27,795 | Pinches are used to generate X-rays and the intense magnetic fields generated are used in electromagnetic forming of metals. They also have applications in particle beams including particle beam weapons, astrophysics studies and it has been proposed to use them in space propulsion. A number of large pinch machines have... | Pinch (plasma physics) | 0.806403 |
27,796 | In physics, a system with a set of conservative forces and an equilibrium point can be approximated as a harmonic oscillator near equilibrium. An example of this is the Lennard-Jones potential, where the potential is given by: The equilibrium points of the function are then found: The second derivative is then found, a... | Electric oscillator | 0.806403 |
27,797 | Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry. Most include the Hartree–Fock (HF) and some post-Hartree–Fock methods. They may also include density functional theory (DFT), molecular mechanics or semi-empirical quantum chemistry methods. The progra... | List of quantum chemistry and solid-state physics software | 0.806402 |
27,798 | In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecti... | Transversality (mathematics) | 0.806401 |
27,799 | Using Sard's theorem, whose hypothesis is a special case of the transversality of maps, it can be shown that transverse intersections between submanifolds of a space of complementary dimensions or between submanifolds and maps to a space are themselves smooth submanifolds. For instance, if a smooth section of an orient... | Transversality (mathematics) | 0.806401 |
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