( see example below. ) after their introduction in the 1968 algol 68 " final report ", w - grammars were widely considered as too powerful and unconstrained to be practical. this was partly a consequence of the way in which they had been applied ; the 1973 algol 68 " revised report " contains a much more readable grammar, without modifying the w - grammar formalism itself. meanwhile, it became clear that w - grammars, when used in their full generality, are indeed too powerful for such practical purposes as serving as the input for a parser generator.


in military acquisition, full operating capability or full operational capability ( foc ) is the completion of a development effort. this is usually preceded by an initial operating capability or initial operational capability ( ioc ) phase. for the united states department of defense military acquisition foc is defined as " in general attained when all units and / or organizations in the force structure scheduled to receive a system have received it and have the ability to employ and maintain it. the specifics for any particular system foc are defined in that system ’ s capability development document ( cdd ) and capability production document ( cpd ).


attention to the location of items in the search can be used to guide visual searches. this was demonstrated by valid cues improving the identification of targets relative to the invalid and neutral conditions. a visual search display can also influence how fast an observer responds to a spatial probe.


for vitamin c, vitamin d, vitamin e, vitamin k, calcium, phosphorus, magnesium, and manganese, the current highest rdas are up to 50 % higher than the older daily values used in labeling, whereas for other nutrients the recommended needs have gone down. a side - by - side table of the old and new adult daily values is provided at reference daily intake. as of october 2010, the only micronutrients that are required to be included on all labels are vitamin a, vitamin c, calcium, and iron.


ashrae guideline 4 - 2014 provides performance indices criteria for model calibration. the performance indices used are normalized mean bias error ( nmbe ), coefficient of variation ( cv ) of the root mean square error ( rmse ), and r2 ( coefficient of determination ). ashrae recommends a r2 greater than 0. 75 for calibrated models. the criteria for nmbe and cv rmse depends on if measured data is available at a monthly or hourly timescale.


in the event of an attack from an aggressor, a state would massively retaliate by using a force disproportionate to the size of the attack. the aim of massive retaliation is to deter another state from attacking first. for such a strategy to work, it must be made public knowledge to all possible aggressors. the aggressor also must believe that the state announcing the policy has the ability to maintain second - strike capability in the event of an attack.


the mips design team that designed the r4300i started the company sandcraft, which designed the r5432 for nec and later produced the sr71000, one of the first out - of - order execution processors for the embedded market. the original dec strongarm team eventually split into two mips - based start - ups : sibyte which produced the sb - 1250, one of the first high - performance mips - based systems - on - a - chip ( soc ) ; while alchemy semiconductor ( later acquired by amd ) produced the au - 1000 soc for low - power uses. lexra used a mips - like architecture and added dsp extensions for the audio chip market and multithreading support for the networking market.


if these decisions change later in the project then the cone will widen. original research for engineering and construction in the chemical industry demonstrated that actual final costs often exceeded the earliest " base " estimate by as much as 100 % ( or underran by as much as 50 % ). research in the software industry on the cone of uncertainty stated that in the beginning of the project life cycle ( i. e. before gathering of requirements ) estimates have in general an uncertainty of factor 4 on both the high side and the low side. this means that the actual effort or scope can be 4 times or 1 / 4 of the first estimates. this uncertainty tends to decrease over the course of a project, although that decrease is not guaranteed.


in some networks, routing is complicated by the fact that no single entity is responsible for selecting paths ; instead, multiple entities are involved in selecting paths or even parts of a single path. complications or inefficiency can result if these entities choose paths to optimize their own objectives, which may conflict with the objectives of other participants. a classic example involves traffic in a road system, in which each driver picks a path that minimizes their travel time. with such routing, the equilibrium routes can be longer than optimal for all drivers.


in numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. these eigenvalue algorithms may also find eigenvectors.


later work by kummer and others always divided the problem into first and second cases. sophie germain primes and safe primes have applications in public key cryptography and primality testing. it has been conjectured that there are infinitely many sophie germain primes, but this remains unproven.


in more recent times, the term bit slicing was reused by matthew kwan to refer to the technique of using a general - purpose cpu to implement multiple parallel simple virtual machines using general logic instructions to perform single - instruction multiple - data ( simd ) operations. this technique is also known as simd within a register ( swar ). this was initially in reference to eli biham's 1997 article a fast new des implementation in software, which achieved significant gains in performance of des by using this method.


in the following query, four different types of data are retrieved from a single table ( status ) and for a single user ( " me " ) : this query can run by querying the facebook graph endpoint / fql with the parameters set to q =


for the 1991 and 1992 seasons, this meant potentially severe angles for short field goal attempts, since the hashmark width remained at 53 ft 4 in ( 16. 26 m ). in 1993, the ncaa narrowed the distance between the hashmarks to 40 ft ( 12. 19 m ), matching what was the width of hashmarks in the nfl from 1945 through 1971 ; as mentioned above, the nfl narrowed the hashmarks in 1972 to goalpost width at 18. 5 feet ( 5. 64 m ). canadian hash marks in amateur play are 51 feet ( 16 m ) apart, 24 yards from each sideline.


in mathematics, a multiply perfect number ( also called multiperfect number or pluperfect number ) is a generalization of a perfect number. for a given natural number k, a number n is called k - perfect ( or k - fold perfect ) if the sum of all positive divisors of n ( the divisor function, σ ( n ) ) is equal to kn ; a number is thus perfect if and only if it is 2 - perfect. a number that is k - perfect for a certain k is called a multiply perfect number. as of 2014, k - perfect numbers are known for each value of k up to 11. it is unknown whether there are any odd multiply perfect numbers other than 1. the first few multiply perfect numbers are : 1, 6, 28, 120, 496, 672, 8128, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240,... ( sequence a007691 in the oeis ).


in scientific inquiry and academic research, data fabrication is the intentional misrepresentation of research results. as with other forms of scientific misconduct, it is the intent to deceive that marks fabrication as unethical, and thus different from scientists deceiving themselves. there are many ways data can be fabricated. experimental data can be fabricated by reporting experiments that were never conducted, and accurate data can be manipulated or misrepresented to suit a desired outcome.


this rule not only replaces the representation of a monophthong with that of a diphthong, but it also destroys the reversibility of any capitalization process in digital environments, as the combination of uppercase letter and uppercase iota would normally be converted back to lowercase letter and lowercase iota. it is therefore strongly recommended, both for the integrity of text and for the practical compatibility with digital environments, that lowercase letter and iota subscript should be capitalized in all situations and contexts as uppercase letter and iota adscript. a future revision of the above - mentioned unicode stipulation is linguistically stipulated and digitally inevitable, as its application is both destructive to the text and impractical in digital applications. in the ascii - based encoding standard beta code, the iota subscript is represented by the pipe character " | " placed after the letter.


in mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where the variables x i { \ displaystyle x _ { i } } are interpreted as having real number values, and where f ( x 1, … x n ) { \ displaystyle f ( x _ { 1 }, \ dots x _ { n } ) } is a quantifier - free formula involving equalities and inequalities of real polynomials. a sentence of this form is true if it is possible to find values for all of the variables that, when substituted into formula f { \ displaystyle f }, make it become true. the decision problem for the existential theory of the reals is the problem of finding an algorithm that decides, for each such sentence, whether it is true or false. equivalently, it is the problem of testing whether a given semialgebraic set is non - empty. this decision problem is np - hard and lies in pspace, giving it significantly lower complexity than alfred tarski's quantifier elimination procedure for deciding statements in the first - order theory of the reals without the restriction to existential quantifiers.


thus in the sentence here is the big house, both house and big house are n - bars, while the big house is a noun phrase. in the sentence i like big houses, both houses and big houses are n - bars, but big houses also functions as a noun phrase ( in this case without an explicit determiner ). in some modern theories of syntax, however, what are called " noun phrases " above are no longer considered to be headed by a noun, but by the determiner ( which may be null ), and they are thus called determiner phrases ( dp ) instead of noun phrases.


given a finite group g = ⟨ s ⟩ and g ∈ g, find a straight - line program computing g over s. the constructive membership problem is often studied in the setting of black box groups. the elements are encoded by bit strings of a fixed length. three oracles are provided for the group - theoretic functions of multiplication, inversion, and checking for equality with the identity.


in reverse mathematics, brouwer's theorem can be proved in the system wkl0, and conversely over the base system rca0 brouwer's theorem for a square implies the weak konig's lemma, so this gives a precise description of the strength of brouwer's theorem.


in practice, a strict adherence to the basic three - structure template of structured programming yields highly nested code, due to inability to exit a structured unit prematurely, and a combinatorial explosion with quite complex program state data to handle all possible conditions. two solutions have been generally adopted : a way to exit a structured unit prematurely, and more generally exceptions – in both cases these go up the structure, returning control to enclosing blocks or functions, but do not jump to arbitrary code locations. these are analogous to the use of a return statement in non - terminal position – not strictly structured, due to early exit, but a mild relaxation of the strictures of structured programming. in c, break and continue allow one to terminate a loop or continue to the next iteration, without requiring an extra while or if statement.


if τ1,..., τm, σ1,..., σn are ramified types then as in simple type theory there is a type ( τ1,..., τm, σ1,..., σn ) of " predicative " propositional functions of τ1,..., τm, σ1,..., σn. however, there are also ramified types ( τ1,..., τm | σ1,..., σn ) that can be thought of as the classes of propositional functions of τ1,... τm obtained from propositional functions of type ( τ1,..., τm, σ1,..., σn ) by quantifying over σ1,..., σn. when n = 0 ( so there are no σs ) these propositional functions are called predicative functions or matrices.


in such a cyberattack the attacker places malware within the networks through a variety of methods ( malware - laden website, targeted email, infected usb stick, socially engineered access, etc. ) and then the malware propagates within the network. most of the time existing cyber defenses clear the attacker tools from standard serves and it workstations ( it endpoints ) but the cyber defense software cannot access the embedded processors within medical devices. most of the embedded operating systems within medical devices are running on microsoft windows 7 and windows xp. the security in these operating systems is no longer supported.


additionally, unlike bounds on the total time, it is a suitable form of analysis even for algorithms that produce an infinite sequence of outputs. the notion of polynomial delay was first introduced by david s. johnson, mihalis yannakakis and christos papadimitriou. = = references = =


in telecommunication, communications survivability is the ability of communications systems to continue to operate effectively under adverse conditions, though portions of the system may be damaged or destroyed. various methods may be used to maintain communications services, such as using alternate routing, different transmission media or methods, redundant equipment, and sites and equipment that are radiation hardened.


an even nontotient may be one more than a prime number, but never one less, since all numbers below a prime number are, by definition, coprime to it. to put it algebraically, for p prime : φ ( p ) = p − 1. also, a pronic number n ( n − 1 ) is certainly not a nontotient if n is prime since φ ( p2 ) = p ( p − 1 ). if a natural number n is a totient, it can be shown that n · 2k is a totient for all natural number k. there are infinitely many even nontotient numbers : indeed, there are infinitely many distinct primes p ( such as 78557 and 271129, see sierpinski number ) such that all numbers of the form 2ap are nontotient, and every odd number has an even multiple which is a nontotient.


in statistics and psychometrics, reliability is the overall consistency of a measure. a measure is said to have a high reliability if it produces similar results under consistent conditions : " it is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.


the theorem also includes a converse : if two quantum states do commute, there is a method for broadcasting them : they must have a common basis of eigenstates diagonalizing them simultaneously, and the map that clones every state of this basis is a legitimate quantum operation, requiring only physical resources independent of the input state to implement — a completely positive map. a corollary is that there is a physical process capable of broadcasting every state in some set of quantum states if, and only if, every pair of states in the set commutes. this broadcasting map, which works in the commuting case, produces an overall state in which the two copies are perfectly correlated in their eigenbasis. remarkably, the theorem does not hold if more than one copy of the initial state is provided : for example, broadcasting six copies starting from four copies of the original state is allowed, even if the states are drawn from a non - commuting set. the purity of the state can even be increased in the process, a phenomenon known as superbroadcasting.


in the united states, in the context of stockholder lawsuits, typically relating to the sale or merger of a public company, the delaware court of chancery has required sufficient disclosures be made to a board of directors and shareholders to “ provide a balanced, truthful account of all matters ” and said “ when a document ventures into certain subjects, it must do so in a manner that is materially complete and unbiased by the omission of material facts. ” in a memorandum opinion in the checkfree / fiserv merger chancellor chandler underlined that the earlier in re pure resources court had established the proper frame of analysis for disclosure of financial data : “ tockholders are entitled to a fair summary of the substantive work performed by the investment bankers upon whose advice the recommendations of their board as to how to vote on a merger or tender rely. ” according to the certification hypothesis fairness opinions may also serve the interest of the shareholders by mitigating informational asymmetries in corporate transactions. = = references = =


in mathematics, a generating set γ of a module m over a ring r is a subset of m such that the smallest submodule of m containing γ is m itself ( the smallest submodule containing a subset is the intersection of all submodules containing the set ). the set γ is then said to generate m. for example, the ring r is generated by the identity element 1 as a left r - module over itself. if there is a finite generating set, then a module is said to be finitely generated. this applies to ideals, which are the submodules of the ring itself.


the pseudo code stores the prefix sum in variable x { \ displaystyle x } and the sum over all nodes in a sub cube in variable σ { \ displaystyle \ sigma }. this makes it possible for all nodes in 1 - sub cube to receive the sum over the 0 - sub cube in every step. this results in a factor of log p { \ displaystyle \ log p } for t start { \ displaystyle t _ { \ text { start } } } and a factor of n log p { \ displaystyle n \ log p } for t byte { \ displaystyle t _ { \ text { byte } } } : t ( n, p ) = ( t start + n t byte ) log p { \ displaystyle t ( n, p ) = ( t _ { \ text { start } } + nt _ { \ text { byte } } ) \ log p }.


rmo and powerpc allow reordering of reads to the same location. these models violate sequential order in examples a and b. an additional relaxation allowed in these models is that memory operations following a read operation can be overlapped and reordered with respect to the read. alpha and rmo allow a read to return the value of another processor's early write. from a programmer's perspective these models must maintain the illusion of write atomicity even though they allow the processor to read its own write early.


dialling 123 from a few mobile services, such as o2, also obtains a speaking clock service. the giffgaff network uses the same service as o2. the service is not available on the 3 mobile telephone network, as they use 123 as the number for their voicemail services.


in mathematics, the pocklington – lehmer primality test is a primality test devised by henry cabourn pocklington and derrick henry lehmer. the test uses a partial factorization of n − 1 { \ displaystyle n - 1 } to prove that an integer n { \ displaystyle n } is prime. it produces a primality certificate to be found with less effort than the lucas primality test, which requires the full factorization of n − 1 { \ displaystyle n - 1 }.


in this way, the first path will be drawn as an x - monotone polyline, a type of curve that is automatically non - self - crossing, and the second path will similarly be drawn as a y - monotone polyline. this type of drawing places the vertices in an integer lattice of dimensions linear in the graph sizes. similarly defined layouts also work, with larger but still linear grid sizes, when both graphs are caterpillars or when both are cycle graphs.


after returning from these recursive calls, vertex 2 is added to x and removed from p. the iteration of the inner loop of the algorithm for v = 4 makes a recursive call to the algorithm with r = { 4 }, p = { 3, 5, 6 }, and x = ø ( although vertex 2 belongs to the set x in the outer call to the algorithm, it is not a neighbor of v and is excluded from the subset of x passed to the recursive call ). this recursive call will end up making three second - level recursive calls to the algorithm that report the three cliques { 3, 4 }, { 4, 5 }, and { 4, 6 }. then, vertex 4 is added to x and removed from p. in the third and final iteration of the inner loop of the algorithm, for v = 6, there is a recursive call to the algorithm with r = { 6 }, p = ø, and x = { 4 }.


there is also generally an expectation that there be a close resemblance between the real world and the features of the model in an ontology. in theory, an ontology is a " formal, explicit specification of a shared conceptualisation ". an ontology renders shared vocabulary and taxonomy which models a domain with the definition of objects and / or concepts and their properties and relations. ontologies are the structural frameworks for organizing information and are used in artificial intelligence, the semantic web, systems engineering, software engineering, biomedical informatics, library science, enterprise bookmarking, and information architecture as a form of knowledge representation about the world or some part of it. the creation of domain ontologies is also essential to the definition and use of an enterprise architecture framework.


in the united states, housing segregation is the practice of denying african americans and other minority groups equal access to housing through the process of misinformation, denial of realty and financing services, and racial steering. housing policy in the united states has influenced housing segregation trends throughout history. key legislation include the national housing act of 1934, the g. i. bill, and the fair housing act.


this has enabled download speeds in excess of 100 mbit / s, over distances up to 35 miles ( 56 km ) from the transmission site. in the early days of mmds, it was known as " wireless cable " and was used in a variety of investment scams that still surface today. frequent solicitations of wireless cable fraud schemes were often heard on talk radio shows like the sonny bloch show in the mid - 1990s. several us telephone companies attempted television services via this system in the mid - 1990s – the tele - tv venture of bell atlantic, nynex and pacific bell ; and the rival americast consortium of ameritech, bellsouth, sbc, snet and gte.


in mathematics, a structure is a set endowed with some additional features on the set ( e. g. an operation, relation, metric, or topology ). often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. a partial list of possible structures are measures, algebraic structures ( groups, fields, etc. ), topologies, metric structures ( geometries ), orders, events, equivalence relations, differential structures, and categories.


an ibm mpic was also used in the rs / 6000 7046 model b50. the apple hydra mac i / o ( mio ) chip ( from the 1990s classic mac os era ) implemented a mpic alongside a scsi controller, adb controller, geoport controller, and timers. the apple implementation of " open pic " ( as the apple documentation of this era spells it ) in their first mio chip for the common hardware reference platform was based on version 1. 2 of the register specification and supported up to two processors and up to 20 interrupt sources. a mpic was also incorporated in the newer k2 i / o controller used in the power mac g5s. freescale also uses a mpic ( " compatible with the open pic " ) on all its powerquicc and qoriq processors. the linux kernel - based virtual machine ( kvm ) supports a virtualized mpic with up to 256 interrupts, based on the freescale variants.


in programming language theory, subtyping ( also subtype polymorphism or inclusion polymorphism ) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype ( the supertype ) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. if s is a subtype of t, the subtyping relation ( written as s < : t, s t, or s ≤ : t ) means that any term of type s can safely be used in any context where a term of type t is expected. the precise semantics of subtyping here crucially depends on the particulars of how " safely be used " and " any context " are defined by a given type formalism or programming language. the type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no ( or very little ) conversion mechanisms.


thus the seeming contradiction is that a model that is itself countable, and which therefore contains only countable sets, satisfies the first - order sentence that intuitively states " there are uncountable sets ". a mathematical explanation of the paradox, showing that it is not a contradiction in mathematics, was given by skolem ( 1922 ). skolem's work was harshly received by ernst zermelo, who argued against the limitations of first - order logic, but the result quickly came to be accepted by the mathematical community.


there are also several methods to approximate a shortest addition chain, and which often require fewer multiplications than binary exponentiation ; binary exponentiation itself is a suboptimal addition - chain algorithm. the optimal algorithm choice depends on the context ( such as the relative cost of the multiplication and the number of times a given exponent is re - used ). the problem of finding the shortest addition chain cannot be solved by dynamic programming, because it does not satisfy the assumption of optimal substructure. that is, it is not sufficient to decompose the power into smaller powers, each of which is computed minimally, since the addition chains for the smaller powers may be related ( to share computations ). for example, in the shortest addition chain for a15 above, the subproblem for a6 must be computed as ( a3 ) 2 since a3 is re - used ( as opposed to, say, a6 = a2 ( a2 ) 2, which also requires three multiplies ).


the category of pointed sets and pointed maps has both products and coproducts, but it is not a distributive category. it is also an example of a category where 0 × a { \ displaystyle 0 \ times a } is not isomorphic to 0 { \ displaystyle 0 }. many algebraic structures are pointed sets in a rather trivial way. for example, groups are pointed sets by choosing the identity element as the basepoint, so that group homomorphisms are point - preserving maps. : 24 this observation can be restated in category theoretic terms as the existence of a forgetful functor from groups to pointed sets. : 582 a pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element. as " rooted set " the notion naturally appears in the study of antimatroids and transportation polytopes.


the range of colors, sizes and shapes is far wider than in those grown or sold in africa, europe or the americas. southeast asian languages do not make the distinction between " bananas " and " plantains " that is made in english ( and spanish ). thus both cavendish cultivars, the classic yellow dessert bananas, and saba cultivars, used mainly for cooking, are called pisang in malaysia and indonesia, kluai in thailand and chuoi in vietnam.


the treaty stipulated that the use of cryptography with short key - lengths ( 56 - bit for symmetric encryption, 512 - bit for rsa ) would no longer be export - controlled. cryptography exports from the us became less strictly regulated as a consequence of a major relaxation in 2000 ; there are no longer very many restrictions on key sizes in us - exported mass - market software.


each choice of definition for'open set'is called a topology. a set with a topology is called a topological space. metric spaces are an important class of topological spaces where a real, non - negative distance, also called a metric, can be defined on pairs of points in the set. having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.


for how long? when do they regress to already seen words?


while the algorithmic complexity implies a deterministic description of an object ( it measures the information content of an individual sequence ), the statistical complexity, like forecasting complexity, implies a statistical description, and refers to an ensemble of sequences generated by a certain source. formally, the statistical complexity reconstructs a minimal model comprising the collection of all histories sharing a similar probabilistic future, and measures the entropy of the probability distribution of the states within this model. it is a computable and observer - independent measure based only on the internal dynamics of the system, and has been used in studies of emergence and self - organization.


in music using the twelve tone technique, combinatoriality is a quality shared by twelve - tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates ( all twelve tones ). much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. arnold schoenberg, creator of the twelve - tone technique, often combined p - 0 / i - 5 to create " two aggregates, between the first hexachords of each, and the second hexachords of each, respectively. " combinatoriality is a side effect of derived rows, where the initial segment or set may be combined with its transformations ( t, r, i, ri ) to create an entire row.


in the compact disc system, cross - interleaved reed – solomon code ( circ ) provides error detection and error correction. circ adds to every three data bytes one redundant parity byte.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2567, 12567, 24567, and 124567 are the patterns related to braille pattern dots - 1345, since the two additional dots of kantenji patterns 01345, 13457, and 013457 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


{ \ displaystyle \ sum _ { v } \ left ( { \ frac { d ( v ) } { | e | } } { \ frac { 1 } { 2 } } \ right ) d ( v ) = { \ frac { \ sum _ { v } d ( v ) ^ { 2 } } { 2 | e | } }. } we know from the definition of variance that v d ( v ) 2 | v | = μ 2 + σ 2, { \ displaystyle { \ frac { \ sum _ { v } d ( v ) ^ { 2 } } { | v | } } = \ mu ^ { 2 } + \ sigma ^ { 2 }, } where σ 2 { \ displaystyle \ sigma ^ { 2 } } is the variance of the degrees in the graph. this allows us to compute the desired expected value as v d ( v ) 2 2 | e | = | v | 2 | e | ( μ 2 + σ 2 ) = μ 2 + σ 2 μ = μ + σ 2 μ.


in most programming languages, the simplest method to convert a floating point number to an integer does not do floor or ceiling, but truncation. the reason for this is historical, as the first machines used ones'complement and truncation was simpler to implement ( floor is simpler in two's complement ). fortran was defined to require this behavior and thus almost all processors implement conversion this way. some consider this to be an unfortunate historical design decision that has led to bugs handling negative offsets and graphics on the negative side of the origin. a bit - wise right - shift of a signed integer x { \ displaystyle x } by n { \ displaystyle n } is the same as x 2 n { \ displaystyle \ left \ lfloor { \ frac { x } { 2 ^ { n } } } \ right \ rfloor }.


moreover, time - sharing was new ground. many of the concepts involved, such as virtual memory, remained unproven. for example : at the time, nobody could explain why the troubled manchester / ferranti atlas virtual memory " didn't work ".


in the context of economics, for example, this is usually economic cost or regret. in classification, it is the penalty for an incorrect classification of an example. in actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of harald cramer in the 1920s. in optimal control, the loss is the penalty for failing to achieve a desired value. in financial risk management, the function is mapped to a monetary loss.


in mathematics, a quadratic irrational number ( also known as a quadratic irrational or quadratic surd ) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their least common denominator, a quadratic irrational is an irrational root of some quadratic equation with integer coefficients. the quadratic irrational numbers, a subset of the complex numbers, are algebraic numbers of degree 2, and can therefore be expressed as a + b c d, { \ displaystyle { a + b { \ sqrt { c } } \ over d }, } for integers a, b, c, d ; with b, c and d non - zero, and with c square - free. when c is positive, we get real quadratic irrational numbers, while a negative c gives complex quadratic irrational numbers which are not real numbers.


these often arise when discretising one - dimensional problems. problems in higher dimensions also lead to banded matrices, in which case the band itself also tends to be sparse. for instance, a partial differential equation on a square domain ( using central differences ) will yield a matrix with a bandwidth equal to the square root of the matrix dimension, but inside the band only 5 diagonals are nonzero. unfortunately, applying gaussian elimination ( or equivalently an lu decomposition ) to such a matrix results in the band being filled in by many non - zero elements.


an early version was demonstrated to a special committee of the society, the recording group, and this was later presented to the aia. this was favourably received and the database has been in development ever since. in 2002 the society received an award from the aia.


{ \ displaystyle 480 = 2! \ cdot 2! \ cdot 5! }. every tree has a number of symmetries that is a jordan – polya number, and every jordan – polya number arises in this way as the order of an automorphism group of a tree. these numbers are named after camille jordan and george polya, who both wrote about them in the context of symmetries of trees. these numbers grow more quickly than polynomials but more slowly than exponentials. as well as in the symmetries of trees, they arise as the numbers of transitive orientations of comparability graphs and in the problem of finding factorials that can be represented as products of smaller factorials.


the paper is also darkened in proportion to its exposure to light, so a second reversal results which restores light and dark to their normal order. negatives were once commonly made on a thin sheet of glass rather than a plastic film, and some of the earliest negatives were made on paper. transparent positive prints can be made by printing a negative onto special positive film, as is done to make traditional motion picture film prints for use in theaters. some films used in cameras are designed to be developed by reversal processing, which produces the final positive, instead of a negative, on the original film. positives on film or glass are known as transparencies or diapositives, and if mounted in small frames designed for use in a slide projector or magnifying viewer they are commonly called slides.


the image on the right shows the permutohedron of order 4, which is the truncated octahedron. its vertices are the 24 permutations of ( 1, 2, 3, 4 ). parallel edges have the same edge color. the 6 edge colors correspond to the 6 possible transpositions of 4 elements, i. e. they indicate in which two places the connected permutations differ. ( e. g. red edges connect permutations that differ in the last two places. )


once researchers determine their preferred statistical model, different forms of regression analysis provide tools to estimate the parameters β { \ displaystyle \ beta }. for example, least squares ( including its most common variant, ordinary least squares ) finds the value of β { \ displaystyle \ beta } that minimizes the sum of squared errors i ( y i − f ( x i, β ) ) 2 { \ displaystyle \ sum _ { i } ( y _ { i } - f ( x _ { i }, \ beta ) ) ^ { 2 } }. a given regression method will ultimately provide an estimate of β { \ displaystyle \ beta }, usually denoted β ^ { \ displaystyle { \ hat { \ beta } } } to distinguish the estimate from the true ( unknown ) parameter value that generated the data.


another category of bug is called a race condition that may occur when programs have multiple components executing at the same time. if the components interact in a different order than the developer intended, they could interfere with each other and stop the program from completing its tasks. these bugs may be difficult to detect or anticipate, since they may not occur during every execution of a program.


in the fair cake - cutting problem, classic allocation rules such as divide and choose are not rm. several rules are known to be rm : when the pieces may be disconnected, any allocation rule maximizing a concave welfare function of the absolute ( not normalized ) utilities is rm. in particular, the nash - optimal rule, absolute - leximin rule and absolute - utilitarian rule are all rm. however, if the maximization uses the relative utilities ( utilities divided by total cake value ) then most of these rules are not rm ; the only one that remains rm is the nash - optimal rule.


the most common and challenging criticism to metalinguistic description theories was put forth by kripke himself : they seem to be an ad hoc explanation of a single linguistic phenomenon. why should there be a metalinguistic theory for proper nouns ( like names ) but not for common nouns, count nouns, verbs, predicates, indexicals and other parts of speech. another recent approach is two - dimensional semantics. the motivations for this approach are rather different from those that inspired other forms of descriptivism, however. two - dimensional approaches are usually motivated by a sense of dissatisfaction with the causal theorist explanation of how it is that a single proposition can be both necessary and a posteriori or contingent and a priori.


the log - logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution. it is similar in shape to the log - normal distribution but has heavier tails. unlike the log - normal, its cumulative distribution function can be written in closed form.


since there can be various levels of data classification and user clearances, this implies a quantified scale for robustness. for example, more robustness is indicated for system environments containing classified top secret information and uncleared users than for one with secret information and users cleared to at least confidential. to promote consistency and eliminate subjectivity in degrees of robustness, an extensive scientific analysis and risk assessment of the topic produced a landmark benchmark standardization quantifying security robustness capabilities of systems and mapping them to the degrees of trust warranted for various security environments.


in the case where all the matrices are hermitian positive definite and all the eigenvalues are distinct, λ i = λ 0 i + x 0 i ( δ k − λ 0 i δ m ) x 0 i x i = x 0 i ( 1 − 1 2 x 0 i δ m x 0 i ) + j = 1 j = i n x 0 j ( δ k − λ 0 i δ m ) x 0 i λ 0 i − λ 0 j x 0 j { \ displaystyle { \ begin { aligned } \ lambda _ { i } & = \ lambda _ { 0i } + \ mathbf { x } _ { 0i } ^ { \ top } \ left ( \ delta \ mathbf { k } - \ lambda _ { 0i } \ delta \ mathbf { m } \ right ) \ mathbf { x } _ { 0i } \ \ \ mathbf { x } _ { i } & = \ mathbf { x } _ { 0i } \ left ( 1 - { \ tfrac { 1 } { 2 } } \ mathbf { x } _ { 0i } ^ { \ top } \ delta \ mathbf { m } \ mathbf { x } _ { 0i } \ right ) + \ sum _ { j = 1 \ atop j \ neq i } ^ { n } { \ frac { \ mathbf { x } _ { 0j } ^ { \ top } \ left ( \ delta \ mathbf { k } - \ lambda _ { 0i } \ delta \ mathbf { m } \ right ) \ mathbf { x } _ { 0i } } { \ lambda _ { 0i } - \ lambda _ { 0j } } } \ mathbf { x } _ { 0j } \ end { aligned } } } for infinitesimal δ k { \ displaystyle \ delta \ mathbf { k } } and δ m { \ displaystyle \ delta \ mathbf { m } } ( the higher order terms in ( 3 ) being neglected ). so far, we have not proved that these higher order terms may be neglected. this point may be derived using the implicit function theorem ; in next section, we summarize the use of this theorem in order to obtain a first order expansion.


in probability a quasi - stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is initially distributed such that it can evolve for a long time without reaching it. the most common example is the evolution of a population : the only equilibrium is when there is no one left, but if we model the number of people it is likely to remain stable for a long period of time before it eventually collapses.


in statistical research, it is an aim to measure the magnitudes of phenomena. for this purpose, phenomena have to be grouped and categorized, so that distinct and discrete counting units can be defined. it must be possible to allocate all observations to mutually exclusive categories, so that they are properly quantifiable.


in statistics, the mean absolute scaled error ( mase ) is a measure of the accuracy of forecasts. it is the mean absolute error of the forecast values, divided by the mean absolute error of the in - sample one - step naive forecast. it was proposed in 2005 by statistician rob j. hyndman and professor of decision sciences anne b. koehler, who described it as a " generally applicable measurement of forecast accuracy without the problems seen in the other measurements. " the mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root - mean - square - deviation, and is therefore recommended for determining comparative accuracy of forecasts.


this can be viewed as a special case of the result relating two minimal stinespring representations. alternatively, there is an isometry scalar matrix { uij } ij ∈ cnm × nm such that a i = j = 1 u i j b j. { \ displaystyle a _ { i } = \ sum _ { j = 1 } u _ { ij } b _ { j }. } this follows from the fact that for two square matrices m and n, m m * = n n * if and only if m = n u for some unitary u.


a measurement system can be accurate but not precise, precise but not accurate, neither, or both. for example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. the result would be a consistent yet inaccurate string of results from the flawed experiment.


in most of these systems, the hardware is not open to run general purpose applications. bare machine computing originated with the application object ( ao ) concept invented by karne at towson university. it evolved over the years into dispersed operating systems ( dosc ), and eventually into the bmc paradigm.


in category theory, a map may refer to a morphism. the term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. there are also a few less common uses in logic and graph theory.


in the foundations of mathematics, formalism is associated with a certain rigorous mathematical method : see formal system. in common usage, a formalism means the out - turn of the effort towards formalisation of a given limited area. in other words, matters can be formally discussed once captured in a formal system, or commonly enough within something formalisable with claims to be one. complete formalisation is in the domain of computer science. formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems, specifically associated with david hilbert. in the philosophy of mathematics, therefore, a formalist is a person who belongs to the school of formalism, which is a certain mathematical - philosophical doctrine descending from hilbert.


the original, strong, form of the conjecture with exponent 1 / 2 has never been disproved, although it is no longer believed to be true and the term hall's conjecture now generally means the version with the ε in it. for example, in 1998, noam elkies found the example 4478849284284020423079182 - 58538865167812233 = - 1641843, for which compatibility with hall's conjecture would require c to be less than. 0214 ≈ 1 / 50, so roughly 10 times smaller than the original choice of 1 / 5 that hall suggested. the weak form of hall's conjecture would follow from the abc conjecture.


in mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. analogously, in any group g, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. in number theory, the more commonly used term is index : we can write x = indr a ( mod m ) ( read " the index of a to the base r modulo m " ) for rx ≡ a ( mod m ) if r is a primitive root of m and gcd ( a, m ) = 1. discrete logarithms are quickly computable in a few special cases. however, no efficient method is known for computing them in general. several important algorithms in public - key cryptography, such as elgamal, base their security on the assumption that the discrete logarithm problem ( dlp ) over carefully chosen groups has no efficient solution.


in relationally synthesized odia words, base morphemes ( root words ) join with bound morphemes to express grammatical function. the odia language has a tendency for commonly used words to have a 2 : 1 morpheme - word ratio i. e. on average ; there are two morphemes in a single word. because of this tendency, odia is said to " possess morphology " since almost each used word has an internal compositional structure in terms of morphemes. in the odia language, generally, separate words are used to express syntactic relationships which imparts an isolating tendency, while using inflectional morphology could have made the language more synthetic.


in mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. the equipollence relation between line segments in geometry is a common example of an equivalence relation. a simpler example is equality. any number a is equal to itself ( reflexive ).


in mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets ( or sometimes to another category, see relative concreteness below ). this functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as structure - preserving functions. many important categories have obvious interpretations as concrete categories, for example the category of topological spaces and the category of groups, and trivially also the category of sets itself. on the other hand, the homotopy category of topological spaces is not concretizable, i. e. it does not admit a faithful functor to the category of sets. a concrete category, when defined without reference to the notion of a category, consists of a class of objects, each equipped with an underlying set ; and for any two objects a and b a set of functions, called morphisms, from the underlying set of a to the underlying set of b. furthermore, for every object a, the identity function on the underlying set of a must be a morphism from a to a, and the composition of a morphism from a to b followed by a morphism from b to c must be a morphism from a to c.


in object - oriented programming, users can inherit the properties and behaviour of a superclass in subclasses. a subclass can override methods of its superclass, substituting its own implementation of the method for the superclass's implementation. sometimes the overriding method will completely replace the corresponding functionality in the superclass, while in other cases the superclass's method must still be called from the overriding method. therefore, most programming languages require that an overriding method must explicitly call the overridden method on the superclass for it to be executed.


in the absence of intervention in the foreign exchange market by national government authorities, the exchange rate of a country's currency is determined, in general, by market forces of supply and demand at a point in time. government authorities may intervene in the market from time to time to achieve specific policy objectives, such as maintaining its balance of trade or to give its exporters a competitive advantage in international trade.


{ \ displaystyle \ mathbf { y } = \ mathbf { x } \ mathbf { \ beta } + \ mathbf { \ varepsilon }, \ qquad \ operatorname { e } = 0, \ \ operatorname { cov } = \ mathbf { \ omega }. } here β ∈ r k { \ displaystyle \ beta \ in \ mathbb { r } ^ { k } } is a vector of unknown constants ( known as “ regression coefficients ” ) that must be estimated from the data. suppose b { \ displaystyle \ mathbf { b } } is a candidate estimate for β { \ displaystyle \ mathbf { \ beta } }.


in statically typed languages ( such as c + + and java ), the term generic functions refers to a mechanism for compile - time polymorphism ( static dispatch ), specifically parametric polymorphism. these are functions defined with typeparameters, intended to be resolved with compile time type information. the compiler uses these types to instantiate suitable versions, resolving any function overloading appropriately.


in queueing theory, a discipline within the mathematical theory of probability, a fork – join queue is a queue where incoming jobs are split on arrival for service by numerous servers and joined before departure. the model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers ( in a warehouse or manufacturing setting ). : 78 – 80 the key quantity of interest in this model is usually the time taken to service a complete job. the model has been described as a " key model for the performance analysis of parallel and distributed systems. " few analytical results exist for fork – join queues, but various approximations are known. the situation where jobs arrive according to a poisson process and service times are exponentially distributed is sometimes referred to as a flatto – hahn – wright model or fhw model.


in mathematics and computer science, a shortest - path tree rooted at a vertex v of a connected, undirected graph g is a spanning tree t of g, such that the path distance from root v to any other vertex u in t is the shortest path distance from v to u in g. in connected graphs where shortest paths are well - defined ( i. e. where there are no negative - length cycles ), we may construct a shortest - path tree using the following algorithm : compute dist ( u ), the shortest - path distance from root v to vertex u in g using dijkstra's algorithm or bellman – ford algorithm. for all non - root vertices u, we can assign to u a parent vertex pu such that pu is connected to u, and that dist ( pu ) + edge _ dist ( pu, u ) = dist ( u ). in case multiple choices for pu exist, choose pu for which there exists a shortest path from v to pu with as few edges as possible ; this tie - breaking rule is needed to prevent loops when there exist zero - length cycles.


these include, among others : the " is greater than ", " is equal to ", and " divides " relations in arithmetic ; the " is congruent to " relation in geometry ; the " is adjacent to " relation in graph theory ; the " is orthogonal to " relation in linear algebra. a function may be defined as a special kind of binary relation. binary relations are also heavily used in computer science.


in order to identify which transitions must be made, the protocol detects sharing using a special bus line named copiesexist. all other caches snoop all memory operations and raise the copiesexist ( c ) if they detect a " snoop hit ", i. e. if they have a copy of the data in their own cache. an arrow that goes from nowhere to a state represents a newly loaded block.


the weights used are usually based on the aggregate input shares either factor earns. this ratio is often quoted as : 33 % return to capital and 67 % return to labor ( in western nations ). in a growing economy, capital is accumulated faster than people are born, so the denominator in the growth function under the mfp calculation is growing faster than in the alp calculation. hence, mfp growth is almost always lower than alp growth. ( therefore, measuring in alp terms increases the apparent capital deepening effect. ) mfp is measured by the " solow residual ", not alp.


the problem is to approximate the integral of a function f as the average of the function evaluated at a set of points x1,..., xn : s f ( u ) d u ≈ 1 n i = 1 n f ( x i ). { \ displaystyle \ int _ { ^ { s } } f ( u ) \, { \ rm { d } } u \ approx { \ frac { 1 } { n } } \, \ sum _ { i = 1 } ^ { n } f ( x _ { i } ). } since we are integrating over the s - dimensional unit cube, each xi is a vector of s elements.


values also have types, which can be checked and queried at runtime. typing of variables also allows polymorphisms to be resolved at compile time. however, this is different from the polymorphism used in object - oriented function calls ( referred to as virtual functions in c + + ) which resolves the call based on the value type as opposed to the supertypes the variable is allowed to have.


in the following soft clustering example, the reference vector y { \ displaystyle y \, } contains sample categories and the joint probability p ( x, y ) { \ displaystyle p ( x, y ) \, } is assumed known. a soft cluster c k { \ displaystyle c _ { k } \, } is defined by its probability distribution over the data samples x i : p ( c k | x i ) { \ displaystyle x _ { i } : \, \, \, p ( c _ { k } | x _ { i } ) }. tishby et al. presented the following iterative set of equations to determine the clusters which are ultimately a generalization of the blahut - arimoto algorithm, developed in rate distortion theory. the application of this type of algorithm in neural networks appears to originate in entropy arguments arising in the application of gibbs distributions in deterministic annealing.


so we must sum over all these possibilities : pr ( median = v ) = i = 0 n k = 0 n n! i! ( n − i − k )!


most computers organize files into hierarchies using folders, directories, or catalogs. the concept is the same irrespective of the terminology used.


in statistics, the 68 – 95 – 99. 7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution : 68 %, 95 %, and 99. 7 % of the values lie within one, two, and three standard deviations of the mean, respectively. in mathematical notation, these facts can be expressed as follows, where pr ( ) is the probability function, χ is an observation from a normally distributed random variable, μ ( mu ) is the mean of the distribution, and σ ( sigma ) is its standard deviation : the usefulness of this heuristic especially depends on the question under consideration. in the empirical sciences, the so - called three - sigma rule of thumb ( or 3σ rule ) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99. 7 % probability as near certainty. in the social sciences, a result may be considered " significant " if its confidence level is of the order of a two - sigma effect ( 95 % ), while in particle physics, there is a convention of a five - sigma effect ( 99. 99994 % confidence ) being required to qualify as a discovery.


in the first version of the above - cited paper, the authors proved the asymptotic time complexity of the algorithm to be o ~ ( log ( n ) 12 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 12 } ) } ( using o from big o notation ) — the twelfth power of the number of digits in n times a factor that is polylogarithmic in the number of digits. however, this upper bound was rather loose ; a widely - held conjecture about the distribution of the sophie germain primes would, if true, immediately cut the worst case down to o ~ ( log ( n ) 6 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 6 } ) }. in the months following the discovery, new variants appeared ( lenstra 2002, pomerance 2002, berrizbeitia 2002, cheng 2003, bernstein 2003a / b, lenstra and pomerance 2003 ), which improved the speed of computation greatly. owing to the existence of the many variants, crandall and papadopoulos refer to the " aks - class " of algorithms in their scientific paper " on the implementation of aks - class primality tests ", published in march 2003.


in the early years of knowledge - based systems the knowledge - bases were fairly small. the knowledge - bases that were meant to actually solve real problems rather than do proof of concept demonstrations needed to focus on well defined problems. so for example, not just medical diagnosis as a whole topic, but medical diagnosis of certain kinds of diseases. as knowledge - based technology scaled up, the need for larger knowledge bases and for modular knowledge bases that could communicate and integrate with each other became apparent.


in doctoral mathematics departments, however, only about 58 % of statistics course instructors had at least a master ’ s degree in statistics or biostatistics as their highest degree earned. in master ’ s - level mathematics departments, the corresponding percentage was near 44 %, and in bachelor ’ s - level departments only 19 % of statistics course instructors had at least a master ’ s degree in statistics or biostatistics as their highest degree earned. as we expected, a large majority of instructors in statistics departments ( 83 % for doctoral departments and 62 % for master ’ s departments ) held doctoral degrees in either statistics or biostatistics.


in more modern terms, a crypt is most often a stone chambered burial vault used to store the deceased. placing a corpse into a crypt can be called immurement, and is a method of final disposition, as an alternative to, for example, cremation. crypts are usually found in cemeteries and under public religious buildings, such as churches or cathedrals, but are also occasionally found beneath mausolea or chapels on personal estates. wealthy or prestigious families will often have a'family crypt'or'vault,'in which all members of the family are interred.


according to the tcp specification, that first sequence number sent by an endpoint can be any value as decided by that endpoint. as the sequence number is chosen by the sender, returned by the recipient, and has no otherwise - defined internal structure, it can be overloaded to carry additional data. the following describes one possible implementation, however as there is no public standard to follow, the order, length, and semantics of the fields may differ between syn cookie implementations.


when using a file transfer protocol, the packets themselves offer their own framing. the packets will always send a continuous stream of data, so the clock cannot " drift " in the same way that it could for data being sent by a user typing on a keyboard. by turning off these framing bits when operating on an error - corrected link, that 20 % overhead can be eliminated.


in stratigraphic excavation, the goal is to remove some or, preferably, all archaeological deposits and features in the reverse order they were created and construct a harris matrix as a chronological record or " sequence " of the site. this harris matrix is used for interpretation and combining contexts into ever larger units of understanding. this stratigraphic removal of the site is crucial for understanding the chronology of events on site. stratigraphic excavation involves a process of cleaning or " troweling back " the surface of the site and isolating contexts and edges which are definable as either : discrete, discernible " edges " that are formed by being completely separated from the surrounding surface and therefore stratigraphically later than its surroundings discrete, discernible " edges " ( as in 1. )


in mathematics, an edge cycle cover ( sometimes called simply cycle cover ) of a graph is a family of cycles which are subgraphs of g and contain all edges of g. if the cycles of the cover have no vertices in common, the cover is called vertex - disjoint or sometimes simply disjoint cycle cover. in this case, the set of the cycles constitutes a spanning subgraph of g. if the cycles of the cover have no edges in common, the cover is called edge - disjoint or simply disjoint cycle cover.


in probability theory, the chain rule ( also called the general product rule ) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities. the rule is notably used in the context of discrete stochastic processes and in applications, e. g. the study of bayesian networks, which describe a probability distribution in terms of conditional probabilities.


thus the number −1, 234, 567 is 7 digits wide and is encoded as : 0001 0010 0011 0100 0101 0110 0111 1101 1 2 3 4 5 6 7 − like character strings, the first byte of the packed decimal – that with the most significant two digits – is usually stored in the lowest address in memory, independent of the endianness of the machine. in contrast, a 4 - byte binary two's complement integer can represent values from −2, 147, 483, 648 to + 2, 147, 483, 647. while packed bcd does not make optimal use of storage ( using about 20 % more memory than binary notation to store the same numbers ), conversion to ascii, ebcdic, or the various encodings of unicode is made trivial, as no arithmetic operations are required.


in programming language theory and type theory, polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different types. the concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. the most commonly recognized major classes of polymorphism are : ad hoc polymorphism : defines a common interface for an arbitrary set of individually specified types. parametric polymorphism : not specifying concrete types and instead use abstract symbols that can substitute for any type. subtyping ( also called subtype polymorphism or inclusion polymorphism ) : when a name denotes instances of many different classes related by some common superclass.


in recent years, considerable effort has been put into improving the performance of existing algorithms. among them are clarans, and birch. with the recent need to process larger and larger data sets ( also known as big data ), the willingness to trade semantic meaning of the generated clusters for performance has been increasing. this led to the development of pre - clustering methods such as canopy clustering, which can process huge data sets efficiently, but the resulting " clusters " are merely a rough pre - partitioning of the data set to then analyze the partitions with existing slower methods such as k - means clustering.


though the transportation network does not depend on the power network to function, the communications network does. thus the deactivation of a critical number of nodes in either the power network or the communication network can lead to a series of cascading failures across the system with potentially catastrophic repercussions. if the two networks were treated in isolation, this important feedback effect would not be seen and predictions of network robustness would be greatly overestimated.


in mathematics, given two groups, ( g, ∗ ) and ( h, · ), a group homomorphism from ( g, ∗ ) to ( h, · ) is a function h : g → h such that for all u and v in g it holds that h ( u ∗ v ) = h ( u ) ⋅ h ( v ) { \ displaystyle h ( u * v ) = h ( u ) \ cdot h ( v ) } where the group operation on the left side of the equation is that of g and on the right side that of h. from this property, one can deduce that h maps the identity element eg of g to the identity element eh of h, h ( e g ) = e h { \ displaystyle h ( e _ { g } ) = e _ { h } } and it also maps inverses to inverses in the sense that h ( u − 1 ) = h ( u ) − 1. { \ displaystyle h \ left ( u ^ { - 1 } \ right ) = h ( u ) ^ { - 1 }. \, } hence one can say that h " is compatible with the group structure ". older notations for the homomorphism h ( x ) may be xh or xh, though this may be confused as an index or a general subscript. in automata theory, sometimes homomorphisms are written to the right of their arguments without parentheses, so that h ( x ) becomes simply x h { \ displaystyle xh }. in areas of mathematics where one considers groups endowed with additional structure, a homomorphism sometimes means a map which respects not only the group structure ( as above ) but also the extra structure. for example, a homomorphism of topological groups is often required to be continuous.


in telecommunication, attack time is the time between the instant that a signal at the input of a device or circuit exceeds the activation threshold of the device or circuit and the instant that the device or circuit reacts in a specified manner, or to a specified degree, to the input. attack time occurs in devices such as clippers, peak limiters, compressors, and voxes.


equipment will search for a bit which has the correct pattern, and will align its framing based on that bit. the pattern sent is 12 bits long, so every group of 12 frames is called a superframe. the pattern used in the 193rd bit is 100011 011100. each channel sends two bits of call supervision data during each superframe using robbed - bit signaling during frames 6 and 12 of the superframe. more specifically, after the 6th and 12th bit in the superframe pattern, the least significant data bit of each channel ( bit 8 ; t1 data is sent big - endian and uses 1 - origin numbering ) is replaced by a " channel - associated signalling " bit ( bits a and b, respectively ). superframe remained in service in many places through the turn of the century, replaced by the improved extended superframe ( esf ) of the 1980s in applications where its additional features were desired.


the cases ( x, y, z ) = ( n, n, 2 ) and all its permutations were proven for n ≥ 4 by darmon and merel in 1995 following work from euler and poonen. the cases ( x, y, z ) = ( n, n, 3 ) and all its permutations were proven for n ≥ 3 by edouard lucas, bjorn poonen, and darmon and merel. the case ( x, y, z ) = ( 2n, 2n, 5 ) and all its permutations were proven for n ≥ 2 by bennett in 2006.


the second expression is evaluated prior to each iteration and the loop is terminated if it evaluates to false. the third expression is evaluated after each iteration, prior to deciding whether to perform the next. this for loop is the only looping construct that can not have a continue block, but expr3 is functionally equivalent.


in practice, the two coordinate - free definitions described above are rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived. the notation ∇ × f has its origins in the similarities to the 3 - dimensional cross product, and it is useful as a mnemonic in cartesian coordinates if ∇ is taken as a vector differential operator del. such notation involving operators is common in physics and algebra. expanded in 3 - dimensional cartesian coordinates ( see del in cylindrical and spherical coordinates for spherical and cylindrical coordinate representations ), ∇ × f is, for f composed of ( where the subscripts indicate the components of the vector, not partial derivatives ) : ∇ × f = | ı ^ ^ k ^ ∂ ∂ x ∂ ∂ y ∂ ∂ z f x f y f z | { \ displaystyle \ nabla \ times \ mathbf { f } = { \ begin { vmatrix } { \ boldsymbol { \ hat { \ imath } } } & { \ boldsymbol { \ hat { \ jmath } } } & { \ boldsymbol { \ hat { k } } } \ \ { \ dfrac { \ partial } { \ partial x } } & { \ dfrac { \ partial } { \ partial y } } & { \ dfrac { \ partial } { \ partial z } } \ \ f _ { x } & f _ { y } & f _ { z } \ end { vmatrix } } } where i, j, and k are the unit vectors for the x -, y -, and z - axes, respectively.


in the eighth chapter titled " the explanatory power of linguistic theory ", chomsky writes a linguistic theory cannot content itself by just generating valid grammatical sentences. it also has to account for other structural phenomena at different levels of linguistic representation. at a certain linguistic level, there can be two items which can be understood having different meanings but they are structurally indistinguishable within that level. this is called a “ constructional homonymity ”.


{ x p ( x ) } = { x q ( x ) } { \ displaystyle \ { x \ mid p ( x ) \ } = \ { x \ mid q ( x ) \ } } if and only if p ( x ) q ( x ). { \ displaystyle p ( x ) \ leftrightarrow q ( x ). }


in probability theory, the doob – dynkin lemma, named after joseph l. doob and eugene dynkin, characterizes the situation when one random variable is a function of another by the inclusion of the σ { \ displaystyle \ sigma } - algebras generated by the random variables. the usual statement of the lemma is formulated in terms of one random variable being measurable with respect to the σ { \ displaystyle \ sigma } - algebra generated by the other. the lemma plays an important role in the conditional expectation in probability theory, where it allows replacement of the conditioning on a random variable by conditioning on the σ { \ displaystyle \ sigma } - algebra that is generated by the random variable.


in public key infrastructure, a validation authority ( va ) is an entity that provides a service used to verify the validity or revocation status of a digital certificate per the mechanisms described in the x. 509 standard and rfc 5280 ( page 69 ). the dominant method used for this purpose is to host a certificate revocation list ( crl ) for download via the http or ldap protocols. to reduce the amount of network traffic required for certificate validation, the ocsp protocol may be used instead. while a validation authority is capable of responding to a network - based request for a crl, it lacks the ability to issue or revoke certificates. it must be continuously updated with current crl information from a certificate authority which issued the certificates contained within the crl.


it shows that it is impossible to express the square root of 2 as a ratio of two integers. another consequential proof of impossibility was ferdinand von lindemann's proof in 1882, which showed that the problem of squaring the circle cannot be solved because the number π is transcendental ( i. e., non - algebraic ), and that only a subset of the algebraic numbers can be constructed by compass and straightedge. two other classical problems — trisecting the general angle and doubling the cube — were also proved impossible in the 19th century, and all of these problems gave rise to research into more complicated mathematical structures.


in mathematics and computing, the hexadecimal ( also base - 16 or simply hex ) numeral system is a positional numeral system that represents numbers using a radix ( base ) of sixteen. unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols " 0 " – " 9 " to represent values 0 to 9, and " a " – " f " ( or alternatively " a " – " f " ) to represent values from ten to fifteen. software developers and system designers widely use hexadecimal numbers because they provide a human - friendly representation of binary - coded values. each hexadecimal digit represents four bits ( binary digits ), also known as a nibble ( or nybble ).


previous studies have been conducted, focusing on priming effects having a rapid rise time and a hasty decay time. for example, an experiment by donald foss researched the decay time of semantic facilitation in lists and sentences. three experiments were conducted and it was found that semantic relationships within words differs when words occur in sentences rather than lists. thus, supporting the ongoing discourse model.


in order to abstract the concept of orientation on the edges of a graph to sets, one needs the ability to assign " direction " to the elements of a set. the way this achieved is with the following definition of signed sets. a signed set, x { \ displaystyle x }, combines a set of objects, x _ { \ displaystyle { \ underline { x } } }, with a partition of that set into two subsets : x + { \ displaystyle x ^ { + } } and x − { \ displaystyle x ^ { - } }. the members of x + { \ displaystyle x ^ { + } } are called the positive elements ; members of x − { \ displaystyle x ^ { - } } are the negative elements. the set x _ = x + ∪ x − { \ displaystyle { \ underline { x } } = x ^ { + } \ cup x ^ { - } } is called the support of x { \ displaystyle x }. the empty signed set, ∅ { \ displaystyle \ emptyset }, is defined as the empty set ∅ _ { \ displaystyle { \ underline { \ emptyset } } } combined with a " partition " of it into two empty sets : ∅ + { \ displaystyle \ emptyset ^ { + } } and ∅ − { \ displaystyle \ emptyset ^ { - } }.


in multiprocessor systems, a processor may send an interrupt request to another processor via inter - processor interrupts ( ipi ).


mdp also used packet - level forward error correction coding concepts as a repair mechanism. encoded parity repair packets were generally sent in response to repair requests by receivers. in this way no additional protocol overhead was added above selective retransmission methods.


in telecommunications, a channel bank is a device that performs multiplexing or demultiplexing ( " demux " ) of a group of communications channels, such as analog or digital telephone lines, into one channel of higher bandwidth or higher digital bit rate, such as a ds - 1 ( t1 ) circuit, so that all the channels can be sent simultaneously over a single cable called a trunkline. a channel bank may be located in a telephone exchange, or in an enterprise's telephone closet or enclosure where it " breaks out " individual telephone lines from a high - capacity telephone trunk line connected to the central telephone office, or the enterprise's pbx system.


in one of google's promotional videos for search published in the summer of 2010, the majority of the links available were reported to be produced at content farms. in late february 2011, google announced it was adjusting search algorithms significantly to " provide better rankings for high - quality sites — sites with original content and information such as research, in - depth reports, thoughtful analysis and so on. " this was reported to be a reaction to content farms and an attempt to reduce their effectiveness in manipulating search result rankings. the privacy - focused search engine duckduckgo does not show results from content farms.


construct the shortest - path tree using the edges between each node and its parent. the above algorithm guarantees the existence of shortest - path trees. like minimum spanning trees, shortest - path trees in general are not unique. in graphs for which all edge weights are equal, shortest path trees coincide with breadth - first search trees.


there is also bell's theorem : no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. while an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single counterexample. such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re - examined.


in telecommunication, the term terminal equipment has the following meanings : communications equipment at either end of a communications link, used to permit the stations involved to accomplish the mission for which the link was established. in radio - relay systems, equipment used at points where data are inserted or derived, as distinct from equipment used only to relay a reconstituted signal. telephone and telegraph switchboards and other centrally located equipment at which communications circuits are terminated.


for the source and destination of every flight i, one adds two nodes to v, node si as the source and node di as the destination node of flight i. one also adds the following edges to e : an edge with capacity between s and each si. an edge with capacity between each di and t. an edge with capacity between each pair of si and di. an edge with capacity between each di and sj, if source sj is reachable with a reasonable amount of time and cost from the destination of flight i. an edge with capacity between s and t. in the mentioned method, it is claimed and proved that finding a flow value of k in g between s and t is equal to finding a feasible schedule for flight set f with at most k crews. another version of airline scheduling is finding the minimum needed crews to perform all the flights.


in mathematics, a surface is a mathematical model of the common concept of a surface. it is a generalization of a plane, but, unlike a plane, it may be curved ; this is analogous to a curve generalizing a straight line. there are several more precise definitions, depending on the context and the mathematical tools that are used for the study. the simplest mathematical surfaces are planes and spheres in the euclidean 3 - space.


as a result, it is common for researchers working in the majority of languages with only one type or the other to simply use the alveolar symbols indifferently for both types, unless they specifically want to call attention to the distinction. the most common sounds are the stops and. more generally, several kinds are distinguished :, voiceless dental plosive, voiced dental plosive, dental ejective, voiced dental implosive = = notes = =


in mathematics, a ternary operation is an n - ary operation with n = 3. a ternary operation on a set a takes any given three elements of a and combines them to form a single element of a. in computer science, a ternary operator is an operator that takes three arguments as input and returns one output.


thus, in each convolutional layer, each neuron takes input from a larger area in the input than previous layers. this is due to applying the convolution over and over, which takes the value of a pixel into account, as well as its surrounding pixels.


in semantics, the most well - known types of semantic equivalence are dynamic equivalence and formal equivalence ( coined by eugene nida ) are associated with two dissimilar translation approaches that are employed to achieve different levels of literalness between the source and target text, as evidenced in biblical translation. the two have been understood basically, with dynamic equivalence as sense - for - sense translation ( translating the meanings of phrases or whole sentences ) with readability in mind, and with formal equivalence as word - for - word translation ( translating the meanings of words and phrases in a more literal way ), keeping literal fidelity.


in software engineering and hardware engineering, serviceability ( also known as supportability ) is one of the - ilities or aspects ( from ibm's ras ( u ) ( reliability, availability, serviceability, and usability ) ). it refers to the ability of technical support personnel to install, configure, and monitor computer products, identify exceptions or faults, debug or isolate faults to root cause analysis, and provide hardware or software maintenance in pursuit of solving a problem and restoring the product into service. incorporating serviceability facilitating features typically results in more efficient product maintenance and reduces operational costs and maintains business continuity. examples of features that facilitate serviceability include : help desk notification of exceptional events ( e. g., by electronic mail or by sending text to a pager ) network monitoring documentation event logging / tracing ( software ) logging of program state, such as execution path and / or local and global variables procedure entry and exit, optionally with incoming and return variable values ( see : subroutine ) exception block entry, optionally with local state ( see : exception handling ) software upgrade graceful degradation, where the product is designed to allow recovery from exceptional events without intervention by technical support staff hardware replacement or upgrade planning, where the product is designed to allow efficient hardware upgrades with minimal computer system downtime ( e. g., hotswap components.


in probability theory and statistics, the zipf – mandelbrot law is a discrete probability distribution. also known as the pareto – zipf law, it is a power - law distribution on ranked data, named after the linguist george kingsley zipf who suggested a simpler distribution called zipf's law, and the mathematician benoit mandelbrot, who subsequently generalized it. the probability mass function is given by : f ( k ; n, q, s ) = 1 / ( k + q ) s h n, q, s { \ displaystyle f ( k ; n, q, s ) = { \ frac { 1 / ( k + q ) ^ { s } } { h _ { n, q, s } } } } where h n, q, s { \ displaystyle h _ { n, q, s } } is given by : h n, q, s = i = 1 n 1 ( i + q ) s { \ displaystyle h _ { n, q, s } = \ sum _ { i = 1 } ^ { n } { \ frac { 1 } { ( i + q ) ^ { s } } } } which may be thought of as a generalization of a harmonic number. in the formula, k { \ displaystyle k } is the rank of the data, and q { \ displaystyle q } and s { \ displaystyle s } are parameters of the distribution.


in the uml superstructure 2. 4. 1 specification document the following definition is given : the notion of power type was inspired by the notion of power set. a power set is defined as a set whose instances are subsets. in essence, then, a power type is a class whose instances are subclasses. = = references = =


in mathematics, a commutative ring is a ring in which the multiplication operation is commutative. the study of commutative rings is called commutative algebra. complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. this distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings.


in symbols, one writes φ i ( n ) = { φ ( n ), if i = 1 φ ( φ i − 1 ( n ) ), if i ≥ 2 { \ displaystyle \ varphi ^ { i } ( n ) = { \ begin { cases } \ varphi ( n ), & { \ text { if } } i = 1 \ \ \ varphi ( \ varphi ^ { i - 1 } ( n ) ), & { \ text { if } } i \ geq 2 \ end { cases } } } for the iterated totient function. then if c is the integer such that φ c ( n ) = 2, { \ displaystyle \ displaystyle \ varphi ^ { c } ( n ) = 2, } one has that n is a perfect totient number if n = i = 1 c + 1 φ i ( n ). { \ displaystyle n = \ sum _ { i = 1 } ^ { c + 1 } \ varphi ^ { i } ( n ). }


in software engineering, canonical schema is a design pattern, applied within the service - orientation design paradigm, which aims to reduce the need for performing data model transformation when services exchange messages that reference the same data model.


the small veblen ordinal θ ω ω ( 0 ) { \ displaystyle \ theta _ { \ omega ^ { \ omega } } ( 0 ) } or ψ ( ω ω ω ) { \ displaystyle \ psi ( \ omega ^ { \ omega ^ { \ omega } } ) } is the limit of ordinals that can be described using a version of veblen functions with finitely many arguments. it is the ordinal that measures the strength of kruskal's theorem. it is also the ordinal type of a certain ordering of rooted trees ( jervell 2005 ).


lovelace went on to write one of history's earliest computer programs that aided babbage in the design of the analytical engine, a machine capable of running programs automatically. lovelace's work with babbage positioned her as a significant pioneer in the field of cybersecurity. kevin kelly, the co - founder of wired magazine, once stated that lovelace played a major role in the invention of computer science, and there are more lines of code written in languages that she created than in c + +, java, javascript, or python combined.


in a priority interrupt system, the flih also ( briefly ) masks other interrupts of equal or lesser priority. a slih completes long interrupt processing tasks similarly to a process. slihs either have a dedicated kernel thread for each handler, or are executed by a pool of kernel worker threads.


extended real - valued function for which the minimization problem is not solved by any one of these three trivial cases are exactly those that are called proper. many ( although not all ) results whose hypotheses require that the function be proper add this requirement specifically to exclude these trivial cases. if the problem is instead a maximization problem ( which would be clearly indicated, such as by the function being concave rather than convex ) then the definition of " proper " is defined in an analogous ( albeit technically different ) manner but with the same goal : to exclude cases where the maximization problem can be answered immediately. specifically, a concave function g { \ displaystyle g } is called proper if its negation − g, { \ displaystyle - g, } which is a convex function, is proper in the sense defined above.


in quantum information theory, the identity channel is a noise - free quantum channel. that is, the channel outputs exactly what was put in. the identity channel is commonly denoted as i { \ displaystyle i }, i d { \ displaystyle { \ mathsf { id } } } or i { \ displaystyle \ mathbb { i } }. = = references = =


in the case of the original gratzel and o'regan design, the cell has 3 primary parts. on top is a transparent anode made of fluoride - doped tin dioxide ( sno2 : f ) deposited on the back of a ( typically glass ) plate. on the back of this conductive plate is a thin layer of titanium dioxide ( tio2 ), which forms into a highly porous structure with an extremely high surface area. the ( tio2 ) is chemically bound by a process called sintering.


in principle fsk can be implemented by using completely independent free - running oscillators, and switching between them at the beginning of each symbol period. in general, independent oscillators will not be at the same phase and therefore the same amplitude at the switch - over instant, causing sudden discontinuities in the transmitted signal. in practice, many fsk transmitters use only a single oscillator, and the process of switching to a different frequency at the beginning of each symbol period preserves the phase. the elimination of discontinuities in the phase ( and therefore elimination of sudden changes in amplitude ) reduces sideband power, reducing interference with neighboring channels.


with since f { \ displaystyle f } does not appear explicitly in l, { \ displaystyle l, } the first term in the euler – lagrange equation vanishes for all f ( x ) { \ displaystyle f ( x ) } and thus, substituting for l { \ displaystyle l } and taking the derivative, thus for some constant c. { \ displaystyle c. } then where solving, we get which implies that is a constant and therefore that the shortest curve that connects two points ( x 1, y 1 ) { \ displaystyle \ left ( x _ { 1 }, y _ { 1 } \ right ) } and ( x 2, y 2 ) { \ displaystyle \ left ( x _ { 2 }, y _ { 2 } \ right ) } is and we have thus found the extremal function f ( x ) { \ displaystyle f ( x ) } that minimizes the functional a { \ displaystyle a } so that a { \ displaystyle a } is a minimum.


in mathematical optimization, bland's rule ( also known as bland's algorithm, bland's anti - cycling rule or bland's pivot rule ) is an algorithmic refinement of the simplex method for linear optimization. with bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling. the original simplex algorithm starts with an arbitrary basic feasible solution, and then changes the basis in order to decrease the minimization target and find an optimal solution. usually, the target indeed decreases in every step, and thus after a bounded number of steps an optimal solution is found. however, there are examples of degenerate linear programs, on which the original simplex algorithm cycles forever.


in number theory, brocard's conjecture is the conjecture that there are at least four prime numbers between ( pn ) 2 and ( pn + 1 ) 2, where pn is the nth prime number, for every n ≥ 2. the conjecture is named after henri brocard. it is widely believed that this conjecture is true.


in mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be euclidean vectors, or more generally, members of a vector space. for representing a vector, the common typographic convention is lower case, upright boldface type, as in v. the international organization for standardization ( iso ) recommends either bold italic serif, as in v, or non - bold italic serif accented by a right arrow, as in v → { \ displaystyle { \ vec { v } } }. in advanced mathematics, vectors are often represented in a simple italic type, like any variable.


the member also has duties to the tax authorities, notably of compliance with the law and the honest presentation of his client's circumstances. it is the taxpayer's responsibility to ensure that returns made to the tax authorities are correct and complete. it is for the member to assist him to decide on the extent and manner of disclosure of facts in relation to his tax affairs.


" phenotypic correlations between psychological traits show significant and substantial genetic mediation. " " the heritability of intelligence increases throughout development. " " age - to - age stability is mainly due to genetics. "


this does not allow for full cross - referencing of information and, according to p. simon and j. stavo - debauge, produces the opposite effect by creating a quasi - hierarchy, with foreigners from outside the european union making up the group with the most difficulties. paradoxically, a highly aggregated country classification is more evocative of ethnic discrimination than a country - level classification. other organizations redact variables such as nationality, necessary for the proper processing of their files, when publishing data.


in some text messaging software products, an ellipsis is displayed while the interlocutor is typing characters. the feature has been referred to as a " typing awareness indicator ", for which patents have been filed since the 1990s.


in mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of lie type, or else it is one of twenty - six or twenty - seven exceptions, called sporadic. the proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. simple groups can be seen as the basic building blocks of all finite groups, reminiscent of the way the prime numbers are the basic building blocks of the natural numbers.


when the commutative diagrams of a category are interpreted as a typed equational theory whose objects are the types, a codiscrete posetal category corresponds to an inconsistent theory understood as one satisfying the axiom x = y at all types. viewing a 2 - category as an enriched category whose hom - objects are categories, the hom - objects of any extension of a posetal category to a 2 - category having the same 1 - cells are monoids. some lattice - theoretic structures are definable as posetal categories of a certain kind, usually with the stronger assumption of being skeletal.


in probability theory and statistics, the normal - gamma distribution ( or gaussian - gamma distribution ) is a bivariate four - parameter family of continuous probability distributions. it is the conjugate prior of a normal distribution with unknown mean and precision.


s. { \ displaystyle \ mathbb { e } \ left = 0, a. s. }


in mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. for example, 1 / 2, 3 / 2, and 3 / 8 are dyadic rationals, but 1 / 3 is not. these numbers are important in computer science because they are the only ones with finite binary representations.


subshells are usually identified by their n { \ displaystyle n } - and ℓ { \ displaystyle \ ell } - values. n { \ displaystyle n } is represented by its numerical value, but ℓ { \ displaystyle \ ell } is represented by a letter as follows : 0 is represented by's ', 1 by'p ', 2 by'd ', 3 by'f ', and 4 by'g '. for instance, one may speak of the subshell with n = 2 { \ displaystyle n = 2 } and ℓ = 0 { \ displaystyle \ ell = 0 } as a'2s subshell '.


in mathematics, the sieve of eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. it does so by iteratively marking as composite ( i. e., not prime ) the multiples of each prime, starting with the first prime number, 2. the multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. this is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.


. ( ( ( ( ( p + p ) + p ) + p ) + … ) + p ) + p = p + p + + p + p { \ displaystyle (.... ( ( ( ( ( p + p ) + p ) + p ) + \ dots ) \ dots + p ) + p = p + p + \ dots + p + p }. note that, this simple algorithm takes at most 2l steps and each step consists of a doubling and ( if ki = 0 ) adding two points. so, this is one of the reasons why addition and doubling formulas are defined. furthermore, this method is applicable to any group and if the group law is written multiplicatively, the double - and - add algorithm is instead called square - and - multiply algorithm.


in mathematics, an associative algebra a is an algebraic structure with compatible operations of addition, multiplication ( assumed to be associative ), and a scalar multiplication by elements in some field k. the addition and multiplication operations together give a the structure of a ring ; the addition and scalar multiplication operations together give a the structure of a vector space over k. in this article we will also use the term k - algebra to mean an associative algebra over the field k. a standard first example of a k - algebra is a ring of square matrices over a field k, with the usual matrix multiplication. a commutative algebra is an associative algebra that has a commutative multiplication, or, equivalently, an associative algebra that is also a commutative ring. in this article associative algebras are assumed to have a multiplicative identity, denoted 1 ; they are sometimes called unital associative algebras for clarification. in some areas of mathematics this assumption is not made, and we will call such structures non - unital associative algebras.


in statistics, the lehmann – scheffe theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. the theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. the lehmann – scheffe theorem is named after erich leo lehmann and henry scheffe, given their two early papers. if t is a complete sufficient statistic for θ and e ( g ( t ) ) = τ ( θ ) then g ( t ) is the uniformly minimum - variance unbiased estimator ( umvue ) of τ ( θ ).


in nonlinear optimization, quasiconvex programming studies iterative methods that converge to a minimum ( if one exists ) for quasiconvex functions. quasiconvex programming is a generalization of convex programming. quasiconvex programming is used in the solution of " surrogate " dual problems, whose biduals provide quasiconvex closures of the primal problem, which therefore provide tighter bounds than do the convex closures provided by lagrangian dual problems. in theory, quasiconvex programming and convex programming problems can be solved in reasonable amount of time, where the number of iterations grows like a polynomial in the dimension of the problem ( and in the reciprocal of the approximation error tolerated ) ; however, such theoretically " efficient " methods use " divergent - series " stepsize rules, which were first developed for classical subgradient methods. classical subgradient methods using divergent - series rules are much slower than modern methods of convex minimization, such as subgradient projection methods, bundle methods of descent, and nonsmooth filter methods.


it takes inspiration from nusap, a method used to qualify the worth ( quality ) of quantitative information with the generation of ` pedigrees'of numbers. likewise, sensitivity auditing has been developed to provide pedigrees of models and model - based inferences.


the notion of a replicating portfolio is fundamental to rational pricing, which assumes that market prices are arbitrage - free – concretely, arbitrage opportunities are exploited by constructing a replicating portfolio. in practice, replicating portfolios are seldom, if ever, exact replications. most significantly, unless they are claims against the same counterparties, there is credit risk. further, dynamic replication is invariably imperfect, since actual price movements are not infinitesimal – they may in fact be large – and transaction costs to change the hedge are not zero.


in the context of biometric systems, presentation attacks may also be called " spoofing attacks ". as per the recent iso / iec 30107 standard, presentation attacks are defined as " presentation to the biometric capture subsystem with the goal of interfering with the operation of the biometric system ". these attacks can be either impersonation or obfuscation attacks.