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12,200 | The Machine Intelligence Research Institute (MIRI), formerly the Singularity Institute for Artificial Intelligence (SIAI), is a non-profit research institute focused since 2005 on identifying and managing potential existential risks from artificial general intelligence. MIRI's work has focused on a friendly AI approach... | Machine Intelligence Research Institute | 0.817253 |
12,201 | If the Markov chain is time-homogeneous, then the transition matrix P is the same after each step, so the k-step transition probability can be computed as the k-th power of the transition matrix, Pk. If the Markov chain is irreducible and aperiodic, then there is a unique stationary distribution π. Additionally, in thi... | Transition probability | 0.817252 |
12,202 | They also allow effective state estimation and pattern recognition. Markov chains also play an important role in reinforcement learning. Markov chains are also the basis for hidden Markov models, which are an important tool in such diverse fields as telephone networks (which use the Viterbi algorithm for error correcti... | Transition probability | 0.817252 |
12,203 | In software engineering, SOLID is a mnemonic acronym for five design principles intended to make object-oriented designs more understandable, flexible, and maintainable. The principles are a subset of many principles promoted by American software engineer and instructor Robert C. Martin, first introduced in his 2000 pa... | SOLID | 0.817251 |
12,204 | There are several well-developed techniques for analyzing nonlinear feedback systems: Describing function method Phase plane method Lyapunov stability analysis Singular perturbation method The Popov criterion and the circle criterion for absolute stability Center manifold theorem Small-gain theorem Passivity analysisCo... | Nonlinear control system | 0.817251 |
12,205 | The Frobenius theorem is a deep result in differential geometry. When applied to nonlinear control, it says the following: Given a system of the form x ˙ = ∑ i = 1 k f i ( x ) u i ( t ) {\displaystyle {\dot {x}}=\sum _{i=1}^{k}f_{i}(x)u_{i}(t)\,} where x ∈ R n {\displaystyle x\in R^{n}} , f 1 , … , f k {\displaystyle f... | Nonlinear control system | 0.817251 |
12,206 | A new person is pointed at as each word is said. The player who is selected at the conclusion of the rhyme is "it" or "out". In an alternate version, the circle of players may each put two feet in and at the conclusion of the rhyme, that player removes one foot and the rhyme starts over with the next person. In this ca... | Counting-out game | 0.817251 |
12,207 | When these statistics are given in a courtroom setting or in a laboratory report they are usually given for the three most common races of that specific area. This is because the allele frequencies at different loci changed based on the individual's ancestry. https://strbase.nist.gov/training/6_Mixture-Statistics.pdf | Forensic DNA analysis | 0.817244 |
12,208 | However, likelihood ratio calculations is becoming the preferred method over the other two most commonly used methods, random man not excluded and combined probability of inclusion. Match statistics are especially important in mixture interpretation where there is more than one contributor to a DNA profile. | Forensic DNA analysis | 0.817244 |
12,209 | Since the values are multiplied together, extremely small numbers can be achieved using CPI. CPI or CPE is considered an acceptable statistical calculation when a mixture is indicated. https://www.promega.com/-/media/files/resources/conference-proceedings/ishi-15/parentage-and-mixture-statistics-workshop/generalpopulat... | Forensic DNA analysis | 0.817244 |
12,210 | Combined probability of inclusion or exclusion calculates the probability that a random, unrelated, person would be a contributor to a DNA profile or DNA mixture. In this method, statistics for each individual locus is determined using population statistics and then combined to get the total CPI or CPE. These calculati... | Forensic DNA analysis | 0.817244 |
12,211 | Likelihood ratios (LR) are a comparison of two different probabilities to determine which one is more likely. When it involves a trial the LR is the probability of the prosecution's argument versus the probability of the defense's argument given their starting assumptions. In this scenario the prosecution's probability... | Forensic DNA analysis | 0.817244 |
12,212 | The above algebraic definition of a semilattice suggests a notion of morphism between two semilattices. Given two join-semilattices (S, ∨) and (T, ∨), a homomorphism of (join-) semilattices is a function f: S → T such that f(x ∨ y) = f(x) ∨ f(y).Hence f is just a homomorphism of the two semigroups associated with each ... | Join semilattice | 0.817242 |
12,213 | Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any such operation induces a partial order (and the respective inverse order) such that the result of the operation for any two elements is the least upper bound (or greatest lower bound) of the... | Join semilattice | 0.817242 |
12,214 | Thus a complete semilattice turns out to be "a complete lattice possibly lacking a top". This definition is of interest specifically in domain theory, where bounded complete algebraic cpos are studied as Scott domains. Hence Scott domains have been called algebraic semilattices. Cardinality-restricted notions of comple... | Join semilattice | 0.817242 |
12,215 | In his second monograph on quartic reciprocity Gauss stated quadratic reciprocity for the ring Z {\displaystyle \mathbb {Z} } of Gaussian integers, saying that it is a corollary of the biquadratic law in Z , {\displaystyle \mathbb {Z} ,} but did not provide a proof of either theorem. Dirichlet showed that the law in ... | Quadratic reciprocity law | 0.817239 |
12,216 | The theorem was formulated in many ways before its modern form: Euler and Legendre did not have Gauss's congruence notation, nor did Gauss have the Legendre symbol. In this article p and q always refer to distinct positive odd primes, and x and y to unspecified integers. | Quadratic reciprocity law | 0.817239 |
12,217 | The supplements provide solutions to specific cases of quadratic reciprocity. They are often quoted as partial results, without having to resort to the complete theorem. | Quadratic reciprocity law | 0.817239 |
12,218 | The observations about −3 and 5 continue to hold: −7 is a residue modulo p if and only if p is a residue modulo 7, −11 is a residue modulo p if and only if p is a residue modulo 11, 13 is a residue (mod p) if and only if p is a residue modulo 13, etc. The more complicated-looking rules for the quadratic characters of 3... | Quadratic reciprocity law | 0.817239 |
12,219 | This proof served as a template for class field theory, which can be viewed as a vast generalization of quadratic reciprocity. Robert Langlands formulated the Langlands program, which gives a conjectural vast generalization of class field theory. He wrote: I confess that, as a student unaware of the history of the subj... | Quadratic reciprocity law | 0.817239 |
12,220 | The early proofs of quadratic reciprocity are relatively unilluminating. The situation changed when Gauss used Gauss sums to show that quadratic fields are subfields of cyclotomic fields, and implicitly deduced quadratic reciprocity from a reciprocity theorem for cyclotomic fields. His proof was cast in modern form by ... | Quadratic reciprocity law | 0.817239 |
12,221 | Then: ( p q ) = ( q ∗ p ) . {\displaystyle \left({\frac {p}{q}}\right)=\left({\frac {q^{*}}{p}}\right).} A number of proofs of the theorem, especially those based on Gauss sums or the splitting of primes in algebraic number fields, derive this formula. | Quadratic reciprocity law | 0.817239 |
12,222 | nonresidue) of p. In the next sentence, he christens it the "fundamental theorem" (Gauss never used the word "reciprocity").Introducing the notation a R b (resp. a N b) to mean a is a quadratic residue (resp. nonresidue) (mod b), and letting a, a′, etc. represent positive primes ≡ 1 (mod 4) and b, b′, etc. positive pri... | Quadratic reciprocity law | 0.817239 |
12,223 | Gauss first proves the supplementary laws. He sets the basis for induction by proving the theorem for ±3 and ±5. Noting that it is easier to state for −3 and +5 than it is for +3 or −5, he states the general theorem in the form: If p is a prime of the form 4n + 1 then p, but if p is of the form 4n + 3 then −p, is a qua... | Quadratic reciprocity law | 0.817239 |
12,224 | This technique doesn't work for Theorem VIII. Let b ≡ B ≡ 3 (mod 4), and assume ( B b ) = ( b B ) = − 1. {\displaystyle \left({\frac {B}{b}}\right)=\left({\frac {b}{B}}\right)=-1.} | Quadratic reciprocity law | 0.817239 |
12,225 | Theorem I is handled by letting a ≡ 1 and b ≡ 3 (mod 4) be primes and assuming that ( b a ) = 1 {\displaystyle \left({\tfrac {b}{a}}\right)=1} and, contrary the theorem, that ( a b ) = − 1. {\displaystyle \left({\tfrac {a}{b}}\right)=-1.} Then x 2 + a y 2 − b z 2 = 0 {\displaystyle x^{2}+ay^{2}-bz^{2}=0} has a solution... | Quadratic reciprocity law | 0.817239 |
12,226 | The attempt to generalize quadratic reciprocity for powers higher than the second was one of the main goals that led 19th century mathematicians, including Carl Friedrich Gauss, Peter Gustav Lejeune Dirichlet, Carl Gustav Jakob Jacobi, Gotthold Eisenstein, Richard Dedekind, Ernst Kummer, and David Hilbert to the study ... | Quadratic reciprocity law | 0.817239 |
12,227 | In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on... | Kinetic diagram | 0.817238 |
12,228 | In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.Defining sets by properties is also known as set comprehension, set abstraction or as ... | Set notation | 0.817237 |
12,229 | Otherwise, the question is asked on the partly instantiated formula Φ{x1=TRUE}, i.e. Φ with the first variable x1 replaced by TRUE, and simplified accordingly. If the answer is "yes", then x1=TRUE, otherwise x1=FALSE. Values of other variables can be found subsequently in the same way. In total, n+1 runs of the algorit... | Propositional satisfiability | 0.817232 |
12,230 | This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem, and it is generally believed that no such algorithm exists; yet this belief ... | Propositional satisfiability | 0.817232 |
12,231 | For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable. SAT is the first problem that was proven to be NP-complete; see Cook–Levin theorem. | Propositional satisfiability | 0.817232 |
12,232 | In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of ... | Propositional satisfiability | 0.817232 |
12,233 | When all literals of a one-in-three 3-SAT formula are positive, the satisfiability problem is called one-in-three positive 3-SAT. One-in-three 3-SAT, together with its positive case, is listed as NP-complete problem "LO4" in the standard reference, Computers and Intractability: A Guide to the Theory of NP-Completeness ... | Propositional satisfiability | 0.817232 |
12,234 | A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to its va... | Propositional satisfiability | 0.817232 |
12,235 | As an example, R(¬x,a,b) is a generalized clause, and R(¬x,a,b) ∧ R(b,y,c) ∧ R(c,d,¬z) is a generalized conjunctive normal form. This formula is used below, with R being the ternary operator that is TRUE just when exactly one of its arguments is. Using the laws of Boolean algebra, every propositional logic formula can ... | Propositional satisfiability | 0.817232 |
12,236 | 1930 (1930): Kurt Gödel announces a proof as an answer to the first two of Hilbert's 1928 questions. "At first he was only angry and frustrated, but then he began to try to deal constructively with the problem... Gödel himself felt—and expressed the thought in his paper—that his work did not contradict Hilbert's forma... | The halting problem | 0.817227 |
12,237 | The usage in Davis's book is as follows: " we wish to determine whether or not Z, if placed in a given initial state, will eventually halt. We call this problem the halting problem for Z. Theorem 2.2 There exists a Turing machine whose halting problem is recursively unsolvable. A related problem is the printing proble... | The halting problem | 0.817227 |
12,238 | In his original proof Turing formalized the concept of algorithm by introducing Turing machines. However, the result is in no way specific to them; it applies equally to any other model of computation that is equivalent in its computational power to Turing machines, such as Markov algorithms, Lambda calculus, Post syst... | The halting problem | 0.817227 |
12,239 | Also, this theorem holds only for properties of the partial function implemented by the program; Rice's Theorem does not apply to properties of the program itself. For example, "halt on input 0 within 100 steps" is not a property of the partial function that is implemented by the program—it is a property of the program... | The halting problem | 0.817227 |
12,240 | Rice's theorem generalizes the theorem that the halting problem is unsolvable. It states that for any non-trivial property, there is no general decision procedure that, for all programs, decides whether the partial function implemented by the input program has that property. (A partial function is a function which may ... | The halting problem | 0.817227 |
12,241 | A machine with finite memory has a finite number of configurations, and thus any deterministic program on it must eventually either halt or repeat a previous configuration: ...any finite-state machine, if left completely to itself, will fall eventually into a perfectly periodic repetitive pattern. The duration of this ... | The halting problem | 0.817227 |
12,242 | When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see Factorization of polynomials). These algorithms are not practicable for hand-written computation, but are available in any computer... | Polynomial curve | 0.817223 |
12,243 | However, root-finding algorithms may be used to find numerical approximations of the roots of a polynomial expression of any degree. The number of solutions of a polynomial equation with real coefficients may not exceed the degree, and equals the degree when the complex solutions are counted with their multiplicity. Th... | Polynomial curve | 0.817223 |
12,244 | There are also formulas for the cubic and quartic equations. For higher degrees, the Abel–Ruffini theorem asserts that there can not exist a general formula in radicals. | Polynomial curve | 0.817223 |
12,245 | A polynomial equation, also called an algebraic equation, is an equation of the form For example, is a polynomial equation. When considering equations, the indeterminates (variables) of polynomials are also called unknowns, and the solutions are the possible values of the unknowns for which the equality is true (in gen... | Polynomial curve | 0.817223 |
12,246 | For example, an algebra problem from the Chinese Arithmetic in Nine Sections, c. 200 BCE, begins "Three sheafs of good crop, two sheafs of mediocre crop, and one sheaf of bad crop are sold for 29 dou." We would write 3x + 2y + z = 29. | Polynomial curve | 0.817223 |
12,247 | Determining the roots of polynomials, or "solving algebraic equations", is among the oldest problems in mathematics. However, the elegant and practical notation we use today only developed beginning in the 15th century. Before that, equations were written out in words. | Polynomial curve | 0.817223 |
12,248 | A 2D geometric model is a geometric model of an object as a two-dimensional figure, usually on the Euclidean or Cartesian plane. Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal. Other ex... | 2D geometric modeling | 0.817223 |
12,249 | The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra. Buchberger's algorithm fo... | Knuth–Bendix algorithm | 0.817219 |
12,250 | A maximum 3-dimensional matching is a largest 3-dimensional matching. In computational complexity theory, this is also the name of the following optimization problem: given a set T, find a 3-dimensional matching M ⊆ T that maximizes |M|. Since the decision problem described above is NP-complete, this optimization probl... | 3-dimensional matching | 0.817218 |
12,251 | In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs, which consist of hyperedges each of which contains 3 vertices (instead of edges containing 2 vertices in a usual graph). 3-dimensional match... | 3-dimensional matching | 0.817218 |
12,252 | Computer vision is a field that includes methods for acquiring, processing, analyzing, and understanding images and high-dimensional data from the real world to produce numerical or symbolic information, e.g., in the forms of decisions. Computer vision has many applications already in use today such as facial recogniti... | Machine perception | 0.817217 |
12,253 | Machine perception is the capability of a computer system to interpret data in a manner that is similar to the way humans use their senses to relate to the world around them. The basic method that the computers take in and respond to their environment is through the attached hardware. Until recently input was limited t... | Machine perception | 0.817217 |
12,254 | The Annals of Applied Probability is a leading peer-reviewed mathematics journal published by the Institute of Mathematical Statistics, which is the main international society for researchers in probability and statistics. The journal was established in 1991 by founding editor J. Michael Steele and is indexed by Mathem... | Annals of Applied Probability | 0.817214 |
12,255 | Its impact factor (measured by JCR/ISI-Thomson) evolved from 1.454 in 2014 to 1.786 in 2017. The journal CiteScore is 3.2 and its SCImago Journal Rank is 1.878, both from 2020. It is currently ranked 9th in the field of Probability & Statistics with Applications according to Google Scholar. | Annals of Applied Probability | 0.817214 |
12,256 | In quantum mechanics, angular momentum (like other quantities) is expressed as an operator, and its one-dimensional projections have quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, implying that at any time, only one projection (also called "component") can be measured with d... | Introduction to angular momentum | 0.817212 |
12,257 | There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (spe... | Internal group | 0.817212 |
12,258 | In quantum chromodynamics, the color field lines are coupled at short distances by gluons, which are polarized by the field and line up with it. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks withi... | Internal group | 0.817212 |
12,259 | It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. For example, quantizing classical electrodynamics gives quantum electro... | Internal group | 0.817212 |
12,260 | The ability of deductive reasoning is an important aspect of intelligence and many tests of intelligence include problems that call for deductive inferences. Because of this relation to intelligence, deduction is highly relevant to psychology and the cognitive sciences. But the subject of deductive reasoning is also pe... | Deductive reasoning | 0.817208 |
12,261 | It gets its name from the forms of mathematical demonstration found in traditional geometry, which are usually based on axioms, definitions, and inferred theorems. An important motivation of the geometrical method is to repudiate philosophical skepticism by grounding one's philosophical system on absolutely certain axi... | Deductive reasoning | 0.817208 |
12,262 | Aristotle, a Greek philosopher, started documenting deductive reasoning in the 4th century BC. René Descartes, in his book Discourse on Method, refined the idea for the Scientific Revolution. Developing four rules to follow for proving an idea deductively, Descartes laid the foundation for the deductive portion of the ... | Deductive reasoning | 0.817208 |
12,263 | Permutation tests are a subset of non-parametric statistics. Assuming that our experimental data come from data measured from two treatment groups, the method simply generates the distribution of mean differences under the assumption that the two groups are not distinct in terms of the measured variable. From this, one... | Permutation test | 0.8172 |
12,264 | The major drawbacks to permutation tests are that they Can be computationally intensive and may require "custom" code for difficult-to-calculate statistics. This must be rewritten for every case. Are primarily used to provide a p-value. The inversion of the test to get confidence regions/intervals requires even more co... | Permutation test | 0.8172 |
12,265 | There are various models for point processes, typically based on but going beyond the classic homogeneous Poisson point process (the basic model for complete spatial randomness) to find expressive models which allow effective statistical methods. The point pattern theory provides a major building block for generation o... | Stochastic geometry | 0.817196 |
12,266 | The name appears to have been coined by David Kendall and Klaus Krickeberg while preparing for a June 1969 Oberwolfach workshop, though antecedents for the theory stretch back much further under the name geometric probability. The term "stochastic geometry" was also used by Frisch and Hammersley in 1963 as one of two s... | Stochastic geometry | 0.817196 |
12,267 | What is meant by a random object? A complete answer to this question requires the theory of random closed sets, which makes contact with advanced concepts from measure theory. The key idea is to focus on the probabilities of the given random closed set hitting specified test sets. There arise questions of inference (fo... | Stochastic geometry | 0.817196 |
12,268 | This brief description has focused on the theory of stochastic geometry, which allows a view of the structure of the subject. However, much of the life and interest of the subject, and indeed many of its original ideas, flow from a very wide range of applications, for example: astronomy, spatially distributed telecommu... | Stochastic geometry | 0.817196 |
12,269 | Line and hyper-flat processes have their own direct applications, but also find application as one way of creating tessellations dividing space; hence for example one may speak of Poisson line tessellations. A notable recent result proves that the cell at the origin of the Poisson line tessellation is approximately cir... | Stochastic geometry | 0.817196 |
12,270 | A complication is that the Euclidean motion symmetries will then be expressed on the representation space in a somewhat unusual way. Moreover, calculations need to take account of interesting spatial biases (for example, line segments are less likely to be hit by random lines to which they are nearly parallel) and this... | Stochastic geometry | 0.817196 |
12,271 | In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures. | Stochastic geometry | 0.817196 |
12,272 | In quantum computing, the Brassard-Høyer-Tapp algorithm or BHT algorithm is a quantum algorithm that solves the collision problem. In this problem, one is given n and an r-to-1 function f: { 1 , … , n } → { 1 , … , n } {\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}} and needs to find two inputs that f ma... | BHT algorithm | 0.817188 |
12,273 | In statistics, a random vector x is classically represented by a probability density function. In a set-membership approach or set estimation, x is represented by a set X to which x is assumed to belong. This means that the support of the probability distribution function of x is included inside X. On the one hand, rep... | Set estimation | 0.817184 |
12,274 | The difference in initial rates of the two steps implies different charge distribution in the transition state (TS). When the addition step occurs more quickly than elimination (an ANDN mechanism), more positive charge develops on the nucleophile, and the transition state is said to be "tight." Conversely, if eliminati... | Nucleotide pyrophosphatase/phosphodiesterase | 0.817182 |
12,275 | NPP catalyses the nucleophilic substitution of one ester bond on a phosphodiester substrate. It has a nucleoside binding pocket that excludes phospholipid substrates from the active site. A threonine nucleophile has been identified through site-directed mutagenesis, and the reaction inverts the stereochemistry of the p... | Nucleotide pyrophosphatase/phosphodiesterase | 0.817182 |
12,276 | The size and strength of the induced vortices around a conducting particle have direct relationship with the applied electric filed and also the size of the conducted surface. This phenomenon is experimentally and numerically proven by several studies, The vortices grow as the external electric field increases and gene... | Induced-charge Electrokinetics | 0.817177 |
12,277 | The induced vortices have many applications in various aspects of electrokinetic microfluidics. There are many micro-mixers that are designed and fabricated based on the existence of their induced vortices in the microfluidics devices. Such micro-mixers which are used for biochemical, medicine, biology applications has... | Induced-charge Electrokinetics | 0.817177 |
12,278 | As a result of this migration, the negative charges move to the side which is close to the positive (or higher) voltage while the positive charges move to the opposite side of the particle. These charges under the skin of the conducting particle attract the counter-ions of the aqueous solution; thus, the electric doubl... | Induced-charge Electrokinetics | 0.817177 |
12,279 | Induced-charge electrokinetics in physics is the electrically driven fluid flow and particle motion in a liquid electrolyte. Consider a metal particle (which is neutrally charged but electrically conducting) in contact with an aqueous solution in a chamber/channel. If different voltages apply to the end of this chamber... | Induced-charge Electrokinetics | 0.817177 |
12,280 | The M22 graph, also called the Mesner graph or Witt graph is the unique strongly regular graph with parameters (77, 16, 0, 4). It is constructed from the Steiner system (3, 6, 22) by representing its 77 blocks as vertices and joining two vertices iff they have no terms in common or by deleting a vertex and its neighbor... | M22 graph | 0.81717 |
12,281 | European Union promoted the Bologna process and the creation of a single European higher education area, both of which require mobility of graduates across Europe. ECTN (European Chemistry Thematic Network) worked in the EU project "Tuning Educational Structures in Europe" and developed Eurobachelor, a framework for a ... | Chemistry Quality Eurolabels | 0.817158 |
12,282 | Euromaster is a registered trademark and an initiative adopted by the EuCheMS General Assembly in 2005. It is associated with the Chemistry Quality Eurolabels. As of 8 April 2013, 36 Euromaster quality labels have been awarded. The label is intended for master's degrees. Euromaster, introduced after Eurobachelor, is in... | Chemistry Quality Eurolabels | 0.817158 |
12,283 | Eurodoctorate is associated with the Chemistry Quality Eurolabels. As of 8 April 2013, 1 Eurodoctorate quality label was awarded. The label is intended for third cycle qualifications (i.e. doctoral degrees).The Tuning Chemistry Subject Area Group (Tuning SAG) discussed with a working party of ECTN (European Chemistry T... | Chemistry Quality Eurolabels | 0.817158 |
12,284 | Eurobachelor is a registered trademark and an initiative adopted by the EuCheMS General Assembly in 2003. It is associated with the Chemistry Quality Eurolabels. As of 8 April 2013, 60 Eurobachelor quality labels have been awarded. The label is intended for first cycle qualifications (bachelor's degrees). Eurobachelor ... | Chemistry Quality Eurolabels | 0.817158 |
12,285 | The Chemistry Quality Eurolabels or European Quality Labels in Chemistry (Labels européens de Qualité en Chimie) is a marketing scheme for chemistry degrees at institutions located within the 45 countries involved in the Bologna process. Labels are awarded to qualifying institutions under the names are Eurobachelor and... | Chemistry Quality Eurolabels | 0.817158 |
12,286 | Reiner Salzer (Chair), TU Dresden, Dresden, Germany Pavel Drašar (Past-Chair), University of Chemistry and Technology, Prague, Czech Republic Evangelia Varella (Secretary), University of Thessaloniki, Thessaloniki, Greece a number of members | Chemistry Quality Eurolabels | 0.817158 |
12,287 | Raffaella Pagani (Chair) Pavel Drašar (Vice-Chair), University of Chemistry and Technology, Prague, Czech Republic Terry Mitchell (Secretary) a number of members | Chemistry Quality Eurolabels | 0.817158 |
12,288 | Pavel Drašar (Chair), University of Chemistry and Technology, Prague, Czech Republic Reiner Salzer (Vice-Chair), TU Dresden, Dresden, Germany Richard Whewell (Secretary 2008), Strathclyde University, Glasgow, Scotland, UK Evangelia Varella (Secretary 2008-2013), University of Thessaloniki, Thessaloniki, Greece a number... | Chemistry Quality Eurolabels | 0.817158 |
12,289 | Terry Mitchell (Chair) Raffaella Pagani (Vice-Chair) David Barr (Secretary), Royal Society of Chemistry, UK a number of members | Chemistry Quality Eurolabels | 0.817158 |
12,290 | Reiner Salzer (Chair), TU Dresden, Dresden, Germany Pavel Drašar (Past-Chair), University of Chemistry and Technology, Prague, Czech Republic Ray Wallace (Secretary), Nottingham Trent University, Nottingham, UK a number of members | Chemistry Quality Eurolabels | 0.817158 |
12,291 | The Wilcox Solar Observatory (WSO) is a solar observatory in Stanford, California that is used to produce daily observations of the magnetic and velocity field at the Sun's surface. It began daily observations of the Sun's mean magnetic field in May 1975. Formerly known as the Stanford Solar Observatory, it is operated... | Wilcox Solar Observatory | 0.817155 |
12,292 | A homomorphism f:A→B of rings is called formally smooth, formally unramified, or formally etale if for every A-algebra R with a nilpotent ideal I, the natural map from HomA(R/I, B) to HomA(R, B) is surjective, injective, or bijective. The algebra B is then called a formally smooth, formally unramified, or formally etal... | Embedding dimension | 0.817153 |
12,293 | 5. The Artin-Rees lemma establishes a certain stability of filtration by an ideal. ASL Acronym for algebra with straightening law. associated An associated prime of a module M over a ring R is a prime ideal p such that M has a submodule isomorphic to R/p. | Embedding dimension | 0.817153 |
12,294 | The altitude of an ideal is another name for its height. analytic 1. The analytic spread of an ideal of a local ring is the Krull dimension of the fiber at the special point of the local ring of the Rees algebra of the ideal. | Embedding dimension | 0.817153 |
12,295 | An absolutely simple point is one with a geometrically regular local ring. acceptable ring Acceptable rings are generalizations of excellent rings, with the conditions about regular rings in the definition replaced by conditions about Gorenstein rings. adic The I-adic topology on a ring has a base of neighborhoods of 0... | Embedding dimension | 0.817153 |
12,296 | absolute integral closure The absolute integral closure is the integral closure of an integral domain in an algebraic closure of the field of fractions of the domain. absolutely The word "absolutely" usually means "not relatively"; i.e., independent of the base field in some sense. It is often synonymous with "geometri... | Embedding dimension | 0.817153 |
12,297 | 3. Noether normalization represents a finitely generated algebra over a field as a finite module over a polynomial ring. normal A normal domain is an integral domain that is integrally closed in its quotient field. | Embedding dimension | 0.817153 |
12,298 | If the module happens to be an algebra this is much stronger than saying it is finitely generated as an algebra. 2. An algebra over a ring is called finitely generated if it is finitely generated as an algebra, which is much weaker than saying it is finitely generated as a module. | Embedding dimension | 0.817153 |
12,299 | finite type An algebra over a ring is said to be of finite type if it is finitely generated as an algebra. finitely generated 1. A module over a ring is called finitely generated if every element is a linear combination of a fixed finite number of elements. | Embedding dimension | 0.817153 |
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