the two codes c 1 { \ displaystyle \ mathbf { c _ { 1 } } } and c 2 { \ displaystyle \ mathbf { c _ { 2 } } } can be constructed as subcodes of the ( 7, 4, 3 ) { \ displaystyle ( 7, 4, 3 ) } hamming code and thus has minimum distance of 3 { \ displaystyle 3 }. given the generator matrix g { \ displaystyle \ mathbf { g } } of the original hamming code, the generator matrix g 1 { \ displaystyle \ mathbf { g _ { 1 } } } for c 1 { \ displaystyle \ mathbf { c _ { 1 } } } is constructed by taking any two rows from g { \ displaystyle \ mathbf { g } }, and g 2 { \ displaystyle \ mathbf { g _ { 2 } } } is constructed by the remaining two rows of g { \ displaystyle \ mathbf { g } }. the corresponding ( 5 × 7 ) { \ displaystyle ( 5 \ times 7 ) } parity - check matrix for each sub - code can be generated according to the generator matrix and used to generate syndrome bits.


in some languages, a pointer can reference executable code, i. e., it can point to a function, method, or procedure. a function pointer will store the address of a function to be invoked. while this facility can be used to call functions dynamically, it is often a favorite technique of virus and other malicious software writers.


unlike other indo - european languages, in slavic languages tense is independent of aspect, with imperfective and perfective aspects being indicated instead by means of prefixes, stem changes, or suppletion. in many west slavic and east slavic languages, the early slavic past tenses have largely merged into a single past tense. in both west and east slavic, verbs in the past tense are conjugated for gender ( masculine, feminine, neuter ) and number ( singular, plural ).


in the bayesian network below, x { \ displaystyle x \, \! } and y { \ displaystyle y \, \! } are parent variables and z { \ displaystyle z \, \! } is the child variable.


in mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group g is the algorithmic problem of deciding whether two words in the generators represent the same element. more precisely, if a is a finite set of generators for g then the word problem is the membership problem for the formal language of all words in a and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on a to the group g. if b is another finite generating set for g, then the word problem over the generating set b is equivalent to the word problem over the generating set a. thus one can speak unambiguously of the decidability of the word problem for the finitely generated group g. the related but different uniform word problem for a class k of recursively presented groups is the algorithmic problem of deciding, given as input a presentation p for a group g in the class k and two words in the generators of g, whether the words represent the same element of g. some authors require the class k to be definable by a recursively enumerable set of presentations.


the theorems are those formulae b { \ displaystyle b } such that b { \ displaystyle \ vdash b } ( with an empty left - hand side ) is the conclusion of a valid proof. ( in some presentations of natural deduction, the a i { \ displaystyle a _ { i } } s and the turnstile are not written down explicitly ; instead a two - dimensional notation from which they can be inferred is used. ) the standard semantics of a judgment in natural deduction is that it asserts that whenever a 1 { \ displaystyle a _ { 1 } }, a 2 { \ displaystyle a _ { 2 } }, etc., are all true, b { \ displaystyle b } will also be true. the judgments a 1, …, a n b { \ displaystyle a _ { 1 }, \ ldots, a _ { n } \ vdash b } and ( a 1 ∧ ∧ a n ) → b { \ displaystyle \ vdash ( a _ { 1 } \ land \ cdots \ land a _ { n } ) \ rightarrow b } are equivalent in the strong sense that a proof of either one may be extended to a proof of the other.


in the field of telephony, quality of service was defined by the itu in 1994. quality of service comprises requirements on all the aspects of a connection, such as service response time, loss, signal - to - noise ratio, crosstalk, echo, interrupts, frequency response, loudness levels, and so on. a subset of telephony qos is grade of service ( gos ) requirements, which comprises aspects of a connection relating to capacity and coverage of a network, for example guaranteed maximum blocking probability and outage probability. in the field of computer networking and other packet - switched telecommunication networks, teletraffic engineering refers to traffic prioritization and resource reservation control mechanisms rather than the achieved service quality. quality of service is the ability to provide different priorities to different applications, users, or data flows, or to guarantee a certain level of performance to a data flow.


in the area of modern algebra known as group theory, the mclaughlin group mcl is a sporadic simple group of order 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11 = 898, 128, 000 ≈ 9×108.


in the bayesian version of binary hypothesis testing one is interested in minimizing the average error probability under both hypothesis, assuming a prior probability of occurrence on each hypothesis. let π 0 { \ displaystyle \ pi _ { 0 } } denote the prior probability of hypothesis h 0 { \ displaystyle h _ { 0 } }. in this case the average error probability is given by p ave = π 0 p ( error h 0 ) + ( 1 − π 0 ) p ( error h 1 ) { \ displaystyle p _ { \ text { ave } } = \ pi _ { 0 } p ( { \ text { error } } \ mid h _ { 0 } ) + ( 1 - \ pi _ { 0 } ) p ( { \ text { error } } \ mid h _ { 1 } ) }. in this setting again a likelihood ratio test is optimal and the optimal error decays as lim n → ∞ − ln p ave n = c ( f 0, f 1 ) { \ displaystyle \ lim _ { n \ to \ infty } { \ frac { - \ ln p _ { \ text { ave } } } { n } } = c ( f _ { 0 }, f _ { 1 } ) } where c ( f 0, f 1 ) { \ displaystyle c ( f _ { 0 }, f _ { 1 } ) } represents the chernoff - information between the two distributions defined as c ( f 0, f 1 ) = max λ ∈ { \ displaystyle c ( f _ { 0 }, f _ { 1 } ) = \ max _ { \ lambda \ in } \ left }. = = references = =


in these examples, the ( negative ) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. this holds in general. when dividing by d, either both remainders are positive and therefore equal, or they have opposite signs. if the positive remainder is r1, and the negative one is r2, then r1 = r2 + d.


the set of positive matrices is a subset of all non - negative matrices. while such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive - definite matrices, which are different. a matrix which is both non - negative and is positive semidefinite is called a doubly non - negative matrix. a rectangular non - negative matrix can be approximated by a decomposition with two other non - negative matrices via non - negative matrix factorization. eigenvalues and eigenvectors of square positive matrices are described by the perron – frobenius theorem.


since its initial sound is aspirated, it can be represented as, and the word's phonetic representation would then be. ( the precise features shown in a phonetic representation depend on whether a narrow or broad transcription is used and which features the writer wishes to draw attention to in a particular context. ) when phones are considered to be realizations of the same phoneme, they are called allophones of that phoneme ( more information on the methods of making such assignments can be found under phoneme ). in english, for example, and are considered allophones of a single phoneme, which is written / p /. the phonemic transcriptions of those two words is thus / spɪn / and / pɪn /, and aspiration is then no longer shown since it is not distinctive.


in number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime - counting problems. the problem was identified and named by atle selberg in 1949. beginning around 1996, john friedlander and henryk iwaniec developed some parity - sensitive sieves that make the parity problem less of an obstacle.


pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e. g. the simply typed lambda calculus allows only terms to depend on terms. pure type systems were independently introduced by stefano berardi ( 1988 ) and jan terlouw ( 1989 ). barendregt discussed them at length in his subsequent papers.


this can make the distribution a useful overdispersed alternative to the poisson distribution, for example for a robust modification of poisson regression. in epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. more generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term. the term " negative binomial " is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.


they must be fitted with a speedometer and may not be used by children under 14. all three classes may be used on footways and cycle paths. class 2 and 3 may be used on dual carriageways with a flashing amber beacon, and otherwise must comply with most other regulations pertaining to use of vehicles on the carriageway ( e. g. lights and reflectors ), though they are specifically excluded from the definition of " motor vehicle ". all are banned from motorways. none of them cover the types described in the section above, which are ordinary motor vehicles subject to all regulations applicable to such.


in software development, obfuscation is the act of creating source or machine code that is difficult for humans or computers to understand. like obfuscation in natural language, it may use needlessly roundabout expressions to compose statements. programmers may deliberately obfuscate code to conceal its purpose ( security through obscurity ) or its logic or implicit values embedded in it, primarily, in order to prevent tampering, deter reverse engineering, or even to create a puzzle or recreational challenge for someone reading the source code. this can be done manually or by using an automated tool, the latter being the preferred technique in industry.


in particle physics, preons are hypothetical point particles, conceived of as sub - components of quarks and leptons. the word was coined by jogesh pati and abdus salam, in 1974. interest in preon models peaked in the 1980s but has slowed, as the standard model of particle physics continues to describe physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found.


in bra – ket notation, this is typically denoted as ψ + = | + ⟩ { \ displaystyle { \ boldsymbol { \ psi } } _ { + } = | + \ rangle }, and ψ − = | − ⟩ { \ displaystyle { \ boldsymbol { \ psi } } _ { - } = | - \ rangle }. as above, kets and bras with the same label are interpreted as kets and bras corresponding to each other using the inner product. in particular, when also identified with row and column vectors, kets and bras with the same label are identified with hermitian conjugate column and row vectors. bra – ket notation was effectively established in 1939 by paul dirac ; it is thus also known as dirac notation, despite the notation having a precursor in hermann grassmann's use of { \ displaystyle } for inner products nearly 100 years earlier.


in number theory, the ideal class group ( or class group ) of an algebraic number field k is the quotient group jk / pk where jk is the group of fractional ideals of the ring of integers of k, and pk is its subgroup of principal ideals. the class group is a measure of the extent to which unique factorization fails in the ring of integers of k. the order of the group, which is finite, is called the class number of k. the theory extends to dedekind domains and their fields of fractions, for which the multiplicative properties are intimately tied to the structure of the class group. for example, the class group of a dedekind domain is trivial if and only if the ring is a unique factorization domain.


one approach would be to modify the program - instructions ( the ones stored in the registers ) so that they contain more than one command. but this too can be exhausted unless an instruction is of ( potentially ) unbounded size. so why not use just one " uber - instruction " – one really really big number – that contains all the program instructions encoded into it!


( the above properties relating to rows may be replaced by the corresponding statements with respect to columns. ) determinants occur throughout mathematics.


in queueing theory, a discipline within the mathematical theory of probability, the flow - equivalent server method ( also known as flow - equivalent aggregation technique, norton's theorem for queueing networks or the chandy – herzog – woo method ) is a divide - and - conquer method to solve product form queueing networks inspired by norton's theorem for electrical circuits. the network is successively split into two, one portion is reconfigured to a closed network and evaluated. marie's algorithm is a similar method where analysis of the sub - network are performed with state - dependent poisson process arrivals. = = references = =


the technique was extended to unit disk graphs by schneider et al. the fastest deterministic algorithms for ( δ + 1 ) - coloring for small δ are due to leonid barenboim, michael elkin and fabian kuhn. the algorithm by barenboim et al. runs in time o ( δ ) + log * ( n ) / 2, which is optimal in terms of n since the constant factor 1 / 2 cannot be improved due to linial's lower bound. panconesi & srinivasan ( 1996 ) use network decompositions to compute a δ + 1 coloring in time 2 o ( log n ) { \ displaystyle 2 ^ { o \ left ( { \ sqrt { \ log n } } \ right ) } }.


a significant invention, which later had a profound effect on electronic music, was the audion in 1906. this was the first thermionic valve, or vacuum tube and which led to the generation and amplification of electrical signals, radio broadcasting, and electronic computation, among other things. other early synthesizers included the telharmonium ( 1897 ), the theremin ( 1919 ), jorg mager's spharophon ( 1924 ) and partiturophone, taubmann's similar electronde ( 1933 ), maurice martenot's ondes martenot ( " martenot waves ", 1928 ), trautwein's trautonium ( 1930 ).


in mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. it is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points ( such as the function's value, gradient, hessian etc. ). the framework has been used to provide tight worst - case guarantees on the number of required iterations, for several important classes of optimization problems.


the distinction between byod and school - issued devices became blurred when many schools started recommending devices for parents to buy ( examples for both ipads and chromebooks being used 1 : 1 in schools, but being paid for by parents exist, there may be similar evidence for other devices ). the term 1 : 1 computing in education is now redefined to a situation where students have access to a device per individual that is used in the teaching as a tool for learning. historically, the programs have centered around the following devices : laptops ( windows and mac ) 1990s - 2010. ipads ( with some competing android and windows devices ) 2010 - 2014 chromebooks ( 2015 – present ) ( with ipad + keyboard and other laptop & tablet - computers competing ).


tuple may be formally defined from ordered pairs by recurrence by starting from ordered pairs ; indeed, a n - tuple can be identified with the ordered pair of its ( n − 1 ) first elements and its nth element. tuples are usually written by listing the elements within parentheses " ( ) ", separated by a comma and a space ; for example, ( 2, 7, 4, 1, 7 ) denotes a 5 - tuple. sometimes other symbols are used to surround the elements, such as square brackets " " or angle brackets " ⟨ ⟩ ".


in the netherlands, there is coverage on all the lines and the old system called telerail was abandoned in favour of gsm - r in 2006.


in order to ensure replica convergence, a system must reconcile differences between multiple copies of distributed data. this consists of two parts : exchanging versions or updates of data between servers ( often known as anti - entropy ) ; and choosing an appropriate final state when concurrent updates have occurred, called reconciliation. the most appropriate approach to reconciliation depends on the application. a widespread approach is " last writer wins ". another is to invoke a user - specified conflict handler.


be aware that roundoff errors can accumulate. if m decimal places are used in the intermediate calculation, we say there are m−n guard digits. guard digits are also used in floating point operations in most computer systems.


in mathematical logic the theory of pure equality is a first - order theory. it has a signature consisting of only the equality relation symbol, and includes no non - logical axioms at all. this theory is consistent but incomplete, as a non - empty set with the usual equality relation provides an interpretation making certain sentences true. it is an example of a decidable theory and is a fragment of more expressive decidable theories, including monadic class of first - order logic ( which also admits unary predicates and is, via skolem normal form, related to set constraints in program analysis ) and monadic second - order theory of a pure set ( which additionally permits quantification over predicates and whose signature extends to monadic second - order logic of k successors ).


hence, it cannot account for the correct or incorrect application of a name. he claimed that there was a natural correctness to names. to do this, he pointed out that compound words and phrases have a range of correctness.


c libraries complying to posix or the single unix specification ( susv3 ) provided such routines as getcontext, setcontext, makecontext and swapcontext, but these functions were declared obsolete in posix 1. 2008. once a second call stack has been obtained with one of the methods listed above, the setjmp and longjmp functions in the standard c library can then be used to implement the switches between coroutines. these functions save and restore, respectively, the stack pointer, program counter, callee - saved registers, and any other internal state as required by the abi, such that returning to a coroutine after having yielded restores all the state that would be restored upon returning from a function call. minimalist implementations, which do not piggyback off the setjmp and longjmp functions, may achieve the same result via a small block of inline assembly which swaps merely the stack pointer and program counter, and clobbers all other registers.


in the distributed environment, one might have difficulties in keeping track of everyone's workload and contribution towards the deliverable. through adoption of agile principles and practices, the visibility is made clearer as there are multiple iterations where one can visualize the issues or criticalities on the initial stages of the project. continuous integration of programming code, which is one of the focal pieces of agile software development, additionally serves to reduce setup of the executive issues. adopting of agile principles appears to positively affect correspondence between groups as advancement in cycles makes it simpler for members to see the short - term objectives.


in mathematics, two non - empty subsets a and b of a given metric space ( x, d ) are said to be positively separated if the infimum inf a ∈ a, b ∈ b d ( a, b ) > 0. { \ displaystyle \ inf _ { a \ in a, b \ in b } d ( a, b ) > 0. } ( some authors also specify that a and b should be disjoint sets ; however, this adds nothing to the definition, since if a and b have some common point p, then d ( p, p ) = 0, and so the infimum above is clearly 0 in that case. ) for example, on the real line with the usual distance, the open intervals ( 0, 2 ) and ( 3, 4 ) are positively separated, while ( 3, 4 ) and ( 4, 5 ) are not. in two dimensions, the graph of y = 1 / x for x > 0 and the x - axis are not positively separated.


formally, given a set of data points x, the k centers ci are to be chosen so as to minimize the sum of the distances from each x to the nearest ci. the criterion function formulated in this way is sometimes a better criterion than that used in the k - means clustering algorithm, in which the sum of the squared distances is used.


the programmer would change the one - word br to the two - word jmp instruction from the next group. as jmp has no conditional forms, the programmer would change beq to a bne that branched around a jmp. sob ( subtract one and branch ) is another conditional branch instruction. the specified register is decremented by 1, and if the result is not zero, a reverse branch is taken based on the 6 bit word offset.


in modern operating systems, non - system ( i. e. user - mode ) applications are prevented from accessing any memory locations not explicitly authorized by the virtual memory controller ( called memory management unit ( mmu ) ). in addition to containing damage that may be caused by software flaws and allowing more efficient use of physical memory, this architecture forms an integral part of the security of the operating system. however, kernel - mode drivers, many hardware devices, and user - mode vulnerabilities allow direct, unimpeded access of the physical memory address space. the physical address space includes all of the main system memory, as well as memory - mapped buses and hardware devices ( which are controlled by the operating system through reads and writes as if they were ordinary ram ).


in mathematics, a nonnegative matrix, written x ≥ 0, { \ displaystyle \ mathbf { x } \ geq 0, } is a matrix in which all the elements are equal to or greater than zero, that is, x i j ≥ 0 i, j. { \ displaystyle x _ { ij } \ geq 0 \ qquad \ forall { i, j }. } a positive matrix is a matrix in which all the elements are strictly greater than zero.


in the eav table itself, this is just an attribute id, a foreign key into an attribute definitions table, as stated above. however, there are usually multiple metadata tables that contain attribute - related information, and these are discussed shortly.


in the 1880s herman hollerith invented the recording of data on a medium that could then be read by a machine. prior uses of machine readable media had been for lists of instructions ( not data ) to drive programmed machines such as jacquard looms and mechanized musical instruments. " after some initial trials with paper tape, he settled on punched cards ".


therefore, equation ( 5 ) applied successively, provides an algorithm to estimate our ground truth x n e w { \ displaystyle \ mathbf { x } _ { new } } by ascending ( since it moves in the direction of the gradient of the likelihood ) in the likelihood landscape. it has not been demonstrated in this derivation that it converges and no dependence on the initial choice is shown. note that equation ( 2 ) provides a way of following the direction that increases the likelihood but the choice of the log - derivative is arbitrary.


more precisely, letting x = x ( t, m ) be the minimal number of cuts required to split the necklace. the following holds as m tends to infinity. for any s < ( t + 1 ) / 2 { \ displaystyle s < ( t + 1 ) / 2 } p ( x = s ) = θ ( m s − ( t + 1 ) / 2 ). { \ displaystyle \ mathbb { p } ( x = s ) = \ theta { \ big ( } m ^ { s - ( t + 1 ) / 2 } { \ big ) }. } for any ( t + 1 ) / 2 < s ≤ t { \ displaystyle ( t + 1 ) / 2


instead of repeating step two to convergence, it may be formulated and solved as a set of linear equations. these equations are merely obtained by making s = s ′ { \ displaystyle s = s'} in the step two equation. thus, repeating step two to convergence can be interpreted as solving the linear equations by relaxation. this variant has the advantage that there is a definite stopping condition : when the array π { \ displaystyle \ pi } does not change in the course of applying step 1 to all states, the algorithm is completed. policy iteration is usually slower than value iteration for a large number of possible states.


in set theory, cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti - diagonal argument, the diagonal method, and cantor's diagonalization proof, was published in 1891 by georg cantor as a mathematical proof that there are infinite sets which cannot be put into one - to - one correspondence with the infinite set of natural numbers. : 20 – such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which cantor began. the diagonal argument was not cantor's first proof of the uncountability of the real numbers, which appeared in 1874.


the discrepancy ( irregularity ) measures how far a given distribution deviates from an ideal one. discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure - theoretic and combinatorial settings. just as ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity. a significant event in the history of discrepancy theory was the 1916 paper of weyl on the uniform distribution of sequences in the unit interval.


in most dialects of american english, speakers have a process known as intervocalic alveolar flapping that changes the consonants / t / and / d / into a quick flap consonant ( ) in words such as " butter " ( ) and " notable " ( ). the stop consonants / t / and / d / only become a flap in between two vowels, where the first vowel is stressed and the second is stressless. it is common to represent phonological rules using formal rewrite rules in the most general way possible. thus, the intervocalic alveolar flapping described above can be formalized as


a rainbow set is a conflict - free set in the special case in which go is made of disjoint cliques, where each clique represents a color. conflict - free set cover is the problem of finding a conflict - free subset of o that is a covering of p. banik, panolan, raman, sahlot and saurabh prove the following for the special case in which the conflict - graph has bounded arboricity : if the geometric cover problem is fixed - parameter tractable ( fpt ), then the conflict - free geometric cover problem is fpt. if the geometric cover problem admits an r - approximation algorithm, then the conflict - free geometric cover problem admits a similar approximation algorithm in fpt time. = = references = =


in mathematical logic, the friedberg – muchnik theorem is a theorem about turing reductions that was proven independently by albert muchnik and richard friedberg in the middle of the 1950s. it is a more general view of the kleene – post theorem. the kleene – post theorem states that there exist incomparable languages a and b below k. the friedberg – muchnik theorem states that there exist incomparable, computably enumerable languages a and b. incomparable meaning that there does not exist a turing reduction from a to b or a turing reduction from b to a. it is notable for its use of the priority finite injury approach.


in probability theory and statistics, the generalized inverse gaussian distribution ( gig ) is a three - parameter family of continuous probability distributions with probability density function f ( x ) = ( a / b ) p / 2 2 k p ( a b ) x ( p − 1 ) e − ( a x + b / x ) / 2, x > 0, { \ displaystyle f ( x ) = { \ frac { ( a / b ) ^ { p / 2 } } { 2k _ { p } ( { \ sqrt { ab } } ) } } x ^ { ( p - 1 ) } e ^ { - ( ax + b / x ) / 2 }, \ qquad x > 0, } where kp is a modified bessel function of the second kind, a > 0, b > 0 and p a real parameter. it is used extensively in geostatistics, statistical linguistics, finance, etc. this distribution was first proposed by etienne halphen. it was rediscovered and popularised by ole barndorff - nielsen, who called it the generalized inverse gaussian distribution. its statistical properties are discussed in bent jørgensen's lecture notes.


in recreational mathematics, many problems concern the properties of numbers under concatenation of their numerals in some base. examples include home primes ( primes obtained by repeatedly factoring the increasing concatenation of prime factors of a given number ), smarandache – wellin numbers ( the concatenations of the first prime numbers ), and the champernowne and copeland – erdos constants ( the real numbers formed by the decimal representations of the positive integers and the prime numbers, respectively ).


language is not an arbitrary set of conventions but a way of thinking and representing the world to oneself. it is not a conditioning process, but one in which the learner actively organizes his perceptions into linguistics concepts. the series method is a variety of the direct method in that experiences are directly connected to the target language. there are three reasons that gouin preceded psycholinguistic theory of the 20th century.


in numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. there is no strict definition regarding the proportion of zero - value elements for a matrix to qualify as sparse but a common criterion is that the number of non - zero elements is roughly equal to the number of rows or columns. by contrast, if most of the elements are non - zero, the matrix is considered dense. the number of zero - valued elements divided by the total number of elements ( e. g., m × n for an m × n matrix ) is sometimes referred to as the sparsity of the matrix.


in a completely regular semigroup, each green h - class is a group and the semigroup is the union of these groups. hence completely regular semigroups are also referred to as " unions of groups ". epigroups generalize this notion and their class includes all completely regular semigroups.


in mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. for example, the formula x + 3 = y { \ displaystyle x + 3 = y } is satisfiable because it is true when x = 3 { \ displaystyle x = 3 } and y = 6 { \ displaystyle y = 6 }, while the formula x + 1 = x { \ displaystyle x + 1 = x } is not satisfiable over the integers. the dual concept to satisfiability is validity ; a formula is valid if every assignment of values to its variables makes the formula true. for example, x + 3 = 3 + x { \ displaystyle x + 3 = 3 + x } is valid over the integers, but x + 3 = y { \ displaystyle x + 3 = y } is not.


in matroid theory, the dual of a matroid m { \ displaystyle m } is another matroid m ∗ { \ displaystyle m ^ { \ ast } } that has the same elements as m { \ displaystyle m }, and in which a set is independent if and only if m { \ displaystyle m } has a basis set disjoint from it. matroid duals go back to the original paper by hassler whitney defining matroids. they generalize to matroids the notions of plane graph duality.


in mathematics, the map segmentation problem is a kind of optimization problem. it involves a certain geographic region that has to be partitioned into smaller sub - regions in order to achieve a certain goal. typical optimization objectives include : minimizing the workload of a fleet of vehicles assigned to the sub - regions ; balancing the consumption of a resource, as in fair cake - cutting. determining the optimal locations of supply depots ; maximizing the surveillance coverage. fair division of land has been an important issue since ancient times, e. g. in ancient greece.


if data models are developed on a system by system basis, then not only is the same analysis repeated in overlapping areas, but further analysis must be performed to create the interfaces between them. most systems within an organization contain the same basic data, redeveloped for a specific purpose. therefore, an efficiently designed basic data model can minimize rework with minimal modifications for the purposes of different systems within the organization


in the early 1990s sun - joo shin presented an extension of existential graphs called venn - ii. syntax and semantics are given formally, together with a set of rules of transformation which are shown to be sound and complete. proofs proceed by applying the rules ( which remove or add syntactic elements to or from diagrams ) sequentially. venn - ii is equivalent in expressive power to a first - order monadic language.


to overcome the problems, some applications may simply attempt to replace the decomposed characters with the equivalent precomposed characters. with an incomplete font, however, precomposed characters may also be problematic – especially if they are more exotic, as in the following example ( showing the reconstructed proto - indo - european word for " dog " ) : kuon ( u + 1e31 u + 1e77 u + 1e53 u + 006e ) kuon ( u + 006b u + 0301 u + 0075 u + 032d u + 006f u + 0304 u + 0301 u + 006e ) in some situations, the precomposed green k, u and o with diacritics may render as unrecognized characters, or their typographical appearance may be very different from the final letter n with no diacritic. on the second line, the base letters should at least render correctly even if the combining diacritics could not be recognized. opentype has the ccmp " feature tag " to define glyphs that are compositions or decompositions involving combining characters.


in painting and other visual arts, two - dimensional color wheels or three - dimensional color solids are used to represent the essential relationships between colors. the split - primary palette is a color - wheel model that attempts to explain, and to compensate for, the unsatisfactory results often produced when mixing the traditional primary colors, red, yellow, and blue. painters have long considered red, yellow, and blue to be primary colors. in practice, however, many of the mixtures produced from these colors lack chromatic intensity.


for instance, the product of type1,..., typen is written type1 *... * typen in ml and ( type1,..., typen ) in haskell. in both these languages, tuples are written ( v1,..., vn ) and the components of a tuple are extracted by pattern - matching. additionally, many functional programming languages provide more general algebraic data types, which extend both product and sum types. product types are the dual of sum types.


in mathematics, the inequality of arithmetic and geometric means, or more briefly the am – gm inequality, states that the arithmetic mean of a list of non - negative real numbers is greater than or equal to the geometric mean of the same list ; and further, that the two means are equal if and only if every number in the list is the same ( in which case they are both that number ). the simplest non - trivial case – i. e., with more than one variable – for two non - negative numbers x and y, is the statement that x + y 2 ≥ x y { \ displaystyle { \ frac { x + y } { 2 } } \ geq { \ sqrt { xy } } } with equality if and only if x = y. this case can be seen from the fact that the square of a real number is always non - negative ( greater than or equal to zero ) and from the elementary case ( a ± b ) 2 = a2 ± 2ab + b2 of the binomial formula : 0 ≤ ( x − y ) 2 = x 2 − 2 x y + y 2 = x 2 + 2 x y + y 2 − 4 x y = ( x + y ) 2 − 4 x y. { \ displaystyle { \ begin { aligned } 0 & \ leq ( x - y ) ^ { 2 } \ \ & = x ^ { 2 } - 2xy + y ^ { 2 } \ \ & = x ^ { 2 } + 2xy + y ^ { 2 } - 4xy \ \ & = ( x + y ) ^ { 2 } - 4xy. \ end { aligned } } } hence ( x + y ) 2 ≥ 4xy, with equality precisely when ( x − y ) 2 = 0, i. e. x = y. the am – gm inequality then follows from taking the positive square root of both sides and then dividing both sides by 2. for a geometrical interpretation, consider a rectangle with sides of length x and y, hence it has perimeter 2x + 2y and area xy.


in public policy a polycentric network is a group of distinct local, regional, or national entities that work co - operatively towards a common goal. proponents claim that such networks can better adapt to changing issues collectively than individually, thus providing network participants better results from relevant efforts.


in recent years, scientists and audio engineers have been developing smartphone apps to conduct sound measurements, similar to the standalone sound level meters and dosimeters. in 2014, the national institute for occupational safety and health ( niosh ) within the centers for disease control and prevention ( cdc ) published a study examining the efficacy of 192 sound measurement apps on apple and android smartphones. the authors found that only 10 apps, all of which were on the app store, met all acceptability criteria. of these 10 apps, only 4 apps met accuracy criteria within 2 db ( a ) from the reference standard. as a result of this study, they created the niosh sound level meter app to increase accessibility and decrease costs of monitoring noise using crowdsourcing data with a tested and highly accurate application.


in practice, signals exhibiting cyclicity with more than one incommensurate period arise and require a generalization of the theory of cyclostationarity. such signals are called polycyclostationary if they exhibit a finite number of incommensurate periods and almost cyclostationary if they exhibit a countably infinite number. such signals arise frequently in radio communications due to multiple transmissions with differing sine - wave carrier frequencies and digital symbol rates. the theory was introduced in for stochastic processes and further developed in for non - stochastic time series.


in mobile networks, the terminal adapter is used by the terminal equipment to access the mobile termination, using at commands ( see hayes command set ). in 2g ( such as gsm or cdma ), the terminal adapter is a theoretically optional while in 3g ( such as w - cdma ), the terminal adapter is mandatory and is part of the mobile termination.


in most regions, google pay on android permits the issuing bank to determine whether to allow its payment cards to be able to transmit when the mobile device is locked under a certain monetary amount. issuers in argentina, brazil, ecuador, mexico, and the united states of america cannot allow locked - device payments except for select transit transactions. on wear os, this option is not available. all transactions for all amounts on wearable devices must be authenticated by opening the wallet app prior to tapping.


in some programming languages, an implicit declaration is provided the first time such a variable is encountered at compile time. in other languages, such a usage is considered to be an error, which may result in a diagnostic message. some languages have started out with the implicit declaration behavior, but as they matured they provided an option to disable it ( e. g. perl's " use strict " or visual basic's " option explicit " ).


in flames'next two albums, soundtrack to your escape ( 2004 ) and come clarity ( 2006 ), peaked at numbers 145 and 58 on the billboard 200, respectively, with the latter album giving in flames a swedish grammy award. the black dahlia murder, arch enemy, children of bodom, and amon amarth also enter the billboard 200 during the 2000s decade. in the mid – late 2000s, melodic metalcore became one of the most popular heavy metal genres, with bands like killswitch engage, unearth, bullet for my valentine, all that remains, shadows fall and atreyu achieving success, headlining major festivals and selling a lot of records.


in the algorithm, αk is chosen such that r k + 1 { \ displaystyle \ mathbf { r } _ { k + 1 } } is orthogonal to r k { \ displaystyle \ mathbf { r } _ { k } }. the denominator is simplified from α k = r k t r k r k t a p k = r k t r k p k t a p k { \ displaystyle \ alpha _ { k } = { \ frac { \ mathbf { r } _ { k } ^ { \ mathsf { t } } \ mathbf { r } _ { k } } { \ mathbf { r } _ { k } ^ { \ mathsf { t } } \ mathbf { a } \ mathbf { p } _ { k } } } = { \ frac { \ mathbf { r } _ { k } ^ { \ mathsf { t } } \ mathbf { r } _ { k } } { \ mathbf { p } _ { k } ^ { \ mathsf { t } } \ mathbf { ap } _ { k } } } } since r k + 1 = p k + 1 − β k p k { \ displaystyle \ mathbf { r } _ { k + 1 } = \ mathbf { p } _ { k + 1 } - \ mathbf { \ beta } _ { k } \ mathbf { p } _ { k } }. the βk is chosen such that p k + 1 { \ displaystyle \ mathbf { p } _ { k + 1 } } is conjugate to p k { \ displaystyle \ mathbf { p } _ { k } }.


in an adaptation of lpt called restricted lpt or rlpt, inputs are assigned in pairs - one to each machine ( for m = 2 machines ). the resulting partition is balanced by design. coffman, frederickson and lueker show that the expected largest sum of rlpt when inputs are uniformly - distributed random variables is exactly n 4 + 1 2 n + 2 { \ displaystyle { \ frac { n } { 4 } } + { \ frac { 1 } { 2n + 2 } } }. the expected difference between the largest and smallest sum is θ ( 1 / n ) { \ displaystyle \ theta ( 1 / n ) }.


the unit number or command code occupies the first 4 of the 5 bits. the final bit is a 0 for a unit code and a 1 for a command code. multiple unit codes may be transmitted in sequence before a command code is finally sent.


if the net gain expressed in db is negative, it is also called the net loss. if the net gain is expressed as a ratio, and the ratio is less than unity, a net loss is indicated. the test signal must be chosen so that its power level is within the usual operating range of the circuit being tested.


let c a { \ displaystyle c ^ { a } } ( also written a c { \ displaystyle ^ { a } c } ) denote the class of sets that fulfill the function property. this is the class of functions from a { \ displaystyle a } to c { \ displaystyle c } in a pure set theory. below the notation x → y { \ displaystyle x \ to y } is also used for y x { \ displaystyle y ^ { x } }, for the sake of distinguishing it from ordinal exponentiation. when functions are understood as just function graphs as above, the membership proposition f ∈ c a { \ displaystyle f \ in c ^ { a } } is also written f : a → c { \ displaystyle f \ colon a \ to c }. the boolean - valued χ b : a → { 0, 1 } { \ displaystyle \ chi _ { b } \ colon a \ to \ { 0, 1 \ } } are among the classes discussed next.


in radio communication systems, information is carried across space using radio waves. at the sending end, the information to be sent is converted by some type of transducer to a time - varying electrical signal called the modulation signal. the modulation signal may be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal consisting of a sequence of bits representing binary data from a computer. the modulation signal is applied to a radio transmitter.


the associativity up to isomorphism is then a way of expressing that different ways of aggregating the same data — such as ( ( a, b ), c ) { \ displaystyle ( ( a, b ), c ) } and ( a, ( b, c ) ) { \ displaystyle ( a, ( b, c ) ) } — store the same information even though the aggregate values need not be the same. the aggregate type may be analogous to the operation of addition ( type sum ) or of multiplication ( type product ). for type product, the identity object is the unit ( ) { \ displaystyle ( ) }, so there is only one inhabitant of the type, and that is why a product with it is always isomorphic to the other operand.


its first known appearance in a technical paper was in a 2003 paper by austrian researcher leo sauermann. many of the existing semantic wiki applications were started in the mid - 2000s, including artificialmemory ( 2004 ), semantic mediawiki ( 2005 ), freebase ( 2005 ), and ontowiki ( 2006 ). june 2006 saw the first meeting dedicated to semantic wikis, the " semwiki " workshop, co - located with the european semantic web conference in montenegro. this workshop ran annually until 2010. the site dbpedia, launched in 2007, though not a semantic wiki, publishes structured data from wikipedia in rdf form, which enables semantic querying of wikipedia's data. in march 2008, wikia, the world's largest wiki farm, made the use of semantic mediawiki available for all their wikis on request, thus allowing all the wikis they hosted to function as semantic wikis. however, since upgrading to version 1. 19 of mediawiki in 2013, they have stopped supporting semantic mediawiki for new requests on the basis of performance problem. in july 2010, google purchased metaweb, the company behind freebase. in april 2012, work began on wikidata, a collaborative, multi - language store of data, whose data could then be used within wikipedia articles, as well as by the outside world.


in the context of classification of groups, there is an essentially unique group containing exactly 2 elements. similarly, there is also an essentially unique group containing exactly 3 elements : the cyclic group of order three. in fact, regardless of how one chooses to write the three elements and denote the group operation, all such groups can be shown to be isomorphic to each other, and hence are " the same ". on the other hand, there does not exist an essentially unique group with exactly 4 elements, as there are in this case two non - isomorphic groups in total : the cyclic group of order 4 and the klein four group.


in mathematics, mirror descent is an iterative optimization algorithm for finding a local minimum of a differentiable function. it generalizes algorithms such as gradient descent and multiplicative weights.


in the early years, a prepaid mobile phone could only be used within the network of the operator from which the customer purchased the phone. it was not possible to roam onto other gsm networks when using the phone abroad. this was because the operator had no way to bill calls in real time from another network.


in number theory, a carmichael number is a composite number n { \ displaystyle n }, which in modular arithmetic satisfies the congruence relation : b n ≡ b ( mod n ) { \ displaystyle b ^ { n } \ equiv b { \ pmod { n } } } for all integers b { \ displaystyle b }. the relation may also be expressed in the form : b n − 1 ≡ 1 ( mod n ) { \ displaystyle b ^ { n - 1 } \ equiv 1 { \ pmod { n } } }. for all integers b { \ displaystyle b } which are relatively prime to n { \ displaystyle n }. carmichael numbers are named after american mathematician robert carmichael, the term having been introduced by nicolaas beeger in 1950 ( øystein ore had referred to them in 1948 as numbers with the " fermat property ", or " f numbers " for short ).


in mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self - adjoint operators. the technique is now commonly applied to problems in physics, but has its origins in attempts to give precise meanings to ill - conditioned sums appearing in number theory.


some significant work was also done on percolation on random graphs. from a physicist's point of view this would still be a mean - field model, so the justification of the research is often formulated in terms of the robustness of the graph, viewed as a communication network. given a random graph of n 1 nodes with an average degree ⟨ k ⟩ { \ displaystyle \ langle k \ rangle }.


third person singular pronouns in english also have a gender feature : " she " is, " he " and " it. different lexical categories realise or are specified for different grammatical features : for example, verbs in english are specified for tense, aspect and mood features, as well as person and number. the features that a category realises can also differ from language to language. there is often a correspondence between morphological and syntactic features, in that certain features, such as person, are relevant to both morphology and syntax ; these are known as morphosyntactic features.


in principle, however, this could also signify that a parametric test has been employed in a situation where all parametric assumptions are fully met, but it is in most cases impossible to prove this completely in a real - world situation. exceptions in which it is certain that parametric tests are exact include tests based on the binomial or poisson distributions. the term permutation test is sometimes used as a synonym for exact test, but it should be kept in mind that all permutation tests are exact tests, but not all exact tests are permutation tests.


this vector corresponds to the stationary distribution of the markov chain represented by the row - normalized adjacency matrix ; however, the adjacency matrix must first be modified to ensure a stationary distribution exists. the second smallest eigenvector can be used to partition the graph into clusters, via spectral clustering. other methods are also available for clustering.


this line of research began with werner heisenberg's matrix mechanics and in a more mathematically developed form with pascual jordan around 1933. subsequently, john von neumann attempted to establish a general framework for these algebras, which culminated in a series of papers on rings of operators. these papers considered a special class of c * - algebras which are now known as von neumann algebras.


another is defined the same way, but using split octonions instead of octonions. the final is constructed from the non - split octonions using a different standard involution. over any algebraically closed field, there is just one albert algebra, and its automorphism group g is the simple split group of type f4.


in mathematics, a set of natural numbers is called a k - trivial set if its initial segments viewed as binary strings are easy to describe : the prefix - free kolmogorov complexity is as low as possible, close to that of a computable set. solovay proved in 1975 that a set can be k - trivial without being computable. the schnorr – levin theorem says that random sets have a high initial segment complexity.


in the united kingdom and other parts of the commonwealth of nations, an equivalent service to direct distance dialing is subscriber trunk dialing ( std ), and isd for international subscriber trunk dialing. queen elizabeth ii inaugurated std on 5 december 1958, when she dialed a call from bristol to edinburgh and spoke to the lord provost.


in the eten ( 天 ) chinese operating system, the following code points are added, to add support for some characters present in the ibm 5550's code page but absent from generic big5 : 0xa3c0 – 0xa3e0 : 33 control characters. 0xc6a1 – 0xc875 : circle 1 – 10, bracket 1 – 10, roman numerals 1 – 9 ( i – ix ), cjk radical glyphs, japanese hiragana, japanese katakana, cyrillic characters 0xf9d6 – 0xf9fe : the characters'','','','','','' and'', followed by 34 additional semigraphic symbols. in some versions of eten, there are extra graphical symbols and simplified chinese characters.


in mathematics, an element ( or member ) of a set is any one of the distinct objects that belong to that set.


in software engineering, overhead can influence the decision whether or not to include features in new products, or indeed whether to fix bugs. a feature that has a high overhead may not be included – or needs a big financial incentive to do so. often, even though software providers are well aware of bugs in their products, the payoff of fixing them is not worth the reward, because of the overhead. for example, an implicit data structure or succinct data structure may provide low space overhead, but at the cost of slow performance ( space / time tradeoff ).


in mathematical optimization, the problem of non - negative least squares ( nnls ) is a type of constrained least squares problem where the coefficients are not allowed to become negative. that is, given a matrix a and a ( column ) vector of response variables y, the goal is to find a r g m i n x ‖ a x − y ‖ 2 2 { \ displaystyle \ operatorname { arg \, min } \ limits _ { \ mathbf { x } } \ | \ mathbf { ax } - \ mathbf { y } \ | _ { 2 } ^ { 2 } } subject to x ≥ 0. here x ≥ 0 means that each component of the vector x should be non - negative, and ‖ · ‖ 2 denotes the euclidean norm. non - negative least squares problems turn up as subproblems in matrix decomposition, e. g. in algorithms for parafac and non - negative matrix / tensor factorization. the latter can be considered a generalization of nnls. another generalization of nnls is bounded - variable least squares ( bvls ), with simultaneous upper and lower bounds αi ≤ xi ≤ βi. : 291


doing this is only a win if the subexpression computation costs more in time than fetching from memory, which in most stack cpus, almost always is the case. it is never worthwhile for simple variables and pointer fetches, because those already have the same cost of one data cache cycle per access. it is only marginally worthwhile for expressions such as x + 1.


in the united states, taxation of sodium has been proposed as a method of decreasing sodium intake and thereby improving health in countries where typical salt consumption is high. taking an alternative view, the salt institute, a salt industry body based in north america, is active in promoting the use of salt, and questioning or opposing the recommended restrictions on salt intake.


in the exhaustive recall method, participants are asked to record all the memories they can access before a specific age. this method, like free recall, relies on participants to come up with memories without cues. exhaustive recall yields a better understanding than others on the number of memories surviving from early childhood but can be demanding for the subjects who often have to spend many hours trying to remember events from their childhood. no major differences among word cued, interview, focused and exhaustive recall have been found.


this problem is np - complete, implying that neither it nor the optimization problem are expected to have polynomial time algorithms. it was one of richard m. karp's original set of 21 np - complete problems ; its np - completeness was proved by karp and eugene lawler by showing that inputs for another hard problem, the vertex cover problem, could be transformed ( " reduced " ) into equivalent inputs to the feedback arc set decision problem. some np - complete problems can become easier when their inputs are restricted to special cases. but for the most important special case of the feedback arc set problem, the case of tournaments, the problem remains np - complete.


most commonly, the conditional mean of the response given the values of the explanatory variables ( or predictors ) is assumed to be an affine function of those values ; less commonly, the conditional median or some other quantile is used. like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis. linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.


in the context of a clinical trial, quality typically refers to the absence of errors which can impact decision making, both during the conduct of the trial and in use of the trial results.


the main market for risc cpus has been systems that need low power or small size. even some cisc processors ( based on architectures that were created before risc grew dominant ), such as newer x86 processors, translate instructions internally into a risc - like instruction set.


in statistics, prediction is a part of statistical inference. one particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. when information is transferred across time, often to specific points in time, the process is known as forecasting.


in the book that was published in 1572, entitled algebra, bombelli gave a comprehensive account of the algebra known at the time. he was the first european to write down the way of performing computations with negative numbers. the following is an excerpt from the text : " plus times plus makes plus minus times minus makes plus plus times minus makes minus minus times plus makes minus plus 8 times plus 8 makes plus 64 minus 5 times minus 6 makes plus 30 minus 4 times plus 5 makes minus 20 plus 5 times minus 4 makes minus 20 " as was intended, bombelli used simple language as can be seen above so that anybody could understand it. but at the same time, he was thorough.


{ \ displaystyle \ mathbb { q } ( { \ sqrt { c } } ). } in this field every element may be uniquely written α + β c, { \ displaystyle \ alpha + \ beta { \ sqrt { c } }, } with α { \ displaystyle \ alpha } and β { \ displaystyle \ beta } being rational numbers. this implies that ± 2 x y { \ displaystyle \ pm 2 { \ sqrt { xy } } } is not rational ( otherwise the right - hand side of the equation would be rational ; but the left - hand side is irrational ).


in some applications, it is more important to minimize the total length of the cuts ( e. g. to minimize the cost of performing the partition, or to minimize the amount of dust ). this problem is called minimum edge - length rectangular partitioning. it was first studied by lingas, pinter, rivest and shamir in 1982. the run - time complexity of this problem crucially depends on whether the raw polygon is allowed to have holes.


the nihr quality, safety and outcomes policy research unit has focused on measuring and assessing the integration of services. they began by examining whether measures were available to assess processes and outcomes of integration of services. they found a very large number of available measures but the infrequent use of any common set of measures made comparisons between systems very difficult.


in model theory, the notion of an algebraic structure is generalized to structures involving both operations and relations. let l be a signature consisting of function and relation symbols, and a, b be two l - structures. then a homomorphism from a to b is a mapping h from the domain of a to the domain of b such that h ( fa ( a1, …, an ) ) = fb ( h ( a1 ), …, h ( an ) ) for each n - ary function symbol f in l, ra ( a1, …, an ) implies rb ( h ( a1 ), …, h ( an ) ) for each n - ary relation symbol r in l. in the special case with just one binary relation, we obtain the notion of a graph homomorphism.


in the body of a generic unit, the ( formal ) type parameter is handled like its upper bound ( expressed with extends ; object if not constrained ). if the return type of a method is the type parameter, the result ( e. g. of type? ) can be referenced by a variable of the type of the upper bound ( or object ). in the other direction, the wildcard fits no other type, not even object : if?


in the case of two enemies sharing a friend, the shared friend is likely to choose one over the other and turn one of his or her friendships into an enemy. antal, krapivsky and reder consider social dynamics as the change in sign on an edge of a signed graph. the social relations with previous friends of a divorcing couple are used to illustrate the evolution of a signed graph in society.


: " addictive * of biblioscopy ". ) to emulate unordered search of the near operator can be done using a combination of ordered searches. for example, to specify a close co - occurrence of " house " and " dog ", the following search - expression could be specified : " house dog " or " dog house " or " house * dog " or " dog * house " or " house * * dog " or " dog * * house ".


in mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. the algorithm is usually formulated in terms of a minimum - cost flow problem. the network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied to general linear program of same dimensions.


recursion though may be achieved by obtaining the same function passed in as an argument, and then using that argument to make the recursive call, instead of using the function's own name, as is done in languages which do support recursion natively. the y combinator demonstrates this style of programming. an example implementation of y combinator in two languages is presented below.


the values iso 639 - 3, clergyman, clergymen are plain character strings. the value eng is taken from the list of languages as defined by iso 639 - 3. with some additional information like dtdversion and feat, the same data can be expressed by the following xml fragment : this example is rather simple, while lmf can represent much more complex linguistic descriptions the xml tagging is correspondingly complex.


in most cases the same mechanisms must be applied as in the positioning of an image or text content.


these occur when microorganisms only come into contact with disinfectants but are not killed by them. when ascertaining the cleanability of a surface with regard to particles, the analysis can be carried out in correlation with the surface cleanliness classes described in vdi 2083 part 9. 1. surface roughness can be measured, for example, using profile methods ( din en iso 11562 ) or afm ( atomic force microscope ). however, no norm is currently in existence which describes a standardized afm procedure.


the request is forwarded to ( performed on ) all objects downwards the tree structure. the nonterminalexpression objects ( ntexpr1, ntexpr2 ) forward the request to their child expressions. the terminalexpression objects ( texpr1, texpr2, … ) perform the interpretation directly.


for example, time may be required to obtain approval of the transaction by government agencies, shareholders, labor unions, lenders, or others. until the transaction is completed, the companies involved go on about their business and are subject to risks. contract terms that deal with material adverse changes are carefully negotiated by the parties and take into account the relevant circumstances of each party.


however, as more classes are added to a program, especially during maintenance and / or refactoring, the problem of communication between these classes may become more complex. this makes the program harder to read and maintain. furthermore, it can become difficult to change the program, since any change may affect code in several other classes.


in mathematics, church encoding is a means of representing data and operators in the lambda calculus. the church numerals are a representation of the natural numbers using lambda notation. the method is named for alonzo church, who first encoded data in the lambda calculus this way.


cbd essentially coincides with the probabilistic part of abramsky's sheaf - theoretic approach if the system is strongly consistently connected, which means that the joint distributions of { r q 1 c, …, r q k c } { \ displaystyle \ left \ { r _ { q _ { 1 } } ^ { c }, \ ldots, r _ { q _ { k } } ^ { c } \ right \ } } and { r q 1 c ′, …, r q k c ′ } { \ displaystyle \ left \ { r _ { q _ { 1 } } ^ { c'}, \ ldots, r _ { q _ { k } } ^ { c'} \ right \ } } coincide whenever q 1, …, q k { \ displaystyle q _ { 1 }, \ ldots, q _ { k } } are measured in contexts c, c ′ { \ displaystyle c, c'}. however, unlike most approaches to contextuality, cbd allows for inconsistent connectedness, with r q c { \ displaystyle r _ { q } ^ { c } } and r q c ′ { \ displaystyle r _ { q } ^ { c'} } differently distributed. this makes cbd applicable to physics experiments in which no - disturbance condition is violated, as well as to human behavior where this condition is violated as a rule. in particular, vctor cervantes, ehtibar dzhafarov, and colleagues have demonstrated that random variables describing certain paradigms of simple decision making form contextual systems, whereas many other decision - making systems are noncontextual once their inconsistent connectedness is properly taken into account.


in the english language, a compound sentence is composed of at least two independent clauses. it does not require a dependent clause. the clauses are joined by a coordinating conjunction, a semicolon that functions as a conjunction, a colon instead of a semicolon between two sentences when the second sentence explains or illustrates the first sentence and no coordinating conjunction is being used to connect the sentences, or a conjunctive adverb preceded by a semicolon. a conjunction can be used to make a compound sentence.


in quantum computing, grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just o ( n ) { \ displaystyle o ( { \ sqrt { n } } ) } evaluations of the function, where n { \ displaystyle n } is the size of the function's domain. it was devised by lov grover in 1996. the analogous problem in classical computation cannot be solved in fewer than o ( n ) { \ displaystyle o ( n ) } evaluations ( because, on average, one has to check half of the domain to get a 50 % chance of finding the right input ). charles h. bennett, ethan bernstein, gilles brassard, and umesh vazirani proved that any quantum solution to the problem needs to evaluate the function ω ( n ) { \ displaystyle \ omega ( { \ sqrt { n } } ) } times, so grover's algorithm is asymptotically optimal.


modern x86 is relatively uncommon in embedded systems, however, and small low power applications ( using tiny batteries ), and low - cost microprocessor markets, such as home appliances and toys, lack significant x86 presence. simple 8 - and 16 - bit based architectures are common here, as well as simpler risc architectures like risc - v, although the x86 - compatible via c7, via nano, amd's geode, athlon neo and intel atom are examples of 32 - and 64 - bit designs used in some relatively low - power and low - cost segments. there have been several attempts, including by intel, to end the market dominance of the " inelegant " x86 architecture designed directly from the first simple 8 - bit microprocessors.


since entrenched ceo pay their workers high salaries, the ceo - worker relationship improves, making workers less likely to unionize. often workers perceive managers'benefits to be more beneficial for them than unions. this leads us to the conclusion that entrenched ceos have the characteristic of being very competitive when it comes to work loyalty. = = references = =


in predicate logic, existential generalization ( also known as existential introduction, ) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. in first - order logic, it is often used as a rule for the existential quantifier ( { \ displaystyle \ exists } ) in formal proofs. example : " rover loves to wag his tail. therefore, something loves to wag its tail. "


differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation ( where the vertices represent pixels and the weighted edges encode pixel similarity based on comparisons of moore neighborhoods or larger windows ), data clustering, data classification, or community detection in a social network ( where the vertices represent users of the network, the edges represent links between users, and the weight function indicates the strength of interactions between users ). the main advantage of finite weighted graphs is that by not being restricted to highly regular structures such as discrete regular grids, lattice graphs, or meshes, they can be applied to represent abstract data with irregular interrelationships. if a finite weighted graph is geometrically embedded in a euclidean space, i. e., the graph vertices represent points of this space, then it can be interpreted as a discrete approximation of a related nonlocal operator in the continuum setting.


( in some accounts that take this approach, the constituent lacking the determiner – that called n - bar above – may be referred to as a noun phrase. ) this analysis of noun phrases is widely referred to as the dp hypothesis. it has been the preferred analysis of noun phrases in the minimalist program from its start ( since the early 1990s ), though the arguments in its favor tend to be theory - internal.


likewise, lattices are directed sets both upward and downward. in topology, directed sets are used to define nets, which generalize sequences and unite the various notions of limit used in analysis. directed sets also give rise to direct limits in abstract algebra and ( more generally ) category theory.


in several languages, the grave accent distinguishes both homophones and words that otherwise would be homographs : in bulgarian and macedonian, it distinguishes the conjunction и ( " and " ) from the short - form feminine possessive pronoun и. in catalan, it distinguishes homophone words such as ma ( " my ( f ) " ) and ma ( " hand " ). in french the grave accent on the letters a and u has no effect on pronunciation and just distinguishes homonyms otherwise spelled the same, for example the preposition a ( " to / belonging to / towards " ) from the verb a ( " has " ) as well as the adverb la ( " there " ) and the feminine definite article la ; it is also used in the words deja ( " already " ), deca ( preceded by en or au, and meaning " closer than " or " inferior to ( a given value ) " ), the phrase ca et la ( " hither and thither " ; without the accents, it would literally mean " it and the " ) and its functional synonym deca, dela. it is used on the letter u only to distinguish ou ( " where " ) and ou ( " or " ). e is rarely used to distinguish homonyms except in des / des ( " since / some " ), es / es ( " in / ( thou ) art " ), and les / les ( " near / the " ).


in mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. some particular topics out of many include ; operations defined on matrices ( such as matrix addition, matrix multiplication and operations derived from these ), functions of matrices ( such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices ), and the eigenvalues of matrices ( eigendecomposition of a matrix, eigenvalue perturbation theory ).


recursive languages are also called decidable. the concept of decidability may be extended to other models of computation. for example, one may speak of languages decidable on a non - deterministic turing machine.


in consequence, mutually exclusive events have the property : p ( a ∩ b ) = 0. for example, in a standard 52 - card deck with two colors it is impossible to draw a card that is both red and a club because clubs are always black. if just one card is drawn from the deck, either a red card ( heart or diamond ) or a black card ( club or spade ) will be drawn. when a and b are mutually exclusive, p ( a ∪ b ) = p ( a ) + p ( b ).


this process is known as regularization. tikhonov regularization is one of the most commonly used for regularization of linear ill - posed problems. the definition of a well - posed problem comes from the work of jacques hadamard on mathematical modeling of physical phenomena.


in some languages, stative and dynamic verbs will use entirely different morphological markers on the verbs themselves. for example, in the mantauran dialect of rukai, an indigenous language of taiwan, the two types of verbs take different prefixes in their finite forms, with dynamic verbs taking o - and stative verbs taking ma -. thus, the dynamic verb " jump " is o - coroko in the active voice, while the stative verb " love " is ma - ðalamə. this sort of marking is characteristic of other formosan languages as well.


short cable lengths and limited physical extent, avoiding signal runtime performance degradation. majority / quorum mechanisms to guarantee data consistency whenever parts of the cluster become inaccessible. indicators for eventually consistent designs ( not suitable for transactional applications! )


the residual, or error, sum - of - squares is sse = i = 1 n ( x i − x ) 2 + i = 1 n ( y i − y ) 2 + i = 1 n ( z i − z ) 2 { \ displaystyle { \ text { sse } } = \ sum _ { i = 1 } ^ { n } ( x _ { i } - { \ bar { x } } ) ^ { 2 } + \ sum _ { i = 1 } ^ { n } ( y _ { i } - { \ bar { y } } ) ^ { 2 } + \ sum _ { i = 1 } ^ { n } ( z _ { i } - { \ bar { z } } ) ^ { 2 } } with 3 ( n−1 ) degrees of freedom. of course, introductory books on anova usually state formulae without showing the vectors, but it is this underlying geometry that gives rise to ss formulae, and shows how to unambiguously determine the degrees of freedom in any given situation.


in practice, stacks of indices can count and remember what rules were applied and in which order. for example, indexed grammars can describe the context - sensitive language of word triples { www : w ∈ { a, b } * } : a derivation of abbabbabb is then s ⇒ s ⇒ s ⇒ s ⇒ t t t ⇒ a t t t ⇒ ab t t t ⇒ abb t t t ⇒ abb t t ⇒... ⇒ abb abb t ⇒... ⇒ abb abb abb. as another example, the grammar g = ⟨ { s, t, a, b, c }, { a, b, c }, { f, g }, p, s ⟩ produces the language { anbncn : n ≥ 1 }, where the production set p consists of an example derivation is s ⇒ t ⇒ t ⇒ a b c ⇒ aa b c ⇒ aa bb c ⇒ aa bb cc ⇒ aa bb cc ⇒ aa bb cc ⇒ aa bb cc. both example languages are not context - free by the pumping lemma.


in mathematics, the rsa numbers are a set of large semiprimes ( numbers with exactly two prime factors ) that were part of the rsa factoring challenge. the challenge was to find the prime factors of each number. it was created by rsa laboratories in march 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. the challenge was ended in 2007. rsa laboratories ( which is an acronym of the creators of the technique ; rivest, shamir and adleman ) published a number of semiprimes with 100 to 617 decimal digits.


in metalogic, formal languages are sometimes called object languages. the language used to make statements about an object language is called a metalanguage. this distinction is a key difference between logic and metalogic. while logic deals with proofs in a formal system, expressed in some formal language, metalogic deals with proofs about a formal system which are expressed in a metalanguage about some object language.


in fact, the consecutive weightings of any digital number system can be employed since they all constitute geometric progressions. for example, the binary, ternary, octal and decimal number systems use a radix ‘ r ’ of 2, 3, 8 and 10 respectively. the value ‘ r ’ is also the common ratio of the geometric progression going up in rank order while ‘ r ’ is the complementary common ratio descending in rank.


x z ) = ( λ x. y z ) { \ displaystyle ( \ lambda x. x \ z ) = ( \ lambda x. y \ z ) } the new rules block this substitution so that it remains as, ( λ x. x z ) = ( λ x. x z ) { \ displaystyle ( \ lambda x. x \ z ) = ( \ lambda x. x \ z ) }


in mathematics, a trivial group or zero group is a group consisting of a single element. all such groups are isomorphic, so one often speaks of the trivial group. the single element of the trivial group is the identity element and so it is usually denoted as such : 0, 1, { \ displaystyle 0, 1, } or e { \ displaystyle e } depending on the context. if the group operation is denoted ⋅ { \ displaystyle \, \ cdot \, } then it is defined by e ⋅ e = e.


it limits the ways that entities can use patients'personal information and protects the privacy of all medical information no matter what form it is in. quality teleradiology must abide by important hipaa rules to ensure patients'privacy is protected. also state laws governing the licensing requirements and medical malpractice insurance coverage required for physicians vary from state to state.


{ \ displaystyle pq - \ varphi ( pq ) = pq - ( p - 1 ) ( q - 1 ) = p + q - 1 = n - 1. \, } it is expected that every even number larger than 6 is a sum of two distinct primes, so probably no odd number larger than 5 is a noncototient. the remaining odd numbers are covered by the observations 1 = 2 − ( 2 ), 3 = 9 − ( 9 ) { \ displaystyle 1 = 2 - \ phi ( 2 ), 3 = 9 - \ phi ( 9 ) } and 5 = 25 − ( 25 ) { \ displaystyle 5 = 25 - \ phi ( 25 ) }. for even numbers, it can be shown 2 p q − φ ( 2 p q ) = 2 p q − ( p − 1 ) ( q − 1 ) = p q + p + q − 1 = ( p + 1 ) ( q + 1 ) − 2 { \ displaystyle 2pq - \ varphi ( 2pq ) = 2pq - ( p - 1 ) ( q - 1 ) = pq + p + q - 1 = ( p + 1 ) ( q + 1 ) - 2 } thus, all even numbers n such that n + 2 can be written as ( p + 1 ) * ( q + 1 ) with p, q primes are cototients.


in the iso 5725 - 1 standard accuracy for measuring instruments is defined as “ the closeness of agreement between a test result and the accepted reference value ”. this term “ accuracy ” includes both the systematic error and the bias component. each device has its manufacturer stated accuracy specification and its tested accuracy. uncertainty takes all the metering system factors that impact measurement accuracy into account.


as a result. the theory is the answer the scientist creates using logic and reason to explain the phenomenon. the scientist then focuses on how to conduct experiments to test the theory incrementally and the theory is either proven to be true or false through repeatable and legitimate experimentation.


thus, the maximum entropy principle is not merely an alternative way to view the usual methods of inference of classical statistics, but represents a significant conceptual generalization of those methods. however these statements do not imply that thermodynamical systems need not be shown to be ergodic to justify treatment as a statistical ensemble. in ordinary language, the principle of maximum entropy can be said to express a claim of epistemic modesty, or of maximum ignorance. the selected distribution is the one that makes the least claim to being informed beyond the stated prior data, that is to say the one that admits the most ignorance beyond the stated prior data.


failing usually results in the student leaving the program or re - taking the test after some time has passed. a second failure normally guarantees dismissal from the graduate program, though progress on previous attempts may convince the student's program to grant a third, final attempt. some schools have an intermediate category, passing at the master's level, which does not permit the student to continue doctoral study, but does allow the student to leave with a master's degree despite not having completed a thesis. in some u. s.


in software engineering, a pipeline consists of a chain of processing elements ( processes, threads, coroutines, functions, etc. ), arranged so that the output of each element is the input of the next ; the name is by analogy to a physical pipeline. usually some amount of buffering is provided between consecutive elements. the information that flows in these pipelines is often a stream of records, bytes, or bits, and the elements of a pipeline may be called filters ; this is also called the pipe ( s ) and filters design pattern.


native data types can be mapped to / from java data types. for compound types such as objects, arrays and strings the native code must explicitly convert the data by calling methods in the jnienv. a jni environment pointer ( jnienv * ) is passed as an argument for each native function mapped to a java method, allowing for interaction with the jni environment within the native method.


in morphology and syntax, words are often organized into lexical categories or word classes, such as " noun ", " verb ", " adjective ", and so on. these word classes have grammatical features ( also called categories or inflectional categories ), which can have one of a set of potential values ( also called the property, meaning, or feature of the category ). for example, consider the pronoun in english. pronouns are a lexical category. pronouns have the person feature, which can have a value of " first ", " second ", or " third ".


despite that, the purely theoretical existence results are nevertheless ubiquitous in contemporary mathematics. for example, john nash's original proof of the existence of a nash equilibrium in 1951 was such an existence theorem. an approach which is constructive was also later found in 1962.


in software development, a given software system's ability to tolerate failures while still ensuring adequate quality of service — often generalized as resilience — is typically specified as a requirement. however, development teams often fail to meet this requirement due to factors such as short deadlines or lack of knowledge of the field. chaos engineering is a technique to meet the resilience requirement. chaos engineering can be used to achieve resilience against infrastructure failures, network failures, and application failures.


the same convention is adopted in functional programming, particularly in haskell. in geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc ( and thus latitude, longitude, elevation and right ascension ). in physics, the prime is used to denote variables after an event.


in probability theory, bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. in the simplest case, let x1,..., xn be independent bernoulli random variables taking values + 1 and −1 with probability 1 / 2 ( this distribution is also known as the rademacher distribution ), then for every positive ε { \ displaystyle \ varepsilon }, p ( | 1 n i = 1 n x i | > ε ) ≤ 2 exp ( − n ε 2 2 ( 1 + ε 3 ) ). { \ displaystyle \ mathbb { p } \ left ( \ left | { \ frac { 1 } { n } } \ sum _ { i = 1 } ^ { n } x _ { i } \ right | > \ varepsilon \ right ) \ leq 2 \ exp \ left ( - { \ frac { n \ varepsilon ^ { 2 } } { 2 ( 1 + { \ frac { \ varepsilon } { 3 } } ) } } \ right ). }


in spherical coordinates, with θ the angle with the z axis and φ the rotation around the z axis, and f again written in local unit coordinates, the divergence is div f = ∇ ⋅ f = 1 r 2 ∂ ∂ r ( r 2 f r ) + 1 r sin θ ∂ ∂ θ ( sin θ f θ ) + 1 r sin θ ∂ f φ ∂ φ. { \ displaystyle \ operatorname { div } \ mathbf { f } = \ nabla \ cdot \ mathbf { f } = { \ frac { 1 } { r ^ { 2 } } } { \ frac { \ partial } { \ partial r } } \ left ( r ^ { 2 } f _ { r } \ right ) + { \ frac { 1 } { r \ sin \ theta } } { \ frac { \ partial } { \ partial \ theta } } ( \ sin \ theta \, f _ { \ theta } ) + { \ frac { 1 } { r \ sin \ theta } } { \ frac { \ partial f _ { \ varphi } } { \ partial \ varphi } }. }


while much of the notation may be applied with any tensors, operations relating to a differential structure are only applicable to tensor fields. where needed, the notation extends to components of non - tensors, particularly multidimensional arrays.


in more general mathematical setting, the boltzmann distribution is also known as the gibbs measure. in statistics and machine learning it is called a log - linear model. in deep learning the boltzmann distribution is used in the sampling distribution of stochastic neural networks such as the boltzmann machine.


all bounds are asymptotically tight when the number of groups is constant. the proofs use discrepancy theory. unanimous envy - freeness with high probability : when all k groups contain the same number of agents, and their valuations are drawn at random, an envy - free allocation exists with high probability if the number of goods is in ω ( n log n ) { \ displaystyle \ omega ( n \ log n ) }, and can be attained by a greedy algorithm that maximizes the sum of utilities. the results can be extended to two groups with different sizes.


the sus has been widely used in the evaluation of a range of systems. bangor, kortum and miller have used the scale extensively over a ten - year period and have produced normative data that allow sus ratings to be positioned relative to other systems. they propose an extension to sus to provide an adjective rating that correlates with a given score. based on a review of hundreds of usability studies, sauro and lewis proposed a curved grading scale for mean sus scores.


in the field of telecommunications, " data retention " generally refers to the storage of call detail records ( cdrs ) of telephony and internet traffic and transaction data ( ipdrs ) by governments and commercial organisations. in the case of government data retention, the data that is stored is usually of telephone calls made and received, emails sent and received, and websites visited. location data is also collected. the primary objective in government data retention is traffic analysis and mass surveillance.


one can logically define a semigroup in which the underlying set s is empty. the binary operation in the semigroup is the empty function from s × s to s. this operation vacuously satisfies the closure and associativity axioms of a semigroup. not excluding the empty semigroup simplifies certain results on semigroups.


in number theory, the totient summatory function φ ( n ) { \ displaystyle \ phi ( n ) } is a summatory function of euler's totient function defined by : φ ( n ) : = k = 1 n φ ( k ), n ∈ n { \ displaystyle \ phi ( n ) : = \ sum _ { k = 1 } ^ { n } \ varphi ( k ), \ quad n \ in \ mathbf { n } } it is the number of coprime integer pairs { p, q }, 1 ≤ p ≤ q ≤ n.


the formulation of the theorem uses the following definition. a word in two variables, say x and y, is an expression of the form w ( x, y ) = x m 1 y n 1 x m 2 y n 2 x m p, { \ displaystyle w ( x, y ) = x ^ { m _ { 1 } } y ^ { n _ { 1 } } x ^ { m _ { 2 } } y ^ { n _ { 2 } } \ cdots x ^ { m _ { p } }, } where m1, n1, m2, n2, …, mp are non - negative integers. the degree of this word is m 1 + n 1 + m 2 + n 2 + + m p.


further inputs to the algorithm are the marginal sample distribution p ( x ) { \ displaystyle p ( x ) \, } which has already been determined by the dominant eigenvector of p { \ displaystyle p \, } and the matrix valued kullback – leibler divergence function d i, j k l = d k l ) { \ displaystyle d _ { i, j } ^ { kl } = d ^ { kl } { \ big } { \ big ) } } derived from the sample spacings and transition probabilities. the matrix p ( y i | c j ) { \ displaystyle p ( y _ { i } | c _ { j } ) \, } can be initialized randomly or with a reasonable guess, while matrix p ( c i | x j ) { \ displaystyle p ( c _ { i } | x _ { j } ) \, } needs no prior values. although the algorithm converges, multiple minima may exist that would need to be resolved.


under such assumptions, the case n < m { \ displaystyle n m { \ displaystyle n > m } and { e i } { \ displaystyle \ { e _ { i } \ } } does not consist of mutually orthogonal projections. for the second possibility, the problem of finding a suitable projection - valued measure now becomes the following problem. by assumption, the non - square matrix m = { \ displaystyle m = { \ begin { bmatrix } x _ { 1 } \ cdots x _ { n } \ end { bmatrix } } } is a co - isometry, that is m m ∗ = i { \ displaystyle mm ^ { * } = i }. if we can find a ( n − m ) × n { \ displaystyle ( n - m ) \ times n } matrix n where u = { \ displaystyle u = { \ begin { bmatrix } m \ \ n \ end { bmatrix } } } is a n × n unitary matrix, the projection - valued measure whose elements are projections onto the column vectors of u will then have the desired properties. in principle, such a n can always be found.


in the beginning of a prefix sum operation, each processing element i { \ displaystyle i } owns a message m i { \ displaystyle m _ { i } }. the goal is to compute 0 ≤ j ≤ i m j { \ displaystyle \ bigoplus _ { 0 \ leq j \ leq i } m _ { j } }, where ⊕ { \ displaystyle \ oplus } is an associative operation. the following pseudo code describes the algorithm. input : message m i { \ displaystyle m _ { i } } of processor i { \ displaystyle i }.


in n dimensions, when all i1,..., in, j1,..., jn take values 1, 2,..., n : where the exclamation mark (! ) denotes the factorial, and δα... β... is the generalized kronecker delta. for any n, the property i, j, k, = 1 n ε i j k … ε i j k … = n! { \ displaystyle \ sum _ { i, j, k, \ dots = 1 } ^ { n } \ varepsilon _ { ijk \ dots } \ varepsilon _ { ijk \ dots } = n! } follows from the facts that every permutation is either even or odd, ( + 1 ) 2 = ( −1 ) 2 = 1, and the number of permutations of any n - element set number is exactly n!. the particular case of ( 8 ) with k = n − 2 { \ textstyle k = n - 2 } is


as a consequence, code quality without the context of the whole system, as w. edwards deming described it, has limited value. to view, explore, analyze, and communicate software quality measurements, concepts and techniques of information visualization provide visual, interactive means useful, in particular, if several software quality measures have to be related to each other or to components of a software or system. for example, software maps represent a specialized approach that " can express and combine information about software development, software quality, and system dynamics ". software quality also plays a role in the release phase of a software project. specifically, the quality and establishment of the release processes ( also patch processes ), configuration management are important parts of an overall software engineering process.


the latter usually applies to a form of argument that does not comply with the valid inference rules of logic, whereas the problematic mathematical step is typically a correct rule applied with a tacit wrong assumption. beyond pedagogy, the resolution of a fallacy can lead to deeper insights into a subject ( e. g., the introduction of pasch's axiom of euclidean geometry, the five colour theorem of graph theory ).


in the early 1990s next computer recognized that connecting to databases was essential to most businesses and yet also potentially complex. every data source has a different data - access language ( or api ), driving up the costs to learn and use each vendor's product. the next engineers wanted to apply the advantages of object - oriented programming, by getting objects to " talk " to relational databases.


items should be empirically related to one another, which leads to the second step of examining their multivariate relationships. third, indexes scores are designed, which involves determining their score ranges and weights for the items.


qualcomm announced a partnership that will allow supported android phones, starting with snapdragon 8 gen 2 chipset, to send and receive text messages via iridium satellites. in 2022, t - mobile formed a partnership to use starlink services via existing lte / 5g nr spectrum. ast spacemobile aims to build a cellular space network from scratch. it will allow existing, unmodified smartphones to connect to satellites in areas with coverage gaps.


in number theory, the chevalley – warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. it was proved by ewald warning ( 1935 ) and a slightly weaker form of the theorem, known as chevalley's theorem, was proved by chevalley ( 1935 ). chevalley's theorem implied artin's and dickson's conjecture that finite fields are quasi - algebraically closed fields ( artin 1982, page x ).


one way to state the conjecture is that if r has no nil ideal, other than { 0 }, then it has no nil one - sided ideal, other than { 0 }. this question was posed in 1930 by gottfried kothe ( 1905 – 1989 ). the kothe conjecture has been shown to be true for various classes of rings, such as polynomial identity rings and right noetherian rings, but a general solution remains elusive.


the hexadecimal notation for null is 00. decoding the base64 string aa = = also yields the null character. in documentation, the null character is sometimes represented as a single - em - width symbol containing the letters " nul ". in unicode, there is a character for this : u + 2400.


in some games, it is possible to partition the elements of x ( or a subset of them ) into a set of pairwise - disjoint pairs. under certain conditions, a player can win using the following greedy strategy : " whenever your opponent picks an element of pair i, pick the other element of pair i ". the " certain conditions " are different for maker and for breaker ; see pairing strategy.


in the omg vision of modeling, data is split into abstract models and concrete models. the abstract models represent the semantic information, whereas the concrete models represent visual diagrams. abstract models are instances of arbitrary mof - based modeling languages such as uml or sysml. for diagrams, the diagram interchange ( di, xmi ) standard is used.


in multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service they have received. the lowest level ( containing jobs which have received the least service ) has the highest priority and higher levels monotonically decreasing priorities. within each level an internal discipline is used. = = references = =


in the united states, the national weather service issues flood watches and warnings for large - scale, gradual river flooding. watches are issued when flooding is possible or expected within 12 – 48 hours, and warnings are issued when flooding over a large area or river flooding is imminent or occurring. both can be issued on a county - by - county basis or for specific rivers or points along a river. when rapid flooding from heavy rain or a dam failure is expected, flash flood watches and warnings are issued.


developers of mobile applications must also consider a large array of devices with different screen sizes, hardware specifications, and configurations because of intense competition in mobile hardware and changes within each of the platforms. today, mobile apps are usually distributed via an official online outlet or marketplace ( e. g. apple - the app store, google - google play ) and there is a formalized process by which developers submit their apps for approval and inclusion in those marketplaces.


in practice, it is difficult to use kuratowski's criterion to quickly decide whether a given graph is planar. however, there exist fast algorithms for this problem : for a graph with n vertices, it is possible to determine in time o ( n ) ( linear time ) whether the graph may be planar or not ( see planarity testing ). for a simple, connected, planar graph with v vertices and e edges and f faces, the following simple conditions hold for v ≥ 3 : theorem 1. e ≤ 3v – 6 ; theorem 2. if there are no cycles of length 3, then e ≤ 2v – 4.


in this context " information " is used to refer to all the details of the state and the statement that information must be preserved means that details corresponding to an earlier time can always be reconstructed at a later time. mathematically, the schrodinger equation implies that the wavefunction at a time t1 can be related to the wavefunction at a time t2 by means of a unitary operator. since the unitary operator is bijective, the wavefunction at t2 can be obtained from the wavefunction at t1 and vice versa.


cantor's theorem had immediate and important consequences for the philosophy of mathematics. for instance, by iteratively taking the power set of an infinite set and applying cantor's theorem, we obtain an endless hierarchy of infinite cardinals, each strictly larger than the one before it. consequently, the theorem implies that there is no largest cardinal number ( colloquially, " there's no largest infinity " ).


in mathematics, the arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by turkish mathematician cahit arf ( 1941 ) when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. the arf invariant is the substitute, in characteristic 2, for the discriminant for quadratic forms in characteristic not 2. arf used his invariant, among others, in his endeavor to classify quadratic forms in characteristic 2. in the special case of the 2 - element field f2 the arf invariant can be described as the element of f2 that occurs most often among the values of the form.


in the feasibility stage, costs of the requirements are determined. for user requirements, the current cost of work is compared to the future projected costs once the new system is in place. questions such as these are asked : “ what are data entry errors costing us now? ” or “ what is the cost of scrap due to operator error with the current interface? ” actually, the need for the new tool is often recognized as these questions come to the attention of financial people in the organization. business costs would include, “ what department has the budget for this? ” “ what is the expected rate of return on the new product in the marketplace? ” “ what ’ s the internal rate of return in reducing costs of training and support if we make a new, easier - to - use system? ” technical costs are related to software development costs and hardware costs.


in quantum information theory, the lieb conjecture is a theorem concerning the wehrl entropy of quantum systems for which the classical phase space is a sphere. it states that no state of such a system has a lower wehrl entropy than the su ( 2 ) coherent states. the analogous property for quantum systems for which the classical phase space is a plane was conjectured by alfred wehrl in 1978 and proven soon afterwards by elliott h. lieb, who at the same time extended it to the su ( 2 ) case. the conjecture was only proven in 2012, by lieb and jan philip solovej.