use of pocsag on the 26 mhz and 27 mhz band has been logged by several listeners in europe, specifically frequencies 26. 350 mhz, 26. 500 mhz, 26. 705 mhz, 26. 725 mhz, 26. 755 mhz, 27. 005 mhz, 27. 007 mhz, 27. 255 mhz ( see note below regarding legal use of 27. 255 mhz for paging in the united states ). it appears that us - specification paging systems operating on 27. 255 mhz have been sold in italy and other european countries. the former monopoly operator sip ( which later became tim ) used the following frequencies for their pager service, called teledrin : 161. 175 mhz ( for tone / voice only and numeric pagers, probably for the alphanumeric pagers ) ; 466. 075 mhz ( for tone / voice only, numeric and alphanumeric pagers, using the narrow frequencies of the tacs phone system ) in france, pocsag is operated by e * message over the alphapage network on the 466 mhz frequency : 466. 025 mhz 466. 050 mhz 466. 075 mhz 466. 175 mhz 466. 20625 mhz 466. 23125 mhz


in order to suppress the ici and thereby reduce snr degradation, the residual cfo must be sufficiently small. for example, when using the 64qam constellation, it is better to keep the residual cfo below 0. 01 / s to ensure that dsnr < 0. 3 db for moderate snr. on the other hand, when qpsk is used, the residual cfo can be up to 0. 03 fs.


in a latter presentation this nominal set of views was presented as an extended rasds semantic information model derivation. hereby rasds stands for reference architecture for space data systems.


in number theory, a diophantine m - tuple is a set of m positive integers { a 1, a 2, a 3, a 4, …, a m } { \ displaystyle \ { a _ { 1 }, a _ { 2 }, a _ { 3 }, a _ { 4 }, \ ldots, a _ { m } \ } } such that a i a j + 1 { \ displaystyle a _ { i } a _ { j } + 1 } is a perfect square for any 1 ≤ i < j ≤ m. { \ displaystyle 1 \ leq i


in statistics, economics, and finance, an index is a statistical measure of change in a representative group of individual data points. these data may be derived from any number of sources, including company performance, prices, productivity, and employment. economic indices track economic health from different perspectives. examples include the consumer price index, which measures changes in retail prices paid by consumers, and the cost - of - living index ( coli ), which measures the relative cost of living over time. influential global financial indices such as the global dow, and the nasdaq composite track the performance of selected large and powerful companies in order to evaluate and predict economic trends.


in section viii, james finally moves beyond what he considers mere preliminaries. here james first identifies areas of belief where he holds that to believe without evidence would be unjustified : " wherever the option between losing truth and gaining it is not momentous, we can throw the chance of gaining truth away, and at any rate save ourselves from any chance of believing falsehood, by not making up our minds at all till objective evidence has come. in scientific questions, this is almost always the case... the questions here are always trivial options, the hypotheses are hardly living ( at any rate not living for us spectators ), the choice between believing truth or falsehood is seldom forced. " james concludes this section by asking us to agree " that wherever there is no forced option, the dispassionately judicial intellect with no pet hypothesis, saving us, as it does from dupery at any rate, ought to be our ideal. "


in the following transcriptions, diacritics may be used to distinguish between apical and laminal. the commonality of cross - linguistically is 6 % in a phonological analysis of 2155 languages.


this idea was well known at the time ; e. g. donald knuth visited the algol 68 design committee while developing his own version of it, attribute grammars. by augmenting the syntax description with attributes, constraints like the above can be checked, ruling many invalid programs out at compile time. as van wijngaarden wrote in his preface : my main objections were certain to me unnecessary restrictions and the definition of the syntax and semantics. actually the syntax viewed in mr 75 produces a large number of programs, whereas i should prefer to have the subset of meaningful programs as large as possible, which requires a stricter syntax.


when a program is stopped to let another run, the program with the highest priority in the run queue is then allowed to execute. processes are also removed from the run queue when they ask to sleep, are waiting on a resource to become available, or have been terminated. in the linux operating system ( prior to kernel 2. 6. 23 ), each cpu in the system is given a run queue, which maintains both an active and expired array of processes.


in number theory, the odd greedy expansion problem asks whether a greedy algorithm for finding egyptian fractions with odd denominators always succeeds. as of 2021, it remains unsolved.


in mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions.


in mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same order. this common order must be a prime number, and the elementary abelian groups in which the common order is p are a particular kind of p - group. a group for which p = 2 ( that is, an elementary abelian 2 - group ) is sometimes called a boolean group. every elementary abelian p - group is a vector space over the prime field with p elements, and conversely every such vector space is an elementary abelian group. by the classification of finitely generated abelian groups, or by the fact that every vector space has a basis, every finite elementary abelian group must be of the form ( z / pz ) n for n a non - negative integer ( sometimes called the group's rank ).


in probability theory and statistics, there are several relationships among probability distributions. these relations can be categorized in the following groups : one distribution is a special case of another with a broader parameter space transforms ( function of a random variable ) ; combinations ( function of several variables ) ; approximation ( limit ) relationships ; compound relationships ( useful for bayesian inference ) ; duality ; conjugate priors.


in probability theory, robbins'problem of optimal stopping, named after herbert robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. let x1,..., xn be independent, identically distributed random variables, uniform on. we observe the xk's sequentially and must stop on exactly one of them. no recall of preceding observations is permitted.


this is an xml - based markup language for technical documentation that bears some resemblance to texinfo, in broad outlines. it is also possible to convert docbook files to texinfo, using the docbook2x program. xml ( generated via makeinfo - - xml. )


in number theory, zolotarev's lemma states that the legendre symbol ( a p ) { \ displaystyle \ left ( { \ frac { a } { p } } \ right ) } for an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation : ( a p ) = ε ( π a ) { \ displaystyle \ left ( { \ frac { a } { p } } \ right ) = \ varepsilon ( \ pi _ { a } ) } where ε denotes the signature of a permutation and πa is the permutation of the nonzero residue classes mod p induced by multiplication by a. for example, take a = 2 and p = 7. the nonzero squares mod 7 are 1, 2, and 4, so ( 2 | 7 ) = 1 and ( 6 | 7 ) = −1. multiplication by 2 on the nonzero numbers mod 7 has the cycle decomposition ( 1, 2, 4 ) ( 3, 6, 5 ), so the sign of this permutation is 1, which is ( 2 | 7 ). multiplication by 6 on the nonzero numbers mod 7 has cycle decomposition ( 1, 6 ) ( 2, 5 ) ( 3, 4 ), whose sign is −1, which is ( 6 | 7 ).


in the field of artificial intelligence ( ai ), ai alignment research aims to steer ai systems towards humans'intended goals, preferences, or ethical principles. an ai system is considered aligned if it advances the intended objectives. a misaligned ai system pursues some objectives, but not the intended ones. it can be challenging for ai designers to align an ai system because it can be difficult for them to specify the full range of desired and undesired behaviors. to avoid this difficulty, they typically use simpler proxy goals, such as gaining human approval.


similarly, the ia - 64 ( itanium ) architecture used variable - sized windows, with 32 global registers and 96 for the windows. in the infineon c166 architecture, most registers are simply locations in internal ram which have the additional property of being accessible as registers.


in mathematics, an endomorphism is a morphism from a mathematical object to itself. an endomorphism that is also an isomorphism is an automorphism. for example, an endomorphism of a vector space v is a linear map f : v → v, and an endomorphism of a group g is a group homomorphism f : g → g. in general, we can talk about endomorphisms in any category. in the category of sets, endomorphisms are functions from a set s to itself. in any category, the composition of any two endomorphisms of x is again an endomorphism of x. it follows that the set of all endomorphisms of x forms a monoid, the full transformation monoid, and denoted end ( x ) ( or endc ( x ) to emphasize the category c ).


some species have several argr paralogs. in a neighbour - joining tree, some of these paralogous sequences show long branches and differ significantly from the well - conserved c - terminal region. = = references = =


in mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. algorithms are used as specifications for performing calculations and data processing. more advanced algorithms can use conditionals to divert the code execution through various routes ( referred to as automated decision - making ) and deduce valid inferences ( referred to as automated reasoning ), achieving automation eventually.


the first 10 superior highly composite numbers and their factorization are listed. for a superior highly composite number n there exists a positive real number ε such that for all natural numbers k smaller than n we have and for all natural numbers k larger than n we have where d ( n ), the divisor function, denotes the number of divisors of n. the term was coined by ramanujan ( 1915 ). for example, the number with the most divisors per square root of the number itself is 12 ; this can be demonstrated using some highly composites near 12. 120 is another superior highly composite number because it has the highest ratio of divisors to itself raised to the. 4 power. the first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 ( sequence a002201 in the oeis ) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum - of - divisors function rather than the number of divisors. neither set, however, is a subset of the other.


in some cases, two transactions may, in the course of their processing, attempt to access the same portion of a database at the same time, in a way that prevents them from proceeding. for example, transaction a may access portion x of the database, and transaction b may access portion y of the database. if at that point, transaction a then tries to access portion y of the database while transaction b tries to access portion x, a deadlock occurs, and neither transaction can move forward. transaction - processing systems are designed to detect these deadlocks when they occur.


open software. promotion of reflexive and interpretive uses of the metrics, to prevent their misuse in quantitative assessments. this definition has been implemented in research programs, like rosi ( reference implementation for open scientometric indicators ). in 2017, the european commission expert group on altmetrics expanded the open metrics program of ulrich herb under a new concept, the next - generation metrics. these metrics should be managed by " open, transparent and linked data infrastructure ". the expert group underline that not everything should be measured and not all metrics are relevants : " measure what matters : the next generation of metrics should begin with those qualities and impacts that european societies most value and need indices for, rather than those which are most easily collected and measure ".


in mathematics, 2e6 is the name of a family of steinberg or twisted chevalley groups. it is a quasi - split form of e6, depending on a quadratic extension of fields k⊂l. unfortunately the notation for the group is not standardized, as some authors write it as 2e6 ( k ) ( thinking of 2e6 as an algebraic group taking values in k ) and some as 2e6 ( l ) ( thinking of the group as a subgroup of e6 ( l ) fixed by an outer involution ). over finite fields these groups form one of the 18 infinite families of finite simple groups, and were introduced independently by tits ( 1958 ) and steinberg ( 1959 ).


in multivariate statistics, exploratory factor analysis ( efa ) is a statistical method used to uncover the underlying structure of a relatively large set of variables. efa is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. it is commonly used by researchers when developing a scale ( a scale is a collection of questions used to measure a particular research topic ) and serves to identify a set of latent constructs underlying a battery of measured variables. it should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables.


in statistics, probability theory and information theory, pointwise mutual information ( pmi ), or point mutual information, is a measure of association. it compares the probability of two events occurring together to what this probability would be if the events were independent. pmi ( especially in its positive pointwise mutual information variant ) has been described as " one of the most important concepts in nlp ", where it " draws on the intuition that the best way to weigh the association between two words is to ask how much more the two words co - occur in corpus than we would have a priori expected them to appear by chance. " the concept was introduced in 1961 by robert fano under the name of " mutual information ", but today that term is instead used for a related measure of dependence between random variables : the mutual information ( mi ) of two discrete random variables refers to the average pmi of all possible events.


dirichlet characters can be seen as a special case of this definition. multiplicative characters are linearly independent, i. e. if χ 1, χ 2, …, χ n { \ displaystyle \ chi _ { 1 }, \ chi _ { 2 }, \ ldots, \ chi _ { n } } are different characters on a group g then from a 1 χ 1 + a 2 χ 2 + + a n χ n = 0 { \ displaystyle a _ { 1 } \ chi _ { 1 } + a _ { 2 } \ chi _ { 2 } + \ cdots + a _ { n } \ chi _ { n } = 0 } it follows that a 1 = a 2 = = a n = 0. { \ displaystyle a _ { 1 } = a _ { 2 } = \ cdots = a _ { n } = 0. }


in natural language processing, linguistics, and neighboring fields, linguistic linked open data ( llod ) describes a method and an interdisciplinary community concerned with creating, sharing, and ( re - ) using language resources in accordance with linked data principles. the linguistic linked open data cloud was conceived and is being maintained by the open linguistics working group ( owlg ) of the open knowledge foundation, but has been a point of focal activity for several w3c community groups, research projects, and infrastructure efforts since then.


every clean ring is an exchange ring. a matrix ring over a clean ring is itself clean. = = references = =


in the context to structural analysis, a structure refers to a body or system of connected parts used to support a load. important examples related to civil engineering include buildings, bridges, and towers ; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. to design a structure, an engineer must account for its safety, aesthetics, and serviceability, while considering economic and environmental constraints. other branches of engineering work on a wide variety of non - building structures.


in number theory and set theory, the minimum overlap problem is a problem proposed by hungarian mathematician paul erdos in 1955.


in other systems ( e. g., ip / rtp systems ), the coded data is carried in packets that are framed by the system transport protocol, and identification of the boundaries of nal units within the packets can be established without use of start code prefix patterns. in such systems, the inclusion of start code prefixes in the data would be a waste of data carrying capacity, so instead the nal units can be carried in data packets without start code prefixes.


in mathematics, a delta - matroid or δ - matroid is a family of sets obeying an exchange axiom generalizing an axiom of matroids. a non - empty family of sets is a delta - matroid if, for every two sets e { \ displaystyle e } and f { \ displaystyle f } in the family, and for every element e { \ displaystyle e } in their symmetric difference e f { \ displaystyle e \ triangle f }, there exists an f ∈ e f { \ displaystyle f \ in e \ triangle f } such that e { e, f } { \ displaystyle e \ triangle \ { e, f \ } } is in the family. for the basis sets of a matroid, the corresponding exchange axiom requires in addition that e ∈ e { \ displaystyle e \ in e } and f ∈ f { \ displaystyle f \ in f }, ensuring that e { \ displaystyle e } and f { \ displaystyle f } have the same cardinality. for a delta - matroid, either of the two elements may belong to either of the two sets, and it is also allowed for the two elements to be equal.


in mathematics, the look - and - say sequence is the sequence of integers beginning as follows : 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221,... ( sequence a005150 in the oeis ). to generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. for example : 1 is read off as " one 1 " or 11. 11 is read off as " two 1s " or 21. 21 is read off as " one 2, one 1 " or 1211.


in set theory, a tree is a partially ordered set ( t, < ) such that for each t ∈ t, the set { s ∈ t : s < t } is well - ordered by the relation <. frequently trees are assumed to have only one root ( i. e. minimal element ), as the typical questions investigated in this field are easily reduced to questions about single - rooted trees.


in some computing environments, user workstations and computing nodes do not host installations of the full range of software that users might want to access. systems may be " imaged " with a minimal or typical cross - section of the most commonly used software. also, in some environments, users might require specialized or occasional access to older versions of software ( for instance, developers may need to perform bug fixes and regression testing, or some users may need access to archived data using outdated tools ). commonly, organizations will provide repositories or " depots " of such software, ready for installation as required.


in mathematics, factorization ( or factorisation, see english spelling differences ) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. for example, 3 × 5 is an integer factorization of 15, and ( x – 2 ) ( x + 2 ) is a polynomial factorization of x2 – 4. factorization is not usually considered meaningful within number systems possessing division, such as the real or complex numbers, since any x { \ displaystyle x } can be trivially written as ( x y ) × ( 1 / y ) { \ displaystyle ( xy ) \ times ( 1 / y ) } whenever y { \ displaystyle y } is not zero. however, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator.


after the news a net is carried out with signal reports exchanged, both with uk listeners and others further afield. this band is unique in the united kingdom insofar as uk 5 mhz operators may also communicate under controlled operating conditions with uk military stations or uk military cadet youth organizations with links to the mod using these frequencies. they use mod allocated call signs, which differ significantly from those issued by ofcom to the amateur radio service in the uk.


but it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. this systematic error can be approximately modeled based on our past data about the measuring instrument and the process.


in probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed bernoulli trials before a specified ( non - random ) number of successes ( denoted r { \ displaystyle r } ) occurs. for example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ( r = 3 { \ displaystyle r = 3 } ). in such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. an alternative formulation is to model the number of total trials ( instead of the number of failures ).


they are also power associative. octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used.


however, the latency across the network makes possible the kind of race condition described. in this case, heading off race conditions by imposing a form of control over access to the shared resource — say, appointing one server to control who holds what privileges — would mean turning the distributed network into a centralized one ( at least for that one part of the network operation ). race conditions can also exist when a computer program is written with non - blocking sockets, in which case the performance of the program can be dependent on the speed of the network link.


higher - order moments and cumulants are obtained by higher derivatives. this technique is often useful when t is a complicated function of the data, whose moments are difficult to calculate by integration. another way to see this that does not rely on the theory of cumulants is to begin from the fact that the distribution of an exponential family must be normalized, and differentiate.


for nine to twenty taxa, it will generally be preferable to use branch - and - bound, which is also guaranteed to return the best tree. for greater numbers of taxa, a heuristic search must be performed. because the most - parsimonious tree is always the shortest possible tree, this means that — in comparison to a hypothetical " true " tree that actually describes the unknown evolutionary history of the organisms under study — the " best " tree according to the maximum - parsimony criterion will often underestimate the actual evolutionary change that could have occurred.


therefore, a word of n bytes can contain up to ( 2n ) −1 decimal digits, which is always an odd number of digits. a decimal number with d digits requires 1 / 2 ( d + 1 ) bytes of storage space. for example, a 4 - byte ( 32 - bit ) word can hold seven decimal digits plus a sign and can represent values ranging from ±9, 999, 999.


at the same time, he was sent to hamburg and geneva to doing some cooperation research in the field of high energy physics. in the 1980s, he began teaching, but at the same time, he still did his research in many physics fields. later, he joined in the ams study ( alfa spectrometer ).


this result is a major application of the large sieve method, which developed rapidly in the early 1960s, from its beginnings in work of yuri linnik two decades earlier. besides bombieri, klaus roth was working in this area. in the late 1960s and early 1970s, many of the key ingredients and estimates were simplified by patrick x. gallagher.


in other words, the ito integral, as a function from the space l a d 2 ( × ω ) { \ displaystyle l _ { \ mathrm { ad } } ^ { 2 } ( \ times \ omega ) } of square - integrable adapted processes to the space l 2 ( ω ) { \ displaystyle l ^ { 2 } ( \ omega ) } of square - integrable random variables, is an isometry of normed vector spaces with respect to the norms induced by the inner products ( x, y ) l a d 2 ( × ω ) : = e ( 0 t x t y t d t ) { \ displaystyle { \ begin { aligned } ( x, y ) _ { l _ { \ mathrm { ad } } ^ { 2 } ( \ times \ omega ) } & : = \ operatorname { e } \ left ( \ int _ { 0 } ^ { t } x _ { t } \, y _ { t } \, \ mathrm { d } t \ right ) \ end { aligned } } } and ( a, b ) l 2 ( ω ) : = e ( a b ). { \ displaystyle ( a, b ) _ { l ^ { 2 } ( \ omega ) } : = \ operatorname { e } ( ab ). } as a consequence, the ito integral respects these inner products as well, i. e. we can write e = e { \ displaystyle \ operatorname { e } \ left = \ operatorname { e } \ left } for x, y ∈ l a d 2 ( × ω ) { \ displaystyle x, y \ in l _ { \ mathrm { ad } } ^ { 2 } ( \ times \ omega ) }.


it is harder to think of words with k as the third letter, such as lake, or acknowledge, although objectively these are three times more common. this leads people to the incorrect conclusion that k is more common at the start of words. in another experiment, subjects heard the names of many celebrities, roughly equal numbers of whom were male and female.


synthetic instruments are implemented on generic hardware, i. e., generic meaning that the underlying hardware is not explicitly designed to perform the particular measurement. this is probably the most salient characteristic of a synthetic instrument. measurement specificity is encapsulated totally in software.


in mathematics, more specifically algebraic topology, a pair ( x, a ) { \ displaystyle ( x, a ) } is shorthand for an inclusion of topological spaces i : a x { \ displaystyle i \ colon a \ hookrightarrow x }. sometimes i { \ displaystyle i } is assumed to be a cofibration. a morphism from ( x, a ) { \ displaystyle ( x, a ) } to ( x ′, a ′ ) { \ displaystyle ( x ', a') } is given by two maps f : x → x ′ { \ displaystyle f \ colon x \ rightarrow x'} and g : a → a ′ { \ displaystyle g \ colon a \ rightarrow a'} such that i ′ ∘ g = f ∘ i { \ displaystyle i'\ circ g = f \ circ i }.


in the early 2000s, speech recognition was still dominated by traditional approaches such as hidden markov models combined with feedforward artificial neural networks. today, however, many aspects of speech recognition have been taken over by a deep learning method called long short - term memory ( lstm ), a recurrent neural network published by sepp hochreiter & jurgen schmidhuber in 1997. lstm rnns avoid the vanishing gradient problem and can learn " very deep learning " tasks that require memories of events that happened thousands of discrete time steps ago, which is important for speech.


in mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. each such matrix, say p, represents a permutation of m elements and, when used to multiply another matrix, say a, results in permuting the rows ( when pre - multiplying, to form pa ) or columns ( when post - multiplying, to form ap ) of the matrix a.


in order to define the data structure difference bound matrix, it is first required to give a data structure to encode atomic constraints. furthermore, we introduce an algebra for atomic constraints. this algebra is similar to the tropical semiring, with two modifications : an arbitrary ordered monoid may be used instead of ℝ. in order to distinguish between " < m { \ displaystyle


however, an exception to this is from using the intptr structure, which is a memory managed equivalent to int *, and does not require the unsafe keyword nor the compilerservices assembly. this type is often returned when using methods from the system. runtime. interopservices, for example : the. net framework includes many classes and methods in the system and system. runtime. interopservices namespaces ( such as the marshal class ) which convert. net types ( for example, system. string ) to and from many unmanaged types and pointers ( for example, lpwstr or void * ) to allow communication with unmanaged code. most such methods have the same security permission requirements as unmanaged code, since they can affect arbitrary places in memory.


on such a machine, an all - to - all algorithm requires at least log 2 n { \ displaystyle \ lceil \ log _ { 2 } n \ rceil } communication rounds. further a minimum of m ( n − 1 ) { \ displaystyle \ left \ lceil m ( n - 1 ) \ right \ rceil } units of data is transferred. optimum for both these measures can not be achieved simultaneously. depending on the network topology ( fully connected, hypercube, ring ), different all - to - all algorithms are required.


retrieval is done by separating the instrument from the balloon after a sufficient amount of exposure, and a parachute opens to somewhat slow the descent of the instrument. although the experiment is designed to meet the structural requirements of the columbia scientific balloon facility, it is inevitable that some damage will be incurred to replaceable parts of the instrument. the main priority is data retrieval ; all other systems are considered secondary at this point.


in natural language processing, textual entailment ( te ), also known as natural language inference ( nli ), is a directional relation between text fragments. the relation holds whenever the truth of one text fragment follows from another text.


in some cases, search engines covering specific regions may provide locally - specific extensions of microdata. for example, yandex, a major search engine in russia, supports microformats such as hcard ( company contact information ), hrecipe ( food recipe ), hreview ( market reviews ) and hproduct ( product data ) and provides its own format for definition of the terms and encyclopedic articles. this extension was made in order to solve transliteration problems between the cyrillic and latin alphabets. after the implementation of additional parameters from schema's vocabulary, indexation of information in russian - language web - pages became more successful.


in queueing theory, a discipline within the mathematical theory of probability, the arrival theorem ( also referred to as the random observer property, rop or job observer property ) states that " upon arrival at a station, a job observes the system as if in steady state at an arbitrary instant for the system without that job. " the arrival theorem always holds in open product - form networks with unbounded queues at each node, but it also holds in more general networks. a necessary and sufficient condition for the arrival theorem to be satisfied in product - form networks is given in terms of palm probabilities in boucherie & dijk, 1997.


exploiting the behavior of a buffer overflow is a well - known security exploit. on many systems, the memory layout of a program, or the system as a whole, is well defined. by sending in data designed to cause a buffer overflow, it is possible to write into areas known to hold executable code and replace it with malicious code, or to selectively overwrite data pertaining to the program's state, therefore causing behavior that was not intended by the original programmer.


k! ( n − k )!.


with the other uses of radio spectrum growing in the 1990s, the fcc made available some bands of spectrum as unlicensed channels. this included spectrum for cordless phones and wi - fi. as a result, some of these channels have been used for news gathering by websites and more informal news outlets. one major disadvantage of unlicensed use is that there is no frequency coordination, which can result in interference or blocking of signals.


in statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. instead, data is evaluated as it is collected, and further sampling is stopped in accordance with a predefined stopping rule as soon as significant results are observed. the generic version is called the optimal bayesian estimator, which is the theoretical underpinning for every sequential estimator ( but cannot be instantiated directly ). it includes a markov process for the state propagation and measurement process for each state, which yields some typical statistical independence relations.


the so - called kommunalka became the most common type of accommodation for the residents of large cities. in each communal apartment one room belonged to one family, while bathroom, toilet and kitchen were shared. such a scheme was widespread until the mid - 1950s, and in some cities there are more communal apartments.


in physics and applied mathematics, analytical regularization is a technique used to convert boundary value problems which can be written as fredholm integral equations of the first kind involving singular operators into equivalent fredholm integral equations of the second kind. the latter may be easier to solve analytically and can be studied with discretization schemes like the finite element method or the finite difference method because they are pointwise convergent. in computational electromagnetics, it is known as the method of analytical regularization. it was first used in mathematics during the development of operator theory before acquiring a name.


in mathematics, statistics and elsewhere, sums of squares occur in a number of contexts :


in mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. more specifically, it usually means a sequence defined by the same recurrence relation as the fibonacci numbers, but with different initial conditions causing all members of the sequence to be composite numbers that do not all have a common divisor. to put it algebraically, a sequence of this type is defined by an appropriate choice of two composite numbers a1 and a2, such that the greatest common divisor g c d ( a 1, a 2 ) { \ displaystyle \ mathrm { gcd } ( a _ { 1 }, a _ { 2 } ) } is equal to 1, and such that for n > 2 { \ displaystyle n > 2 } there are no primes in the sequence of numbers calculated from the formula a n = a n − 1 + a n − 2 { \ displaystyle a _ { n } = a _ { n - 1 } + a _ { n - 2 } }. the first primefree sequence of this type was published by ronald graham in 1964.


in the early years of windows mobile devices were able to be managed and synced from a remote computer using activesync ; a data synchronization technology and protocol developed by microsoft, originally released in 1996. this allowed servers running microsoft exchange server, or other third party variants, to act as a personal information manager and share information such as email, calendar appointments, contacts or internet favorites. with the release of windows vista, activesync was replaced with windows mobile device center. device center is included with vista and windows 7 and provides many front end enhancements, allowing a home user to sync pim information with microsoft outlook 2003 and later, photos from windows photo gallery, videos or music from windows media player and favorites with internet explorer ; without the need for a server back end. devices at this time also included a base driver compatible with mobile device center so a user can connect to a computer without a need for any configuration.


in statistics, a paired difference test is a type of location test that is used when comparing two sets of paired measurements to assess whether their population means differ. a paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power, or to reduce the effects of confounders. specific methods for carrying out paired difference tests are, for normally distributed difference t - test ( where the population standard deviation of difference is not known ) and the paired z - test ( where the population standard deviation of the difference is known ), and for differences that may not be normally distributed the wilcoxon signed - rank test as well as the paired permutation test.


in the erasure channel model a symbol gets either transmitted correctly with probability 1 − p e { \ displaystyle 1 - p _ { e } } or is erased with probability p e { \ displaystyle p _ { e } } ( see figure \ ref { fig : sudoku3x3channel } ). the channel introduces no errors, i. e. no channel input is changed to another symbol. the example in figure \ ref { fig : sudoku3x3bsc } shows the transmission of a 3 × 3 { \ displaystyle 3 \ times 3 } sudoku code.


write operations invalidate other copies, but often don't wait for their acknowledgements. read operations typically don't check every redundant copy prior to answering, potentially missing the preceding write operation. the large amount of metadata signal traffic would require specialized hardware and short distances to be handled with acceptable performance ( i. e., act like a non - clustered storage device or database ). whenever strong data consistency is expected, look for these indicators : the use of infiniband, fibrechannel or similar low - latency networks to avoid performance degradation with increasing cluster size and number of redundant copies.


in mathematics, the matrix ( 1 − 1 1 1 ) { \ displaystyle { \ begin { pmatrix } 1 & - 1 \ \ 1 & 1 \ end { pmatrix } } } is sometimes called the quincunx matrix. it is a 2×2 hadamard matrix, and its rows form the basis of a diagonal square lattice consisting of the integer points whose coordinates both have the same parity ; this lattice is a two - dimensional analogue of the three - dimensional body - centered cubic lattice.


but, in balanced ternary, we can't omit the rightmost trailing infinite −1s after the radix point in order to gain a representations of integer or terminating fraction. donald knuth has pointed out that truncation and rounding are the same operation in balanced ternary — they produce exactly the same result ( a property shared with other balanced numeral systems ). the number 1 / 2 is not exceptional ; it has two equally valid representations, and two equally valid truncations : 0. 1 ( round to 0, and truncate to 0 ) and 1. ( round to 1, and truncate to 1 ).


in the umts cellular communication system, received signal code power ( rscp ) denotes the power measured by a receiver on a particular physical communication channel. it is used as an indication of signal strength, as a handover criterion, in downlink power control, and to calculate path loss. in cdma systems, a physical channel corresponds to a particular spreading code, hence the name ( received signal code power ). rscp is also called receiver side call power.


with an odd radix, double rounding is also equivalent to directly rounding to the final precision, unlike with an even radix. the basic operations — addition, subtraction, multiplication, and division — are done as in regular ternary. multiplication by two can be done by adding a number to itself, or subtracting itself after a - trit - left - shifting. an arithmetic shift left of a balanced ternary number is the equivalent of multiplication by a ( positive, integral ) power of 3 ; and an arithmetic shift right of a balanced ternary number is the equivalent of division by a ( positive, integral ) power of 3.


in strategic planning, resource allocation is a plan for using available resources, for example human resources, especially in the near term, to achieve goals for the future. it is the process of allocating scarce resources among the various projects or business units. there are a number of approaches to solving resource allocation problems e. g. resources can be allocated using a manual approach, an algorithmic approach ( see below ), or a combination of both. there may be contingency mechanisms such as a priority ranking of items excluded from the plan, showing which items to fund if more resources should become available and a priority ranking of some items included in the plan, showing which items should be sacrificed if total funding must be reduced.


in order to match certain signatures, an ids is required to keep state related to the connections it is monitoring. for example, an ids must maintain " tcp control blocks " ( tcbs ), chunks of memory which track information such as sequence numbers, window sizes, and connection states ( established, related, closed, etc. ), for each tcp connection monitored by the ids. once all of the ids's random - access memory ( ram ) is consumed, it is forced to utilize virtual memory on the hard disk which is much slower than ram, leading to performance problems and dropped packets similar to the effects of cpu exhaustion. if the ids doesn't garbage collect tcbs correctly and efficiently, an attacker can exhaust the ids's memory by starting a large number of tcp connections very quickly. similar attacks can be made by fragmenting a large number of packets into a larger number of smaller packets, or send a large number of out - of - order tcp segments.


in mathematics and computer science, the middle - square method is a method of generating pseudorandom numbers. in practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some severe weaknesses ; repeated enough times, the middle - square method will either begin repeatedly generating the same number or cycle to a previous number in the sequence and loop indefinitely.


in probability theory and statistics, fisher's noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified by weight factors. it can also be defined as the conditional distribution of two or more binomially distributed variables dependent upon their fixed sum. the distribution may be illustrated by the following urn model.


instead, they bear a legend statement " authorized by drawer ". this type of instrument is usually used by credit card companies, utility companies, or telemarketers. remotely created checks are vulnerable to fraud.


in the united states, privacy concerns have been addressed by the us congress via the passage of regulatory controls such as the health insurance portability and accountability act ( hipaa ). the hipaa requires individuals to give their " informed consent " regarding information they provide and its intended present and future uses. according to an article in biotech business week, "'n practice, hipaa may not offer any greater protection than the longstanding regulations in the research arena,'says the aahc. more importantly, the rule's goal of protection through informed consent is approach a level of incomprehensibility to average individuals. "


in response to a series of earthquakes near comrie in scotland in 1839, a committee was formed in the united kingdom in order to produce better detection devices for earthquakes. the outcome of this was an inverted pendulum seismometer constructed by james david forbes, first presented in a report by david milne - home in 1842, which recorded the measurements of seismic activity through the use of a pencil placed on paper above the pendulum. the designs provided did not prove effective, according to milne's reports. it was milne who coined the word seismometer in 1841, to describe this instrument.


merchant codes and product codes are used at the point of sale ( required by law by certain merchants by certain states in the u. s. ) to restrict sales if they do not qualify. because of the extra checking and documenting that goes on, later, the statement can be used to substantiate these purchases for tax deductions.


at the same time, the availability of published material online opens more doors for plagiarism, unauthorized use, or re - use of the material. some publishers are trying to address these concerns. for example, in 2011, harpercollins limited the number of times that one of its e - books could be lent in a public library. other publishers, such as penguin, are attempting to incorporate e - book elements into their regular paper publications.


in simplest terms it is a measure of the probability of finding a particle at a distance of r { \ displaystyle r } away from a given reference particle, relative to that for an ideal gas. the general algorithm involves determining how many particles are within a distance of r { \ displaystyle r } and r + d r { \ displaystyle r + dr } away from a particle. this general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those whose centers are within the circular shell, dotted in orange.


in mathematics, the caratheodory kernel theorem is a result in complex analysis and geometric function theory established by the greek mathematician constantin caratheodory in 1912. the uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. the kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the loewner differential equation.


in probability theory and statistics, given two jointly distributed random variables x { \ displaystyle x } and y { \ displaystyle y }, the conditional probability distribution of y { \ displaystyle y } given x { \ displaystyle x } is the probability distribution of y { \ displaystyle y } when x { \ displaystyle x } is known to be a particular value ; in some cases the conditional probabilities may be expressed as functions containing the unspecified value x { \ displaystyle x } of x { \ displaystyle x } as a parameter. when both x { \ displaystyle x } and y { \ displaystyle y } are categorical variables, a conditional probability table is typically used to represent the conditional probability. the conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.


that is, we want to find a channel code, which is able to partition the space of input x { \ displaystyle x } into several cosets, where each coset has a unique syndrome associated with it. with a given coset and y { \ displaystyle \ mathbf { y } }, there is only one x { \ displaystyle \ mathbf { x } } that is possible to be the input given the correlation between two sources. in this example, we can use the ( 7, 4, 3 ) { \ displaystyle ( 7, 4, 3 ) } binary hamming code c { \ displaystyle \ mathbf { c } }, with parity check matrix h { \ displaystyle \ mathbf { h } }.


in mathematics, negafibonacci coding is a universal code which encodes nonzero integers into binary code words. it is similar to fibonacci coding, except that it allows both positive and negative integers to be represented. all codes end with " 11 " and have no " 11 " before the end.


in number theory, a pierpont prime is a prime number of the form for some nonnegative integers u and v. that is, they are the prime numbers p for which p − 1 is 3 - smooth. they are named after the mathematician james pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. the same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding. except for 2 and the fermat primes, every pierpont prime must be 1 modulo 6. the first few pierpont primes are : it has been conjectured that there are infinitely many pierpont primes, but this remains unproven.


in the example 3 4 -, first the 3 is put onto the stack, then the 4 ; the 4 is now on top and the 3 below it. the subtraction operator removes the top two items from the stack, performs 3 - 4, and puts the result of - 1 onto the stack. the common terminology is that added items are pushed on the stack and removed items are popped. the advantage of reverse polish notation is that it removes the need for order of operations and parentheses that are required by infix notation and can be evaluated linearly, left - to - right. for example, the infix expression ( 3 × 4 ) + ( 5 × 6 ) becomes 3 4 × 5 6 × + in reverse polish notation.


the axiom of choice is also rejected in most intuitionistic set theories, though in some versions it is accepted. in intuitionism, the term " explicit construction " is not cleanly defined, and that has led to criticisms. attempts have been made to use the concepts of turing machine or computable function to fill this gap, leading to the claim that only questions regarding the behavior of finite algorithms are meaningful and should be investigated in mathematics. this has led to the study of the computable numbers, first introduced by alan turing. not surprisingly, then, this approach to mathematics is sometimes associated with theoretical computer science.


in mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. it refines the concept of a monotone function. if a, b are posets, a function f : a → b is defined to be monotone if it is order - preserving : that is, if x ≤ y implies f ( x ) ≤ f ( y ). this is equivalent to the condition that the preimage under f of every down - set of b is a down - set of a. we define a principal down - set to be one of the form ↓ { b } = { b'∈ b : b'≤ b }.


in statistics, the residual sum of squares ( rss ), also known as the sum of squared residuals ( ssr ) or the sum of squared estimate of errors ( sse ), is the sum of the squares of residuals ( deviations predicted from actual empirical values of data ). it is a measure of the discrepancy between the data and an estimation model, such as a linear regression. a small rss indicates a tight fit of the model to the data.


in real world application, one often observe only a few entries corrupted at least by a small amount of noise. for example, in the netflix problem, the ratings are uncertain. candes and plan showed that it is possible to fill in the many missing entries of large low - rank matrices from just a few noisy samples by nuclear norm minimization. the noisy model assumes that we observe y i j = m i j + z i j, ( i, j ) ∈ ω, { \ displaystyle y _ { ij } = m _ { ij } + z _ { ij }, ( i, j ) \ in \ omega, } where z i j : ( i, j ) ∈ ω { \ displaystyle { z _ { ij } : ( i, j ) \ in \ omega } } is a noise term.


in physics, the bekenstein bound ( named after jacob bekenstein ) is an upper limit on the thermodynamic entropy s, or shannon entropy h, that can be contained within a given finite region of space which has a finite amount of energy — or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. it implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. in computer science this implies that non - finite models such as turing machines are not realizable as finite devices.


here, the original observations are effectively mapped into a higher dimensional non - linear space. linear classification in this non - linear space is then equivalent to non - linear classification in the original space. the most commonly used example of this is the kernel fisher discriminant.


a surface is a two - dimensional space ; this means that a moving point on a surface may move in two directions ( it has two degrees of freedom ). in other words, around almost every point, there is a coordinate patch on which a two - dimensional coordinate system is defined. for example, the surface of the earth resembles ( ideally ) a two - dimensional sphere, and latitude and longitude provide two - dimensional coordinates on it ( except at the poles and along the 180th meridian ). the concept of surface is widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. for example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.


in practice, one sets y 2 = x 3 + a x + b { \ displaystyle y ^ { 2 } = x ^ { 3 } + ax + b }, and then ψ 2 m + 1 ∈ z { \ displaystyle \ psi _ { 2m + 1 } \ in \ mathbb { z } } and ψ 2 m ∈ 2 y z { \ displaystyle \ psi _ { 2m } \ in 2y \ mathbb { z } }. the division polynomials form a generic elliptic divisibility sequence over the ring q / ( y 2 − x 3 − a x − b ) { \ displaystyle \ mathbb { q } / ( y ^ { 2 } - x ^ { 3 } - ax - b ) }. if an elliptic curve e { \ displaystyle e } is given in the weierstrass form y 2 = x 3 + a x + b { \ displaystyle y ^ { 2 } = x ^ { 3 } + ax + b } over some field k { \ displaystyle k }, i. e. a, b ∈ k { \ displaystyle a, b \ in k }, one can use these values of a, b { \ displaystyle a, b } and consider the division polynomials in the coordinate ring of e { \ displaystyle e }. the roots of ψ 2 n + 1 { \ displaystyle \ psi _ { 2n + 1 } } are the x { \ displaystyle x } - coordinates of the points of e { o } { \ displaystyle e \ setminus \ { o \ } }, where e { \ displaystyle e } is the ( 2 n + 1 ) th { \ displaystyle ( 2n + 1 ) ^ { \ text { th } } } torsion subgroup of e { \ displaystyle e }.


conceptual errors are a developer's misunderstanding of what the software must do. the resulting software may perform according to the developer's understanding, but not what is really needed. other types :


in the continuing struggle to create the fastest and most advanced 3d accelerator, ati came up with the rage 128. the chip was announced in two flavors, the rage 128 gl and the rage 128 vr. aside from the vr chip's lower price, the main difference was that the former was a full 128 - bit design, while the vr, still a 128 - bit processor internally, used a 64 - bit external memory interface. magnum - a workstation board for oems with 32 mb sdram.


in the deques of this structure, elements are kept in sorted order according to their working set size. formally, element x { \ displaystyle x } lies after y { \ displaystyle y } in deque q i { \ displaystyle q _ { i } } if and only if w ( x ) < w ( y ) { \ displaystyle w ( x )


in mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. every automatic sequence is morphic.


in statistics and signal processing, the orthogonality principle is a necessary and sufficient condition for the optimality of a bayesian estimator. loosely stated, the orthogonality principle says that the error vector of the optimal estimator ( in a mean square error sense ) is orthogonal to any possible estimator. the orthogonality principle is most commonly stated for linear estimators, but more general formulations are possible. since the principle is a necessary and sufficient condition for optimality, it can be used to find the minimum mean square error estimator.


in the turkish terms for the constructive and inflectional endings, three roots are involved : ek " supplement, affix " ( notably turkish has no prefixes ) yap - " make " cek - " pull, draw " for the last two verbal roots, the constructive suffix - im can be added to form nouns for instances of the actions denoted by the roots : yapım " construction " ; cekim " pull or draw " ( or a " take " in cinema ). either of these nouns can be compounded with the noun ek, resulting in an indefinite compound ( belirtisiz tamlama ), the sign of which is the inflectional suffix - i attached to ek : yapım eki " structure - suffix " ; cekim eki " inflection - suffix ". the inflectional suffix - ler comes before the - i to form the plural, so yapım ekleri, cekim ekleri. many words in turkish — particularly many grammatical terms — are neologisms invented to replace earlier words borrowed from arabic or persian, which have largely been successful at permanently superseding the previously used foreign terms. ( see the main article on turkish language. ) in some cases, the foreign term continues to be in use alongside the neologism.


in multiprocessing, omega networks may be used as connectors between the cpus and their shared memory, in order to decrease the probability that the cpu - to - memory connection becomes a bottleneck. this class of networks has been built into the illinois cedar multiprocessor, into the ibm rp3, and into the nyu ultracomputer.


for example, for p = 1, the latent variables of all entities i = 1,...


in mathematical logic, computer programming, philosophy and linguistics fuzzy concepts can be analyzed and defined more accurately or comprehensively, by describing or modelling the concepts using the terms of fuzzy logic or other substructural logics. more generally, clarification techniques can be used such as : 1. contextualizing the concept by defining the setting or situation in which the concept is used, or how it is used appropriately ( context ). 2.


it is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self - interaction feedback. regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. however, it is now well understood and has proven to yield useful, accurate predictions.


it also depends on f { \ displaystyle f }, α 0 { \ displaystyle \ alpha _ { 0 } }, τ { \ displaystyle \ tau } and c { \ displaystyle c } of course, although these dependencies can be left implicit if they are assumed to be fixed with respect to the optimization problem. the detailed steps are thus, see armijo ( 1966 ), bertsekas ( 2016 ) : choose an initial starting point x 0 { \ displaystyle \ mathbf { x } _ { 0 } } and set the iteration counter n = 0 { \ displaystyle n = 0 }. until some stopping condition is satisfied, choose a descent direction p n { \ displaystyle \ mathbf { p } _ { n } }, increment n { \ displaystyle n }, and update the position to x n + 1 = x n + α ( x n, p n ) p n { \ displaystyle \ mathbf { x } _ { n + 1 } = \ mathbf { x } _ { n } + \ alpha ( \ mathbf { x } _ { n }, \ mathbf { p } _ { n } ) \, \ mathbf { p } _ { n } }.


in some languages, certain digraphs and trigraphs are counted as distinct letters in themselves, and assigned to a specific place in the alphabet, separate from that of the sequence of characters that composes them, for purposes of orthography and collation. for example : in the gaj ’ s latin alphabet used to write serbo - croatian, the digraphs ⟨ dz ⟩, ⟨ lj ⟩ and ⟨ nj ⟩, which correspond to the single cyrillic letters ⟨ ⟩, ⟨ љ ⟩, ⟨ њ ⟩, are treated as distinct letters. in the czech and slovak alphabet, ⟨ ch ⟩ is treated as a distinct letter, coming after ⟨ h ⟩ in the alphabet. also, in the slovak alphabet the relatively rare digraphs ⟨ dz ⟩ and ⟨ dz ⟩ are treated as distinct letters.


such experiments allow researchers to quantify the role of historical contingency and repeatability in network evolution, enabling predictions about the architecture and dynamics of large networks of interacting species. the inclusion of ecological interactions in digital systems enables new research avenues : investigations using self - replicating computer programs complement laboratory efforts by broadening the breadth of viable experiments focused on the emergence and diversification of coevolving interactions in complex communities. this cross - disciplinary research program provides fertile grounds for new collaborations between computer scientists and evolutionary biologists.


in number theory, a sierpinski number is an odd natural number k such that k × 2 n + 1 { \ displaystyle k \ times 2 ^ { n } + 1 } is composite for all natural numbers n. in 1960, wacław sierpinski proved that there are infinitely many odd integers k which have this property. in other words, when k is a sierpinski number, all members of the following set are composite : { k ⋅ 2 n + 1 : n ∈ n }. { \ displaystyle \ left \ { \, k \ cdot 2 ^ { n } + 1 : n \ in \ mathbb { n } \, \ right \ }. } if the form is instead k × 2 n − 1 { \ displaystyle k \ times 2 ^ { n } - 1 }, then k is a riesel number.


this idea can be applied to any commutative monoid. on the other hand, the set of integers z requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation n + m = n ′ { \ displaystyle n + m = n'} by writing m = ( n ′ − n ) { \ displaystyle m = ( n'- n ) }. a mathematical hierarchy ( a pre - ordered set ) should not be confused with the more general concept of a hierarchy in the social realm, particularly when one is constructing computational models that are used to describe real - world social, economic or political systems. these hierarchies, or complex networks, are much too rich to be described in the category set of sets.


{ \ displaystyle { \ begin { pmatrix } 0 & 0 & 2 & 0 \ \ 0 & 2 & - 1 & 1 \ \ 2 & - 1 & 2 & - 1 \ \ 0 & 1 & - 1 & 2 \ end { pmatrix } } ; \ quad { \ begin { pmatrix } 0 & 0 & 2 & 0 & 0 \ \ 0 & 1 & - 1 & 2 & 0 \ \ 2 & - 1 & - 1 & 0 & 2 \ \ 0 & 0 & 2 & 0 & 0 \ \ 0 & 2 & 0 & 0 & 0 \ end { pmatrix } } ; \ quad { \ begin { pmatrix } 0 & 0 & 0 & 2 \ \ 0 & 2 & 0 & 0 \ \ 2 & - 2 & 2 & 0 \ \ 0 & 2 & 0 & 0 \ end { pmatrix } } ; \ quad { \ begin { pmatrix } 0 & 2 & 0 & 0 \ \ 0 & 0 & 0 & 2 \ \ 2 & 0 & 0 & 0 \ \ 0 & 0 & 2 & 0 \ end { pmatrix } }. } the set of hsasms is a superset of the asms. the extreme points of the convex hull of the set of r - spin hsasms are themselves integer multiples of the usual asms. = = references = =


in the following, f k { \ displaystyle f _ { k } } denotes the value of the function f : { 0, 1 } n → { 0, 1 } { \ displaystyle f : \ { 0, 1 \ } ^ { n } \ rightarrow \ { 0, 1 \ } } when applied to an input vector of weight k { \ displaystyle k }.


in mathematics, an aperiodic semigroup is a semigroup s such that every element is aperiodic, that is, for each x in s there exists a positive integer n such that xn = xn + 1. an aperiodic monoid is an aperiodic semigroup which is a monoid.


.., m a x d − 1, + ∞ } { \ displaystyle k _ { max } = \ { max _ { 0 }, + \ infty, max _ { 1 }, + \ infty,..., max _ { d - 1 }, + \ infty \ } }


in some cases the observations may be weighted — for example, they may not be equally reliable. in this case, one can minimize the weighted sum of squares : where wi > 0 is the weight of the ith observation, and w is the diagonal matrix of such weights. the weights should, ideally, be equal to the reciprocal of the variance of the measurement. ( this implies that the observations are uncorrelated.


we use the potential function φ = σ ( u ) ( i. e. φ is the sum of the labels of all active nodes ). it is obvious that φ is 0 initially and stays nonnegative throughout the execution of the algorithm. both relabels and saturating pushes can increase φ. however, the value of φ must be equal to 0 at termination since there cannot be any remaining active nodes at the end of the algorithm's execution.


in such theories, the speech act of assertion is often analyzed as a proposal to add an additional proposition to the common ground. similarly, presuppositions are taken to be licensed when they are already established in the common ground. while such approaches are typically construed as pragmatic, the framework of dynamic semantics treats the semantic denotations of sentences as functions which update the common ground. in many theories, the common ground is one of several elements of the conversational scoreboard.


brent's method is due to richard brent and builds on an earlier algorithm by theodorus dekker. consequently, the method is also known as the brent – dekker method. modern improvements on brent's method include chandrupatla's method, which is simpler and faster for functions that are flat around their roots ; ridders'method, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations ; and the itp method which is a hybrid between regula - falsi and bisection that achieves optimal worst - case and asymptotic guarantees.


in probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. the hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse - cosh distribution. generalisation of the distribution gives rise to the meixner distribution, also known as the natural exponential family - generalised hyperbolic secant or nef - ghs distribution.


if we restrict loops to be of a predictably finite size ( like the for loop in basic ), we can express all of the primitive recursive functions ( meyer and ritchie, 1967 ). an example of such a machine is provided by the toy programming language pl - { goto } of brainerd and landweber ( 1974 ).


furthermore, the objective should be to obtain an experts'carefully considered judgment based on a systematic consideration of all relevant evidence. for this reason one should take care to adopt strategies designed to help the expert being interviewed to avoid overlooking relevant evidence. additionally, vocabulary used should face intense scrutiny ; qualitative uncertainty words such as " likely " and " unlikely " are not sufficient and can lead to confusion. such words can mean very different things to different people, or to the same people in different situations.


in some parts of the world, including the united kingdom, 2g remains widely used for older feature phones and for internet of things ( iot ) devices such as smart meters, ecall systems and vehicle trackers to avoid the high patent licensing cost of newer technologies. terminating 2g services could leave vulnerable people who rely on 2g infrastructure unable to communicate even with emergency contacts, causing harm and possibly deaths.


in optimization and other branches of mathematics, and in search algorithms ( a topic in computer science ), a candidate solution is a member of the set of possible solutions in the feasible region of a given problem. a candidate solution does not have to be a likely or reasonable solution to the problem — it is simply in the set that satisfies all constraints ; that is, it is in the set of feasible solutions. algorithms for solving various types of optimization problems often narrow the set of candidate solutions down to a subset of the feasible solutions, whose points remain as candidate solutions while the other feasible solutions are henceforth excluded as candidates.


most gsm / umts phones support all four bands, while most cdma2000 / 1xrtt phones ( mostly north america and voice transmission only ) do not, and so are considered only dual - band devices. a few phones support both of the domestic frequencies but only one foreign one for limited roaming, making them tri - band phones. the term penta - band describes a device that supports a fifth frequency band, commonly the 1700 / 2100 mhz band in much of the world. the advanced wireless services ( aws ) 1700 mhz band is also seeing increased usage.


2d spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3d are equivalent to a point on the unit sphere. the normalized vector u of a non - zero vector u is the unit vector in the direction of u, i. e., u ^ = u ‖ u ‖ { \ displaystyle \ mathbf { \ hat { u } } = { \ frac { \ mathbf { u } } { \ | \ mathbf { u } \ | } } } where ‖ u ‖ is the norm ( or length ) of u. the term normalized vector is sometimes used as a synonym for unit vector. unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors.


in standard matrix notation, each element of rn is typically written as a column vector and sometimes as a row vector : the coordinate space rn may then be interpreted as the space of all n × 1 column vectors, or all 1 × n row vectors with the ordinary matrix operations of addition and scalar multiplication. linear transformations from rn to rm may then be written as m × n matrices which act on the elements of rn via left multiplication ( when the elements of rn are column vectors ) and on elements of rm via right multiplication ( when they are row vectors ). the formula for left multiplication, a special case of matrix multiplication, is : any linear transformation is a continuous function ( see below ). also, a matrix defines an open map from rn to rm if and only if the rank of the matrix equals to m.


in mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. for example : 7 = 71, 9 = 32 and 64 = 26 are prime powers, while 6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not. the sequence of prime powers begins : 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, … ( sequence a246655 in the oeis ). the prime powers are those positive integers that are divisible by exactly one prime number ; in particular, the number 1 is not a prime power. prime powers are also called primary numbers, as in the primary decomposition.


in software engineering, profiling ( " program profiling ", " software profiling " ) is a form of dynamic program analysis that measures, for example, the space ( memory ) or time complexity of a program, the usage of particular instructions, or frequency and duration of function calls. the most common use of profiling information is to aid program optimization. profiling is achieved by instrumenting either the program source code or its binary executable form using a tool called a profiler ( or code profiler ). a number of different techniques may be used by profilers, such as event - based, statistical, instrumented, and simulation methods.


in robust statistics, the convex hull provides one of the key components of a bagplot, a method for visualizing the spread of two - dimensional sample points. the contours of tukey depth form a nested family of convex sets, with the convex hull outermost, and the bagplot also displays another polygon from this nested family, the contour of 50 % depth. in statistical decision theory, the risk set of a randomized decision rule is the convex hull of the risk points of its underlying deterministic decision rules.


beta langfi pointed out that " it is not only to study parts and processes in isolation, but also to study the interaction of various parts. the organism should be considered as a whole or system. environmental protection requires systematic thinking. landscape planning is required for overall planning.


typically, people try to systematically " retrace their steps " to determine all of the possible places where the item might be located. based on the role that context plays in determining recall, it is not at all surprising that individuals often quite easily discover the lost item upon returning to the correct context. this concept is heavily related to the encoding specificity principle.


the selection of central office names was conducted in a careful manner to avoid misunderstanding of the verbal requests. for automatic telephone service, impulse senders ( dials ) were installed on customer telephones, so that subscribers did not need operators to initiate a call, but simply dial the directory number themselves. this required a digit or letter identification of central offices, so that the central office for the recipient could be dialed before the line number. telephone dials were typically supplemented with letters next to the numerals on the dial, as seen in the right - hand photo, so that a name could be dialed by its first letter, or by multiple letters.


using bayes'theorem ). having made explicit the expected loss for each given x { \ displaystyle x \, \! } separately, we can define a decision rule δ { \ displaystyle \ delta \, \! }


in the context of digital privacy, communication privacy is the notion that individuals should have the freedom, or right, to communicate information digitally with the expectation that their communications are secure — meaning that messages and communications will only be accessible to the sender's original intended recipient. however, communications can be intercepted or delivered to other recipients without the sender's knowledge, in a multitude of ways. communications can be intercepted directly through various hacking methods, such as the man - in - the - middle attack ( mitm ). communications can also be delivered to recipients unbeknown to the sender due to false assumptions made regarding the platform or medium that was used to send information.


in the design of algorithms, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by splitting its sets into a larger number of smaller sets. in that sense it is dual to the union - find data structure, which also maintains a partition into disjoint sets but in which the operations merge pairs of sets. in some applications of partition refinement, such as lexicographic breadth - first search, the data structure maintains as well an ordering on the sets in the partition. partition refinement forms a key component of several efficient algorithms on graphs and finite automata, including dfa minimization, the coffman – graham algorithm for parallel scheduling, and lexicographic breadth - first search of graphs.


in functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. in theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. the most general setting for the strict notion of currying and uncurrying is in the closed monoidal categories, which underpins a vast generalization of the curry – howard correspondence of proofs and programs to a correspondence with many other structures, including quantum mechanics, cobordisms and string theory.


the s - box used is derived from the multiplicative inverse over gf ( 28 ), known to have good non - linearity properties. to avoid attacks based on simple algebraic properties, the s - box is constructed by combining the inverse function with an invertible affine transformation. the s - box is also chosen to avoid any fixed points ( and so is a derangement ), i. e., s ( a i, j ) = a i, j { \ displaystyle s ( a _ { i, j } ) \ neq a _ { i, j } }, and also any opposite fixed points, i. e., s ( a i, j ) ⊕ a i, j = ff 16 { \ displaystyle s ( a _ { i, j } ) \ oplus a _ { i, j } \ neq { \ text { ff } } _ { 16 } }. while performing the decryption, the invsubbytes step ( the inverse of subbytes ) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.


in quantum computing, a graph state is a special type of multi - qubit state that can be represented by a graph. each qubit is represented by a vertex of the graph, and there is an edge between every interacting pair of qubits. in particular, they are a convenient way of representing certain types of entangled states. graph states are useful in quantum error - correcting codes, entanglement measurement and purification and for characterization of computational resources in measurement based quantum computing models. a graph state is a particular case of a 2 - uniform hypergraph state, a generalization where the edges have n cardinality.


the challenge problems do not require the formalisation of large programming languages, but they do require sophistication in reasoning about : binding most programming languages have some form of binding, ranging in complexity from the simple binders of simply typed lambda calculus to complex, potentially infinite binders needed in the treatment of record patterns. induction properties such as subject reduction and strong normalisation often require complex induction arguments. reuse furthering collaboration being a key aim of the challenge, the solutions are expected to contain reusable components that would allow researchers to share language features and designs without requiring them to start from scratch every time.


in software engineering, a monolithic application describes a software application that is designed as a single service. multiple services can be desirable in certain scenarios as it can facilitate maintenance by allowing repair or replacement of parts of the application without requiring wholesale replacement. modularity is achieved to various extents by different modular programming approaches.


in mathematics, welch bounds are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space. the bounds are important tools in the design and analysis of certain methods in telecommunication engineering, particularly in coding theory. the bounds were originally published in a 1974 paper by l. r. welch.


in mathematics, the wiener – wintner theorem, named after norbert wiener and aurel wintner, is a strengthening of the ergodic theorem, proved by wiener and wintner ( 1941 ).


in mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. a theory is a consistent, relatively - self - contained body of knowledge which usually contains an axiomatic system and all its derived theorems. an axiomatic system that is completely described is a special kind of formal system. a formal theory is an axiomatic system ( usually formulated within model theory ) that describes a set of sentences that is closed under logical implication. a formal proof is a complete rendition of a mathematical proof within a formal system.


each work item consists of a series of instructions, to be executed sequentially, but in the course of its execution, a work item may also spawn new work items that can feasibly be executed in parallel with its other work. these new items are initially put on the queue of the processor executing the work item. when a processor runs out of work, it looks at the queues of the other processors and " steals " their work items.


{ \ displaystyle \ | t \ | _ { 1 } \ geq \ | t \ | _ { p } \ geq \ | t \ | _ { p'} \ geq \ | t \ | _ { \ infty }. } duality : let h 1, h 2 { \ displaystyle h _ { 1 }, h _ { 2 } } be finite - dimensional hilbert spaces, p ∈ { \ displaystyle p \ in } and q { \ displaystyle q } such that 1 p + 1 q = 1 { \ displaystyle { \ frac { 1 } { p } } + { \ frac { 1 } { q } } = 1 }, then ‖ s ‖ p = sup { | ⟨ s, t ⟩ | ‖ t ‖ q = 1 }, { \ displaystyle \ | s \ | _ { p } = \ sup \ lbrace | \ langle s, t \ rangle | \ mid \ | t \ | _ { q } = 1 \ rbrace, } where ⟨ s, t ⟩ = t r ( s ∗ t ) { \ displaystyle \ langle s, t \ rangle = \ mathrm { tr } ( s ^ { * } t ) } denotes the hilbert – schmidt inner product. let ( e k ) k, ( f k ′ ) k ′ { \ displaystyle ( e _ { k } ) _ { k }, ( f _ { k'} ) _ { k'} } be two orthonormal basis of the hilbert spaces h 1, h 2 { \ displaystyle h _ { 1 }, h _ { 2 } }, then for p = 1 { \ displaystyle p = 1 } ‖ t ‖ 1 ≤ k, k ′ | t k, k ′ | { \ displaystyle \ | t \ | _ { 1 } \ leq \ sum _ { k, k'} \ left | t _ { k, k'} \ right | }.


in statistics, the generalized canonical correlation analysis ( gcca ), is a way of making sense of cross - correlation matrices between the sets of random variables when there are more than two sets. while a conventional cca generalizes principal component analysis ( pca ) to two sets of random variables, a gcca generalizes pca to more than two sets of random variables. the canonical variables represent those common factors that can be found by a large pca of all of the transformed random variables after each set underwent its own pca.


for example, it can be used about primes in an arithmetic progression of the form a n + b { \ displaystyle an + b }, where a and b are coprime which according to dirichlet's theorem on arithmetic progressions contains infinitely many primes, along with infinitely many composites. for integer k ≥ 3, an ap - k ( also called pap - k ) is any sequence of k primes in arithmetic progression. an ap - k can be written as k primes of the form a · n + b, for fixed integers a ( called the common difference ) and b, and k consecutive integer values of n. an ap - k is usually expressed with n = 0 to k − 1. this can always be achieved by defining b to be the first prime in the arithmetic progression.


in queueing theory, a discipline within the mathematical theory of probability, an m / d / c queue represents the queue length in a system having c servers, where arrivals are determined by a poisson process and job service times are fixed ( deterministic ). the model name is written in kendall's notation. agner krarup erlang first published on this model in 1909, starting the subject of queueing theory. the model is an extension of the m / d / 1 queue which has only a single server.


in network science, ingredient - flavor networks are networks describing the sharing of flavor compounds of culinary ingredients. in the bipartite form, an ingredient - flavor network consist of two different types of nodes : the ingredients used in the recipes and the flavor compounds that contributes to the flavor of each ingredients. the links connecting different types of nodes are undirected, represent certain compound occur in each ingredients. the ingredient - flavor network can also be projected in the ingredient or compound space where nodes are ingredients or compounds, links represents the sharing of the same compounds to different ingredients or the coexistence in the same ingredient of different compounds.


there are a finite number of possible configurations in the section between two walls so the automaton must eventually start repeating inside each section, though the period may be very long if the section is wide enough. these walls will form with probability 1 for completely random initial conditions.


in order to assign a digital representation to an entity, the attributing party must trust that the claim of an attribute ( such as name, location, role as an employee, or age ) is correct and associated with the person or thing presenting the attribute. conversely, the individual claiming an attribute may only grant selective access to its information ( e. g., proving identity in a bar or paypal authentication for payment at a website ). in this way, digital identity is better understood as a particular viewpoint within a mutually - agreed relationship than as an objective property.


in mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. this is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice.


a typical pole stage plantation tree is 7 – 30 cm in diameter at breast height ( dbh ). such trees are sometimes not suitable for timber, but are used as pulp for paper and particleboard, and as chips for oriented strand board. as the trees grow and become dense and crowded again, the thinning process is repeated.


when employed in parallel connected electric distribution systems, closed - core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. blathy had suggested the use of closed cores, zipernowsky had suggested the use of parallel shunt connections, and deri had performed the experiments ; in early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores. transformers today are designed on the principles discovered by the three engineers. they also popularized the word'transformer'to describe a device for altering the emf of an electric current although the term had already been in use by 1882. in 1886, the zbd engineers designed, and the ganz factory supplied electrical equipment for, the world's first power station that used ac generators to power a parallel connected common electrical network, the steam - powered rome - cerchi power plant.


for an example, given set y { \ displaystyle y }, let q ( n ) { \ displaystyle q ( n ) } denote the existential statement that a certain function space set exist, h. h y { 0, 1, …, n − 1 } { \ displaystyle \ exists h. h \ simeq y ^ { \ { 0, 1, \ dots, n - 1 \ } } }. here the existential quantifier is not merely one over natural numbers or bounded by any other set.


in statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output binary variable. generally the probability of the two alternatives is modeled, instead of simply outputting a single value, as in linear regression. binary regression is usually analyzed as a special case of binomial regression, with a single outcome ( n = 1 { \ displaystyle n = 1 } ), and one of the two alternatives considered as " success " and coded as 1 : the value is the count of successes in 1 trial, either 0 or 1. the most common binary regression models are the logit model ( logistic regression ) and the probit model ( probit regression ).


the multinational control of the export of cryptography on the western side of the cold war divide was done via the mechanisms of cocom. by the 1960s, however, financial organizations were beginning to require strong commercial encryption on the rapidly growing field of wired money transfer. the u. s. government's introduction of the data encryption standard in 1975 meant that commercial uses of high quality encryption would become common, and serious problems of export control began to arise. generally these were dealt with through case - by - case export license request proceedings brought by computer manufacturers, such as ibm, and by their large corporate customers.


this approach is good solely for instructive purposes. the euler – lagrange equation will now be used to find the extremal function f ( x ) { \ displaystyle f ( x ) } that minimizes the functional a. { \ displaystyle a. }


when clock speeds of cpus began to move into the 3 – 5 ghz range, cpu power dissipation and other problems became more important. the ability of industry to produce ever - faster single cpu systems ( linked to moore's law about the periodic doubling of transistor counts ) began to be threatened. in the early 21st century, many flavors of parallel computing began to proliferate, including multi - core architectures at the low - end and massively parallel processing at the high end.


the simple logistic function varies by less than 0. 01 from the cumulative normal ogive across the range, given an arbitrary scale factor. in the btl model, the probability that object j is judged to have more of an attribute than object i is : pr { x j i = 1 } = e δ j − δ i 1 + e δ j − δ i = σ ( δ j − δ i ), { \ displaystyle \ pr \ { x _ { ji } = 1 \ } = { \ frac { e ^ { { \ delta _ { j } } - { \ delta _ { i } } } } { 1 + e ^ { { \ delta _ { j } } - { \ delta _ { i } } } } } = \ sigma ( \ delta _ { j } - \ delta _ { i } ), } where δ i { \ displaystyle \ delta _ { i } } is the scale location of object i { \ displaystyle i } ; σ { \ displaystyle \ sigma } is the logistic function ( the inverse of the logit ). for example, the scale location might represent the perceived quality of a product, or the perceived weight of an object.


they were introduced in the course of stanley's enumeration of the reduced decompositions of permutations, and in particular his proof that the permutation w0 = n ( n − 1 )... 21 ( written here in one - line notation ) has exactly ( n 2 )! 1 n − 1 ⋅ 3 n − 2 ⋅ 5 n − 3 ( 2 n − 3 ) 1 { \ displaystyle { \ frac { { \ binom { n } { 2 } }! } { 1 ^ { n - 1 } \ cdot 3 ^ { n - 2 } \ cdot 5 ^ { n - 3 } \ cdots ( 2n - 3 ) ^ { 1 } } } } reduced decompositions. ( here ( n 2 ) { \ displaystyle { \ binom { n } { 2 } } } denotes the binomial coefficient n ( n − 1 ) / 2 and! denotes the factorial. )


subscribers are often provided with several set - top boxes as part of their subscription, and can give or sell unneeded activated boxes to neighboring nonsubscribers who can use them in their own residences, though a provider using ip location using the cable modem within a set - top box featuring advanced two - way features can avert this situation. this system is dependent on the security of the encryption system chosen by the cable company in question. old cable equipment used an analog signal that was scrambled by tuning the signal so the picture was unsteady, just as macrovision does at an attempt to copy a video.


in order to gain access to the software, the scientologists must first sign a contract. section 7 of this contract states that the members must agree to " use the specific internet filter program that csi has provided to you which allows you freedom to view other sites on dianetics, scientology or its principals without threat of accessing sites deemed to be using the marks or works in an unauthorized fashion or deemed to be improper or discreditable to the scientology religion. " the program works by preventing the user from accessing sites with certain keywords which scientology has identified as being objectionable material for viewing by their members. this use of keywords functions as a way to prevent members from learning of guarded scientology doctrine, such as xenu, ot iii, and other material relating to space opera in scientology scripture.


but then, by the same argument as before, 2 divides b2, so b must be even. however, if a and b are both even, they have 2 as a common factor. this contradicts our previous statement that a and b have no common factor, so we must conclude that 2 { \ displaystyle { \ sqrt { 2 } } } is an irrational number. to paraphrase : if one could write 2 { \ displaystyle { \ sqrt { 2 } } } as a fraction, this fraction could never be written in lowest terms, since 2 could always be factored from numerator and denominator.


part of the overhead is transmitted, then part of the payload, then the next part of the overhead, then the next part of the payload, until the entire frame has been transmitted. in the case of an sts - 1, the frame is 810 octets in size, while the stm - 1 / sts - 3c frame is 2, 430 octets in size. for sts - 1, the frame is transmitted as three octets of overhead, followed by 87 octets of payload.


in mathematics, legendre's equation is the diophantine equation the equation is named for adrien - marie legendre who proved in 1785 that it is solvable in integers x, y, z, not all zero, if and only if −bc, −ca and −ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, square - free, pairwise relatively prime integers, not all positive or all negative.


in 1819, charles babbage showed the same congruence modulo p2, which holds for p ≥ 3 { \ displaystyle p \ geq 3 }. an equivalent formulation is the congruence ( a p b p ) ≡ ( a b ) ( mod p 3 ) { \ displaystyle { ap \ choose bp } \ equiv { a \ choose b } { \ pmod { p ^ { 3 } } } } for p ≥ 5 { \ displaystyle p \ geq 5 }, which is due to wilhelm ljunggren ( and, in the special case b = 1 { \ displaystyle b = 1 }, to j. w. l. glaisher ) and is inspired by lucas'theorem. no known composite numbers satisfy wolstenholme's theorem and it is conjectured that there are none ( see below ).


a read from one such memory can happen before the write to this memory completes. therefore, the data read can be stale. thus, a processor under pc can execute a younger load when an older store needs to be stalled.


in the following section it is shown that for 455 spheres the sausage packing is non - optimal, and that there instead exists a special cluster packing that occupies a smaller volume. the volume of a convex hull of a sausage packing with n { \ displaystyle n } spheres of radius r { \ displaystyle r } is calculable with elementary geometry. the middle part of the hull is a cylinder with length h = 2 r ⋅ ( n − 1 ) { \ displaystyle h = 2r \ cdot ( n - 1 ) } while the caps at the end are half - spheres with radius r { \ displaystyle r }. the total volume v w { \ displaystyle v _ { w } } is therefore given by.


one of the most notably cyber attacks that had a physical impact, causing significant degradation of a target system, were the stuxnet and aurora worms. the stuxnet worm was first revealed in 2010 and specially targeted weaknesses in programmable logic controllers ( plcs ), devices in the scada category of systems. though it was never positivity attributed, it is widely believed that the malicious software was developed jointly by the united states and israel to disrupt the iranian nuclear enrichment facility at natanz.


in number theory, euler's theorem ( also known as the fermat – euler theorem or euler's totient theorem ) states that, if n and a are coprime positive integers, and φ ( n ) { \ displaystyle \ varphi ( n ) } is euler's totient function, then a raised to the power φ ( n ) { \ displaystyle \ varphi ( n ) } is congruent to 1 modulo n ; that is a φ ( n ) ≡ 1 ( mod n ). { \ displaystyle a ^ { \ varphi ( n ) } \ equiv 1 { \ pmod { n } }. } in 1736, leonhard euler published a proof of fermat's little theorem ( stated by fermat without proof ), which is the restriction of euler's theorem to the case where n is a prime number. subsequently, euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is not prime. the converse of euler's theorem is also true : if the above congruence is true, then a { \ displaystyle a } and n { \ displaystyle n } must be coprime.


in the field of recorded music, a hidden track ( sometimes called a ghost track, secret track or unlisted track ) is a song or a piece of audio that has been placed on a cd, audio cassette, lp record, or other recorded medium, in such a way as to avoid detection by the casual listener. in some cases, the piece of music may simply have been left off the track listing, while in other cases, more elaborate methods are used. in rare cases, a'hidden track'is actually the result of an error that occurred during the mastering stage production of the recorded media. however, since the rise of digital and streaming services such as itunes and spotify in the late 2000s and early 2010s, the inclusion of hidden tracks has declined on studio albums.


it is the starting point for understanding the structure of semigroups. it serves as a counterexample in illuminating many situations. for example, the semigroup with one element is the only semigroup in which 0 = 1, that is, the zero element and the identity element are equal. further, if s is a semigroup with one element, the semigroup obtained by adjoining an identity element to s is isomorphic to the semigroup obtained by adjoining a zero element to s. the semigroup with one element is also a group. in the language of category theory, any semigroup with one element is a terminal object in the category of semigroups.


2 s ( n + 1, j + 1 ) s ( k + 1, j + 1 ), { \ displaystyle b _ { n } ^ { ( - k ) } = \ sum _ { j = 0 } ^ { \ min ( n, k ) } ( j! ) ^ { 2 } s ( n + 1, j + 1 ) s ( k + 1, j + 1 ), } where s ( n, k ) { \ displaystyle s ( n, k ) } is the number of ways to partition a size n { \ displaystyle n } set into k { \ displaystyle k } non - empty subsets ( the stirling number of the second kind ). a combinatorial interpretation is that the poly - bernoulli numbers of negative index enumerate the set of n { \ displaystyle n } by k { \ displaystyle k } ( 0, 1 ) - matrices uniquely reconstructible from their row and column sums.


in mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points ( sets of values of the choice variables ) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. this is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. for example, consider the problem of minimizing the function x 2 + y 4 { \ displaystyle x ^ { 2 } + y ^ { 4 } } with respect to the variables x { \ displaystyle x } and y, { \ displaystyle y, } subject to 1 ≤ x ≤ 10 { \ displaystyle 1 \ leq x \ leq 10 } and 5 ≤ y ≤ 12. { \ displaystyle 5 \ leq y \ leq 12. \, } here the feasible set is the set of pairs ( x, y ) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12.


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


in order to implement general - purpose coroutines, a second call stack must be obtained, which is a feature not directly supported by the c language. a reliable ( albeit platform - specific ) way to achieve this is to use a small amount of inline assembly to explicitly manipulate the stack pointer during initial creation of the coroutine. this is the approach recommended by tom duff in a discussion on its relative merits vs. the method used by protothreads. on platforms which provide the posix sigaltstack system call, a second call stack can be obtained by calling a springboard function from within a signal handler to achieve the same goal in portable c, at the cost of some extra complexity.


, a n ( r ) { \ displaystyle \ pi _ { a _ { 1 },..., a _ { n } } ( r ) }, where r { \ displaystyle r } is a relation and a 1,...