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9,300 | Researchers at Bell Telephone Laboratories like John R. Arthur. Alfred Y. Cho, and Art C. Gossard developed and implemented MBE as a research tool in the late 1960s and 1970s. Samples made by MBE were key to the discovery of the fractional quantum Hall effect for which the 1998 Nobel Prize in Physics was awarded. | Nano sciences | 0.820361 |
9,301 | The precursors of these techniques preceded the nanotech era, and are extensions in the development of scientific advancements rather than techniques which were devised with the sole purpose of creating nanotechnology and which were results of nanotechnology research.The top-down approach anticipates nanodevices that m... | Nano sciences | 0.820361 |
9,302 | There are several important modern developments. The atomic force microscope (AFM) and the Scanning Tunneling Microscope (STM) are two early versions of scanning probes that launched nanotechnology. There are other types of scanning probe microscopy. Although conceptually similar to the scanning confocal microscope dev... | Nano sciences | 0.820361 |
9,303 | Some examples include the Silver Nano platform for using silver nanoparticles as an antibacterial agent, nanoparticle-based transparent sunscreens, carbon fiber strengthening using silica nanoparticles, and carbon nanotubes for stain-resistant textiles.Governments moved to promote and fund research into nanotechnology,... | Nano sciences | 0.820361 |
9,304 | Controversies emerged regarding the definitions and potential implications of nanotechnologies, exemplified by the Royal Society's report on nanotechnology. Challenges were raised regarding the feasibility of applications envisioned by advocates of molecular nanotechnology, which culminated in a public debate between D... | Nano sciences | 0.820361 |
9,305 | C60 was not initially described as nanotechnology; the term was used regarding subsequent work with related carbon nanotubes (sometimes called graphene tubes or Bucky tubes) which suggested potential applications for nanoscale electronics and devices. The discovery of carbon nanotubes is largely attributed to Sumio Iij... | Nano sciences | 0.820361 |
9,306 | These seek to arrange smaller components into more complex assemblies. DNA nanotechnology utilizes the specificity of Watson–Crick basepairing to construct well-defined structures out of DNA and other nucleic acids. Approaches from the field of "classical" chemical synthesis (Inorganic and organic synthesis) also aim a... | Nano sciences | 0.820361 |
9,307 | Peter Grünberg and Albert Fert received the Nobel Prize in Physics in 2007 for their discovery of Giant magnetoresistance and contributions to the field of spintronics. Solid-state techniques can also be used to create devices known as nanoelectromechanical systems or NEMS, which are related to microelectromechanical s... | Nano sciences | 0.820361 |
9,308 | These seek to create smaller devices by using larger ones to direct their assembly. Many technologies that descended from conventional solid-state silicon methods for fabricating microprocessors are now capable of creating features smaller than 100 nm, falling under the definition of nanotechnology. Giant magnetoresist... | Nano sciences | 0.820361 |
9,309 | The microscope's developers Gerd Binnig and Heinrich Rohrer at IBM Zurich Research Laboratory received a Nobel Prize in Physics in 1986. Binnig, Quate and Gerber also invented the analogous atomic force microscope that year. Second, fullerenes were discovered in 1985 by Harry Kroto, Richard Smalley, and Robert Curl, wh... | Nano sciences | 0.820361 |
9,310 | The emergence of nanotechnology as a field in the 1980s occurred through convergence of Drexler's theoretical and public work, which developed and popularized a conceptual framework for nanotechnology, and high-visibility experimental advances that drew additional wide-scale attention to the prospects of atomic control... | Nano sciences | 0.820361 |
9,311 | The concepts that seeded nanotechnology were first discussed in 1959 by renowned physicist Richard Feynman in his talk There's Plenty of Room at the Bottom, in which he described the possibility of synthesis via direct manipulation of atoms. The term "nano-technology" was first used by Norio Taniguchi in 1974, though i... | Nano sciences | 0.820361 |
9,312 | The double negation introduction rule may be written in sequent notation: P ⊢ ¬ ¬ P {\displaystyle P\vdash \neg \neg P} The double negation elimination rule may be written as: ¬ ¬ P ⊢ P {\displaystyle \neg \neg P\vdash P} In rule form: P ¬ ¬ P {\displaystyle {\frac {P}{\neg \neg P}}} and ¬ ¬ P P {\displaystyle {\frac {... | Double negation elimination | 0.820357 |
9,313 | The octonions are a normed division algebra over the real numbers, the largest such algebra. Mathematically they can be specified by 8-tuplets of real numbers, so form an 8-dimensional vector space over the reals, with addition of vectors being the addition in the algebra. A normed algebra is one with a product that sa... | Eight-dimensional space | 0.820349 |
9,314 | The complexified quaternions C ⊗ H {\displaystyle \mathbb {C} \otimes \mathbb {H} } , or "biquaternions," are an eight-dimensional algebra dating to William Rowan Hamilton's work in the 1850s. This algebra is equivalent (that is, isomorphic) to the Clifford algebra C ℓ 2 ( C ) {\displaystyle C\ell _{2}(\mathbb {C} )} a... | Eight-dimensional space | 0.820349 |
9,315 | Over fields of characteristic zero another equivalent definition of a reductive group is a connected group G {\displaystyle G} admitting a faithful semisimple representation which remains semisimple over its algebraic closure k a l {\displaystyle k^{al}} page 424. | Semi-simple group | 0.820345 |
9,316 | An important simple group is the symplectic group Sp(2n) over a field k, the subgroup of GL(2n) that preserves a nondegenerate alternating bilinear form on the vector space k2n. Likewise, the orthogonal group O(q) is the subgroup of the general linear group that preserves a nondegenerate quadratic form q on a vector sp... | Semi-simple group | 0.820345 |
9,317 | For a Lie group G, a lattice in G means a discrete subgroup Γ of G such that the manifold G/Γ has finite volume (with respect to a G-invariant measure). For example, a discrete subgroup Γ is a lattice if G/Γ is compact. The Margulis arithmeticity theorem says, in particular: for a simple Lie group G of real rank at lea... | Semi-simple group | 0.820345 |
9,318 | Let G be a linear algebraic group over the rational numbers Q. Then G can be extended to an affine group scheme G over Z, and this determines an abstract group G(Z). An arithmetic group means any subgroup of G(Q) that is commensurable with G(Z). (Arithmeticity of a subgroup of G(Q) is independent of the choice of Z-str... | Semi-simple group | 0.820345 |
9,319 | In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: e.g. mixing paint, mixing drinks, industrial mixing. The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dyna... | Strong mixing | 0.820338 |
9,320 | Artificial intelligence (AI) is used in robotic control to make it able to process and adapt to its surroundings. It is able to be programmed to do a certain task, for instance, walk up a hill. The technology is relatively new, and is being experimented in several fields, such as the military. | Robot control | 0.820329 |
9,321 | Robotic control is the system that contributes to the movement of robots. This involves the mechanical aspects and programmable systems that makes it possible to control robots. Robotics can be controlled by various means including manual, wireless, semi-autonomous (a mix of fully automatic and wireless control), and f... | Robot control | 0.820329 |
9,322 | In the transition phase of the development, the robots were semi-automatic, being able to be controlled remotely by a human controller. The advancements made in sensors and processors lead to advancements in capabilities of military robots. Since the mid-20th century, the technology of artificial intelligence (A.I.) be... | Robot control | 0.820329 |
9,323 | When the “Atlas” is being controlled, the control software doesn’t explicitly tell the robot how to move its joints, but rather it employs mathematical models of the underlying physics of the robot’s body and how it interacts with the environment”. Instead of inputting data into every single joint of the robot, the eng... | Robot control | 0.820329 |
9,324 | A leaf subroutine is a subroutine which cannot in turn call another subroutine. Some compilers can apply special program optimizations to leaf subroutines, such as the use of link registers to avoid having to push the return address on the stack. The term "leaf" refers to their position as leaf nodes in the call graph ... | Leaf subroutine | 0.820327 |
9,325 | Square-free monomial ideal in a polynomial ring and Stanley–Reisner ring of a simplicial complex. Cohen–Macaulay ring. Monomial ring, closely related to an affine semigroup ring and to the coordinate ring of an affine toric variety. Algebra with a straightening law. There are several versions of those, including Hodge ... | Combinatorial commutative algebra | 0.820323 |
9,326 | While the problem can be formulated purely in geometric terms, the methods of the proof drew on commutative algebra techniques. A signature theorem in combinatorial commutative algebra is the characterization of h-vectors of simplicial polytopes conjectured in 1970 by Peter McMullen. Known as the g-theorem, it was prov... | Combinatorial commutative algebra | 0.820323 |
9,327 | Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedr... | Combinatorial commutative algebra | 0.820323 |
9,328 | Infinite sequences of digits (or characters) drawn from a finite alphabet are of particular interest in theoretical computer science. They are often referred to simply as sequences or streams, as opposed to finite strings. Infinite binary sequences, for instance, are infinite sequences of bits (characters drawn from th... | Mathematical sequence | 0.82032 |
9,329 | In mathematics, the coset construction (or GKO construction) is a method of constructing unitary highest weight representations of the Virasoro algebra, introduced by Peter Goddard, Adrian Kent and David Olive (1986). The construction produces the complete discrete series of highest weight representations of the Viraso... | Coset construction | 0.820319 |
9,330 | In the mathematics of combinatorial games, the sum or disjunctive sum of two games is a game in which the two games are played in parallel, with each player being allowed to move in just one of the games per turn. The sum game finishes when there are no moves left in either of the two parallel games, at which point (in... | Sum of combinatorial games | 0.820317 |
9,331 | In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one tran... | Labeled transition system | 0.820315 |
9,332 | A 14 TMS topology with periplasmic N- and C-termini has been established for the Vibrio parahaemolyticus SglT carrier. SglT transports sugar:Na with a 1:1 stoichiometry. However, MctP of Rhizobium leguminosarum may take up monocarboxylates via an H+ symport mechanism as a dependency on Na+ could not be demonstrated and... | Sodium-motive force | 0.820313 |
9,333 | Proteins of the SSS vary in size from about 400 residues to about 700 residues and probably possess thirteen to fifteen putative transmembrane helical spanners (TMSs). They generally share a core of 13 TMSs, but different members of the family have different numbers of TMSs. A 13 TMS topology with a periplasmic N-termi... | Sodium-motive force | 0.820313 |
9,334 | The neural network for biological motion is highly sensitive to the observer's prior experience with the action's biological motions, allowing for embodied learning. This is related to a research field that is broadly known as embodied cognitive science, along with research on mirror neurons. For instance, a well known... | Biological motion | 0.820308 |
9,335 | Recent cognitive neuroscience research has begun to focus on the brain structures and neural networks that are involved in biological motion processing. The use of transcranial magnetic stimulation methods provided with evidence that suggests that biological motion processing occurs outside of the MT+/V5 area, which ca... | Biological motion | 0.820308 |
9,336 | Interest in biological motion was renewed with the publication of a 1996 article on mirror neurons. Mirror neurons were found to be active in an animal's brain both when that animal observed another animal making a movement and when that animal made the same movement. The mirror neurons were initially observed in the p... | Biological motion | 0.820308 |
9,337 | Findings from research on biological motion has shown that humans are highly sensitive to biological motions of actions and those observations has developed into studies on different possible factors in the perception and understanding of the biological motions of bodily actions. Through studies with point-light displa... | Biological motion | 0.820308 |
9,338 | In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds π. Riemann's elliptic geometry over Ω(t) consists of the projective plane over Ω(t), which can be identified wi... | Semi-Euclidean geometry | 0.820306 |
9,339 | hema.to is a web service for the classification of flow cytometry data of patients suspected to have lymphoma. The artificial intelligence within the tool uses a deep convolutional neural network to recognize patterns of distinct subtypes. All data and code is open access. It processes raw data, which makes gating unne... | Flow cytometry bioinformatics | 0.820306 |
9,340 | It is also possible to characterize data in more comprehensive ways, such as the density-guided binary space partitioning technique known as probability binning, or by combinatorial gating. Finally, diagnosis using flow cytometry data can be aided by supervised learning techniques, and discovery of new cell types of bi... | Flow cytometry bioinformatics | 0.820306 |
9,341 | Flow cytometry bioinformatics is the application of bioinformatics to flow cytometry data, which involves storing, retrieving, organizing and analyzing flow cytometry data using extensive computational resources and tools. Flow cytometry bioinformatics requires extensive use of and contributes to the development of tec... | Flow cytometry bioinformatics | 0.820306 |
9,342 | Despite rapid development in the field of flow cytometry bioinformatics, several problems remain to be addressed. Variability across flow cytometry experiments arises from biological variation among samples, technical variations across instruments used, as well as methods of analysis. In 2010, a group of researchers fr... | Flow cytometry bioinformatics | 0.820306 |
9,343 | As in other bioinformatics fields, development of new methods has primarily taken the form of free open source software, and several databases have been created for depositing open data. | Flow cytometry bioinformatics | 0.820306 |
9,344 | Particularly in newer, high-throughput experiments, there is a need for visualization methods to help detect technical errors in individual samples. One approach is to visualize summary statistics, such as the empirical distribution functions of single dimensions of technical or biological replicates to ensure they are... | Flow cytometry bioinformatics | 0.820306 |
9,345 | The molecular clock hypothesis predicts that the rate of amino acid substitution in a particular protein will be approximately constant over time, though this rate may vary between protein families. This suggests that the number of mutations per amino acid in a protein increases approximately linearly with time. Determ... | Point Accepted Mutation | 0.820305 |
9,346 | In bioinformatics, PAM matrices are sometimes used as substitution matrices to score sequence alignments for proteins. Each entry in a PAM matrix indicates the likelihood of the amino acid of that row being replaced with the amino acid of that column through a series of one or more point accepted mutations during a spe... | Point Accepted Mutation | 0.820305 |
9,347 | One cause was the discovery in 1982 by Celso Costa of a surface that disproved the conjecture that the plane, the catenoid, and the helicoid are the only complete embedded minimal surfaces in R3 of finite topological type. This not only stimulated new work on using the old parametric methods, but also demonstrated the ... | Minimal surface equation | 0.820297 |
9,348 | The way the MV-algebra characterizes all possible MV-algebras parallels the well-known fact that identities holding in the two-element Boolean algebra hold in all possible Boolean algebras. Moreover, MV-algebras characterize infinite-valued Łukasiewicz logic in a manner analogous to the way that Boolean algebras chara... | MV-algebra | 0.820291 |
9,349 | Chang's (1958, 1959) completeness theorem states that any MV-algebra equation holding in the standard MV-algebra over the interval will hold in every MV-algebra. Algebraically, this means that the standard MV-algebra generates the variety of all MV-algebras. Equivalently, Chang's completeness theorem says that MV-alge... | MV-algebra | 0.820291 |
9,350 | C. C. Chang devised MV-algebras to study many-valued logics, introduced by Jan Łukasiewicz in 1920. In particular, MV-algebras form the algebraic semantics of Łukasiewicz logic, as described below. Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of propositional formulas (in the language consis... | MV-algebra | 0.820291 |
9,351 | Being defined by identities, MV-algebras form a variety of algebras. The variety of MV-algebras is a subvariety of the variety of BL-algebras and contains all Boolean algebras. An MV-algebra can equivalently be defined (Hájek 1998) as a prelinear commutative bounded integral residuated lattice ⟨ L , ∧ , ∨ , ⊗ , → , 0 ,... | MV-algebra | 0.820291 |
9,352 | An MV-algebra is an algebraic structure ⟨ A , ⊕ , ¬ , 0 ⟩ , {\displaystyle \langle A,\oplus ,\lnot ,0\rangle ,} consisting of a non-empty set A , {\displaystyle A,} a binary operation ⊕ {\displaystyle \oplus } on A , {\displaystyle A,} a unary operation ¬ {\displaystyle \lnot } on A , {\displaystyle A,} and a constant ... | MV-algebra | 0.820291 |
9,353 | If G is such a group with strong (order) unit u, then the "unit interval" { x ∈ G | 0 ≤ x ≤ u } can be equipped with ¬x = u − x, x ⊕ y = u ∧G (x + y), and x ⊗ y = 0 ∨G (x + y − u). This construction establishes a categorical equivalence between lattice-ordered abelian groups with strong unit and MV-algebras. An effect ... | MV-algebra | 0.820291 |
9,354 | Another important example is Chang's MV-algebra, consisting just of infinitesimals (with the order type ω) and their co-infinitesimals. Chang also constructed an MV-algebra from an arbitrary totally ordered abelian group G by fixing a positive element u and defining the segment as { x ∈ G | 0 ≤ x ≤ u }, which becomes ... | MV-algebra | 0.820291 |
9,355 | If instead the axiom added is x ⊕ x ⊕ x = x ⊕ x {\displaystyle x\oplus x\oplus x=x\oplus x} , then the axioms define the MV3 algebra corresponding to the three-valued Łukasiewicz logic Ł3. Other finite linearly ordered MV-algebras are obtained by restricting the universe and operations of the standard MV-algebra to the... | MV-algebra | 0.820291 |
9,356 | {\displaystyle \lnot 0=0.} The two-element MV-algebra is actually the two-element Boolean algebra { 0 , 1 } , {\displaystyle \{0,1\},} with ⊕ {\displaystyle \oplus } coinciding with Boolean disjunction and ¬ {\displaystyle \lnot } with Boolean negation. In fact adding the axiom x ⊕ x = x {\displaystyle x\oplus x=x} to ... | MV-algebra | 0.820291 |
9,357 | A simple numerical example is A = , {\displaystyle A=,} with operations x ⊕ y = min ( x + y , 1 ) {\displaystyle x\oplus y=\min(x+y,1)} and ¬ x = 1 − x . {\displaystyle \lnot x=1-x.} In mathematical fuzzy logic, this MV-algebra is called the standard MV-algebra, as it forms the standard real-valued semantics of Łukasi... | MV-algebra | 0.820291 |
9,358 | MV-algebras were related by Daniele Mundici to approximately finite-dimensional C*-algebras by establishing a bijective correspondence between all isomorphism classes of approximately finite-dimensional C*-algebras with lattice-ordered dimension group and all isomorphism classes of countable MV algebras. Some instances... | MV-algebra | 0.820291 |
9,359 | For the axiomatically more complicated (finitely) n-valued Łukasiewicz logics, suitable algebras were published in 1977 by Revaz Grigolia and called MVn-algebras. MVn-algebras are a subclass of LMn-algebras; the inclusion is strict for n ≥ 5.The MVn-algebras are MV-algebras that satisfy some additional axioms, just lik... | MV-algebra | 0.820291 |
9,360 | In the 1940s Grigore Moisil introduced his Łukasiewicz–Moisil algebras (LMn-algebras) in the hope of giving algebraic semantics for the (finitely) n-valued Łukasiewicz logic. However, in 1956 Alan Rose discovered that for n ≥ 5, the Łukasiewicz–Moisil algebra does not model the Łukasiewicz n-valued logic. Although C. C... | MV-algebra | 0.820291 |
9,361 | There are multiple frameworks implementing fuzzy logic (type II), and most of them implement what has been called a multi-adjoint logic. This is no more than the implementation of an MV-algebra. | MV-algebra | 0.820291 |
9,362 | In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation ⊕ {\displaystyle \oplus } , a unary operation ¬ {\displaystyle \neg } , and the constant 0 {\displaystyle 0} , satisfying certain axioms. MV-algebras are the algebraic semantics of Łukasiewicz logic; the l... | MV-algebra | 0.820291 |
9,363 | In this approach the strength and type, excitatory or inhibitory, of synaptic connections are represented by the magnitude and sign of weights, that is, numerical coefficients w ′ {\displaystyle w'} in front of the inputs x {\displaystyle x} to a particular neuron. The response of the j {\displaystyle j} -th neuron is ... | Models of neural computation | 0.820288 |
9,364 | The most widely used models of information transfer in biological neurons are based on analogies with electrical circuits. The equations to be solved are time-dependent differential equations with electro-dynamical variables such as current, conductance or resistance, capacitance and voltage. | Models of neural computation | 0.820288 |
9,365 | A linear system is one whose response in a specified unit of measure, to a set of inputs considered at once, is the sum of its responses due to the inputs considered individually. Linear systems are easier to analyze mathematically and are a persuasive assumption in many models including the McCulloch and Pitts neuron,... | Models of neural computation | 0.820288 |
9,366 | The Hodgkin–Huxley model, widely regarded as one of the great achievements of 20th-century biophysics, describes how action potentials in neurons are initiated and propagated in axons via voltage-gated ion channels. It is a set of nonlinear ordinary differential equations that were introduced by Alan Lloyd Hodgkin and ... | Models of neural computation | 0.820288 |
9,367 | In theoretical computer science, the time hierarchy is a classification of decision problems according to the amount of time required to solve them. | Hierarchy (mathematics) | 0.820284 |
9,368 | This is not just a pedantic claim; there are also mathematical hierarchies, in the general sense, that are not describable using set theory.Other natural hierarchies arise in computer science, where the word refers to partially ordered sets whose elements are classes of objects of increasing complexity. In that case, t... | Hierarchy (mathematics) | 0.820284 |
9,369 | Using the extended real number line, take a + b to be the minimum of a and b and ab to be the ordinary sum of a and b (with the sum of +∞ and −∞ being defined as +∞). a* is defined to be the real number zero for nonnegative a and −∞ for negative a. This is a Kleene algebra with zero element +∞ and one element the real ... | Regular algebra | 0.820282 |
9,370 | Define 1 = span {I}, the span of the unit of the algebra. The closure of V is the direct sum of all powers of V. Suppose M is a set and A is the set of all binary relations on M. Taking + to be the union, · to be the composition and * to be the reflexive transitive closure, we obtain a Kleene algebra. Every Boolean alg... | Regular algebra | 0.820282 |
9,371 | The linear subspaces of a unital algebra over a field form a Kleene algebra. Given linear subspaces V and W, define V + W to be the sum of the two subspaces, and 0 to be the trivial subspace {0}. Define V · W = span {v · w | v ∈ V, w ∈ W}, the linear span of the product of vectors from V and W respectively. | Regular algebra | 0.820282 |
9,372 | Let M be a monoid with identity element e and let A be the set of all subsets of M. For two such subsets S and T, let S + T be the union of S and T and set ST = {st: s in S and t in T}. S* is defined as the submonoid of M generated by S, which can be described as {e} ∪ S ∪ SS ∪ SSS ∪ ... Then A forms a Kleene algebra w... | Regular algebra | 0.820282 |
9,373 | Again let Σ be an alphabet. Let A be the set of all regular languages over Σ (or the set of all context-free languages over Σ; or the set of all recursive languages over Σ; or the set of all languages over Σ). Then the union (written as +) and the concatenation (written as ·) of two elements of A again belong to A, and... | Regular algebra | 0.820282 |
9,374 | Let Σ be a finite set (an "alphabet") and let A be the set of all regular expressions over Σ. We consider two such regular expressions equal if they describe the same language. Then A forms a Kleene algebra. In fact, this is a free Kleene algebra in the sense that any equation among regular expressions follows from the... | Regular algebra | 0.820282 |
9,375 | The problem of providing a complete set of axioms, which would allow derivation of all equations among regular expressions, was intensively studied by John Horton Conway under the name of regular algebras, however, the bulk of his treatment was infinitary. In 1981, Kozen gave a complete infinitary equational deductive ... | Regular algebra | 0.820282 |
9,376 | Kleene introduced regular expressions and gave some of their algebraic laws. Although he didn't define Kleene algebras, he asked for a decision procedure for equivalence of regular expressions. Redko proved that no finite set of equational axioms can characterize the algebra of regular languages. Salomaa gave complete ... | Regular algebra | 0.820282 |
9,377 | Kleene algebras are a particular case of closed semirings, also called quasi-regular semirings or Lehmann semirings, which are semirings in which every element has at least one quasi-inverse satisfying the equation: a* = aa* + 1 = a*a + 1. This quasi-inverse is not necessarily unique. In a Kleene algebra, a* is the lea... | Regular algebra | 0.820282 |
9,378 | In mathematics, a Kleene algebra ( KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions. | Regular algebra | 0.820282 |
9,379 | Knowing the first N bits of Ω, one could calculate the halting problem for all programs of a size up to N. Let the program p for which the halting problem is to be solved be N bits long. In dovetailing fashion, all programs of all lengths are run, until enough have halted to jointly contribute enough probability to mat... | Halting probability | 0.820282 |
9,380 | Low cost for control achieved High torque at startup and low speeds Ruggedness Simplicity of construction Can operate in an open loop control system Low maintenance (high reliability) Less likely to stall or slip Will work in any environment Can be used in robotics in a wide scale. High reliability The rotation angle o... | Stepper motors | 0.820273 |
9,381 | This language is intended to be easy to use for mathematicians, and many parts of the system are indeed written in the Macaulay2 language. The algebraic algorithms that form the core functionality are written in C++ for speed. The interpreter itself is written in a custom type safety layer over C. Both the system and t... | Macaulay computer algebra system | 0.820272 |
9,382 | Nearly 200 packages are included in the distribution of Macaulay2 as of 2019, and notable package authors include Craig Huneke and Frank-Olaf Schreyer. The Journal of Software for Algebra and Geometry has published numerous packages and programs for Macaulay2.Macaulay2 has an interactive command-line interface used fro... | Macaulay computer algebra system | 0.820272 |
9,383 | Macaulay2 is built around fast implementations of algorithms useful for computation in commutative algebra and algebraic geometry. This core functionality includes arithmetic on rings, modules, and matrices, as well as algorithms for Gröbner bases, free resolutions, Hilbert series, determinants and Pfaffians, factoring... | Macaulay computer algebra system | 0.820272 |
9,384 | Macaulay2 is a free computer algebra system created by Daniel Grayson (from the University of Illinois at Urbana–Champaign) and Michael Stillman (from Cornell University) for computation in commutative algebra and algebraic geometry. | Macaulay computer algebra system | 0.820272 |
9,385 | Bradley, James (1727–1728). "A Letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr.Edmond Halley Astronom. Reg. | Velocity addition | 0.820269 |
9,386 | It can be rewritten in terms of four-velocities as The correct expression for the flux, published by Christian Møller in 1945, is given by One notes that for collinear velocities, F = n 1 n 2 | v 2 − v 1 | = n 1 n 2 v r {\displaystyle F=n_{1}n_{2}|\mathbf {v} _{2}-\mathbf {v} _{1}|=n_{1}n_{2}v_{r}} . In order to get a ... | Velocity addition | 0.820269 |
9,387 | The relative velocity is incorrectly given in most, perhaps all books on particle physics and quantum field theory. This is mostly harmless, since if either one particle type is stationary or the relative motion is collinear, then the right result is obtained from the incorrect formulas. The formula is invariant, but n... | Velocity addition | 0.820269 |
9,388 | : 12-11: 359 The fundamental theories for forces developed from the unification of different ideas. For example, Newton's universal theory of gravitation showed that the force responsible for objects falling near the surface of the Earth is also the force responsible for the falling of celestial bodies about the Earth ... | Physical force | 0.820268 |
9,389 | All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charge... | Physical force | 0.820268 |
9,390 | In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-m... | Physical force | 0.820268 |
9,391 | Sega have since continued to manufacture motion simulator cabinets for arcade games through to the 2010s.In the mid-1980s, Codemasters and the Oliver Twins released a number of games with "Simulator" in the title, including BMX Simulator (1986), Grand Prix Simulator (1986), and Pro Boxing Simulator (1988). Richard and ... | Simulation games | 0.820267 |
9,392 | It follows from the compactness theorem and the upward Löwenheim–Skolem theorem that it is not possible to characterize finiteness or countability, respectively, in first-order logic. Certain fragments of second-order logic like ESO are also more expressive than first-order logic even though they are strictly less expr... | Second-order logic | 0.820264 |
9,393 | On the other hand, the set of first-order sentences valid in the reals has arbitrarily large models due to the compactness theorem. Thus the least-upper-bound property cannot be expressed by any set of sentences in first-order logic. (In fact, every real-closed field satisfies the same first-order sentences in the sign... | Second-order logic | 0.820264 |
9,394 | In popular culture, forensic biology is frequently portrayed in shows like Law & Order, Hannibal, Bones, CSI, Dexter and Castle. However thanks to Hollywood's depiction of forensic science, the analysis of biological evidence has fallen prey to the CSI Effect, which results in the public's perception of its capabilitie... | Forensic biology | 0.82026 |
9,395 | Forensic toxicology is the use of toxicology and other disciplines such as analytical chemistry, pharmacology and clinical chemistry to aid medical or legal investigation of death, poisoning, and drug use. The primary concern for forensic toxicology is not the legal outcome of the toxicological investigation or the tec... | Forensic biology | 0.82026 |
9,396 | Forensic biology is the application of biology into law enforcement investigations.Forensic biology primarily involves the DNA sequencing of biological matter at crime scenes. This assists investigators in identifying possible suspects, or unidentified bodies. Forensic biology has many sub-branches, such as forensic an... | Forensic biology | 0.82026 |
9,397 | Journey into Geometries is written as a conversation between three characters: Alice, from Alice's Adventures in Wonderland (but older and familiar with Euclidean geometry), Lewis Carroll, the author of Alice's adventures, and a modern mathematician named "Dr. Whatif". Its topics include hyperbolic geometry, inversive ... | Journey into Geometries | 0.82026 |
9,398 | Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd, and published in 1991 by the Mathematical Association of America in their MAA Spectrum book series. | Journey into Geometries | 0.82026 |
9,399 | Reviewer William E. Fenton is unsure of the audience of the book, writing that it is not suitable as a textbook and would scare most undergraduates, but is too unserious for graduate students. David A. Thomas identifies the audience as "people who like to play with mathematical ideas".Fenton criticizes the book's style... | Journey into Geometries | 0.82026 |
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