In packed BCD (or simply packed decimal), each nibble represent a decimal digit. Packed BCD has been in use since at least the 1960s and is implemented in all IBM mainframe hardware since then. Most implementations are big endian, i.e. with the more significant digit in the upper half of each byte, and with the leftmost byte (residing at the lowest memory address) containing the most significant digits of the packed decimal value. The lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag.


In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. It is a time-reversed dual to the no-cloning theorem, which states that arbitrary states cannot be copied. This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust.


The idea originated with the Scottish physicist Alexander Crichton Mitchell, who was helped by the Royal Navy at HMS Tarlair. He had shown that the passage of a submarine past a cable formed an induction loop which induced a voltage of approximately a millivolt, detectable by a sensitive galvanometer. Voltages were also induced in the cable by random fluctuations in the Earth's magnetic field and electrical noise from the Glasgow tram lines.


For example, while the word representation properly designates a group homomorphism from a group G to GL(V), where V is a vector space, it is common to call V "a representation of G". Another common abuse of language consists in identifying two mathematical objects that are different, but canonically isomorphic. Other examples include identifying a constant function with its value, identifying a group with a binary operation with the name of its underlying set, or identifying to R 3 {\displaystyle \mathbb {R} ^{3}} the Euclidean space of dimension three equipped with a Cartesian coordinate system.


They are the with-carry analog of m-sequences or maximum length sequences. There are efficient algorithms for FCSR synthesis. This is the problem: given a prefix of a sequence, construct a minimal length FCSR that outputs the sequence.


In mathematics, the Littlewood–Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood–Richardson rule describes as counting certain skew tableaux. They occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of finite-dimensional representations of general linear groups, or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials. Littlewood–Richardson coefficients depend on three partitions, say λ , μ , ν {\displaystyle \lambda ,\mu ,\nu } , of which λ {\displaystyle \lambda } and μ {\displaystyle \mu } describe the Schur functions being multiplied, and ν {\displaystyle \nu } gives the Schur function of which this is the coefficient in the linear combination; in other words they are the coefficients c λ , μ ν {\displaystyle c_{\lambda ,\mu }^{\nu }} such that s λ s μ = ∑ ν c λ , μ ν s ν . {\displaystyle s_{\lambda }s_{\mu }=\sum _{\nu }c_{\lambda ,\mu }^{\nu }s_{\nu }.} The Littlewood–Richardson rule states that c λ , μ ν {\displaystyle c_{\lambda ,\mu }^{\nu }} is equal to the number of Littlewood–Richardson tableaux of skew shape ν / λ {\displaystyle \nu /\lambda } and of weight μ {\displaystyle \mu } .


In probability theory, Dudley's theorem is a result relating the expected upper bound and regularity properties of a Gaussian process to its entropy and covariance structure.


In some languages, including a number of Chinese varieties, many of the words that serve as prepositions can also be used as verbs. For instance, in Standard Chinese, 到 dào can be used in either a prepositional or a verbal sense: 我到北京去 wǒ dào Běijīng qù ("I go to Beijing"; qù, meaning "to go", is the main verb, dào is prepositional meaning "to") 我到了 wǒ dào le ("I have arrived"; dào is the main verb, meaning "to arrive")Because of this overlap, and the fact that a sequence of prepositional phrases and verb phrases often resembles a serial verb construction, Chinese prepositions (and those of other languages with similar grammatical structures) are often referred to as coverbs. As noted in previous sections, Chinese can also be said to have postpositions, although these can be analyzed as nominal (noun) elements. For more information, see the article on Chinese grammar, particularly the sections on coverbs and locative phrases.


Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences in the terminology they use and their particular rules. In modern usage, the first letter of the generic name is always capitalized in writing, while that of the specific epithet is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized in normal text (or underlined in handwriting).


These kinds of contemporary features help gain citizen a new level of technology. Majority of space in the chip has been made available for the private sector to use for their products and services. It might appear expensive for the private sector to use this card initially but once the number of citizens having critical mass is reached, it will be more profitable for the private sector to use this secure and universal platform.


In multitasking computing an operating system can handle several programs, both native applications or emulated software, that are running independent, parallel, together in the same time in the same device, using separated or shared resources and/or data, executing their tasks separately or together, while a user can switch on the fly between them or groups of them to use obtained effects or supervise purposes, without waste of time or waste of performance. In operating systems using GUI very often it is done by switching from an active window (or an object playing similar role) of a particular software piece to another one but of another software. A computer can compute results on the fly, or retrieve a previously stored result.


When the value of a large quantity of items has a Zipf's law distribution, the total value of the n most-valuable items is proportional to the n-th harmonic number. This leads to a variety of surprising conclusions regarding the long tail and the theory of network value. The Bertrand-Chebyshev theorem implies that, except for the case n = 1, the harmonic numbers are never integers.


In mathematics, the Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. It is named after Maurice Fréchet.


In number theory, integer factorization is the decomposition, of a positive integer into a product of integers. If the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime (in this case, one has a "product" of a single factor). When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist.


The newly created package provided a standard collection of common numerical operations on top of the Numeric array data structure. Shortly thereafter, Fernando Pérez released IPython, an enhanced interactive shell widely used in the technical computing community, and John Hunter released the first version of Matplotlib, the 2D plotting library for technical computing. Since then the SciPy environment has continued to grow with more packages and tools for technical computing.


In sociology a social rule refers to any social convention commonly adhered to in a society. These rules are not written in law or otherwise formalized. In social constructionism there is a great focus on social rules. It is argued that these rules are socially constructed, that these rules act upon every member of a society, but at the same time, are re-produced by the individuals.


In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods.


The coefficient field is called the base field. If constructive and algorithmic methods are the main issue it is Q ( x , y ) {\displaystyle \mathbb {Q} (x,y)} . The respective ring of differential operators is denoted by D = Q ( x , y )  {\displaystyle {\mathcal {D}}=\mathbb {Q} (x,y)} or D = F  {\displaystyle {\mathcal {D}}={\mathcal {F}}} .


The conditioning event is interpreted as evidence for the conditioned event. That is, P(A) is the probability of A before accounting for evidence E, and P(A|E) is the probability of A after having accounted for evidence E or after having updated P(A). This is consistent with the frequentist interpretation, which is the first definition given above.


Such strings may be translated into English by using "and", "while", "(in order) to" or other connectives, but some may have a more compact translation, as in the following example (from Hayao Miyazaki's Mononoke Hime) in which the actions of "following" and "coming" are simultaneous: The following sentence from Mandarin Chinese can be considered to contain four verb phrases in sequence: In Chinese, however, there is often no clear distinction between serial verb phrases and prepositional phrases. The first three "verbs" in the above sentence may alternatively be regarded as prepositions (this applies particularly to words like cóng which do not normally appear as independent verbs). Words used in that way in Chinese and in some other languages are commonly referred to as coverbs.


In the category of algebraic varieties, the product is given by the Segre embedding. In the category of semi-abelian monoids, the product is given by the history monoid.


In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224). These conditions are used in many proofs of Kurt Gödel's second incompleteness theorem. They are also closely related to axioms of provability logic.


In several interesting cases, the functor G {\displaystyle G} is an inclusion of a full subcategory not admitting a left adjoint. For example, the codensity monad of the inclusion of FinSet into Set is the ultrafilter monad associating to any set M {\displaystyle M} the set of ultrafilters on M . {\displaystyle M.} This was proven by Kennison and Gildenhuys, though without using the term "codensity".


Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science.


The solution of eq. 108 has the form where la, ma, ρ, are arbitrary functions of coordinates x, y bound by condition eq. 110 derived from eq. 107. To find higher terms of this decomposition, it is convenient to write the matrix of required quantities γab in the form where the symbol ~ means matrix transposition. Matrix H is symmetric and its trace is zero.


In most major handicapping systems, a golfer does not use their exact handicap (or handicap index) directly, but use it to produce their playing or course handicap. For some systems, this means simply rounding the exact handicap to the nearest whole number; however, systems that use slope ratings require a more complex calculation to produce a course handicap with some also factoring in the course rating: Course handicap = ( handicap index × slope rating ) 113 {\displaystyle {\mbox{Course handicap}}={\frac {({\mbox{handicap index}}\times {\mbox{slope rating}})}{\mbox{113}}}} or Course handicap = ( handicap index × slope rating ) 113 + ( course rating − par ) {\displaystyle {\mbox{Course handicap}}={\frac {({\mbox{handicap index}}\times {\mbox{slope rating}})}{\mbox{113}}}+({\mbox{course rating}}-{\mbox{par}})} The USGA and Golf Australia systems use the first calculation; the WHS, EGA, and Golf RSA systems use the second. Under CONGU's Unified Handicapping System the exact handicap is rounded to the nearest whole number to produce the playing handicap, and in the Argentinian system the exact handicap is used directly. A playing handicap may also refer to the stroke allowance for a given competition dependent on playing format, and is generally calculated as a percentage of the course handicap.


If tests are developed without an understanding of what the business considers to be an acceptable level of risk, it is possible to have a release candidate that passes all the available tests, but which the business leaders would not consider to be ready for release. For the test results to accurately indicate whether each release candidate meets business expectations, the approach to designing tests must be based on the business's tolerance for risks related to security, performance, reliability, and compliance. In addition to having unit tests that check code at a very granular bottom-up level, there is a need for a broader suite of tests to provide a top-down assessment of the release candidate's business risk.


In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x ‖ A x − y ‖ 2 + λ ‖ x ‖ 2 {\displaystyle \min _{x}\|Ax-y\|^{2}+\lambda \|x\|^{2}} to find a vector x {\displaystyle x} that is a stable solution to the regression problem.


In the NFS games Underground 2 to Carbon, the network (as Cingular) was shown as the mobile internet provider in the ingame voice/text message.


In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid. Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs, even sets in families of sets, and general position of point sets. It is hard to compute, but fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation.


Most mobile phone operators had charged for such calls previously, with Orange being the final major network to introduce such charges during December 2005. Certain helplines, such as those in the 0808 80x xxxx series had remained free from most networks on a voluntary basis and some niche operators, such as Giffgaff always offered freephone calls at no charge.The UK mobile operators offer an alternative product to organisations who wish to provide toll-free services - 5-digit voice short codes which are sold through mobile aggregators. 0500 numbers, introduced by Mercury Communications (later known as Cable & Wireless, now Vodafone) in 1982, were also freephone numbers (known as "FreeCall"), but were officially withdrawn by Ofcom on 3 June 2017.


In mechanical typewriters, the shift key functions by mechanically shifting some component so an alternate row of characters on typebars hits the paper. In an electronic system, by contrast, there is no necessary connection between the code points of unshifted and shifted values, though implementation is simpler if the code points of unshifted and shifted keys are related, most simply by a single bit differing. In electromechanical systems, this makes a significant difference in ease of implementation, as shifting must be accomplished by some physical linkage. For this reason, among others (such as ease of collation), the ASCII standard strove to organize the code points so that shifting could be implemented by simply toggling a bit.


In practice, implementations of Optimality Theory often make use of many concepts of phonological theories of representations, such as the syllable, the mora, or feature geometry. Completely distinct from these, there are sub-theories which have been proposed entirely within Optimality Theory, such as positional faithfulness theory, correspondence theory (McCarthy & Prince 1995), sympathy theory, stratal OT, and a number of theories of learnability, most notably by Bruce Tesar. Other theories within Optimality Theory are concerned with issues like the need for derivational levels within the phonological domain, the possible formulations of constraints, and constraint interactions other than strict domination.


If the tactic is applied to the second case, then the resulting partition can be considered as the standard partition for that operator. Stocks and Carrington in (Stocks & Carrington 1996) illustrate this situation with R ⊕ G = ( dom G ⋪ R ) ∪ G {\displaystyle R\oplus G=({\text{dom }}G\ntriangleleft R)\cup G} , where ⋪ {\displaystyle \ntriangleleft } means domain anti-restriction, by giving standard partitions for ⋪ {\displaystyle \ntriangleleft } and ∪ {\displaystyle \cup } and propagating them to calculate a partition for ⊕ {\displaystyle \oplus } . Specification Mutation (SM).


For example, a common weighting scheme consists in giving each neighbor a weight of 1/d, where d is the distance to the neighbor.The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required. A peculiarity of the k-NN algorithm is that it is sensitive to the local structure of the data.


In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir  ( α ) {\displaystyle \operatorname {Dir} ({\boldsymbol {\alpha }})} , is a family of continuous multivariate probability distributions parameterized by a vector α {\displaystyle {\boldsymbol {\alpha }}} of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process.


Its powers have poles of order 4 , 6 {\displaystyle 4,6} and so on. Therefore, such a P {\displaystyle P} has the gap sequence 1 , 3 , 5 , … , 2 g − 1. {\displaystyle 1,3,5,\dots ,2g-1.}


In project management, risk assessment is an integral part of the risk management plan, studying the probability, the impact, and the effect of every known risk on the project, as well as the corrective action to take should an incident be implied by a risk occur. Of special consideration in this area are the relevant codes of practice that are enforced in the specific jurisdiction. Understanding the regime of regulations that risk management must abide by is integral to formulating safe and compliant risk assessment practices.


In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division). However, other conventions are possible. Computers and calculators have various ways of storing and representing numbers; thus their definition of the modulo operation depends on the programming language or the underlying hardware. In nearly all computing systems, the quotient q and the remainder r of a divided by n satisfy the following conditions: This still leaves a sign ambiguity if the remainder is non-zero: two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur.


In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states. The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT algorithm. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison, hence the name.


If the univariate polynomial Ψ ℓ ( X , j ( E ) ) {\displaystyle \Psi _{\ell }(X,j(E))} has a root in F q {\displaystyle \mathbb {F} _{q}} , where j ( E ) {\displaystyle j(E)} denotes the j-invariant of E {\displaystyle E} , then ℓ {\displaystyle \ell } is an Elkies prime, and otherwise it is an Atkin prime. In the Elkies case, further computations involving modular polynomials are used to obtain a proper factor of the division polynomial ψ ℓ {\displaystyle \psi _{\ell }} . The degree of this factor is O ( ℓ ) {\displaystyle O(\ell )} , whereas ψ ℓ {\displaystyle \psi _{\ell }} has degree O ( ℓ 2 ) {\displaystyle O(\ell ^{2})} .


In the definition of NP-complete given above, the term reduction was used in the technical meaning of a polynomial-time many-one reduction. Another type of reduction is polynomial-time Turing reduction. A problem X {\displaystyle \scriptstyle X} is polynomial-time Turing-reducible to a problem Y {\displaystyle \scriptstyle Y} if, given a subroutine that solves Y {\displaystyle \scriptstyle Y} in polynomial time, one could write a program that calls this subroutine and solves X {\displaystyle \scriptstyle X} in polynomial time. This contrasts with many-one reducibility, which has the restriction that the program can only call the subroutine once, and the return value of the subroutine must be the return value of the program.


In particular, GXL was developed to enable interoperability between software reengineering tools and components, such as code extractors (parsers), analyzers and visualizers. GXL allows software reengineers to combine single-purpose tools especially for parsing, source code extraction, architecture recovery, data flow analysis, pointer analysis, program slicing, query techniques, source code visualization, object recovery, restructuring, refactoring, remodularization, etc., into a single powerful reengineering workbench. There are two innovative features in GXL that make it well-suited to an exchange format for software data. The conceptual data model is a typed, attributed, directed graph.


The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from a ( v ) = b ( v ) = d ( v ) = 1 , and e ( v ) = 0 . {\displaystyle a(v)=b(v)=d(v)=1,{\text{ and }}e(v)=0\,.}


In some economic models, the role of social networks in job searching often use exogenous job networks. Using this framework, Calvo-Armegnol and Jackson were able to point out some network related labor market issues.


In the early seventies Stephen Wiesner introduced a primitive called multiplexing in his seminal paper "Conjugate Coding", which was the starting point of quantum cryptography. Unfortunately it took more than ten years to be published. Even though this primitive was equivalent to what was later called 1–2 oblivious transfer, Wiesner did not see its application to cryptography.


These evolutionary lineages can thereby be portrayed through a phylogenetic tree, or cladogram, where varying relatedness amongst species is evidently depicted. Through this tree, organisms can be categorized by divergence from the common ancestor, and primitive characters, to clades of organisms with shared derived character states. Furthermore, cladograms allow researchers to view the changes and evolutionary alterations occurring in a species over time as they move from primitive characters to varying derived character states.Cladograms are important for scientists as they allow them to classify and hypothesize the origin and future of organisms. Cladograms allow scientists to propose their evolutionary scenarios about the lineage from a primitive trait to a derived one. By understanding how the trait came to be, scientists can hypothesize the environment that specific organism was in and how that affected the evolutionary adaptations of the trait that came to be.Other, more technical, terms for these two conditions—for example, "plesiomorphic" and "synapomorphic"—are frequently encountered; see the table below.


In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be.


Two moves in: At this point, the requirement that the graph be proper comes into effect, as a red area must be made which does not touch the existing one: Once the third region is coloured: Note that areas only count as touching if they share edges, not if they only share vertices, so this move is legal. The game continues, players moving alternately, until one player cannot make a move. This player loses. A possible continuation of the game is as follows (with each move numbered for clarity): Game over: In this outcome, the blue player has lost.


Scheme theory also unifies algebraic geometry with much of number theory, which eventually led to Wiles's proof of Fermat's Last Theorem. Formally, a scheme is a topological space together with commutative rings for all of its open sets, which arises from gluing together spectra (spaces of prime ideals) of commutative rings along their open subsets. In other words, it is a ringed space which is locally a spectrum of a commutative ring.


In recent years, several students of Jean-Paul Benzécri have refined MCA and incorporated it into a more general framework of data analysis known as geometric data analysis. This involves the development of direct connections between simple correspondence analysis, principal component analysis and MCA with a form of cluster analysis known as Euclidean classification.Two extensions have great practical use. It is possible to include, as active elements in the MCA, several quantitative variables.


If an industry uses little of a factor of production, a small increase in the output of that industry will not bid the price of that factor up. To a first-order approximation, firms in the industry will experience constant costs, and the industry supply curves will not slope up. If an industry uses an appreciable amount of that factor of production, an increase in the output of that industry will exhibit increasing costs.


The SQL standard defines the following properties: Language - defines the programming language in which the user-defined function is implemented; examples include SQL, C, C# and Java. Parameter style - defines the conventions that are used to pass the function parameters and results between the implementation of the function and the database system (only applicable if language is not SQL). Specific name - a name for the function that is unique within the database.


Links not in the MCF are paid nothing. This routing problem is one of the cases for which VCG is strategyproof and minimum. In 2004, it was shown that the expected VCG overpayment of an Erdős–Rényi random graph with n nodes and edge probability p, G ∈ G ( n , p ) {\displaystyle \scriptstyle G\in G(n,p)} approaches p 2 − p {\displaystyle {\frac {p}{2-p}}} as n, approaches ∞ {\displaystyle \scriptstyle \infty } , for n p = ω ( n log  n ) {\displaystyle np=\omega ({\sqrt {n\log n}})} . Prior to this result, it was known that VCG overpayment in G(n, p) is Ω ( 1 n p ) {\displaystyle \Omega \left({\frac {1}{np}}\right)} and O ( 1 ) {\displaystyle O(1)\,} with high probability given n p = ω ( log  n ) . {\displaystyle np=\omega (\log n).\,}


In order to effectively aid marketers in fully understanding customers and subsequently developing a strategic marketing plan, marketing automation platforms (MAPs) are designed to perform eight key tasks: Development and analysis of marketing campaigns and customers Management of marketing campaigns Appropriate customer data organization and storage Moving contacts from leads (marketing prospects) to customers Lead scoring to qualify leads by measuring their engagement level Integration of multiple touch-points such as email and social media Lead management Campaign performance analytics (i.e. open rate or click-through rates on emails, conversion rates on landing pages)


In mathematics, mathematical optimization (or optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives. In the simplest case, an optimization problem involves maximizing or minimizing a real function by selecting input values of the function and computing the corresponding values of the function. The solution process includes satisfying general necessary and sufficient conditions for optimality. For optimization problems, specialized notation may be used as to the function and its input(s).


The negation of an event in probability theory: Pr(A′) = 1 − Pr(A) (other notation also exists). The result of a transformation: Tx = x′ The transpose of a matrix (other notation also exists) The dual of a vector spaceThe prime is said to "decorate" the letter to which it applies.


In physics, the impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of a potential field U(r) created by an object that the projectile is approaching (see diagram). It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics. The impact parameter is related to the scattering angle θ by θ = π − 2 b ∫ r min ∞ d r r 2 1 − ( b / r ) 2 − 2 U / ( m v ∞ 2 ) , {\displaystyle \theta =\pi -2b\int _{r_{\text{min}}}^{\infty }{\frac {dr}{r^{2}{\sqrt {1-(b/r)^{2}-2U/(mv_{\infty }^{2})}}}},} where v∞ is the velocity of the projectile when it is far from the center, and rmin is its closest distance from the center.


In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or B . {\displaystyle \mathbb {B} .} The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements.


"The text also states that, "... over most of the area affected by the EMP the electric field strength on the ground would exceed 0.5Emax. For yields of less than a few hundred kilotons, this would not necessarily be true because the field strength at the Earth's tangent could be substantially less than 0.5Emax.


Supposing that the Kempe chain is connecting the green and yellow neighbors, red and blue must then necessarily not have a Kempe chain between them. So, when placing the original vertex v back into the graph, we can simply reverse the colors of the red vertex and its neighbors (including the red vertex, making it blue) and color vertex v as red. This results in a four-colored graph.


Such a formula can be made either true or false based on the values assigned to its propositional variables. The double turnstile notation ⊨ S {\displaystyle \vDash S} is used to indicate that S is a tautology. Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq".


In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality ρ(X1)+ρ(X2)+ρ(X1∪X2∪X3)+ρ(X1∪X2∪X4)+ρ(X3∪X4) ≤ ρ(X1∪X2)+ρ(X1∪X3)+ρ(X1∪X4)+ρ(X2∪X3)+ρ(X2∪X4) is satisfied.Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.


In some states, grand theft of a vehicle may be charged as "grand theft auto" (see motor vehicle theft for more information). Repeat offenders who continue to steal may become subject to life imprisonment in certain states.Sometimes the federal anti-theft-of-government-property law 18 U.S.C. § 640 is used to prosecute cases where the Espionage Act would otherwise be involved; the theory being that by retaining sensitive information, the defendant has taken a 'thing of value' from the government. For examples, see the Amerasia case and United States v. Manning.


Areas most at risk for flooding could be put to valuable uses that could be abandoned temporarily as people retreat to safer areas when a flood is imminent. Planning for flood safety involves many aspects of analysis and engineering, including: observation of previous and present flood heights and inundated areas, statistical, hydrologic, and hydraulic model analyses, mapping inundated areas and flood heights for future flood scenarios, long-term land use planning and regulation, engineering design and construction of structures to control or withstand flooding, intermediate-term monitoring, forecasting, and emergency-response planning, and short-term monitoring, warning, and response operations.Each topic presents distinct yet related questions with varying scope and scale in time, space, and the people involved. Attempts to understand and manage the mechanisms at work in floodplains have been made for at least six millennia.In the United States, the Association of State Floodplain Managers works to promote education, policies, and activities that mitigate current and future losses, costs, and human suffering caused by flooding and to protect the natural and beneficial functions of floodplains – all without causing adverse impacts. A portfolio of best practice examples for disaster mitigation in the United States is available from the Federal Emergency Management Agency.


In simple type theory objects are elements of various disjoint "types". Types are implicitly built up as follows. If τ1,...,τm are types then there is a type (τ1,...,τm) that can be thought of as the class of propositional functions of τ1,...,τm (which in set theory is essentially the set of subsets of τ1×...×τm). In particular there is a type () of propositions, and there may be a type ι (iota) of "individuals" from which other types are built.


If it is consistent with either state, Bob announces that the bit is invalid, since he cannot distinguish which state was transmitted based on the measurement. If on the other hand, one of the two candidate states was inconsistent with the observed measurement, Bob announces that the bit is valid since he can deduce the state (and therefore the secret bit). Consider for example the scenario that Alice transmits | ψ 00 ⟩ {\displaystyle |\psi _{00}\rangle } and announces the two states | ψ 00 ⟩ {\displaystyle |\psi _{00}\rangle } and | ψ 01 ⟩ {\displaystyle |\psi _{01}\rangle } .


In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters μ and b, then Y = eX has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.


The linear form ⟨ ϕ | {\displaystyle \langle \phi |} is a covector to | ϕ ⟩ {\displaystyle |\phi \rangle } , and the set of all covectors form a subspace of the dual vector space V ∨ {\displaystyle V^{\vee }} , to the initial vector space V {\displaystyle V} . The purpose of this linear form ⟨ ϕ | {\displaystyle \langle \phi |} can now be understood in terms of making projections on the state ϕ {\displaystyle {\boldsymbol {\phi }}} , to find how linearly dependent two states are, etc. For the vector space C n {\displaystyle \mathbb {C} ^{n}} , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplication.


Since you and your opponent are each infinitely wealthy, there is no limit to how long the game can last. This means the sample space Ω must consist of all possible infinite sequences of H {\displaystyle H} or T: {\displaystyle T:} However, after n {\displaystyle n} flips of the coin, you may want to determine or revise your betting strategy in advance of the next flip. The observed information at that point can be described in terms of the 2n possibilities for the first n {\displaystyle n} flips. Formally, since you need to use subsets of Ω, this is codified as the σ-algebra Observe that then where G ∞ {\displaystyle {\mathcal {G}}_{\infty }} is the smallest σ-algebra containing all the others.


Now we are taking balls randomly in such a way that the probability of taking a particular ball is proportional to its weight, but independent of what happens to the other balls. The number of balls taken of a particular color follows the binomial distribution. If the total number n of balls taken is known then the conditional distribution of the number of taken red balls for given n is Fisher's noncentral hypergeometric distribution.


In some types of computer video displays, the related technique of double buffering may be used to improve video performance. In this case, while the processor is updating the contents of one set of physical memory locations, the video generation hardware is accessing and displaying the contents of a second set. When the processor has completed its update, it can signal to the video display hardware to swap active banks, so that the transition visible on screen is free of artifacts or distortion. In this case, the processor may have access to all the memory at once, but the video display hardware is bank-switched between parts of the video memory. If the two (or more) banks of video memory contain slightly different images, rapidly cycling (page-flipping) between them can create animation or other visual effects that the processor might otherwise be too slow to carry out directly.


This always includes the content of general-purpose CPU registers, the CPU process status word, stack and frame pointers, etc. During context switch, the running process is stopped and another process runs. The kernel must stop the execution of the running process, copy out the values in hardware registers to its PCB, and update the hardware registers with the values from the PCB of the new process. Process control information is used by the OS to manage the process itself. This includes: Process scheduling state – The state of the process in terms of "ready", "suspended", etc., and other scheduling information as well, such as priority value, the amount of time elapsed since the process gained control of the CPU or since it was suspended. Also, in case of a suspended process, event identification data must be recorded for the event the process is waiting for; Process structuring information – the process's children id's, or the id's of other processes related to the current one in some functional way, which may be represented as a queue, a ring or other data structures; Interprocess communication information – flags, signals and messages associated with the communication among independent processes; Process Privileges – allowed/disallowed access to system resources; Process State – new, ready, running, waiting, dead; Process Number (PID) – unique identification number for each process (also known as Process ID); Program Counter (PC) – a pointer to the address of the next instruction to be executed for this process; CPU Registers – register set where process needs to be stored for execution for running state; CPU Scheduling Information – information scheduling CPU time; Memory Management Information – page table, memory limits, segment table; Accounting Information – amount of CPU used for process execution, time limits, execution ID etc.; I/O Status Information – list of I/O devices allocated to the process.


In mathematics, in particular number theory, an odd composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence U ( P , Q ) {\displaystyle U(P,Q)} with the discriminant D = P 2 − 4 Q , {\displaystyle D=P^{2}-4Q,} such that gcd ( N , D ) = 1 {\displaystyle \gcd(N,D)=1} and the rank appearance of N in the sequence U(P, Q) is 1 d ( N − ( D N ) ) , {\displaystyle {\frac {1}{d}}\left(N-\left({\frac {D}{N}}\right)\right),} where ( D N ) {\displaystyle \left({\frac {D}{N}}\right)} is the Jacobi symbol.


However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in Mesopotamia, where the Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving equations like the quadratic equation.


SQL query is tightly coupled and rigidly constrained by datatype within the specific database and can join tables and extract data from tables, and the result is generally a table, and a query can join tables by any columns which match by datatype. SPARQL query is the standard query language and protocol for Linked Open Data on the web and loosely coupled with the database so that it facilitates the reusability and can extract data through the relations free from the datatype, and not only extract but also generate additional knowledge graph with more sophisticated operations(logic: transitive/symmetric/inverseOf/functional). The inference based query (query on the existing asserted facts without the generation of new facts by logic) can be fast comparing to the reasoning based query (query on the existing plus the generated/discovered facts based on logic).


(TCP's sister protocol, UDP, does not do this. UDP simply sends data packets over the network in a best effort manner and assumes the packets are well-received.) An early problem noted with TCP's ACK mechanism was it did not work well in large multicast group communications.


The first of these is that the context changes functional interpretations of the same behaviors, such as the way “wright, right, right, rite, and write” are interpreted based on the context of the sentence. “Right” can be interpreted as a direction or as something good depending on the context. A second line of evidence says that errors are involved in human behavior as hierarchical organization.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 258, 1258, 2458, and 12458 are the patterns related to Braille pattern dots-146, since the two additional dots of kantenji patterns 0146, 1467, and 01467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in specific applications with various definitions.


The main reason for the design of this format is that it fits the maximum amount of data on a standard 80-character-wide screen or printer, while still being very easy to read and skim visually. Here the leftmost column represents the address at which the bytes represented by the following columns are located. CP/M and various DOS systems ran in real mode on the x86 CPUs, where addresses are composed of two parts (base and offset). In the above examples the final 00s are non-existent bytes beyond the end of the file. Some dump tools display other characters so that it is clear they are beyond the end of the file, typically using spaces or asterisks, e.g.: or


In programming languages that support recursive data types, it is possible to type the Y combinator by appropriately accounting for the recursion at the type level. The need to self-apply the variable x can be managed using a type (Rec a), which is defined so as to be isomorphic to (Rec a -> a). For example, in the following Haskell code, we have In and out being the names of the two directions of the isomorphism, with types: which lets us write: Or equivalently in OCaml: Alternatively:


In the Philippines, The Data Privacy Act of 2012 mandated the creation of the National Privacy Commission that would monitor and maintain policies that involve information privacy and personal data protection in the country. Modeled after the EU Data Protection Directive and the Asia-Pacific Economic Cooperation (APEC) Privacy Framework, the independent body would ensure compliance of the country with international standards set for data protection. The law requires government and private organizations composed of at least 250 employees or those which have access to the personal and identifiable information of at least 1000 people to appoint a Data Protection Officer that would assist in regulating the management of personal information in such entities.In summary, the law identifies important points regarding the handling of personal information as follows: Personal information must be collected for reasons that are specified, legitimate, and reasonable.


In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we have y x = ( − 1 ) | x | | y | x y , {\displaystyle yx=(-1)^{|x||y|}xy,} where |x| denotes the grade of the element and is 0 or 1 (in Z2) according to whether the grade is even or odd, respectively. Equivalently, it is a superalgebra where the supercommutator  = x y − ( − 1 ) | x | | y | y x {\displaystyle =xy-(-1)^{|x||y|}yx} always vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as skew-commutative associative algebras to emphasize the anti-commutation, or, to emphasize the grading, graded-commutative or, if the supercommutativity is understood, simply commutative. Any commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even).


In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set.


This is possible because the logarithm of a product is the sum of the logarithms of the factors: provided that b, x and y are all positive and b ≠ 1. The slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century, and who also introduced the letter e as the base of natural logarithms.Logarithmic scales reduce wide-ranging quantities to smaller scopes.


In USAID, the use of a program cycle, "codified in the Automated Directive Systems (ADS) 201, is USAID's operational model for planning, delivering, assessing, and adapting development programming in a given region or country to achieve more effective and sustainable results in order to advance U.S. foreign policy". Relatedly, within the agency there exists resources regarding adaptive management decision cycles.


As properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set { 1 , 2 , … , n } {\displaystyle \{1,2,\ldots ,n\}} that are considered for studying permutations. In elementary combinatorics, the k-permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. When k is equal to the size of the set, these are the permutations of the set.


In meteorology a ridge or barometric ridge is an elongated area of relatively high atmospheric pressure compared to the surrounding environment, without being a closed circulation. It is associated with an area of maximum anticyclonic curvature of wind flow. The ridge originates in the center of an anticyclone and sandwiched between two low-pressure areas, and the locus of the maximum curvature is called the ridge line. This phenomenon is the opposite of a trough.


For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth. : 694 However, the concept of multisets predates the coinage of the word multiset by many centuries.


In the SVP, a basis of a vector space V and a norm N (often L2) are given for a lattice L and one must find the shortest non-zero vector in V, as measured by N, in L. In other words, the algorithm should output a non-zero vector v such that ‖ v ‖ N = λ ( L ) {\displaystyle \|v\|_{N}=\lambda (L)} . In the γ-approximation version SVPγ, one must find a non-zero lattice vector of length at most γ ⋅ λ ( L ) {\displaystyle \gamma \cdot \lambda (L)} for given γ ≥ 1 {\displaystyle \gamma \geq 1} .


Error correction does not seem to have a direct influence on learning a second language. Instruction may affect the rate of learning, but the stages remain the same.


In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take "on average" over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of this probability space.


In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc. Various notations have been used to represent hyperoperations. One such notation is H n ( a , b ) {\displaystyle H_{n}(a,b)} . Knuth's up-arrow notation ↑ {\displaystyle \uparrow } is another. For example: the single arrow ↑ {\displaystyle \uparrow } represents exponentiation (iterated multiplication) the double arrow ↑↑ {\displaystyle \uparrow \uparrow } represents tetration (iterated exponentiation) the triple arrow ↑↑↑ {\displaystyle \uparrow \uparrow \uparrow } represents pentation (iterated tetration) The general definition of the up-arrow notation is as follows (for a ≥ 0 , n ≥ 1 , b ≥ 0 {\displaystyle a\geq 0,n\geq 1,b\geq 0} ): Here, ↑ n {\displaystyle \uparrow ^{n}} stands for n arrows, so for example The square brackets are another notation for hyperoperations.


This is a PBE - it is a best-response for both sender and receiver. The sender's strategy is: never give. Suppose the receiver's beliefs when receiving a gift is that the sender is a friend with probability q {\displaystyle q} , where q {\displaystyle q} is any number in  {\displaystyle } .


The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions and to systems of equations.


In one special case two covariates, say j and k, are identical for each observation, so that x ( j ) = x ( k ) {\displaystyle x_{(j)}=x_{(k)}} , where x ( j ) , i = x ( k ) , i {\displaystyle x_{(j),i}=x_{(k),i}} . Then the values of β j {\displaystyle \beta _{j}} and β k {\displaystyle \beta _{k}} that minimize the lasso objective function are not uniquely determined. In fact, if some β ^ {\displaystyle {\hat {\beta }}} in which β ^ j β ^ k ≥ 0 {\displaystyle {\hat {\beta }}_{j}{\hat {\beta }}_{k}\geq 0} , then if s ∈  {\displaystyle s\in } replacing β ^ j {\displaystyle {\hat {\beta }}_{j}} by s ( β ^ j + β ^ k ) {\displaystyle s({\hat {\beta }}_{j}+{\hat {\beta }}_{k})} and β ^ k {\displaystyle {\hat {\beta }}_{k}} by ( 1 − s ) ( β ^ j + β ^ k ) {\displaystyle (1-s)({\hat {\beta }}_{j}+{\hat {\beta }}_{k})} , while keeping all the other β ^ i {\displaystyle {\hat {\beta }}_{i}} fixed, gives a new solution, so the lasso objective function then has a continuum of valid minimizers. Several variants of the lasso, including the Elastic net regularization, have been designed to address this shortcoming.


Whatever we may say something 'is' obviously is not the 'something' on the silent levels." By making it a 'mental' habit to find and keep one's bearings among the ordered stages, general semantics training seeks to sharpen internal orientation much as a GPS device may sharpen external orientation. Once trained, general semanticists affirm, a person will act, respond, and make decisions more appropriate to any given set of happenings.


Given a data array X, the basic Backus-Gilbert inverse is: H θ = C − 1 G θ G θ T C − 1 G θ {\displaystyle \mathbf {H} _{\theta }={\frac {\mathbf {C} ^{-1}\mathbf {G} _{\theta }}{\mathbf {G} _{\theta }^{T}\mathbf {C} ^{-1}\mathbf {G} _{\theta }}}} where C is the covariance matrix of the data, and Gθ is an a priori constraint representing the source θ for which a solution is sought. Regularization is implemented by "whitening" the covariance matrix: C ′ = C + λ I {\displaystyle \mathbf {C} '=\mathbf {C} +\lambda \mathbf {I} } with C′ replacing C in the equation for Hθ. Then, H θ T X {\displaystyle \mathbf {H} _{\theta }^{T}\mathbf {X} } is an estimate of the activity of the source θ.


In some countries such as Germany, the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with the first digit of the multiplier: 23958233 · 5830 ——————————————— 119791165 191665864 71874699 00000000 ——————————————— 139676498390 Below pseudocode describes the process of above multiplication. It keeps only one row to maintain the sum which finally becomes the result. Note that the '+=' operator is used to denote sum to existing value and store operation (akin to languages such as Java and C) for compactness.


{\cdot }\,} _{i\in I}A_{i}} ). A standard way for building the disjoint union is to define A {\displaystyle A} as the set of ordered pairs ( x , i ) {\displaystyle (x,i)} such that x ∈ A i , {\displaystyle x\in A_{i},} and the injection A i → A {\displaystyle A_{i}\to A} as x ↦ ( x , i ) . {\displaystyle x\mapsto (x,i).}


In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data.


We can show that c = 2 ℵ 0 {\displaystyle {\mathfrak {c}}=2^{\aleph _{0}}} , this also being the cardinality of the set of all subsets of the natural numbers. The continuum hypothesis says that ℵ 1 = 2 ℵ 0 {\displaystyle \aleph _{1}=2^{\aleph _{0}}} , i.e. 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} is the smallest cardinal number bigger than ℵ 0 {\displaystyle \aleph _{0}} , i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers. The continuum hypothesis is independent of ZFC, a standard axiomatization of set theory; that is, it is impossible to prove the continuum hypothesis or its negation from ZFC—provided that ZFC is consistent. For more detail, see § Cardinality of the continuum below.


For instance, the set of all integers (including negative numbers) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still (only) countably infinite. Nevertheless, there are sets, such as the set of real numbers, that can be shown to be "too large" to admit a bijection with the natural numbers, and these sets are called "uncountable." Sets for which there exists a bijection between them are said to have the same cardinality, and in the most general sense counting a set can be taken to mean determining its cardinality.


In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue.


A line l in a projective plane Π is a translation line if the group of all elations with axis l acts transitively on the points of the affine plane obtained by removing l from the plane Π, Πl (the affine derivative of Π). A projective plane with a translation line is called a translation plane. The affine plane obtained by removing the translation line is called an affine translation plane. While it is often easier to work with projective planes, in this context several authors use the term translation plane to mean affine translation plane.


The LRN removes the need for the public telephone number to identify the local exchange carrier. If a subscriber changes to another telephone service provider, the current telephone number can be retained, and only the LRN needs to be changed. In addition to supporting service provider telephone number portability, an LRN also supports the possibility of two other types of number portability: service portability (for example, ordinary service to ISDN) and geographic portability.


In order to define a custom structure type using Oracle Database one could use statements such as these:Such structure type can be then used to create a table that would also hold all columns defined in Person_Type:Custom structure types support inheritance, which means that one can create another type that inherits from previous. NOT FINAL statement must be however included in a base structure type definition in order to allow for creation of any other subtypes.Student_Type then could be used in order to create a Student_Table which will include all columns defined in Person_Type as well. Primary Key and Constraints should be defined during or after creation of table and cannot be defined inside structure type itself.Each custom structure type can also contain other types in order to support more complex structures:


In the 19th century, Sir William Thomson made a hypothesis that the chemical elements were based upon knotted vortices in the aether. In an attempt to make a periodic table of the elements, P. G. Tait, C. N. Little and others started to attempt to count all possible knots. Because their work predated the invention of the digital computer, all work had to be done by hand.


VoIP systems are based on Internet standards and technology which have not previously attempted to satisfy such complex and demanding requirements as those that specify call control. An alternative name often used is call processing.In a VoIP network, call control is one of three major categories of communications traffic, the other two being call signaling and media communications. Call control uses Q.931, a connection protocol for digital networks, especially VoIP systems. Messages are transmitted as octets as specified in ITU H.245, which resolves the type of call media to be used (for example, conventional call, videoconferencing, or VoIP), and then manages the connection after it has been established. Call control functions include, but are not limited to, the determination of master/slave status for the endpoints, monitoring of the status of the endpoints, modification of the parameters of a connection, termination of a connection, and restarting a terminated or failed connection.


These critics suggest that direct parameters would be better placed on the operational uses of data in general. Opponents of regulatory reform say this would, perhaps unintentionally, drastically inhibit businesses ability to utilize the data for positive measures. Furthermore, because singular data points may be used across a large array of industries, sector-specific legislation may prove fruitless.


In pseudocode the algorithm can be stated as: Begin 1) Objective function: f ( x ) , x = ( x 1 , x 2 , . . .


An example is the assignment of the code EUR to the euro. ISO 4217 amendment 94, which created this code, states "The code element 'EU' has been reserved by the ISO 3166 Maintenance Agency for use within ISO 4217 where 'R' has been appended to make an acceptable mnemonic code." Here the R comes from the third letter in the word "euro".


The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it.The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems.


When an item in the left column is related to an item across the top, a mark is placed in the intersecting cell. The number of relationships are added up for each row and each column.


Thus, metaheuristics usually allow to meet the resolution delays imposed in the industrial field as well as they allow to study general problem classes instead that particular problem instances. In general, many of the best performing techniques in precision and effort to solve complex and real-world problems are metaheuristics. Their fields of application range from combinatorial optimization, bioinformatics, and telecommunications to economics, software engineering, etc. These fields are full of many tasks needing fast solutions of high quality.


In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. This is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. The name comes from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling.


In test-driven development (TDD), which is frequently used in both extreme programming and scrum, unit tests are created before the code itself is written. When the tests pass, that code is considered complete. The same unit tests are run against that function frequently as the larger code base is developed either as the code is changed or via an automated process with the build. If the unit tests fail, it is considered to be a bug either in the changed code or the tests themselves. The unit tests then allow the location of the fault or failure to be easily traced. Since the unit tests alert the development team of the problem before handing the code off to testers or clients, potential problems are caught early in the development process.


In the 1970s, there was a two-player game made by Tri-ang Toys & Games called Check Lines, in which the board consisted of eleven holes arranged in a geometrical pattern of twelve straight lines each containing three of the holes. Each player had exactly five tokens and played in turn placing one token in any of the holes. The winner was the first player whose tokens were arranged in two lines of three (which by definition were intersecting lines). If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.


In optimal control theory, the evolution of n state variables through time depends at any time on their own values and on the values of k control variables. With linear evolution, matrices of coefficients appear in the state equation (equation of evolution). In some problems the values of the parameters in these matrices are not known with certainty, in which case there are random matrices in the state equation and the problem is known as one of stochastic control. : ch. 13 A key result in the case of linear-quadratic control with stochastic matrices is that the certainty equivalence principle does not apply: while in the absence of multiplier uncertainty (that is, with only additive uncertainty) the optimal policy with a quadratic loss function coincides with what would be decided if the uncertainty were ignored, the optimal policy may differ if the state equation contains random coefficients.


The position of an element in a sequence is its rank or index; it is the natural number for which the element is the image. The first element has index 0 or 1, depending on the context or a specific convention. In mathematical analysis, a sequence is often denoted by letters in the form of a n {\displaystyle a_{n}} , b n {\displaystyle b_{n}} and c n {\displaystyle c_{n}} , where the subscript n refers to the nth element of the sequence; for example, the nth element of the Fibonacci sequence F {\displaystyle F} is generally denoted as F n {\displaystyle F_{n}} . In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory; infinite sequences are called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.


In most languages that provide this feature, a procedural parameter f of a subroutine P can be called inside the body of P as if it were an ordinary procedure: procedure P(f): return f(6,3) * f(2,1) When calling the subroutine P, one must give it one argument, that must be some previously defined function compatible with the way P uses its parameter f. For example, if we define procedure plus(x, y): return x + y then we may call P (plus), and the result will be plus(6,3) * plus(2,1) = (6 + 3)*(2 + 1) = 27. On the other hand, if we define procedure quot(u, v): return u/v then the call P (quot) will return quot(6,3)*quot(2,1) = (6/3)*(2/1) = 4. Finally, if we define procedure evil(z) return z + 100 then the call P (evil) will not make much sense, and may be flagged as an error.


In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem. Since the theorem has now been proven, these are now of mainly historical significance, though the Mirimanoff polynomials are interesting in their own right. The theorem is due to Dmitry Mirimanoff.


In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.


In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter. This distribution is flexible in terms of its ability to allow a moderate over-dispersion in the data. The authors Kemp and Kemp have called it "Hermite distribution" from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of (modified) Hermite polynomials.


The typical metric used in this case the Lee distance. There exist a Gray isometry between Z 2 2 m {\displaystyle \mathbb {Z} _{2}^{2m}} (i.e. GF(22m)) with the Hamming distance and Z 4 m {\displaystyle \mathbb {Z} _{4}^{m}} (also denoted as GR(4,m)) with the Lee distance. == References ==


In mathematical logic, proof compression by splitting is an algorithm that operates as a post-process on resolution proofs. It was proposed by Scott Cotton in his paper "Two Techniques for Minimizing Resolution Proof".The Splitting algorithm is based on the following observation: Given a proof of unsatisfiability π {\displaystyle \pi } and a variable x {\displaystyle x} , it is easy to re-arrange (split) the proof in a proof of x {\displaystyle x} and a proof of ¬ x {\displaystyle \neg x} and the recombination of these two proofs (by an additional resolution step) may result in a proof smaller than the original. Note that applying Splitting in a proof π {\displaystyle \pi } using a variable x {\displaystyle x} does not invalidates a latter application of the algorithm using a differente variable y {\displaystyle y} . Actually, the method proposed by Cotton generates a sequence of proofs π 1 π 2 … {\displaystyle \pi _{1}\pi _{2}\ldots } , where each proof π i + 1 {\displaystyle \pi _{i+1}} is the result of applying Splitting to π i {\displaystyle \pi _{i}} .


In political science, the policy cycle is a tool used for analyzing the development of a policy. It can also be referred to as a "stages model" or "stages heuristic". It is thus a rule of thumb rather than the actual reality of how policy is created, but has been influential in how political scientists looked at policy in general. It was developed as a theory from Harold Lasswell's work.


This is primarily because adding another Opteron processor increases memory bandwidth, while that is not always the case for Xeon systems, and the fact that the Opterons use a switched fabric, rather than a shared bus. In particular, the Opteron's integrated memory controller allows the CPU to access local RAM very quickly. In contrast, multiprocessor Xeon system CPUs share only two common buses for both processor-processor and processor-memory communication. As the number of CPUs increases in a typical Xeon system, contention for the shared bus causes computing efficiency to drop. Intel migrated to a memory architecture similar to the Opteron's for the Intel Core i7 family of processors and their Xeon derivatives.


Then, they consider the above LP with one additional constraint:The additional constraint guarantees that the "vacant space" in the bins can be filled by the small items. The dual of this LP is more complex and cannot be solved by a simple knapsack-problem separation oracle. Csirik, Johnson and Kenyon present a different method to solve it approximately in time exponential in 1/epsilon. Jansen and Solis-Oba present an improved method to solve it approximately in time exponential in 1/epsilon.


In mathematics, especially group theory, the centralizer (also called commutant) of a subset S in a group G is the set C G  ( S ) {\displaystyle \operatorname {C} _{G}(S)} of elements of G that commute with every element of S, or equivalently, such that conjugation by g {\displaystyle g} leaves each element of S fixed. The normalizer of S in G is the set of elements N G ( S ) {\displaystyle \mathrm {N} _{G}(S)} of G that satisfy the weaker condition of leaving the set S ⊆ G {\displaystyle S\subseteq G} fixed under conjugation. The centralizer and normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers and normalizers of suitable subsets S. Suitably formulated, the definitions also apply to semigroups.


In mathematics, the Mertens conjecture is the statement that the Mertens function M ( n ) {\displaystyle M(n)} is bounded by ± n {\displaystyle \pm {\sqrt {n}}} . Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in Stieltjes (1905)), and again in print by Franz Mertens (1897), and disproved by Andrew Odlyzko and Herman te Riele (1985). It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor.


relation algebra to specify information systems.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 58, 158, 458, and 1458 are the patterns related to Braille pattern dots-46, since the two additional dots of kantenji patterns 046, 467, and 0467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Let ℓ {\displaystyle \ell } be the single literal of the unit clause of η ′ {\displaystyle \eta ^{\prime }} . Then any occurrence of ℓ ¯ {\displaystyle {\overline {\ell }}} in the subproof above η {\displaystyle \eta } will not be cancelled by resolution inferences with η ′ {\displaystyle \eta ^{\prime }} anymore. Consequently, ℓ ¯ {\displaystyle {\overline {\ell }}} will be propagated downwards when the proof is fixed and will appear in the clause of η {\displaystyle \eta } .


In some texts, especially in random matrix theory, authors have found it more convenient to use a matrix argument in the Jack function. The connection is simple. If X {\displaystyle X} is a matrix with eigenvalues x 1 , x 2 , … , x m {\displaystyle x_{1},x_{2},\ldots ,x_{m}} , then J κ ( α ) ( X ) = J κ ( α ) ( x 1 , x 2 , … , x m ) . {\displaystyle J_{\kappa }^{(\alpha )}(X)=J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m}).}


In some cases, FPUs may be specialized, and divided between simpler floating-point operations (mainly addition and multiplication) and more complicated operations, like division. In some cases, only the simple operations may be implemented in hardware or microcode, while the more complex operations are implemented as software. In some current architectures, the FPU functionality is combined with SIMD units to perform SIMD computation; an example of this is the augmentation of the x87 instructions set with SSE instruction set in the x86-64 architecture used in newer Intel and AMD processors.


In some older virtual memory operating systems, space in swap backing store is reserved when programs allocate memory for runtime data. Operating system vendors typically issue guidelines about how much swap space should be allocated.


In most legal proceedings, one party has a burden of proof, which requires it to present prima facie evidence for all of the essential facts in its case. If it cannot, its claim may be dismissed without any need for a response by other parties. A prima facie case might not stand or fall on its own; if an opposing party introduces other evidence or asserts an affirmative defense, it can be reconciled only with a full trial.


and by Stanley P. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers. Over-relaxation methods had been used before the work of Young and Frankel. An example is the method of Lewis Fry Richardson, and the methods developed by R. V. Southwell. However, these methods were designed for computation by human calculators, requiring some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young Jr.


In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.


In the 1993 book "Information Coordination: The Management of Information Models, Systems, and Organizations" Veryard gives a snapshot of the state of the art around these subjects. "Maximizing the value of corporate data depends upon being able to manage information models both within and between businesses. A centralized information model is not appropriate for many organizations," Veryard explains.His book "takes the approach that multiple information models exist and the differences and links between them have to be managed. Coordination is currently an area of both intensive theoretical speculation and of practical research and development. Information Coordination explains practical guidelines for information management, both from on-going research and from recent field experience with CASE tools and methods".


Only call packets from or destined to a phone serviced by the concentrator actually are processed by the concentrator — nonlocal phones' time slots just pass through the concentrator unchanged. If the concentrator malfunctions, a fail-safe relay connects the "in" wires to the "out" wires, and nonlocal phones detect no difference. The central switch periodically counts concentrators, and schedules maintenance, probably before users notice the failure. Concentrators for several hundred customers can be threaded on this loop like pearls. The interface between remote concentrators and their parent telephone switches has been standardised by ETSI as the V5 interface.


Considering even the simple case of exponentiation as a primitive recursive function, and that the composition of primitive recursive functions is primitive recursive, one can begin to see how quickly a primitive recursive function can grow. And any function that can be computed by a Turing machine in a running time bounded by a primitive recursive function is itself primitive recursive. So it is difficult to imagine a practical use for full μ-recursion where primitive recursion will not do, especially since the former can be simulated by the latter up to exceedingly long running times. And in any case, Kurt Gödel's first incompleteness theorem and the halting problem imply that there are while loops that always terminate but cannot be proven to do so; thus it is unavoidable that any requirement for a formal proof of termination must reduce the expressive power of a programming language. While we have shown that every loop that terminates has a variant, this does not mean that the well-foundedness of the loop iteration can be proven.


Abstract datatypes are structures of concrete datatypes, with a new name assigned. For example, a list of integers could be called integer_list. In object-oriented jargon, abstract datatypes are called classes.


Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence without an outside argument. The values of the loadings L {\displaystyle L} , the averages μ {\displaystyle \mu } , and the variances of the "errors" ε {\displaystyle \varepsilon } must be estimated given the observed data X {\displaystyle X} and F {\displaystyle F} (the assumption about the levels of the factors is fixed for a given F {\displaystyle F} ). The "fundamental theorem" may be derived from the above conditions: ∑ i z a i z b i = ∑ j ℓ a j ℓ b j + ∑ i ε a i ε b i {\displaystyle \sum _{i}z_{ai}z_{bi}=\sum _{j}\ell _{aj}\ell _{bj}+\sum _{i}\varepsilon _{ai}\varepsilon _{bi}} The term on the left is the ( a , b ) {\displaystyle (a,b)} -term of the correlation matrix (a p × p {\displaystyle p\times p} matrix derived as the product of the p × N {\displaystyle p\times N} matrix of standardized observations with its transpose) of the observed data, and its p {\displaystyle p} diagonal elements will be 1 {\displaystyle 1} s. The second term on the right will be a diagonal matrix with terms less than unity.


The equivalence class of a set A under this relation, then, consists of all those sets which have the same cardinality as A. There are two ways to define the "cardinality of a set": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each equivalence class.


In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. For a directed graph, a similar problem is known as Minimum Bottleneck Spanning Arborescence (MBSA).


In telephony, a service switching point (SSP) is the telephone exchange that initially responds, when a telephone caller dials a number, by sending a query to a central database called a service control point (SCP) so that the call can be handled. The service switching point uses the Signalling System No. 7 (SS7) protocols which are responsible for the call setup, management, and termination with other service switching points.


In mathematics and statistics, the arithmetic mean ( arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic. In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent.


Clustering of machines and parts is one of the most popular production flow analysis methods. The algorithms for machine part grouping include Rank Order Clustering, Modified Rank Order Clustering, and Similarity coefficients. There are also a number of mathematical models and algorithms to aid in planning a cellular manufacturing center, which take into account a variety of important variables such as, "multiple plant locations, multi-market allocations with production planning and various part mix." Once these variables are determined with a given level of uncertainty, optimizations can be performed to minimize factors such as, "total cost of holding, inter-cell material handling, external transportation, fixed cost for producing each part in each plant, machine and labor salaries."


In some data exfiltration scenarios, a large amount of aggregated data may be exfiltrated. However, in these and other scenarios, it is likely that certain types of data may be targeted. Types of data that are targeted includes: Usernames, associated passwords, and other system authentication related information Information associated with strategic decisions Cryptographic keys Personal financial information Social security numbers and other personally identifiable information (PII) Mailing addresses United States National Security Agency hacking tools


In the 1960s, theoretical research in computer science on regular expressions and finite automata led to the discovery that context-free grammars are equivalent to nondeterministic pushdown automata. These grammars were thought to capture the syntax of computer programming languages. The first high-level computer programming languages were under development at the time (see History of programming languages) and writing compilers was difficult. But using context-free grammars to help automate the parsing part of the compiler simplified the task.


In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of invertible 2 × 2 integer matrices of determinant 1 in which the off-diagonal entries are even. More generally, the notion of congruence subgroup can be defined for arithmetic subgroups of algebraic groups; that is, those for which we have a notion of 'integral structure' and can define reduction maps modulo an integer. The existence of congruence subgroups in an arithmetic group provides it with a wealth of subgroups, in particular it shows that the group is residually finite. An important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. Congruence subgroups of 2×2 matrices are fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more general arithmetic groups.


In mathematics, a self-descriptive number is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b−1) counts how many instances of digit n are in m.


In music theory, an inversion is a type of change to intervals, chords, voices (in counterpoint), and melodies. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.


It is not a cogent and simple way. It is claimed to be precise, but precise for what purpose?


In software engineering, a software development process is a process of planning and managing software development. It typically involves dividing software development work into smaller, parallel, or sequential steps or sub-processes to improve design and/or product management. It is also known as a software development life cycle (SDLC).


In software, a stack buffer overflow or stack buffer overrun occurs when a program writes to a memory address on the program's call stack outside of the intended data structure, which is usually a fixed-length buffer. Stack buffer overflow bugs are caused when a program writes more data to a buffer located on the stack than what is actually allocated for that buffer. This almost always results in corruption of adjacent data on the stack, and in cases where the overflow was triggered by mistake, will often cause the program to crash or operate incorrectly. Stack buffer overflow is a type of the more general programming malfunction known as buffer overflow (or buffer overrun).


In order to formulate a classical field theory, the following structures are needed:


The classes in a class diagram represent both the main elements, interactions in the application, and the classes to be programmed. In the diagram, classes are represented with boxes that contain three compartments: The top compartment contains the name of the class. It is printed in bold and centered, and the first letter is capitalized.


The algorithm performs a series of iterations, each consisting of two basic steps: Authority update: Update each node's authority score to be equal to the sum of the hub scores of each node that points to it. That is, a node is given a high authority score by being linked from pages that are recognized as Hubs for information. Hub update: Update each node's hub score to be equal to the sum of the authority scores of each node that it points to.


The term generalized inverse is sometimes used as a synonym for pseudoinverse. A common use of the pseudoinverse is to compute a "best fit" (least squares) solution to a system of linear equations that lacks a solution (see below under § Applications). Another use is to find the minimum (Euclidean) norm solution to a system of linear equations with multiple solutions.


In the absence of interference, there are two factors at play when recalling a list of items: the recency and the primacy effects. The recency effect occurs when the short-term memory is used to remember the most recent items, and the primacy effect occurs when the long-term memory has encoded the earlier items. The recency effect can be eliminated if there is a period of interference between the input and the output of information extending longer than the holding time of short-term memory (15–30 seconds). This occurs when a person is given subsequent information to recall preceding the recall of the initial information.


The trade secret law varies from country to country, unlike the case for patents, trademarks and copyright for which there are formal conventions through which subscribing countries grant the same protection to the property as the others; examples of which are the Paris Convention for the Protection of Industrial Property and the World Intellectual Property Organization (WIPO), under United Nations, a supportive organization designed "to encourage creative activity,  to promote the protection of intellectual property throughout the world". The World Trade Organization defined a trade secret by the following criteria: Natural and legal persons shall have the possibility of preventing information lawfully within their control from being disclosed to, acquired by, or used by others without their consent in a manner contrary to honest commercial practices (10) so long as such information: (a) is secret in the sense that it is not, as a body or in the precise configuration and assembly of its components, generally known among or readily accessible to persons within the circles that normally deal with the kind of information in question; (b) has commercial value because it is secret; and (c) has been subject to reasonable steps under the circumstances, by the person lawfully in control of the information, to keep it secret. For purposes of illustration, the following may be a provision in a license agreement serving to define know-how:- Know-how shall mean technical data, formulas, standards, technical information, specifications, processes, methods, codebooks, raw materials, as well as all information, knowledge, assistance, trade practices and secrets, and improvements thereto, divulged, disclosed, or in any way communicated to the Licensee under this Agreement, unless such information was, at the time of disclosure, or thereafter becomes part of the general knowledge or literature which is generally available for public use from other lawful sources. The burden of proving that any information disclosed hereunder is not confidential information shall rest on the licensee.


Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them. In this context, statements become well-formed formulas of some formal language.


Rack (1984 and 2013), for the case n = 3, the explicit values of the optimal (unique and zero-symmetric) 4 interpolation nodes and the explicit value of the minimal Lebesgue constant are known. All arbitrary optimal sets of 4 interpolation nodes in  when n = 3 have been explicitly determined, in two different but equivalent fashions, by H.-J. Rack and R. Vajda (2015). The Padua points provide another set of nodes with slow growth (although not as slow as the Chebyshev nodes) and with the additional property of being a unisolvent point set.


While Principles of Operation discusses the TLB in general terms, the details are not part of the architecture and vary from model to model. Starting with the 3031, 3032, and 3033 processor complexes, IBM offered a feature called Dual-address Space: 5-13–5-17, Dual-Address-Space Control: 5-17–5-20, DAS Authorization Mechanisms: 5-21–5-24, PC-Number Translation (DAS), which allows a program to switch between the translation tables for two address spaces, referred to as primary address space (CR1) and secondary address space (CR7), and to move data between the address spaces subject to protection key. DAS supports a translation table to convert a 16-bit address space number (ASN) to an STD, with privileged instructions to load the STD into CR1 (primary) or CR7 (secondary).


10 consecutive 0 bits followed by a 1 bit provide frame synchronization.One frame is sent at the desired sample rate, for a bit rate of 256×48 kHz = 12.288 Mbit/s. This is twice the baud rate used by S/PDIF (3.072 Mbit/s, doubled by biphase coding to 6.144 MBd), but still within the specified 15 Mbaud capacity of the popular TOTX147 /TORX147  TOSLINK transceivers. User data bit allocations: User bit 0 is designated for Timecode transport User bit 1 is designated for MIDI data transport User bit 2 is designated for S/Mux indication (96 kHz sample rate mode) User bit 3 is reserved and set to 0The transmission speed of the user bits is equal to the sampling rate (e.g. 48,000 bits per second)


In mathematics texts it is customary to denote permutations using lowercase Greek letters. Commonly, either α {\displaystyle \alpha } and β , {\displaystyle \beta ,} or σ , τ {\displaystyle \sigma ,\tau } and π {\displaystyle \pi } are used.Permutations can be defined as bijections from a set S onto itself. All permutations of a set with n elements form a symmetric group, denoted S n {\displaystyle S_{n}} , where the group operation is function composition. Thus for two permutations, π {\displaystyle \pi } and σ {\displaystyle \sigma } in the group S n {\displaystyle S_{n}} , the four group axioms hold: Closure: If π {\displaystyle \pi } and σ {\displaystyle \sigma } are in S n {\displaystyle S_{n}} then so is π σ .


In the following example, the vector p does not escape into g, so it can be allocated on the stack and then removed from the stack before calling g. If, however, we had then either p would need to be allocated on the heap or (if g is known to the compiler when f is compiled, and behaves well) allocated on the stack in such a fashion that it can remain in place when g is called. If continuations are used to implement exception-like control structures, escape analysis can often detect this to avoid having to actually allocate a continuation and copy the call stack into it. For example, in escape analysis will determine that the continuation captured by call/cc doesn't escape, so no continuation structure needs to be allocated, and invoking the continuation by calling continuation can be implemented by unwinding the stack.


In subtyping systems, the bottom type is a subtype of all types. It is dual to the top type, which spans all possible values in a system. If a type system is sound, the bottom type is uninhabited and a term of bottom type represents a logical contradiction. In such systems, typically no distinction is drawn between the bottom type and the empty type, and the terms may be used interchangeably.


In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually denoted by B2 (sequence A065421 in the OEIS). Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.


That provides a clear and structured approach to the description of shared data and the coordination and communication between concurrent processes. This method is flexible in its ability to express timing, and can be used in different ways. In addition, path expressions are useful for process synchronization for two reasons: first, the close relationship between stream expressions and regular expressions that simplify the task of writing and reasoning about programs that use this synchronization mechanism.


In the Bantu languages, attributive verbs are formed by the addition of the "pre-prefix" (or "initial vowel"). For example, in Luganda: Abasajja batambula "The men walk" (predicative) Abasajja abatambula "The men who walk" (attributive)This is similar to the behaviour of attributive adjectives: Abasajja bagagga "The men are rich" (predicative) Abasajja abagagga "The men who are rich" (i.e "the rich men") (attributive)The attributive verb formation is the usual way of forming relatives in Luganda when the antecedent is the subject of the subordinate verb, and is sometimes called the "subject relative". Relative pronouns do exist, but they are only used for "object relatives", i.e. relative clauses where the antecedent is the object of the subordinate verb.


In metadata, a synonym ring or synset, is a group of data elements that are considered semantically equivalent for the purposes of information retrieval. These data elements are frequently found in different metadata registries. Although a group of terms can be considered equivalent, metadata registries store the synonyms at a central location called the preferred data element. According to WordNet, a synset or synonym set is defined as a set of one or more synonyms that are interchangeable in some context without changing the truth value of the proposition in which they are embedded.