The PRISM design was notable for several aspects of its instruction set. Notably, PRISM included Epicode (extended processor instruction code), which defined a number of "special" instructions intended to offer the operating system a stable ABI across multiple implementations. Epicode was given its own set of 22 32-bit registers to use. A set of vector processing instructions were later added as well, supported by an additional sixteen 64-bit vector registers that could be used in a variety of ways.


At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself. For example, to calculate 132 ÷ 8, one might successively subtract 80, 40 and 8 to leave 4: 132 80 (10 × 8) -- 52 40 ( 5 × 8) -- 12 8 ( 1 × 8) -- 4 -------- 132 = 16 × 8 + 4 Because 10 + 5 + 1 = 16, 132 ÷ 8 is 16 with 4 remaining. In the UK, this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the National Numeracy Strategy in its "numeracy hour" brought in a new emphasis on more free-form oral and mental strategies for calculations, rather than the rote learning of standard methods.Compared to the short division and long division methods that are traditionally taught, chunking may seem strange, unsystematic, and arbitrary.


In the English language, a hate crime (also known as a "bias-motivated crime") generally refers to criminal acts which are seen to have been motivated by hate. Those who commit hate crimes target victims because of their perceived membership in a certain social group, usually defined by race, gender, religion, sexual orientation, mental disorder, disability, class, ethnicity, nationality, age, gender identity, or political affiliation. Incidents may involve physical assault, destruction of property, bullying, harassment, verbal abuse or insults, or offensive graffiti or letters (hate mail).Hate speech is speech perceived to disparage a person or group of people based on their social or ethnic group, such as race, sex, age, ethnicity, nationality, religion, sexual orientation, gender identity, mental disorder, disability, language ability, ideology, social class, occupation, appearance (height, weight, skin color, etc.), mental capacity, and any other distinction that might be considered a liability.


When the action executes, and what its actual inputs are, is determined by the concrete action and the behaviors in which it is used. An action is the specification of an executable statement and is the fundamental unit of processing or behavior in an activity node that represents some transformation in the modeled system. An action forms an abstraction of a computational procedure which is an atomic execution and therefore completes without interruption.


A song sold on iTunes gives the artist 9 cents in profit. They also reported that customers were purchasing 2.5 million songs a week which translates to a projected annual run rate of 130 million songs a year. The 50 millionth song was "The Path of Thorns" by Sarah McLachlan.On April 28, 2004, iTunes Music Store marked its first anniversary with 70 million songs sold, clear dominance in the paid online music market and a slight profit.


It can be proved by a back-and-forth method that is also sometimes attributed to Cantor but was actually published later, by Felix Hausdorff. The same back-and-forth method also proves that countable dense unbounded orders are highly symmetric, and can be applied to other kinds of structures. However, Cantor's original proof only used the "going forth" half of this method.


In semantic hashing documents are mapped to memory addresses by means of a neural network in such a way that semantically similar documents are located at nearby addresses. Deep neural network essentially builds a graphical model of the word-count vectors obtained from a large set of documents. Documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. This way of extending the efficiency of hash-coding to approximate matching is much faster than locality sensitive hashing, which is the fastest current method.


In more sophisticated systems such as large cities, this concept is further extended: some streets are marked as being one-way, and on those streets all traffic must flow in only one direction. Pedestrians on the sidewalks are generally not limited to one-way movement. Drivers wishing to reach a destination they have already passed must return via other streets. One-way streets, despite the inconveniences to some individual drivers, can greatly improve traffic flow since they usually allow traffic to move faster and tend to simplify intersections.


As per the standard: "An equal month is presumed to have 30.41666 days (i.e. 365/12) regardless of whether or not it is a leap year." The result is to be expressed to at least one decimal place.


In the field of textual scholarship and the editing of historic texts, the term "normalization" implies a degree of modernization and standardization – for example in the extension of scribal abbreviations and the transliteration of the archaic glyphs typically found in manuscript and early printed sources. A normalized edition is therefore distinguished from a diplomatic edition (or semi-diplomatic edition), in which some attempt is made to preserve these features. The aim is to strike an appropriate balance between, on the one hand, rigorous fidelity to the source text (including, for example, the preservation of enigmatic and ambiguous elements); and, on the other, producing a new text that will be comprehensible and accessible to the modern reader. The extent of normalization is therefore at the discretion of the editor, and will vary. Some editors, for example, choose to modernize archaic spellings and punctuation, but others do not.


Genus types with sufficient vertical extent to occupy more than one level do not carry any altitude-related prefixes. They are classified formally as low- or mid-level depending on the altitude at which each initially forms, and are also more informally characterized as multi-level or vertical. Most of the ten genera derived by this method of classification can be subdivided into species and further subdivided into varieties.


The even dimensional space of dimension d {\displaystyle d} can be described using complex coordinates w i ∈ C d / 2 {\displaystyle w_{i}\in \mathbb {C} ^{d/2}} with a metric g i j ¯ = ( 1 + ρ d r d ) 2 / d  , {\displaystyle g_{i{\bar {j}}}={\bigg (}1+{\frac {\rho ^{d}}{r^{d}}}{\bigg )}^{2/d}{\bigg },} where ρ {\displaystyle \rho } is a scale setting constant and r 2 = | w | C d / 2 2 {\displaystyle r^{2}=|w|_{\mathbb {C} ^{d/2}}^{2}} . Aside from its inherent importance in pure geometry, the space is important in string theory. Certain types of K3 surfaces can be approximated as a combination of several Eguchi–Hanson metrics since both have the same holonomy group.


In music, a rewrite rule is a recursive generative grammar, which creates a chord progression from another. Steedman (1984) has proposed a set of recursive "rewrite rules" which generate all well-formed transformations of jazz, basic I–IV–I–V–I twelve-bar blues chord sequences, and, slightly modified, non-twelve-bar blues I–IV–V sequences ("rhythm changes"). The typical 12-bar blues progression can be notated 1 2 3 4 5 6 7 8 9 10 11 12 I / I / I / I // IV /IV / I / I // V / IV / I / I where the top line numbers each bar, one slash indicates a bar line, two indicate both a bar line and a phrase ending and a Roman numeral indicates the chord function. Important transformations include replacement or substitution of a chord by its dominant or subdominant: 1 2 3 4 5 6 7 8 9 10 11 12 I / IV / I / I7 // IV / VII7 / III7 / VI7 // II7 / V7 / I / I // use of chromatic passing chords: ...7 8 9 ... ...III7 / ♭III7 / II7... and chord alterations such as minor chords, diminished sevenths, etc.Sequences by fourth, rather than fifth, include Jimi Hendrix's version of "Hey Joe" and Deep Purple's "Hush": 1 2 3 4 5 6 7 8 9 10 11 12 ♭VI, ♭III / ♭VII, IV / I / I // ♭VI, ♭III / ♭VII, IV / I / I // ♭VI, ♭III / ♭VII, IV / I / I // These often result in Aeolian harmony and lack perfect cadences (V–I).


OSes have grown immensely in their size and complexity resulting in attempts to reduce OS overhead and improve performance including Microkernel, Exokernel, Tiny-OS, OS-Kit, Palacios and Kitten, IO_Lite, bare-metal Linux, IBM-Libra and other lean kernels. In addition to the above approaches, in embedded systems such as smart phones, a small and dedicated portion of an OS and a given set of applications are closely integrated with the hardware. There are also a myriad of industrial control and gaming applications that run directly on the hardware.


In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by Kolyvagin (1990) in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the work of Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles.


Other regression methods that can be used in place of ordinary least squares include least absolute deviations (minimizing the sum of absolute values of residuals) and the Theil–Sen estimator (which chooses a line whose slope is the median of the slopes determined by pairs of sample points). Deming regression (total least squares) also finds a line that fits a set of two-dimensional sample points, but (unlike ordinary least squares, least absolute deviations, and median slope regression) it is not really an instance of simple linear regression, because it does not separate the coordinates into one dependent and one independent variable and could potentially return a vertical line as its fit. The remainder of the article assumes an ordinary least squares regression. In this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.


The case (x, y, z) = (2, 6, n) and all its permutations were proven for n ≥ 3 by Michael Bennett and Imin Chen in 2011 and by Bennett, Chen, Dahmen and Yazdani in 2014. The case (x, y, z) = (2, 2n, 3) and all its permutations were proven for 3 ≤ n ≤ 107 except n = 7 and various modulo congruences when n is prime to have no non-Catalan solution by Bennett, Chen, Dahmen and Yazdani. The cases (x, y, z) = (2, 2n, 9), (2, 2n, 10), (2, 2n, 15) and all their permutations were proven for n ≥ 2 by Bennett, Chen, Dahmen and Yazdani in 2014.


Z i {\displaystyle Z_{i}} is the idiosyncratic component, the ‘strength’ of entity i, possibly measured by entity i's stock price return. From equation (10) we see, that the correlation between entities i is modeled indirectly by conditioning the latent variable x i {\displaystyle x_{i}} on the common factor M {\displaystyle M} .


In the Java programming language, heap pollution is a situation that arises when a variable of a parameterized type refers to an object that is not of that parameterized type. This situation is normally detected during compilation and indicated with an unchecked warning. Later, during runtime heap pollution will often cause a ClassCastException.Heap pollution in Java can occur when type arguments and variables are not reified at run-time.


In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3. The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n2, usually pronounced as "n squared". The name square number comes from the name of the shape.


Almost all even positive numbers can be expressed as the sum of two primes. : 489 Almost all primes are isolated. Moreover, for every positive integer g, almost all primes have prime gaps of more than g both to their left and to their right; that is, there is no other prime between p − g and p + g.


In the case of indivisible item assignment, when the utility functions of all agents are GS (and thus an equilibrium exists), it is possible to find a competitive equilibrium using an ascending auction. In an ascending auction, the auctioneer publishes a price vector, initially zero, and the buyers declare their favorite bundle under these prices. In case each item is desired by at most a single bidder, the items are divided and the auction is over.


In the Unix-world, there is commonly a special filesystem mounted at /proc. This filesystem is implemented within the kernel and publishes information about processes. For each process, there is a directory (named by the process ID), containing detailed information about the process: status, open files, memory maps, mounts, etc. /proc first appeared in Unix 8th Edition, and its functionality was greatly expanded in Plan 9 from Bell Labs.


To this end the 56800 series added a complete MCU which created a single-chip "DSPcontroller" solution, while the opposite occurred in the 68456, a 68000 with a 56000 on it. A still quite prevalent model of the 56000 is the third generation 56300 family, starting with the 56301, which features several models with special applications hard- and firmware built-in, like PCI interface logic, CRC processors, or audio companders. Core clock frequencies ranged up to 250 MHz.


The receiver un-does these transformations in reverse order: demodulation, trellis decoding, error detection and correction, decompression. Some communication systems omit one or more of these steps, or use techniques that combine several of these steps together. For example, a Morse code transmitter combines source coding, channel coding, and line coding into one step, typically followed by an amplitude modulation step. Barcodes, on the other hand, add a checksum digit during channel coding, then translate each digit into a barcode symbol during line coding, omitting modulation.


The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic F β {\displaystyle F_{\beta }} score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the lowest possible value is 0, if either precision or recall are zero.


In mathematics, an algebra such as ( R , + , ⋅ ) {\displaystyle (\mathbb {R} ,+,\cdot )} has multiplication ⋅ {\displaystyle \cdot } whose associativity is well-defined on the nose. This means for any real numbers a , b , c ∈ R {\displaystyle a,b,c\in \mathbb {R} } we have a ⋅ ( b ⋅ c ) − ( a ⋅ b ) ⋅ c = 0 {\displaystyle a\cdot (b\cdot c)-(a\cdot b)\cdot c=0} .But, there are algebras R {\displaystyle R} which are not necessarily associative, meaning if a , b , c ∈ R {\displaystyle a,b,c\in R} then a ⋅ ( b ⋅ c ) − ( a ⋅ b ) ⋅ c ≠ 0 {\displaystyle a\cdot (b\cdot c)-(a\cdot b)\cdot c\neq 0} in general. There is a notion of algebras, called A ∞ {\displaystyle A_{\infty }} -algebras, which still have a property on the multiplication which still acts like the first relation, meaning associativity holds, but only holds up to a homotopy, which is a way to say after an operation "compressing" the information in the algebra, the multiplication is associative. This means although we get something which looks like the second equation, the one of inequality, we actually get equality after "compressing" the information in the algebra.


In number theory, Proth's theorem is a primality test for Proth numbers. It states that if p is a Proth number, of the form k2n + 1 with k odd and k < 2n, and if there exists an integer a for which a p − 1 2 ≡ − 1 ( mod p ) , {\displaystyle a^{\frac {p-1}{2}}\equiv -1{\pmod {p}},} then p is prime. In this case p is called a Proth prime. This is a practical test because if p is prime, any chosen a has about a 50 percent chance of working, furthermore, since the calculation is mod p, only values of a smaller than p have to be taken into consideration.


In parallel to the development of L4Ka::Hazelnut, in 1998 the Operating Systems Group TUD:OS of the TU Dresden started to develop their own C++ implementation of the L4 kernel interface, named L4/Fiasco. In contrast to L4Ka::Hazelnut, which allows no concurrency in the kernel, and its successor L4Ka::Pistachio, which allows interrupts in the kernel only at specific preemption points, L4/Fiasco was fully preemptible (with the exception of extremely short atomic operations) to achieve a low interrupt latency. This was considered necessary because L4/Fiasco is used as the basis of DROPS, a hard real-time computing capable operating system, also developed at the TU Dresden. However, the complexities of a fully preemptible design prompted later versions of Fiasco to return to the traditional L4 approach of running the kernel with interrupts disabled, except for a limited number of preemption points.


In text-based electronic communication, the sign of the horns is represented with the \../, \m/ or |m| emoticon and sometimes with /../. The Unicode character U+1F918 🤘 SIGN OF THE HORNS was introduced in Unicode 8.0 as an emoji, on June 17, 2015.


In terms of sieve theory the Selberg sieve is of combinatorial type: that is, derives from a careful use of the inclusion–exclusion principle. Selberg replaced the values of the Möbius function which arise in this by a system of weights which are then optimised to fit the given problem. The result gives an upper bound for the size of the sifted set. Let A {\displaystyle A} be a set of positive integers ≤ x {\displaystyle \leq x} and let P {\displaystyle P} be a set of primes.


Modern power systems are designed to be resistant to this sort of cascading failure, but it may be unavoidable (see below). Moreover, since there is no short-term economic benefit to preventing rare large-scale failures, researchers have expressed concern that there is a tendency to erode the resilience of the network over time, which is only corrected after a major failure occurs. In a 2003 publication, Carreras and co-authors claimed that reducing the likelihood of small outages only increases the likelihood of larger ones.


In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry".He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.


Suppose the documentation associated with these types specifies that type Stack's methods shall behave as expected for stacks (i.e. they shall exhibit LIFO behavior), and that type Queue's methods shall behave as expected for queues (i.e. they shall exhibit FIFO behavior). Suppose, now, that type Stack was declared as a subclass of type Queue. Most programming language compilers ignore documentation and perform only the checks that are necessary to preserve type safety.


In software development, a test suite, less commonly known as a validation suite, is a collection of test cases that are intended to be used to test a software program to show that it has some specified set of behaviors. A test suite often contains detailed instructions or goals for each collection of test cases and information on the system configuration to be used during testing. A group of test cases may also contain prerequisite states or steps, and descriptions of the following tests. Collections of test cases are sometimes termed a test plan, a test script, or even a test scenario.


They can also be described as subsets of a set of 24 elements, where addition is defined as taking the symmetric difference of the subsets. In the extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 16, or 24. Code words of weight 8 are called octads and code words of weight 12 are called dodecads.


In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.


In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer.


In structural typing, an element is considered to be compatible with another if, for each feature within the second element's type, a corresponding and identical feature exists in the first element's type. Some languages may differ on the details, such as whether the features must match in name. This definition is not symmetric, and includes subtype compatibility. Two types are considered to be identical if each is compatible with the other.


Again in contrast to linear regression, there may be many local minima of the function to be optimized and even the global minimum may produce a biased estimate. In practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares. For details concerning nonlinear data modeling see least squares and non-linear least squares.


In measure theory, given a measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} and a signed measure μ {\displaystyle \mu } on it, a set A ∈ Σ {\displaystyle A\in \Sigma } is called a positive set for μ {\displaystyle \mu } if every Σ {\displaystyle \Sigma } -measurable subset of A {\displaystyle A} has nonnegative measure; that is, for every E ⊆ A {\displaystyle E\subseteq A} that satisfies E ∈ Σ , {\displaystyle E\in \Sigma ,} μ ( E ) ≥ 0 {\displaystyle \mu (E)\geq 0} holds. Similarly, a set A ∈ Σ {\displaystyle A\in \Sigma } is called a negative set for μ {\displaystyle \mu } if for every subset E ⊆ A {\displaystyle E\subseteq A} satisfying E ∈ Σ , {\displaystyle E\in \Sigma ,} μ ( E ) ≤ 0 {\displaystyle \mu (E)\leq 0} holds. Intuitively, a measurable set A {\displaystyle A} is positive (resp. negative) for μ {\displaystyle \mu } if μ {\displaystyle \mu } is nonnegative (resp.


In software testing, error guessing is a test method in which test cases used to find bugs in programs are established based on experience in prior testing. The scope of test cases usually rely on the software tester involved, who uses experience and intuition to determine what situations commonly cause software failure, or may cause errors to appear. Typical errors include divide by zero, null pointers, or invalid parameters.Error guessing has no explicit rules for testing; test cases can be designed depending on the situation, either drawing from functional documents or when an unexpected/undocumented error is found while testing operations. == References ==


In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient.


In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine transformations that combine both variables. It can be calculated in O ( n 2 ) {\displaystyle O(n^{2})} time by brute force, in O ( n log 2  n ) {\displaystyle O(n\log ^{2}n)} time using more sophisticated techniques, or in O ( n log  n ) {\displaystyle O(n\log n)} randomized expected time. It may also be calculated using an on-line algorithm with O ( n ) {\displaystyle O(n)} update time.


A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852. The four color theorem was ultimately proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer.


In focused calculi, it is possible to define positive connectives by giving only their introduction rules, with the shape of the elimination rules being forced by this choice. (Symmetrically, negative connectives can be defined in focused calculi by giving only the elimination rules, with the introduction rules forced by this choice.) The second view, which might be termed the computational or Brouwer–Heyting–Kolmogorov interpretation of propositions, takes the view that we fix a computational system up front, and then give a realizability interpretation of propositions to give them constructive content.


The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.


Next, Kleene proceeds to present "Turing's thesis", where results are shown to be uncomputable, using his simplified derivation of a Turing machine based on the work of Emil Post. Both theses are proven equivalent by use of "Theorem XXX". Thesis I. Every effectively calculable function (effectively decidable predicate) is general recursive. Theorem XXX: The following classes of partial functions are coextensive, i.e. have the same members: (a) the partial recursive functions, (b) the computable functions ... Turing's thesis: Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. Kleene, finally, uses for the first time the term the "Church-Turing thesis" in a section in which he helps to give clarifications to concepts in Alan Turing's paper "The Word Problem in Semi-Groups with Cancellation", as demanded in a critique from William Boone.


In the 2-ary case, there can be zero or one identity elements: the empty set is a 2-ary group, since the empty set is both a semigroup and a quasigroup, and every inhabited 2-ary group is a group. In n-ary groups for n ≥ 3 there can be zero, one, or many identity elements. An n-ary groupoid (G, f) with f = (x1 ◦ x2 ◦ ⋯ ◦ xn), where (G, ◦) is a group is called reducible or derived from the group (G, ◦). In 1928 Dörnte published the first main results: An n-ary groupoid which is reducible is an n-ary group, however for all n > 2 there exist inhabited n-ary groups which are not reducible.


In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle A} , the set of all subsets of A , {\displaystyle A,} the power set of A , {\displaystyle A,} has a strictly greater cardinality than A {\displaystyle A} itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n {\displaystyle n} elements has a total of 2 n {\displaystyle 2^{n}} subsets, and the theorem holds because 2 n > n {\displaystyle 2^{n}>n} for all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.


It follows that, as with LFSRs and linear complexity, any stream cipher whose N-adic complexity is low should not be used for cryptography. FCSRs and LFSRs are special cases of a very general algebraic construction of sequence generators called Algebraic Feedback Shift Registers (AFSRs) in which the integers are replaced by an arbitrary ring R and N is replaced by an arbitrary non-unit in R. A general reference on the subject of LFSRs, FCSRs, and AFSRs is the book. == References ==


In the United States, the books were most popular as A5-sized paperback volumes, and were usually between 150 and 200 pages long, divided into just under thirty chapters. The front covers featured images of the narrating Animorph undergoing the various stages of one of the morphs from the story, with a few exceptions (noted in each book's article). Behind the morphing character were images of clouds and skies, which became more colorful and elaborate as the series progressed. All the covers of the regular series books had a small cutout over part of the full morph's anatomy, revealing a computer-generated illustration on the first page, which was printed on glossy paper.


The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.


In message queueing a dead letter queue (DLQ) is a service implementation to store messages that the messaging system cannot or should not deliver. Although implementation-specific, messages can be routed to the DLQ for the following reasons: The message is sent to a queue that does not exist. The maximum queue length is exceeded. The message exceeds the size limit.


CDMA, by comparison, supports "soft hand-off" which allows a mobile phone to be in communication with up to 6 base stations simultaneously, a type of "same-frequency handover". The incoming packets are compared for quality, and the best one is selected. CDMA's "cell breathing" characteristic, where a terminal on the boundary of two congested cells will be unable to receive a clear signal, can often negate this advantage during peak periods.


Other applications are in statistics, and another is in elliptic geometry.For n > 1, there are two kinds of conference matrix. Let us normalize C by, first (if the more general definition is used), rearranging the rows so that all the zeros are on the diagonal, and then negating any row or column whose first entry is negative. (These operations do not change whether a matrix is a conference matrix.)


has been applied as the formal type parameter of a method, no actual parameters can be passed to it. However, objects of the unknown type can be read from the generic object and assigned to a variable of a supertype of the upperbound. Sample code for the Generic class: Sample code that uses the Generic class:


The groups of each of these 8 types were classified by various authors. They consist mainly of groups of Lie type with all roots of the same length over the field with 2 elements, but also include many exceptional cases, including the majority of the sporadic simple groups. Smith (1980) gave a survey of this work. Smith (1979, p.279) gives a table of simple groups containing a large extraspecial 2-group.


In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent set.


In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proved without these theorems. The inequality can be viewed intuitively in either R2 or R3.


In telecommunications, the term cyclic prefix refers to the prefixing of a symbol with a repetition of the end. The receiver is typically configured to discard the cyclic prefix samples, but the cyclic prefix serves two purposes: It provides a guard interval to eliminate intersymbol interference from the previous symbol. It repeats the end of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as circular convolution, which in turn may transform to the frequency domain via a discrete Fourier transform. This approach accommodates simple frequency domain processing, such as channel estimation and equalization.For the cyclic prefix to serve its objectives, it must have a length at least equal to the length of the multipath channel. The concept of a cyclic prefix is traditionally associated with OFDM systems, however the cyclic prefix is now also used in single carrier systems to improve the robustness to multipath propagation.


It is used in polynomial factorization, a problem for which all known efficient algorithms use modular arithmetic. It is used by the most efficient implementations of polynomial greatest common divisor, exact linear algebra and Gröbner basis algorithms over the integers and the rational numbers. As posted on Fidonet in the 1980s and archived at Rosetta Code, modular arithmetic was used to disprove Euler's sum of powers conjecture on a Sinclair QL microcomputer using just one-fourth of the integer precision used by a CDC 6600 supercomputer to disprove it two decades earlier via a brute force search.In computer science, modular arithmetic is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures.


Data collection with proton precession instruments was slow, making high sample density surveys impracticable. Data were manually recorded and plotted.


Many linguistic anthropologists have come to understand that language and culture are not separate entities, but are in fact processes that work hand in hand. These contextualization cues are culturally specific and usually unconscious. Linguistic anthropology helps make explicit the implicit features of culture that can often be unknown to the speaker.


In standard linear regression models one observes data { y i , x i j } i = 1 , … , n , j = 2 , … , k {\displaystyle \{y_{i},x_{ij}\}_{i=1,\dots ,n,j=2,\dots ,k}} on n statistical units. The response values are placed in a vector y = ( y 1 , … , y n ) T {\displaystyle \mathbf {y} =\left(y_{1},\dots ,y_{n}\right)^{\mathsf {T}}} , and the predictor values are placed in the design matrix X = ( x 1 T , … , x n T ) T {\displaystyle \mathbf {X} =\left(\mathbf {x} _{1}^{\mathsf {T}},\dots ,\mathbf {x} _{n}^{\mathsf {T}}\right)^{\mathsf {T}}} , where x i = ( 1 , x i 2 , … , x i k ) {\displaystyle \mathbf {x} _{i}=\left(1,x_{i2},\dots ,x_{ik}\right)} is a vector of the k predictor variables (including a constant) for the ith unit. The model forces the conditional mean of y {\displaystyle \mathbf {y} } given X {\displaystyle \mathbf {X} } to be a linear function of X {\displaystyle \mathbf {X} } and assumes the conditional variance of the error term given X {\displaystyle \mathbf {X} } is a known nonsingular covariance matrix Ω {\displaystyle \mathbf {\Omega } } . This is usually written as y = X β + ε , E   = 0 , Cov   = Ω .


The trainer gets active when the object has been allocated and deactivates itself again when the object is freed. Modern operating systems also come with position-independent executables (PIE) for security. Together with ASLR, the binaries are loaded to a different virtual memory address each code execution.


In 2009, Gu et al. presented a class of infinite physical systems that exhibits non-computable macroscopic properties. More precisely, if one could compute certain macroscopic properties of these systems from the microscopic description of these systems, then one would be able to solve computational problems known to be undecidable in computer science. These results concern infinite systems, finite systems being considered computable.


In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which the elements are partitioned into different categories. For each category, there is a capacity constraint - a maximum number of allowed elements from this category. The independent sets of a partition matroid are exactly the sets in which, for each category, the number of elements from this category is at most the category capacity.


In telecommunications, a multi-band device (including (2) dual-band, (3) tri-band, (4) quad-band and (5) penta-band devices) is a communication device (especially a mobile phone) that supports multiple radio frequency bands. All devices which have more than one channel use multiple frequencies; a band however is a group of frequencies containing many channels. Multiple bands in mobile devices support roaming between different regions where different standards are used for mobile telephone services. Where the bands are widely separated in frequency, parallel transmit and receive signal path circuits must be provided, which increases the cost, complexity and power demand of multi-band devices.The term quad-band describes a device that supports four frequency bands: the 850 and 1900 MHz bands, which are used in the Americas, and 900 / 1800, which are used in most other parts of the world.


In mathematics, the Hartogs–Rosenthal theorem is a classical result in complex analysis on the uniform approximation of continuous functions on compact subsets of the complex plane by rational functions. The theorem was proved in 1931 by the German mathematicians Friedrich Hartogs and Arthur Rosenthal and has been widely applied, particularly in operator theory.


In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying certain objects into tests on groups of items, rather than on individual ones. First studied by Robert Dorfman in 1943, group testing is a relatively new field of applied mathematics that can be applied to a wide range of practical applications and is an active area of research today. A familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken. The objective is to find the broken bulb using the smallest number of tests (where a test is when some of the bulbs are connected to a power supply).


, 1123456789, 10123456789, ... (sequence A134596 in the OEIS)Primeval numbers can be composite. The first is 1037 = 17×61. A Primeval prime is a primeval number which is also a prime number: 2, 13, 37, 107, 113, 137, 1013, 1237, 1367, 10079, 10139, 12379, 13679, 100279, 100379, 123479, 1001237, 1002347, 1003679, 1012379, ... (sequence A119535 in the OEIS)The following table shows the first seven primeval numbers with the obtainable primes and the number of them.


In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation (also called rotation), or multiplicative operations (such as the cycle of fourths and cycle of fifths transforms). These may produce reorderings of the members of the set, or may simply map the set onto itself.


Eventually, one ends up with a day-count to which one applies modulo 7 to determine the day of the week of the date.Some methods do all the additions first and then cast out sevens, whereas others cast them out at each step, as in Lewis Carroll's method. Either way is quite viable: the former is easier for calculators and computer programs, the latter for mental calculation (it is quite possible to do all the calculations in one's head with a little practice). None of the methods given here perform range checks, so unreasonable dates will produce erroneous results.


If we make a change of variables, w k = v k + 1 − v k , k = 0 , . . .


The Requires constraint states that if cause 1 is true, then cause 2 must be true, and it is impossible for 1 to be true and 2 to be false. For effects, valid constraint symbol is M (Mask). The mask constraint states that if effect 1 is true then effect 2 is false.


In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials on elliptic curves. EDS were first defined, and their arithmetic properties studied, by Morgan Ward in the 1940s. They attracted only sporadic attention until around 2000, when EDS were taken up as a class of nonlinear recurrences that are more amenable to analysis than most such sequences. This tractability is due primarily to the close connection between EDS and elliptic curves. In addition to the intrinsic interest that EDS have within number theory, EDS have applications to other areas of mathematics including logic and cryptography.


In programming languages with a built-in Boolean data type, such as Pascal and Java, the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions. Languages with no explicit Boolean data type, like C90 and Lisp, may still represent truth values by some other data type. Common Lisp uses an empty list for false, and any other value for true.


Thus ¬ is a dual automorphism of (A, ∨, ∧, 0, 1). If the lattice is defined in terms of the order instead, i.e. (A, ≤) is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, and the meet and join operations so defined satisfy the distributive law, then the complementation can also be defined as an involutive anti-automorphism, that is, a structure A = (A, ≤, ¬) such that: (A, ≤) is a bounded distributive lattice, and ¬¬x = x, and x ≤ y → ¬y ≤ ¬x.De Morgan algebras were introduced by Grigore Moisil around 1935, although without the restriction of having a 0 and a 1. They were then variously called quasi-boolean algebras in the Polish school, e.g. by Rasiowa and also distributive i-lattices by J. A. Kalman.


A formal proof or derivation is a finite sequence of well-formed formulas (which may be interpreted as sentences, or propositions) each of which is an axiom or follows from the preceding formulas in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system. Formal proofs are useful because their theorems can be interpreted as true propositions.


They have introduced finite and infinite mixture models of inverted Dirichlet distributions using the Newton–Raphson technique to estimate the parameters and the Dirichlet process to model infinite mixtures. T. Bdiri et al. have also used the inverted Dirichlet distribution to propose an approach to generate Support Vector Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering. == References ==


In most experiments, measurements are repeatedly made at the same two locations. A local hidden variable theory could exploit the memory of past measurement settings and outcomes in order to increase the violation of a Bell inequality. Moreover, physical parameters might be varying in time. It has been shown that, provided each new pair of measurements is done with a new random pair of measurement settings, that neither memory nor time inhomogeneity have a serious effect on the experiment.


In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If d ∗ {\displaystyle d^{*}} is the optimal dual value and p ∗ {\displaystyle p^{*}} is the optimal primal value then the duality gap is equal to p ∗ − d ∗ {\displaystyle p^{*}-d^{*}} . This value is always greater than or equal to 0 (for minimization problems). The duality gap is zero if and only if strong duality holds.


7. Examining how likely it is that the concept applies, statistically or intuitively (probability theory).


The software can be more usable and has a better chance to focus on business problems that are critical to end users rather than technical problems of interest to developers. However, this excludes other categories of what are usually known as Non-functional requirements (AKA constraints or quality attributes) including security and portability. Risk control.


In statistical classification, the rule which assigns a class to a new data-item can be considered to be a special type of estimator. A number of invariance-type considerations can be brought to bear in formulating prior knowledge for pattern recognition.


In the area of nonmonotonic logics, a group of logics related to artificial intelligence, he focused on investigations of Reiter's default logic, and autoepistemic logic of R. Moore. These investigations led to a form of logic programming called answer set programming a computational knowledge representation formalism, studied both in Europe and in the United States. Together with Mirosław Truszczynski, he proved that the problem of existence of stable models of logic programs is NP-complete. In a stronger formalism admitting function symbols, along with Nerode and Remmel he showed that the analogous problem is Σ11-complete.


In the conventional sequential BFS algorithm, two data structures are created to store the frontier and the next frontier. The frontier contains all vertices that have the same distance (also called "level") from the source vertex, these vertices need to be explored in BFS. Every neighbor of these vertices will be checked, some of these neighbors which are not explored yet will be discovered and put into the next frontier. At the beginning of the BFS algorithm, a given source vertex s is the only vertex in the frontier.


In the example test case graph, all test cases and their isolated conditions are marked by colors, and the remaining paths are implicitly passed.


Personal information must be handled properly. Information must be kept accurate and relevant, used only for the stated purposes, and retained only for as long as reasonably needed. The law required entities to be active in ensuring that unauthorized parties do not have access to their customers' information. Personal information must be disposed in way that unauthorized third parties could not access the discarded data.


An eight step policy cycle is developed in detail in The Australian Policy Handbook by Peter Bridgman and Glyn Davis: (now with Catherine Althaus in its 4th and 5th editions) Issue identification Policy analysis Consultation (which permeates the entire process) Policy instrument development Building coordination and coalitions Program Design: Decision making Policy Implementation Policy EvaluationThe Althaus, Bridgman & Davis model is heuristic and iterative. It is intentionally normative and not meant to be diagnostic or predictive.


In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals.


The signature of the form determines the group up to isomorphism; interchanging p with q amounts to replacing the metric by its negative, and so gives the same group. If either p or q equals zero, then the group is isomorphic to the ordinary orthogonal group O(n). We assume in what follows that both p and q are positive.


Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization and discrete logarithm problem have served as the base for public key cryptography since the early 1980s. An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem can be used to solve a version of the shortest vector problem (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented).


It is usually least stiff in the radial direction (between the growth rings), and is intermediate in the circumferential direction. This anisotropy was provided by evolution, as it best enables the tree to remain upright.


In protected mode with paging enabled (bit 31, PG, of control register CR0 is set), but without PAE, x86 processors use a two-level page translation scheme. Control register CR3 holds the page-aligned physical address of a single 4 KB long page directory. This is divided into 1024 four-byte page directory entries that in turn, if valid, hold the page-aligned physical addresses of page tables, each 4 KB in size. These similarly consist of 1024 four-byte page table entries which, if valid, hold the page-aligned physical addresses of 4 KB long pages of physical memory (RAM).


These human computers worked with electrical engineers to help figure out how to boost signals with vacuum tube amplifiers. One of the computers, Clara Froelich, was eventually moved along with the other computers to their own division where they worked with a mathematician, Thornton Fry, to create new computational methods. Froelich studied IBM tabulating equipment and desk calculating machines to see if she could adapt the machine method to calculations.Edith Clarke was the first woman to earn a degree in electrical engineering and who worked as the first professionally employed electrical engineer in the United States.


In set theory and related branches of mathematics, a family (or collection) can mean any of set indexed set multiset classdepending upon the context. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S . {\displaystyle S.} More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system.


And these will always start as there blanks with the scanned square on the left: i.e. bbb. With two symbols 1, 0 and blank we can have 27 distinct configurations: bbb, bb0, bb1, b0b, b00, b01, b1b, b10, b11, 0bb, 0b0, 0b1, 00b, 000, 001, 01b, 010, 011, 1bb, 1b0, 1b1, 10b, 100, 101, 11b, 110, 111 We must be careful here, because it is quite possible that an algorithm will (temporarily) leave blanks in between figures, then come back and fill something in. More likely, an algorithm may do this intentionally.


If the smallest item size is eB (for some fraction e in (0,1)), then there can be up to 1/e items in each bin, so the number of configurations C ~ S1/e, which can be very large if e is small (if e is considered a constant, then the integer LP can be solved by exhaustive search: there are at most S1/e configurations, and for each configuration there are at most n possible values, so there are at most n S 1 / e {\displaystyle n^{S^{1/e}}} combinations to check. For each combination, we have to check S constraints, so the run-time is S ⋅ n S 1 / e {\displaystyle S\cdot n^{S^{1/e}}} , which is polynomial in n when S, e are constant).However, this ILP serves as a basis for several approximation algorithms. The main idea of these algorithms is to reduce the original instance into a new instance in which S is small and e is large, so C is relatively small. Then, the ILP can be solved either by complete search (if S, C are sufficiently small), or by relaxing it into a fractional LP.


These three operations are repeated until no new states can be added to the set. The set is generally implemented as a queue of states to process, with the operation to be performed depending on what kind of state it is. The algorithm accepts if (X → γ •, 0) ends up in S(n), where (X → γ) is the top level-rule and n the input length, otherwise it rejects.


However, unlike Conway's Life, cells that have become dead never become alive again. It can also be viewed as an epidemic model in which inactive cells are considered as infected and active cells with too many infected neighbors become infected themselves. The smallest threshold that allows some cells of an initial cluster to survive is called the degeneracy of its adjacency graph, and the remnant of a cluster that survives with threshold k is called the k-core of this graph.One application of bootstrap percolation arises in the study of fault tolerance for distributed computing.


In social psychology, ambiguity is a factor used in determining peoples' responses to various situations. High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for help) elicit more consistent intervention and assistance. With regard to the bystander effect, studies have shown that emergencies deemed ambiguous trigger the appearance of the classic bystander effect (wherein more witnesses decrease the likelihood of any of them helping) far more than non-ambiguous emergencies.


In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log2 n⌋ + 1 bits) is of the form exp  ( ( ( 64 / 9 ) 1 / 3 + o ( 1 ) ) ( log  n ) 1 / 3 ( log  log  n ) 2 / 3 ) = L n  {\displaystyle \exp \left(\left((64/9)^{1/3}+o(1)\right)\left(\log n\right)^{1/3}\left(\log \log n\right)^{2/3}\right)=L_{n}\left} in O and L-notations. It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots).


The Power ISA v3.0 allows 64 bits for an effective address, mapped to a segmented address with between 65 and 78 bits allowed, for virtual memory, and, for any given processor, up to 60 bits for physical memory.The Oracle SPARC Architecture 2015 allows 64 bits for virtual memory and, for any given processor, between 40 and 56 bits for physical memory.The ARM AArch64 Virtual Memory System Architecture allows 48 bits for virtual memory and, for any given processor, from 32 to 48 bits for physical memory.The DEC Alpha specification requires minimum of 43 bits of virtual memory address space (8 TiB) to be supported, and hardware need to check and trap if the remaining unsupported bits are zero (to support compatibility on future processors). Alpha 21064 supported 43 bits of virtual memory address space (8 TiB) and 34 bits of physical memory address space (16 GiB). Alpha 21164 supported 43 bits of virtual memory address space (8 TiB) and 40 bits of physical memory address space (1 TiB). Alpha 21264 supported user-configurable 43 or 48 bits of virtual memory address space (8 TiB or 256 TiB) and 44 bits of physical memory address space (16 TiB).


In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing all elements of A {\displaystyle A} that also belong to B {\displaystyle B} or equivalently, all elements of B {\displaystyle B} that also belong to A . {\displaystyle A.}


In natural language processing, semantic role labeling (also called shallow semantic parsing or slot-filling) is the process that assigns labels to words or phrases in a sentence that indicates their semantic role in the sentence, such as that of an agent, goal, or result. It serves to find the meaning of the sentence. To do this, it detects the arguments associated with the predicate or verb of a sentence and how they are classified into their specific roles. A common example is the sentence "Mary sold the book to John." The agent is "Mary," the predicate is "sold" (or rather, "to sell,") the theme is "the book," and the recipient is "John." Another example is how "the book belongs to me" would need two labels such as "possessed" and "possessor" and "the book was sold to John" would need two other labels such as theme and recipient, despite these two clauses being similar to "subject" and "object" functions.


Linguistic signs may also derive nonreferential meaning from indexicality, for example when features of a speaker's register indexically signal their social class. Nonlinguistic signs may also display indexicality: for example, a pointing index finger may index (without referring to) some object in the direction of the line implied by the orientation of the finger, and smoke may index the presence of a fire. In linguistics and philosophy of language, the study of indexicality tends to focus specifically on deixis, while in semiotics and anthropology equal attention is generally given to nonreferential indexicality, including altogether nonlinguistic indexicality.


In the PIC instruction set, the REPEAT and DO instructions implement zero-overhead loops. REPEAT only repeats a single instruction, while DO repeats a specified number of following instructions.


In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet.


In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.


Beginning in 1969 the U.S. Army Mobility Equipment Research and Development Command (MERADCOM) reverse-engineered the Russian PMP design to develop the improved float bridge (IFB), later known as the standard ribbon bridge (SRB). The IFB/SRB was type classified in 1972 and first deployed in service in 1976.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2358, 12358, 23458, and 123458 are the patterns related to Braille pattern dots-1246, since the two additional dots of kantenji patterns 01246, 12467, and 012467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


However, it does compile in C/C++ and some other languages, yielding surprising result (as true would be represented by the number 1 here). It is possible to give the expression x < y < z its familiar mathematical meaning, and some programming languages such as Python and Raku do that. Others, such as C# and Java, do not, partly because it would differ from the way most other infix operators work in C-like languages. The D programming language does not do that since it maintains some compatibility with C, and "Allowing C expressions but with subtly different semantics (albeit arguably in the right direction) would add more confusion than convenience".Some languages, like Common Lisp, use multiple argument predicates for this. In Lisp (<= 1 x 10) is true when x is between 1 and 10.


In some languages, a pointer can reference another pointer, requiring multiple dereference operations to get to the original value. While each level of indirection may add a performance cost, it is sometimes necessary in order to provide correct behavior for complex data structures. For example, in C it is typical to define a linked list in terms of an element that contains a pointer to the next element of the list: This implementation uses a pointer to the first element in the list as a surrogate for the entire list. If a new value is added to the beginning of the list, head has to be changed to point to the new element. Since C arguments are always passed by value, using double indirection allows the insertion to be implemented correctly, and has the desirable side-effect of eliminating special case code to deal with insertions at the front of the list: In this case, if the value of item is less than that of head, the caller's head is properly updated to the address of the new item. A basic example is in the argv argument to the main function in C (and C++), which is given in the prototype as char **argv—this is because the variable argv itself is a pointer to an array of strings (an array of arrays), so *argv is a pointer to the 0th string (by convention the name of the program), and **argv is the 0th character of the 0th string.


Russian нос "nose" (unpalatalized /n/)нёс "(he) carried" (palatalized /nʲ/)Irish bó "cow" (velarized b)beo "alive" (palatalized b)Some palatalized phonemes undergo change beyond phonetic palatalization. For instance, the unpalatalized sibilant (Irish /sˠ/, Scottish /s̪/) has a palatalized counterpart that is actually postalveolar , not phonetically palatalized , and the velar fricative /x/ in both languages has a palatalized counterpart that is actually palatal  rather than palatalized velar . These shifts in primary place of articulation are examples of the sound change of palatalization.


In signalling models, one party chooses how and whether or not to present information about itself to another party to reduce the information asymmetry between them. In signaling models, the signaling party agent and the receiving party principal have access to different information. The challenge for the receiving party is to decipher the credibility of the signaling party so as to assess their capabilities.


In the Post-Soviet states DD.MM.YYYY format is used with dot as a separator.


In the Classic Mac OS, Multiprocessing Services is not the only threading mechanism; cooperatively scheduled threads can be created with the Thread Manager. While applications using Multiprocessing Services have their threads preemptively scheduled, the application as a whole is still cooperatively scheduled with other running applications. Non-Multiprocessing Services tasks remain scheduled on a single processor, and tasks using the Macintosh Toolbox cannot be preemptively scheduled.When a process uses Multiprocessing Services, in addition to the preemptive tasks it creates, an additional task exists, deth, which waits for other tasks created by the process to terminate and cleans up their resources when they do.


In mathematics, the matching distance is a metric on the space of size functions. The core of the definition of matching distance is the observation that the information contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively cornerlines and cornerpoints. Given two size functions ℓ 1 {\displaystyle \ell _{1}} and ℓ 2 {\displaystyle \ell _{2}} , let C 1 {\displaystyle C_{1}} (resp. C 2 {\displaystyle C_{2}} ) be the multiset of all cornerpoints and cornerlines for ℓ 1 {\displaystyle \ell _{1}} (resp.


Suppose that when the screening test is applied to a person not having the disease, there is a 1% chance of getting a false positive result (and hence 99% chance of getting a true negative result, a number known as the specificity of the test), i.e. P ( positive | well ) = 1 % , and P ( negative | well ) = 99 % . {\displaystyle P({\text{positive}}|{\text{well}})=1\%,{\text{ and }}P({\text{negative}}|{\text{well}})=99\%.} Finally, suppose that when the test is applied to a person having the disease, there is a 1% chance of a false negative result (and 99% chance of getting a true positive result, known as the sensitivity of the test), i.e. P ( negative | ill ) = 1 % and P ( positive | ill ) = 99 % . {\displaystyle P({\text{negative}}|{\text{ill}})=1\%{\text{ and }}P({\text{positive}}|{\text{ill}})=99\%.}


In mathematics, an E n {\displaystyle {\mathcal {E}}_{n}} -algebra in a symmetric monoidal infinity category C consists of the following data: An object A ( U ) {\displaystyle A(U)} for any open subset U of Rn homeomorphic to an n-disk. A multiplication map: μ: A ( U 1 ) ⊗ ⋯ ⊗ A ( U m ) → A ( V ) {\displaystyle \mu :A(U_{1})\otimes \cdots \otimes A(U_{m})\to A(V)} for any disjoint open disks U j {\displaystyle U_{j}} contained in some open disk Vsubject to the requirements that the multiplication maps are compatible with composition, and that μ {\displaystyle \mu } is an equivalence if m = 1 {\displaystyle m=1} . An equivalent definition is that A is an algebra in C over the little n-disks operad.


In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematician Peter L. Montgomery.Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder.


Prior to coding, the algorithm had been identified and understood. The flowchart represented a high level definition of the solution to be implemented on a machine. Although they were working only with numerical algorithms, they proposed a programming methodology which has since become standard practice in the computer programming field.


In order to limit production cost, Busicom wanted to design a calculator engine that would be based on a few integrated circuits (ICs), containing some ROMs and shift registers and that could be adapted to a broad range of calculators by just changing the ROM IC chips. Busicom's engineers came up with a design that required 12 ICs: 263–265 and asked Intel, a company founded one year earlier in 1968 for the purpose of making solid state random-access memory (RAM), to finalize and manufacture their calculator engine. People who were influential in convincing Busicom to switch to using microprocessors were Tadashi Sasaki and Robert Noyce.Intel's Ted Hoff was assigned to studying Busicom's design, and came up with a much more elegant, 4 ICs architecture centered on what was to become the 4004 microprocessor surrounded by a mixture of 3 different ICs containing ROM, shift registers, input/output ports and RAM—Intel's first product (1969) was the 3101 Schottky TTL bipolar 64-bit SRAM.Busicom's management agreed to Hoff's new approach and the chips' implementation was led by Federico Faggin who had previously developed the Silicon Gate Technology at Fairchild Semiconductor. It was this technology that made possible the design of the microprocessor and the dynamic RAMs. The 4 ICs were delivered to Busicom in January 1971.In mid-1971 Busicom, which had exclusive right to the design and its components, asked Intel to lower their prices. Intel renegotiated their contract and Busicom gave up its exclusive rights to the chips.A few months later, on November 15, 1971, Intel announced the immediate availability of the first microprocessor chipset family, the MCS-4 micro computer set (all from the Busicom design) with an advertisement in Electronic News.


. . , n − 1.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 357, 1357, 3457, and 13457 are the patterns related to Braille pattern dots-234, since the two additional dots of kantenji patterns 0234, 2347, and 02347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


The accuracy of flowmeters could be used in two different metering systems that ultimately have different calculated uncertainties due to other factors in the system that affect flow calculations. Uncertainty even includes such factors as the flow computer's A/D converter accuracy. The quest for accuracy in a custody transfer system requires meticulous attention to detail.


So if for some 1 ⩽ i ⩽ N , c i 1 ≠ c i 2 {\displaystyle 1\leqslant i\leqslant N,c_{i}^{1}\neq c_{i}^{2}} and the code C i n i {\displaystyle C_{in}^{i}} has distance ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k , {\displaystyle \geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k,} then Δ ( C i n i ( c i 1 ) , C i n i ( c i 2 ) ) ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k . {\displaystyle \Delta \left(C_{in}^{i}\left(c_{i}^{1}\right),C_{in}^{i}\left(c_{i}^{2}\right)\right)\geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k.} Further, if we have T {\displaystyle T} numbers 1 ⩽ i ⩽ N {\displaystyle 1\leqslant i\leqslant N} such that c i 1 ≠ c i 2 {\displaystyle c_{i}^{1}\neq c_{i}^{2}} and the code C i n i {\displaystyle C_{in}^{i}} has distance ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k , {\displaystyle \geqslant H_{q}^{-1}({\tfrac {1}{2}}-\varepsilon )\cdot 2k,} then Δ ( C ∗ ( m 1 ) , C ∗ ( m 2 ) ) ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k ⋅ T .


Symbolically, if the cardinality of N {\displaystyle \mathbb {N} } is denoted as ℵ 0 {\displaystyle \aleph _{0}} , the cardinality of the continuum is This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them.


In modern digital communications, Gray codes play an important role in error correction. For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise.


In order to understand ODS, it is necessary to understand the normal anatomy and defecation process.The pelvic floor (pelvic diaphragm) can be divided into 4 compartments: Anterior or urinary (bladder, bladder neck, and urethra), Middle or genital (vagina and uterus in women, prostate in men), Posterior (anus, anal canal, sigmoid, and rectum), and Peritoneal (endopelvic fascia and perineal membrane).Defecation is a complex physiologic process, involving interaction between neural processes, reflexes, colorectal contractility and the biomechanics of straining.When feces reach the rectum, the rectal walls become naturally distended, stimulating nerve receptors. Brain centres for defecation respond to this sensation and stimulate mass colonic movement in the colon and the rectum. These mass contractions move feces along the colon and into the rectum. Occasionally some straining helps, which normally transmits forces to the upper part of the rectum, and aids defecation.


Stemming and lemmatization Different tokens might carry out similar information (e.g. tokenization and tokenizing). And we can avoid calculating similar information repeatedly by reducing all tokens to its base form using various stemming and lemmatization dictionaries. 3.


Historically, however, that was not always the case. Mobile UIs, or front-ends, rely on mobile back-ends to support access to enterprise systems. The mobile back-end facilitates data routing, security, authentication, authorization, working off-line, and service orchestration. This functionality is supported by a mix of middleware components including mobile app server, mobile backend as a service (MBaaS), and service-oriented architecture (SOA) infrastructure.


In the case where the order s {\displaystyle s} is an integer, it will be represented by s = n {\displaystyle s=n} (or s = − n {\displaystyle s=-n} when negative). It is often convenient to define μ = ln  ( z ) {\displaystyle \mu =\ln(z)} where ln  ( z ) {\displaystyle \ln(z)} is the principal branch of the complex logarithm Ln  ( z ) {\displaystyle \operatorname {Ln} (z)} so that − π < Im  ( μ ) ≤ π . {\displaystyle -\pi <\operatorname {Im} (\mu )\leq \pi .} Also, all exponentiation will be assumed to be single-valued: z s = exp  ( s ln  ( z ) ) .


The language of thought theory allows the mind to process more complex representations with the help of semantics. (See below in semantics of mental states). Recent work has suggested that we make a distinction between the mind and cognition.


In recent research, storage strength (how well an item is learned) and retrieval strength (how well an item can be retrieved) have become separate measures for retrieval practice. Retrieval strength (also known as recall accuracy) is typically higher for restudied words when tested immediately after practice, whereas tested words were higher as time moves on. This suggests using tests is more beneficial for long term memory and retrieval which some authors believe is due to limited retrieval success during practice supporting the idea that tests are learning opportunities.Functional magnetic resonance imaging suggests that retrieval practice strengthens subsequent retention of learning through a "dual action" affecting the anterior and posterior hippocampus regions of the brain.


In probability theory, more specifically the study of random matrices, the circular law concerns the distribution of eigenvalues of an n × n random matrix with independent and identically distributed entries in the limit n → ∞. It asserts that for any sequence of random n × n matrices whose entries are independent and identically distributed random variables, all with mean zero and variance equal to 1/n, the limiting spectral distribution is the uniform distribution over the unit disc.


In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by: f ( x , y ) = ( x 2 + y − 11 ) 2 + ( x + y 2 − 7 ) 2 . {\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\quad } It has one local maximum at x = − 0.270845 {\displaystyle x=-0.270845} and y = − 0.923039 {\displaystyle y=-0.923039} where f ( x , y ) = 181.617 {\displaystyle f(x,y)=181.617} , and four identical local minima: f ( 3.0 , 2.0 ) = 0.0 , {\displaystyle f(3.0,2.0)=0.0,\quad } f ( − 2.805118 , 3.131312 ) = 0.0 , {\displaystyle f(-2.805118,3.131312)=0.0,\quad } f ( − 3.779310 , − 3.283186 ) = 0.0 , {\displaystyle f(-3.779310,-3.283186)=0.0,\quad } f ( 3.584428 , − 1.848126 ) = 0.0. {\displaystyle f(3.584428,-1.848126)=0.0.\quad } The locations of all the minima can be found analytically. However, because they are roots of cubic polynomials, when written in terms of radicals, the expressions are somewhat complicated.The function is named after David Mautner Himmelblau (1924–2011), who introduced it.


Policy cycles are typically characterized as adopting a classical approach, and tend to describe processes from the perspective of policy decision makers. Accordingly, some postpositivist academics challenge cyclical models as unresponsive and unrealistic, preferring systemic and more complex models. They consider a broader range of actors involved in the policy space that includes civil society organisations, the media, intellectuals, think tanks or policy research institutes, corporations, lobbyists, etc.


(X is a developable space. )Moore spaces are generally interesting in mathematics because they may be applied to prove interesting metrization theorems. The concept of a Moore space was formulated by R. L. Moore in the earlier part of the 20th century.


In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity. Consider a finite group ( G , ∘ ) {\displaystyle \left(G,\circ \right)} , and any set of generators S. Define D S {\displaystyle D_{S}} to be the graph diameter of the Cayley graph Λ = ( G , S ) {\displaystyle \Lambda =\left(G,S\right)} . Then the diameter of ( G , ∘ ) {\displaystyle \left(G,\circ \right)} is the largest value of D S {\displaystyle D_{S}} taken over all generating sets S. For instance, every finite cyclic group of order s, the Cayley graph for a generating set with one generator is an s-vertex cycle graph. The diameter of this graph, and of the group, is ⌊ s / 2 ⌋ {\displaystyle \lfloor s/2\rfloor } .It is conjectured, for all non-abelian finite simple groups G, that diam  ( G ) ⩽ ( log  | G | ) O ( 1 ) .


In telecommunications, a point-to-point connection refers to a communications connection between two communication endpoints or nodes. An example is a telephone call, in which one telephone is connected with one other, and what is said by one caller can only be heard by the other. This is contrasted with a point-to-multipoint or broadcast connection, in which many nodes can receive information transmitted by one node. Other examples of point-to-point communications links are leased lines and microwave radio relay.


In the first 16 terms of the binary Van der Corput sequence 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15one of the longest increasing subsequences is 0, 2, 6, 9, 11, 15.This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, 0, 4, 6, 9, 11, 15 0, 2, 6, 9, 13, 15 0, 4, 6, 9, 13, 15are other increasing subsequences of equal length in the same input sequence.


2. In telecommunications management, a resource within the telecommunications environment that may be managed through the use of operation, administration, maintenance, and provisioning (OAMP) application protocols.


In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties. The proofs are probabilistic — they work by showing that a random object, chosen from some probability distribution, has the desired properties with positive probability. Consequently, they are nonconstructive — they don't explicitly describe an efficient method for computing the desired objects. The method of conditional probabilities (Spencer 1987), (Raghavan 1988) converts such a proof, in a "very precise sense", into an efficient deterministic algorithm, one that is guaranteed to compute an object with the desired properties.


In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.


In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.


In natural science, impossibility assertions (like other assertions) come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying theory, very successful in making predictions, whose assumptions lead logically to the conclusion that something is impossible. Two examples of widely accepted impossibilities in physics are perpetual motion machines, which violate the law of conservation of energy, and exceeding the speed of light, which violates the implications of special relativity. Another is the uncertainty principle of quantum mechanics, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle.


An infix operator is positioned in between a left and a right operand, as in x+y. Some languages, most notably the C-syntax family, stretches this conventional terminology and speaks also of ternary infix operators (a?b:c). Theoretically it would even be possible (but not necessarily practical) to define parenthesization as a unary bifix operation.


In number theory the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers.


In telecommunication, the term transmission block has the following meanings: A group of characters or bits transmitted as a block, unit, message, or packet. It usually includes additional encoded characters for error detection and correction. In data transmission, a group of records sent, processed, or recorded as a unit.Some protocols require each transmission block to end with an end-of-message marker. This is often a control character such as End-of-Text (ETX), End-of-Transmission-Block (ETB), or End-of-Transmission (EOT). Some protocols (especially those requiring ETX) require each transmission block to begin with a Start-of-Text character (STX).


Post strongly disagreed with Church's "identification" of effective computability with the λ-calculus and recursion, stating: Actually the work already done by Church and others carries this identification considerably beyond the working hypothesis stage. But to mask this identification under a definition… blinds us to the need of its continual verification. Rather, he regarded the notion of "effective calculability" as merely a "working hypothesis" that might lead by inductive reasoning to a "natural law" rather than by "a definition or an axiom".


The combination of possible states can generate a wide variety of events, thus defining a more complex production cycle. As a consequence, cycles are usually far to be simple linear sequences. There are commonly parallel branches running together and alternatives selected according to different events, schematically represented below: s:stage c:condition s1 | |-c2 | s2 | ---------- | | |-c31 |-c32 | | s31 s32 | | |-c41 |-c42 | | ---------- | s4


In sociology, dirty data refer to secretive data the discovery of which is discrediting to those who kept the data secret. Following the definition of Gary T. Marx, Professor Emeritus of MIT, dirty data are one among four types of data: Nonsecretive and nondiscrediting data: Routinely available information. Secretive and nondiscrediting data: Strategic and fraternal secrets, privacy. Nonsecretive and discrediting data: sanction immunity, normative dissensus, selective dissensus, making good on a threat for credibility, discovered dirty data. Secretive and discrediting data: Hidden and dirty data.


Against Method (3rd ed.). p.


Williams showed that the first moment can be matched as far as N − 2 {\displaystyle ~N^{-2}~} if the test statistic is divided by a factor given by q 1 = 1 + ∑ i = 1 k π i − 1 − 1 6 N ( k − 1 ) . {\displaystyle ~q_{1}=1+{\frac {\;\sum _{i=1}^{k}\pi _{i}^{-1}\,-\,1\;}{6N(k-1)}}~.} In the special case where the null hypothesis is that all the values π i {\displaystyle \pi _{i}} are equal to 1 / k {\displaystyle ~1/k~} (i.e. it stipulates a uniform distribution), this simplifies to q 1 = 1 + k + 1 6 N .


In the demographic transition model, the size and shape of population pyramids vary. In stage one of the demographic transition model, the pyramids have the most defined shape. They have the ideal big base and a skinny top. In stage two, the pyramid looks similar but starts to widen in the middle age groups.


Most basic metaheuristics are sequential. Although their utilization allows to significantly reduce the temporal complexity of the search process, this latter remains high for real-world problems arising in both academic and industrial domains. Therefore, parallelism comes as a natural way not to only reduce the search time, but also to improve the quality of the provided solutions. For a comprehensive discussion on how parallelism can be mixed with metaheuristics see .


In spite of various uncertainties or possible criticisms of cost–benefit analysis, it does have several strengths: It offers an internally consistent and global comprehensive analysis of impacts. : 955 Sensitivity analysis allows critical assumptions in the analysis to be changed. This can identify areas where the value of information is highest and where additional research might have the highest payoffs. : 119 As uncertainty is reduced, the integrated models used in producing cost–benefit analysis might become more realistic and useful.


In shared memory model the processors are all connected to a "globally available" memory, via either software or hardware means. The operating system usually maintains its memory coherence.From a programmer's point of view, this memory model is better understood than the distributed memory model. Another advantage is that memory coherence is managed by the operating system and not the written program. Two known disadvantages are: scalability beyond thirty-two processors is difficult, and the shared memory model is less flexible than the distributed memory model.There are many examples of shared memory (multiprocessors): UMA (uniform memory access), COMA (cache-only memory access).


In the early 1970s, ICL signed an OEM agreement with the Canadian company, Consolidated Computers Ltd (later Consolidated Computer Inc.) to distribute CCL's key-to-disk data entry product, Key-Edit, in the British Commonwealth of countries as well as in western and eastern Europe. Models included Key Edit 100, 50, 59, 1000, and 2000. In the mid-1980s a version of the Key Edit 59 operating system was ported (in emulation mode) to the DRS 20 series and marketed as Data Entry 20.


The legitimacy of this method relies on the assumption that the observed coincidences constitute a fair sample of the emitted pairs. Following local realist assumptions as in Bell's paper, the estimated quantum correlation converges after a sufficient number of trials to Q C ( a , b ) = ∫ d λ ρ ( λ ) A ( a , λ ) B ( b , λ ) {\displaystyle QC(a,b)=\int d\lambda \rho (\lambda )A(a,\lambda )B(b,\lambda )} where a and b are detector settings and λ is the hidden variable, drawn from a distribution ρ(λ). The quantum correlation is the key statistic in the CHSH inequality and some of the other Bell inequalities, tests that open the way for experimental discrimination between quantum mechanics and local realism or local hidden-variable theory.


Virtual memory was introduced to the x86 architecture with the protected mode of the Intel 80286 processor, but its segment swapping technique scaled poorly to larger segment sizes. The Intel 80386 introduced paging support underneath the existing segmentation layer, enabling the page fault exception to chain with other exceptions without double fault. However, loading segment descriptors was an expensive operation, causing operating system designers to rely strictly on paging rather than a combination of paging and segmentation.


The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square, for example, 4 9 = ( 2 3 ) 2 {\displaystyle \textstyle {\frac {4}{9}}=\left({\frac {2}{3}}\right)^{2}} . Starting with 1, there are ⌊ m ⌋ {\displaystyle \lfloor {\sqrt {m}}\rfloor } square numbers up to and including m, where the expression ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } represents the floor of the number x.


A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints, allowing an easier relaxed problem to be solved. Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming and Lagrangian relaxations are used to obtain bounds in branch-and-bound algorithms for integer programming.The modeling strategy of relaxation should not be confused with iterative methods of relaxation, such as successive over-relaxation (SOR); iterative methods of relaxation are used in solving problems in differential equations, linear least-squares, and linear programming. However, iterative methods of relaxation have been used to solve Lagrangian relaxations.


In mathematics, a relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalence relation needs to be transitive.


That is why there arises the following natural question. Suppose that the conditions of the characterization theorem are fulfilled not exactly but only approximately. May we assert that the conclusion of the theorem is also fulfilled approximately? The theorems in which the problems of this kind are considered are called stability characterizations of probability distributions.


Comparisons can be made between the clusters and how they show up more or less in certain features in contrast to each other. To calculate a cluster's presence within a certain feature, it is determined if a nuclear profile is present within a window that is detected within a feature. The percentage of how often nuclear profiles within a cluster occur within the same windows that are detected within a feature are then displayed by the radar chart.


This is called the cyclic or adjacency property of the code.In modern digital communications, Gray codes play an important role in error correction. For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point.


In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system A x = b {\displaystyle {\boldsymbol {Ax}}={\boldsymbol {b}}} where A {\displaystyle {\boldsymbol {A}}} is symmetric positive-definite. The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. The intent of this article is to document the important steps in these derivations.


In propositional logic a resolution proof of a clause κ {\displaystyle \kappa } from a set of clauses C is a directed acyclic graph (DAG): the input nodes are axiom inferences (without premises) whose conclusions are elements of C, the resolvent nodes are resolution inferences, and the proof has a node with conclusion κ {\displaystyle \kappa } .The DAG contains an edge from a node η 1 {\displaystyle \eta _{1}} to a node η 2 {\displaystyle \eta _{2}} if and only if a premise of η 1 {\displaystyle \eta _{1}} is the conclusion of η 2 {\displaystyle \eta _{2}} . In this case, η 1 {\displaystyle \eta _{1}} is a child of η 2 {\displaystyle \eta _{2}} , and η 2 {\displaystyle \eta _{2}} is a parent of η 1 {\displaystyle \eta _{1}} . A node with no children is a root. A proof compression algorithm will try to create a new DAG with fewer nodes that represents a valid proof of κ {\displaystyle \kappa } or, in some cases, a valid proof of a subset of κ {\displaystyle \kappa } .


Satisfiability and validity are defined for a single formula, but can be generalized to an arbitrary theory or set of formulas: a theory is satisfiable if at least one interpretation makes every formula in the theory true, and valid if every formula is true in every interpretation. For example, theories of arithmetic such as Peano arithmetic are satisfiable because they are true in the natural numbers.


The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite. From the late 1980s, the first algorithms were developed to find solutions for these equations. Sergei A. Abramov, Marko Petkovšek and Mark van Hoeij described algorithms to find polynomial, rational, hypergeometric and d'Alembertian solutions.


In the area of modern algebra known as group theory, the Held group He is a sporadic simple group of order 210 · 33 · 52 · 73 · 17 = 4030387200 ≈ 4×109.


In order to apply the theory of NP-completeness to the minimum feedback arc set, it is necessary to modify the problem from being an optimization problem (how few edges can be removed to break all cycles) to an equivalent decision version, with a yes or no answer (is it possible to remove k {\displaystyle k} edges). Thus, the decision version of the feedback arc set problem takes as input both a directed graph and a number k {\displaystyle k} . It asks whether all cycles can be broken by removing at most k {\displaystyle k} edges, or equivalently whether there is an acyclic subgraph with at least | E ( G ) | − k {\displaystyle |E(G)|-k} edges.


In practice the use of MAST includes three steps: Preceding assessment Multidisciplinary assessment Transferability assessmentFirstly, the assessment must start with preceding considerations in order to determine whether it is relevant for an institution at a given point in time to carry out the assessment. This step involves mainly assessment of the maturity of the technology and the organization planning to use it. If the technology is not matured and have not been tested in practice, then pilot studies must be carried out to mature the technology before a multidisciplinary study is initiated. Secondly, after the preceding considerations, the multidisciplinary assessment is carried out in order to describe and assess the different outcomes of the telemedicine application. This involves assessment of outcomes within the following seven domains: Domain 1: Health problem and characteristics of the application Domain 2: Safety Domain 3: Clinical effectiveness Domain 4: Patient perspectives Domain 5: Economic aspects Domain 6: Organizational aspects Domain 7: Socio-cultural, ethical and legal aspectsThirdly, in relation to the description of the outcomes, an assessment should also be made of the transferability of the results to other settings or countries.


In the 1960s, Chomsky introduced two central ideas relevant to the construction and evaluation of grammatical theories.


In recent times, the use of blessed salt is found within some Catholic and Anglican liturgies of Holy Baptism, and in the blessing of holy water, sometimes called lustral water. The Anglican Missal, used by some Anglo-Catholics, in The Order of Blessing Water, includes an English translation of traditional prayers for the exorcism and blessing of salt. The Collect reads: Almighty and everlasting God, we humbly beseech thy infinite goodness, that thou wouldest vouchsafe of thy mercy to ble+ss and sanct+ify this thy creature of salt, which thou hast bestowed for the necessities of mankind: let it be profitable for all them that receive it for their healing both in body and soul: and grant that all such things as are touched or sprinkled with the same may be delivered from all uncleanliness, and defended against the assaults of all spiritual wickedness. Through Jesus Christ our Lord.


In measure theory, the following implications hold between measures: So every probability measure is a sub-probability measure, but the converse is not true. Also every sub-probability measure is a finite measure and a σ-finite measure, but the converse is again not true.


In mathematics, given a partial order ⪯ {\displaystyle \preceq } and ⊑ {\displaystyle \sqsubseteq } on a set A {\displaystyle A} and B {\displaystyle B} , respectively, the product order (also called the coordinatewise order or componentwise order) is a partial ordering ≤ {\displaystyle \leq } on the Cartesian product A × B . {\displaystyle A\times B.} Given two pairs ( a 1 , b 1 ) {\displaystyle \left(a_{1},b_{1}\right)} and ( a 2 , b 2 ) {\displaystyle \left(a_{2},b_{2}\right)} in A × B , {\displaystyle A\times B,} declare that ( a 1 , b 1 ) ≤ ( a 2 , b 2 ) {\displaystyle \left(a_{1},b_{1}\right)\leq \left(a_{2},b_{2}\right)} if a 1 ⪯ a 2 {\displaystyle a_{1}\preceq a_{2}} and b 1 ⊑ b 2 . {\displaystyle b_{1}\sqsubseteq b_{2}.}


Each finite continued fraction of the sequence is obtained by using a finite prefix of the infinite continued fraction's defining sequence of integers. Moreover, every irrational number α {\displaystyle \alpha } is the value of a unique infinite regular continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values α {\displaystyle \alpha } and 1.