the modern formulation of the conjecture relates arithmetic data associated with an elliptic curve e over a number field k to the behaviour of the hasse – weil l - function l ( e, s ) of e at s = 1. more specifically, it is conjectured that the rank of the abelian group e ( k ) of points of e is the order of the zero of l ( e, s ) at s = 1, and the first non - zero coefficient in the taylor expansion of l ( e, s ) at s = 1 is given by more refined arithmetic data attached to e over k ( wiles 2006 ). the conjecture was chosen as one of the seven millennium prize problems listed by the clay mathematics institute, which has offered a $ 1, 000, 000 prize for the first correct proof.


in object - oriented jargon, abstract datatypes are called classes. however, a class is only a definition ; no memory is allocated. when memory is allocated to a class, it's called an object. object - oriented imperative languages developed by combining the need for classes and the need for safe functional programming.


the seidel matrix of g is also the adjacency matrix of a signed complete graph kg in which the edges of g are negative and the edges not in g are positive. it is also the adjacency matrix of the two - graph associated with g and kg. the eigenvalue properties of the seidel matrix are valuable in the study of strongly regular graphs.


these would be rendered at the same width as the other single - byte characters, making them half - width kana characters rather than normally proportioned kana. although the jis x 0201 standard itself did not specify half - width display for katakana, this became the visually distinguishing feature in shift jis between the single - byte jis x 0201 and double - byte jis x 0208 katakana. some ibm code pages used a similar treatment for korean jamo, based on the n - byte hangul code and its ebcdic translation.


in the united kingdom, the data protection acts and later the freedom of information act 2000 gave patients or their representatives the right to a copy of their record, except where information breaches confidentiality ( e. g., information from another family member or where a patient has asked for information not to be disclosed to third parties ) or would be harmful to the patient's wellbeing ( e. g., some psychiatric assessments ). also, the legislation gives patients the right to check for any errors in their record and insist that amendments be made if required.


the sole aim of the design was to eliminate the mains transformer. the lower cost of transformerless designs remained popular with manufacturers long after dc power distribution had disappeared.


in telecommunication, a coded set is a set of elements onto which another set of elements has been mapped according to a code. examples of coded sets include the list of names of airports that is mapped onto a set of corresponding three - letter representations of airport names, the list of classes of emission that is mapped onto a set of corresponding standard symbols, and the names of the months of the year mapped onto a set of two - digit decimal numbers. this article incorporates public domain material from federal standard 1037c. general services administration. archived from the original on 2022 - 01 - 22.


in the first section, christian interweaves discussions of the history of artificial intelligence research, particularly the machine learning approach of artificial neural networks such as the perceptron and alexnet, with examples of how ai systems can have unintended behavior. he tells the story of julia angwin, a journalist whose propublica investigation of the compas algorithm, a tool for predicting recidivism among criminal defendants, led to widespread criticism of its accuracy and bias towards certain demographics. one of ai's main alignment challenges is its black box nature ( inputs and outputs are identifiable but the transformation process in between is undetermined ). the lack of transparency makes it difficult to know where the system is going right and where it is going wrong.


, x 1, y i − 1, y i − 2,...


in programming, a docstring is a string literal specified in source code that is used, like a comment, to document a specific segment of code. unlike conventional source code comments, or even specifically formatted comments like docblocks, docstrings are not stripped from the source tree when it is parsed and are retained throughout the runtime of the program. this allows the programmer to inspect these comments at run time, for instance as an interactive help system, or as metadata. languages that support docstrings include python, lisp, elixir, clojure, gherkin, julia and haskell.


( 1964 – 1977 ). by the early 2010s videotelephony and videophones had become commonplace and unremarkable in various forms of media, in part due to their real and ubiquitous presence in common electronic devices and laptop computers.


it depends on the models, which one to use and requires experience to choose the right one. in most cases, the goal is to estimate the state sequence from the measurements. in other cases, one can use the description to estimate the parameters of a noise process for example.


in mathematics the symmetrization methods are algorithms of transforming a set a ⊂ r n { \ displaystyle a \ subset \ mathbb { r } ^ { n } } to a ball b ⊂ r n { \ displaystyle b \ subset \ mathbb { r } ^ { n } } with equal volume vol ( b ) = vol ( a ) { \ displaystyle \ operatorname { vol } ( b ) = \ operatorname { vol } ( a ) } and centered at the origin. b is called the symmetrized version of a, usually denoted a ∗ { \ displaystyle a ^ { * } }. these algorithms show up in solving the classical isoperimetric inequality problem, which asks : given all two - dimensional shapes of a given area, which of them has the minimal perimeter ( for details see isoperimetric inequality ). the conjectured answer was the disk and steiner in 1838 showed this to be true using the steiner symmetrization method ( described below ).


in matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex - disjoint paths in a directed graph. the concept of a gammoid was introduced and shown to be a matroid by hazel perfect ( 1968 ), based on considerations related to menger's theorem characterizing the obstacles to the existence of systems of disjoint paths. gammoids were given their name by pym ( 1969 ) and studied in more detail by mason ( 1972 ).


in the following the ranked pairs winner for the first group of voters is determined. the results would be tabulated as follows : indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column captionthe sorted list of victories would be : result : b > c and a > b are locked in first ( and c > a can't be locked in after that ), so the full ranking is a > b > c. thus, a is elected ranked pairs winner by the first group of voters.


in parallel computing, folded cube graphs have been studied as a potential network topology, as an alternative to the hypercube. compared to a hypercube, a folded cube with the same number of nodes has nearly the same vertex degree but only half the diameter. efficient distributed algorithms ( relative to those for a hypercube ) are known for broadcasting information in a folded cube.


it is a tool that postal management uses to redistribute and eliminate overtime costs, based on consultation with the carrier about his / her estimated workload for the day and mail volume projections from the dois ( delivery operations information system ) computer program. routes are adjusted and / or eliminated based on information ( length, time, and overall workload ) also controlled by this program, consultations with the carrier assigned to the route, and a current ps form 3999 ( street observation by a postal supervisor to determine accurate times spent on actual delivery of mail ). rural carriers are under a form of salary called " evaluated hours ", usually with overtime built into their pay.


in physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement. an experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on. experimental uncertainty estimates are needed to assess the confidence in the results. a related field is design of experiments.


in fact, subjects actually named predictable words faster than they did unpredictable words. whittlesea was able to conclude from this study that subjects misattributed their fast responses for highly predictable words as an indication that they had previously experienced the word whereas in fact that was incorrect. as a result, the fluency of processing caused the subjects to misinterpret their quickness as a case of familiarity.


in mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. for " pure " vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures.


in most tabletop role - playing games, die rolls required by the system are given in the form adx. a and x are variables, separated by the letter d, which stands for die or dice. the letter d is most commonly lower - case, but some forms of notation use upper - case d ( non - english texts can use the equivalent form of the first letter of the given language's word for " dice ", but also often use the english " d " ). a is the number of dice to be rolled ( usually omitted if 1 ).


in number theory, sylvester's sequence is an integer sequence in which each term is the product of the previous terms, plus one. the first few terms of the sequence are 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 ( sequence a000058 in the oeis ). sylvester's sequence is named after james joseph sylvester, who first investigated it in 1880. its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions. the recurrence by which it is defined allows the numbers in the sequence to be factored more easily than other numbers of the same magnitude, but, due to the rapid growth of the sequence, complete prime factorizations are known only for a few of its terms. values derived from this sequence have also been used to construct finite egyptian fraction representations of 1, sasakian einstein manifolds, and hard instances for online algorithms.


in mid - 2001, the xeon brand was introduced ( " pentium " was dropped from the name ). the initial variant that used the new netburst microarchitecture, " foster ", was slightly different from the desktop pentium 4 ( " willamette " ). it was a decent chip for workstations, but for server applications it was almost always outperformed by the older cascades cores with a 2 mb l2 cache and amd's athlon mp. combined with the need to use expensive rambus dynamic ram, the foster's sales were somewhat unimpressive.


in practice, the easiest way to find an optimal bfs is to use the simplex algorithm. it keeps, at each point of its execution, a " current basis " b ( a subset of m out of n variables ), a " current bfs ", and a " current tableau ". the tableau is a representation of the linear program where the basic variables are expressed in terms of the non - basic ones : : 65 where x b { \ displaystyle x _ { b } } is the vector of m basic variables, x n { \ displaystyle x _ { n } } is the vector of n non - basic variables, and z { \ displaystyle z } is the maximization objective. since non - basic variables equal 0, the current bfs is p { \ displaystyle p }, and the current maximization objective is z 0 { \ displaystyle z _ { 0 } }.


division by a power of 2 is often written as a right - shift, not for optimization as might be assumed, but because the floor of negative results is required. assuming such shifts are " premature optimization " and replacing them with division can break software. many programming languages ( including c, c + +, c #, java, php, r, and python ) provide standard functions for floor and ceiling, usually called floor and ceil, or less commonly ceiling. the language apl uses x for floor.


the spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix a satisfying the equation a * a = aa * is diagonalizable. the converse does not hold because diagonalizable matrices may have non - orthogonal eigenspaces. the left and right singular vectors in the singular value decomposition of a normal matrix a = u σ v ∗ { \ displaystyle \ mathbf { a } = \ mathbf { u } { \ boldsymbol { \ sigma } } \ mathbf { v } ^ { * } } differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values.


compound or " query - based " operations on groups of identifiers, based on the namespaces in which they are declared, are rendered unwieldy or unfeasible. in languages with restricted identifier length, the use of prefixes limits the number of characters that can be used to identify what the function does. this is a particular problem for packages originally written in fortran 77, which offered only 6 characters per identifier.


square matrices are often used to represent simple linear transformations, such as shearing or rotation. for example, if r { \ displaystyle r } is a square matrix representing a rotation ( rotation matrix ) and v { \ displaystyle \ mathbf { v } } is a column vector describing the position of a point in space, the product r v { \ displaystyle r \ mathbf { v } } yields another column vector describing the position of that point after that rotation. if v { \ displaystyle \ mathbf { v } } is a row vector, the same transformation can be obtained using v r t { \ displaystyle \ mathbf { v } r ^ { \ mathsf { t } } }, where r t { \ displaystyle r ^ { \ mathsf { t } } } is the transpose of r { \ displaystyle r }.


examples are " sales department ", " procurement department ", etc. it is represented as an ellipse with a vertical line. information, material, or resource object in the event - driven process chain, the information, material, or resource objects portray objects in the real world, for example business objects, entities, etc., which can be input data serving as the basis for a function, or output data produced by a function. examples are " material ", " order ", etc. in the epc graph such an object is represented as rectangle. logical connector in the event - driven process chain the logical relationships between elements in the control flow, that is, events and functions are described by logical connectors. with the help of logical connectors it is possible to split the control flow from one flow to two or more flows and to synchronize the control flow from two or more flows to one flow. logical relationshipsthere are three kinds of logical relationships defined in event - driven process chains : branch / merge : branch and merge correspond to making decision of which path to choose among several control flows.


in mathematics, richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln 2, { \ displaystyle \ ln 2, } and exponential and sine functions. it was proved in 1968 by mathematician and computer scientist daniel richardson of the university of bath. specifically, the class of expressions for which the theorem holds is that generated by rational numbers, the number π, the number ln 2, the variable x, the operations of addition, subtraction, multiplication, composition, and the sin, exp, and abs functions. for some classes of expressions ( generated by other primitives than in richardson's theorem ) there exist algorithms that can determine whether an expression is zero.


in some cases, it is easy to calculate t ( g ) directly : if g is itself a tree, then t ( g ) = 1. when g is the cycle graph cn with n vertices, then t ( g ) = n. for a complete graph with n vertices, cayley's formula gives the number of spanning trees as nn − 2. if g is the complete bipartite graph k p, q { \ displaystyle k _ { p, q } }, then t ( g ) = p q − 1 q p − 1 { \ displaystyle t ( g ) = p ^ { q - 1 } q ^ { p - 1 } }. for the n - dimensional hypercube graph q n { \ displaystyle q _ { n } }, the number of spanning trees is t ( g ) = 2 2 n − n − 1 k = 2 n k ( n k ) { \ displaystyle t ( g ) = 2 ^ { 2 ^ { n } - n - 1 } \ prod _ { k = 2 } ^ { n } k ^ { n \ choose k } }.


in mathematics, the paley – zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moments. the inequality was proved by raymond paley and antoni zygmund. theorem : if z ≥ 0 is a random variable with finite variance, and if 0 ≤ θ ≤ 1 { \ displaystyle 0 \ leq \ theta \ leq 1 }, then p ( z > θ e ) ≥ ( 1 − θ ) 2 e 2 e. { \ displaystyle \ operatorname { p } ( z > \ theta \ operatorname { e } ) \ geq ( 1 - \ theta ) ^ { 2 } { \ frac { \ operatorname { e } ^ { 2 } } { \ operatorname { e } } }. }


it is very difficult to support new peers joining part - way through a game. each peer must communicate with all other peers, limiting the number of connected players. each peer must wait for every other peer's message before simulating the next " network frame ", resulting in all players experiencing the same latency as the player with the worst connection.


when n = 2 r { \ displaystyle n = 2r } there are other equally - large families, but for larger values of n { \ displaystyle n } only the families constructed in this way can be largest. the erdos – ko – rado theorem can also be described in terms of hypergraphs or independent sets in kneser graphs. several analogous theorems apply to other kinds of mathematical object than sets, including linear subspaces, permutations, and strings. they again describe the largest possible intersecting families as being formed by choosing an element and forming the family of all objects that contain the chosen element.


} } \ right ) \ \ \ \ & { } = \ lambda e ^ { - \ lambda t } - e ^ { - \ lambda t } \ sum _ { u = 1 } ^ { x - 1 } \ left ( { \ frac { \ lambda ^ { u } t ^ { u - 1 } } { ( u - 1 )! } } - { \ frac { \ lambda ^ { u + 1 } t ^ { u } } { u! } } \ right ) \ end { aligned } } } the sum telescopes, leaving f ( t ) = λ x t x − 1 e − λ t ( x − 1 )!. { \ displaystyle f ( t ) = { \ frac { \ lambda ^ { x } t ^ { x - 1 } e ^ { - \ lambda t } } { ( x - 1 )! } }. }


a field has a consistent tensorial character wherever it is defined : i. e. a field cannot be a scalar field somewhere and a vector field somewhere else. for example, the newtonian gravitational field is a vector field : specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. moreover, within each category ( scalar, vector, tensor ), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. in this theory an equivalent representation of field is a field particle, for instance a boson.


so, 30 z { \ displaystyle 30 \ mathbb { z } } is a semiprime ideal of the integers ( because 30 = 2 × 3 × 5, with no repeated prime factors ), but 12 z { \ displaystyle 12 \ mathbb { z } \, } is not ( because 12 = 22 × 3, with a repeated prime factor ). the class of semiprime rings includes semiprimitive rings, prime rings and reduced rings. most definitions and assertions in this article appear in ( lam 1999 ) and ( lam 2001 ).


in mathematics, euler's idoneal numbers ( also called suitable numbers or convenient numbers ) are the positive integers d such that any integer expressible in only one way as x2 ± dy2 ( where x2 is relatively prime to dy2 ) is a prime power or twice a prime power. in particular, a number that has two distinct representations as a sum of two squares is composite. every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.


in the unicode standard, the symbol £ is called pound sign, and the symbol ₤ is the lira sign. these have respective code points : u + 00a3 £ pound sign ( £ · inherited from latin - 1 ) u + 20a4 ₤ lira signunicode notes that the " lira sign " is not widely used and was added due to both it and the pound sign being available on hp printers. the encoding of the £ symbol in position xa3 ( 16310 ) was first standardised by iso latin - 1 ( an " extended ascii " ) in 1985. position xa3 was used by the digital equipment corporation vt220 terminal, mac os roman, amstrad cpc, amiga, and acorn archimedes. many early computers ( limited to a 7 - bit, 128 - position character set ) used a variant of ascii with one of the less - frequently used characters replaced by the £.


in netstalking, there are two general methods for finding unusual information : a deli - search and a net - random. deli - search, or " deliberated search ", is a targeted search for objects of interest whose characteristics are already known. this method usually uses the language of search queries and web archives, with which one can view old or deleted versions of these pages. net - random searches for hidden and unknown information through the process of trial and error.


the b { \ displaystyle b } on the right - hand side can also be written as b 1 { \ displaystyle b ^ { 1 } }, giving b r + r = b 1 { \ displaystyle b ^ { r + r } = b ^ { 1 } }. equating the exponents on both sides, we have r + r = 1 { \ displaystyle r + r = 1 }.


in the age of information, the amount of the written material we encounter each day is simply beyond our processing capacity. topic models can help to organize and offer insights for us to understand large collections of unstructured text bodies. originally developed as a text - mining tool, topic models have been used to detect instructive structures in data such as genetic information, images, and networks. they also have applications in other fields such as bioinformatics and computer vision.


if the components of the gradient of a function f { \ displaystyle f }, ( ∇ f ) i { \ displaystyle ( \ nabla f ) ^ { i } }, are expressed in terms of a given basis, e i { \ displaystyle \ mathbf { e } _ { i } }, then these components will in fact still vary oppositely to that of the basis vectors, as can be seen by observing ( using the einstein summation convention ) : where δ j i { \ displaystyle \ delta _ { j } ^ { i } } is the kronecker delta symbol, and ( t ) k i { \ displaystyle ( t ) _ { k } ^ { i } } represents the components of some transformation matrix corresponding to the transformation t { \ displaystyle t }. as can be seen, whatever transformation acts on the basis vectors, the inverse transformation must act on the components. a third concept related to covariance and contravariance is invariance.


in mathematics, the free matroid over a given ground - set e is the matroid in which the independent sets are all subsets of e. it is a special case of a uniform matroid. the unique basis of this matroid is the ground - set itself, e. among matroids on e, the free matroid on e has the most independent sets, the highest rank, and the fewest circuits.


in the united kingdom, mobile phone network providers are not obliged to provide unlocking, even after the end of the contract. ofcom, uk's telecom regulator, allowed 3 uk to sell a mobile phone with the sim card permanently superglued to the phone. most operators offer some form of unlocking service, depending on the state of the contract and the model of phone, but usually for a charge. the full oftel 2002 sim - lock position paper specifies that there is no sim - locking law in the uk ; the regulator wants only " consumer awareness ".


following is another example : table 1 the join dependencies of the table are { medic name, occupation }, { medic name, practice in years } and { medic name, type }. hence we could see that such table is 2nf ( due to the appearance of transitive dependency ). the following tables try to bring it to 6nf : table 2. 1 table 2. 2 table 2. 3 table 2. 4


in programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way.


in simple cases, the user can compute the path delay between elements manually. if the design is more than a dozen or so elements this is impractical. for example, the time delay along a path from the output of a d - flip flop, through combinatorial logic gates, then into the next d - flip flop input must satisfy ( be less than ) the time period between synchronizing clock pulses to the two flip flops. when the delay through the elements is greater than the clock cycle time, the elements are said to be on the critical path.


in recent years the model formulating approach of considering a " typical user " in cellular ( or other ) networks has been used considerably. this is, however, just a first approach which allows one to characterize only the spectral efficiency ( or information rate ) of the network. in other words, this approach captures the best possible service that can be given to a single user who does not need to share wireless network resources with other users. models beyond the typical user approach have been proposed with the aim of analyzing qos metrics of a population of users, and not just a single user.


over a perfect field of non - zero characteristic p, this quotient is the product of the a i { \ displaystyle a _ { i } } such that i is not a multiple of p. further gcd computations and exact divisions allow computing the square - free factorization ( see square - free factorization over a finite field ). in characteristic zero, a better algorithm is known, yun's algorithm, which is described below. its computational complexity is, at most, twice that of the gcd computation of the input polynomial and its derivative. more precisely, if t n { \ displaystyle t _ { n } } is the time needed to compute the gcd of two polynomials of degree n { \ displaystyle n } and the quotient of these polynomial by the gcd, then 2 t n { \ displaystyle 2t _ { n } } is an upper bound for the time needed to compute the square free decomposition. there are also known algorithms for the computation of the square - free decomposition of multivariate polynomials, that proceed generally by considering a multivariate polynomial as a univariate polynomial with polynomial coefficients, and applying recursively a univariate algorithm.


however, the size of each table does not change, so both table and directory now have only 512 entries. because this allows only one half of the entries of the original scheme, an extra level of hierarchy has been added, so cr3 now points physically to a page directory pointer table, a short table containing four pointers to page directories. supporting 64 bit addresses in the page - table is a significant change as this enables two changes to the processor addressing.


in mathematics, especially homotopy theory, the mapping cone is a construction c f { \ displaystyle c _ { f } } of topology, analogous to a quotient space. it is also called the homotopy cofiber, and also notated c f { \ displaystyle cf }. its dual, a fibration, is called the mapping fibre. the mapping cone can be understood to be a mapping cylinder m f { \ displaystyle mf }, with one end of the cylinder collapsed to a point. thus, mapping cones are frequently applied in the homotopy theory of pointed spaces.


in the field of information theory shannon entropy is defined to quantify the complexity of a distribution p as p log p { \ displaystyle p \ log p \, }. therefore, higher entropy means p is more complex hence more unpredictable. to measure the complexity of an image region { x, r } { \ displaystyle \ { x, r \ } } around point x { \ displaystyle x } with shape r { \ displaystyle r }, a descriptor d { \ displaystyle d } that takes on values d 1, …, d r { \ displaystyle { d _ { 1 }, \ dots, d _ { r } } } ( e. g., in an 8 bit grey level image, d would range from 0 to 255 for each pixel ) is defined so that p d ( d i, x, r ) { \ displaystyle p _ { d } ( d _ { i }, x, r ) }, the probability of descriptor value d i { \ displaystyle d _ { i } } occurs in region { x, r } { \ displaystyle \ { x, r \ } } can be computed. further, the entropy of image region r x { \ displaystyle r _ { x } } can compute as h d ( x, r ) = − i ∈ ( 1 … r ) p d ( d i, x, r ) log p d ( d i, x, r ).


in physics, it is conventional to denote a lorentz transformation λ ∈ so + ( 1, 3 ) { \ displaystyle \ lambda \ in \ operatorname { so } ^ { + } ( 1, 3 ) } as λ μ ν, { \ displaystyle { \ lambda ^ { \ mu } } _ { \ nu } ~, } thus showing the matrix with spacetime indexes μ, ν = 0, 1, 2, 3. { \ displaystyle \ mu, \ nu = 0, 1, 2, 3. } a four - vector can be created from the pauli matrices in two different ways : as σ μ = ( i, σ → ) { \ displaystyle \ sigma ^ { \ mu } = ( i, { \ vec { \ sigma } } ) } and as σ μ = ( i, − σ → ).


in mathematics, a plane is a two - dimensional space or flat surface that extends indefinitely. a plane is the two - dimensional analogue of a point ( zero dimensions ), a line ( one dimension ) and three - dimensional space. when working exclusively in two - dimensional euclidean space, the definite article is used, so the euclidean plane refers to the whole space. many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two - dimensional or planar space.


in number theory, a branch of mathematics, the carmichael function λ ( n ) of a positive integer n is the smallest positive integer m such that a m ≡ 1 ( mod n ) { \ displaystyle a ^ { m } \ equiv 1 { \ pmod { n } } } holds for every integer a coprime to n. in algebraic terms, λ ( n ) is the exponent of the multiplicative group of integers modulo n. the carmichael function is named after the american mathematician robert carmichael who defined it in 1910. it is also known as carmichael's λ function, the reduced totient function, and the least universal exponent function. the following table compares the first 36 values of λ ( n ) ( sequence a002322 in the oeis ) with euler's totient function φ ( in bold if they are different ; the ns such that they are different are listed in oeis : a033949 ).


the most prominent of these models has been the penn discourse treebank ( pdtb ). pdtb is focusing on the annotation of discourse cues ( discourse markers, discourse connectives ), which are assigned an internal argument ( to which the discourse marker is attached ), an external argument ( target or attachment point of the relation ) and a sense ( discourse relation ). both arguments are defined as the smallest string that expresses the meaning of the utterances to be connected.


it was an upgrade path for users who had outgrown the ibm system / 3. it ran cobol - 74, rpg2, fortran, and assembler. the instruction set of the 90 / xx series was implemented in microcode and was loaded into control storage as part of the boot up process, before loading the operating system. shortly after the 90 / 30 was introduced, sperry univac introduced the 90 / 25 which was the same basic hardware, however had an option for a smaller 80 column card reader and was a bit slower.


a common variant on the risc design employs the harvard architecture, versus von neumann architecture or stored program architecture common to most other designs. in a harvard architecture machine, the program and data occupy separate memory devices and can be accessed simultaneously. in von neumann machines, the data and programs are mixed in one memory device, requiring sequential accessing which produces the so - called von neumann bottleneck.


in these examples, the ranks are assigned to values in ascending order. ( in some other cases, descending ranks are used. ) ranks are related to the indexed list of order statistics, which consists of the original dataset rearranged into ascending order.


in order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. an example would be where one is given one positive x2 tile, three positive x tiles, and two positive unit tiles. the student forms the rectangle by having the x2 tile in the upper right corner, then one has two x tiles on the right side of the x2 tile, one x tile underneath the x2 tile, and two unit tiles are in the bottom right corner.


in order to bound the time complexity of the algorithm, we must analyze the number of push and relabel operations which occur within the main loop. the numbers of relabel, saturating push and nonsaturating push operations are analyzed separately. in the algorithm, the relabel operation can be performed at most ( 2 | v | − 1 ) ( | v | − 2 ) < 2 | v | 2 times. this is because the labeling ( u ) value for any node u can never decrease, and the maximum label value is at most 2 | v | − 1 for all nodes.


and edges connect different types of nodes ( i. e. actors to movies ) if they have a relationship ( actors in a movie ). initially the network was found to have a small - world property. afterwards, it was discovered that it exhibits a scale - free ( power - law ) behavior. the parlor game of six degrees of kevin bacon involves finding paths in this network from specified actors to kevin bacon.


in terms of integer operations, the prism architecture was similar to the mips designs. of the 32 - bits in the instructions, the 6 highest and 5 lowest bits were the instruction, leaving the other 21 bits of the word for encoding either a constant or register locations. sixty - four 32 - bit registers were included, as opposed to thirty - two in the mips, but usage was otherwise similar. prism and mips both lack the register windows that were a hallmark of the other major risc design, berkeley risc.


in the domain of computer vision, efforts have been made to model the mechanism of human attention, especially the bottom - up intentional mechanism and its semantic significance in classification of video contents. both spatial attention and temporal attention have been incorporated in such classification efforts. generally speaking, there are two kinds of models to mimic the bottom - up salience mechanism in static images.


in terms of components, let a = a i d x i, { \ displaystyle a = a _ { i } dx ^ { i }, } where d x i { \ displaystyle dx ^ { i } } is the standard one - form coordinate bases on the cotangent bundle t * m. inserting into the above, and expanding, one obtains ( using the summation convention ) : f = 1 2 ( ∂ a j ∂ x i − ∂ a i ∂ x j + ) d x i ∧ d x j. { \ displaystyle f = { \ frac { 1 } { 2 } } \ left ( { \ frac { \ partial a _ { j } } { \ partial x ^ { i } } } - { \ frac { \ partial a _ { i } } { \ partial x ^ { j } } } + \ right ) dx ^ { i } \ wedge dx ^ { j }. } keep in mind that for an n - dimensional vector space, each a i { \ displaystyle a _ { i } } is an n×n matrix, the indices of which have been suppressed, whereas the indices i and j run over 1,..., m, with m being the dimension of the underlying manifold. both of these indices can be made simultaneously manifest, as shown in the next section. the notation presented here is that which is commonly used in physics ; for example, it can be immediately recognizable as the gluon field strength tensor. for the abelian case, n = 1, and the vector bundle is one - dimensional ; the commutator vanishes, and the above can then be recognized as the electromagnetic tensor in more or less standard physics notation.


however, they are only assumed identical or nearly identical in musical set theory. sets are said to be inversionally symmetrical if they map onto themselves under inversion. the pitch that the sets must be inverted around is said to be the axis of symmetry ( or center ).


find k ∈ z { \ displaystyle k \ in \ mathbb { z } } such that p = r + k ⋅ q { \ displaystyle p = r + k \ cdot q } is a p { \ displaystyle p } - bit prime with p ≡ 2 mod 3 { \ displaystyle p \ equiv 2 \ { \ text { mod } } \ 3 }. correctness of algorithm a : it remains to check that q p 2 − p + 1 { \ displaystyle q \ mid p ^ { 2 } - p + 1 } because all the other necessary properties are obviously satisfied per definition of p { \ displaystyle p } and q { \ displaystyle q }. we easily see that p 2 − p + 1 = r 2 + 2 r k q + k 2 q 2 − r − k q + 1 = r 2 − r + 1 + q ( 2 r k + k 2 q − k ) = q ( 1 + 2 r k + k 2 q − k ) { \ displaystyle p ^ { 2 } - p + 1 = r ^ { 2 } + 2rkq + k ^ { 2 } q ^ { 2 } - r - kq + 1 = r ^ { 2 } - r + 1 + q ( 2rk + k ^ { 2 } q - k ) = q ( 1 + 2rk + k ^ { 2 } q - k ) } which implies that q p 2 − p + 1 { \ displaystyle q \ mid p ^ { 2 } - p + 1 }. algorithm a is very fast and can be used to find primes p { \ displaystyle p } that satisfy a degree - two polynomial with small coefficients. such p { \ displaystyle p } lead to fast arithmetic operations in g f ( p ) { \ displaystyle gf ( p ) }.


in the background there is an update stream that runs a series of insert / delete operations ( one pair for each query user ). the choice of the number of users is at the discretion of the test sponsor. the throughput metric is computed as the total amount of work ( s×17 ), converted to hours from seconds ( 3600 seconds per hour ), scaled by the database volume ( sf ) and divided by the total elapsed time ( ts ) required between the first query starting and the last query or update function completing. therefore, the complete formulation is : q t h d = s × 17 × 3600 t s × s f { \ displaystyle { \ mathit { qthd } } = { \ frac { s \ times 17 \ times 3600 } { t _ { s } } } \ times { \ mathit { sf } } } = = references = =


to generate this distribution experimentally, we have to repeat the experiment until it happens to give n balls. if we want to fix the value of n prior to the experiment then we have to take the balls one by one until we have n balls. the balls are therefore no longer independent.


in probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso - density plots. in statistics, the normal distribution is used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t - distribution, or light ( in comparison with the normal distribution ). some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions ( with finite variance ), particularly for spherical distributions ( which are defined below ). elliptical distributions are also used in robust statistics to evaluate proposed multivariate - statistical procedures.


in the hermite polynomial hen ( x ) of variance 1, the absolute value of the coefficient of xk is the number of ( unordered ) partitions of an n - element set into k singletons and n − k / 2 ( unordered ) pairs. equivalently, it is the number of involutions of an n - element set with precisely k fixed points, or in other words, the number of matchings in the complete graph on n vertices that leave k vertices uncovered ( indeed, the hermite polynomials are the matching polynomials of these graphs ). the sum of the absolute values of the coefficients gives the total number of partitions into singletons and pairs, the so - called telephone numbers 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496,... ( sequence a000085 in the oeis ). this combinatorial interpretation can be related to complete exponential bell polynomials as where xi = 0 for all i > 2. these numbers may also be expressed as a special value of the hermite polynomials :


while classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an ontology. metaclasses are supported in the ontology language owl and the data - modeling vocabulary rdfs. metaclasses are often modeled by setting them as the object of claims involving rdf : type and rdfs : subclassof — built - in properties commonly referred to as instance of and subclass of.


in the united kingdom, the term " back - to - back agreement " refers to an nda entered into with a third party who legitimately receives confidential information, putting them under similar non - disclosure obligations as the initial party granted the information. case law in a 2013 court of appeal decision ( dorchester project management v bnp paribas ) confirmed that a confidentiality agreement will be interpreted as a contract subject to the rules of contractual interpretation which generally apply in the english courts. ndas are often used as a condition of a financial settlement in an attempt to silence whistleblowing employees from making public the misdeeds of their former employers. there is law, the public interest disclosure act 1998, which allows " protected disclosure " despite the existence of an nda, although employers sometimes intimidate the former employee into silence despite this.


in the fields of computational linguistics and applied linguistics, a morphological dictionary is a linguistic resource that contains correspondences between surface form and lexical forms of words. surface forms of words are those found in natural language text. the corresponding lexical form of a surface form is the lemma followed by grammatical information ( for example the part of speech, gender and number ).


store : data - collection or some sort of material. flow : movement of data or material in the process. external entity : external to the modeled system, but interacts with it. now, with these symbols, a process can be represented as a network of these symbols. this decomposed process is a dfd, data flow diagram. in dynamic enterprise modeling a division is made in the control model, function model, process model and organizational model.


with object - oriented programming the memory objects are often stored dynamically on the heap but modern operating systems use address space layout randomization ( aslr ). therefore, the only way to modify such memory in a reproducible manner is to get information from inside the game process. this requires reverse engineering methods like api hooking of malloc ( ) and free ( ), code injection or searching for static access pointers.


this problem has initialized a significant effort in developing automated detection methods for misinformation on social media platforms. social media platforms allow for easy spread of misinformation. the specific reasons why misinformation spreads through social media so easily remain unknown. a 2018 study of twitter determined that, compared to accurate information, false information spread significantly faster, further, deeper, and more broadly.


in mathematics, kuiper's theorem ( after nicolaas kuiper ) is a result on the topology of operators on an infinite - dimensional, complex hilbert space h. it states that the space gl ( h ) of invertible bounded endomorphisms of h is such that all maps from any finite complex y to gl ( h ) are homotopic to a constant, for the norm topology on operators. a significant corollary, also referred to as kuiper's theorem, is that this group is weakly contractible, ie. all its homotopy groups are trivial. this result has important uses in topological k - theory.


in network science, the strength notated as si of a node i is defined as si = σjwij, where wij is the weight of the link between i and j. in order to apply the disparity filter algorithm without overlooking nodes with low strength, a normalized weight pij is defined as pij = wij / si. in the null model, the normalized weights of a certain node with degree k is generated like this : k − 1 pins are randomly assigned between the interval 0 and 1. the interval is then divided into k subintervals. the length of the subinterval represents the normalized weight of each link in the null model. consecutively, and based on the null model, we can derive that the normalized weight distribution of a node with degree k follows ρ ( x ) d x = ( k − 1 ) ( 1 − x ) k − 2 d x { \ displaystyle \ rho ( x ) \, dx = ( k - 1 ) ( 1 - x ) ^ { k - 2 } \, dx }.


in the case where a parametrized family has a location parameter, a slightly different definition is often used as follows. if we denote the location parameter by m { \ displaystyle m }, and the scale parameter by s { \ displaystyle s }, then we require that f ( x ; s, m, θ ) = f ( ( x − m ) / s ; 1, 0, θ ) { \ displaystyle f ( x ; s, m, \ theta ) = f ( ( x - m ) / s ; 1, 0, \ theta ) } where f ( x, s, m, θ ) { \ displaystyle f ( x, s, m, \ theta ) } is the cmd for the parametrized family. this modification is necessary in order for the standard deviation of a non - central gaussian to be a scale parameter, since otherwise the mean would change when we rescale x { \ displaystyle x }. however, this alternative definition is not consistently used.


in the examination of individual scripts, the study of writing systems has developed along partially independent lines. thus, the terminology employed differs somewhat from field to field.


some terminals and editing programs could not deal with double - byte characters starting at odd columns, only even ones ( some could not even put double - byte and single - byte characters in the same line ). so the dbcs sets generally included roman characters and digits also, for use alongside the cjk characters in the same line. on the other hand, early japanese computing used a single - byte code page called jis x 0201 for katakana.


in software engineering, these activities are known as software maintenance ( cf. iso / iec 9126 ). closely related concepts in the software engineering domain are evolvability, modifiability, technical debt, and code smells. the maintainability index is calculated with certain formulae from lines - of - code measures, mccabe measures and halstead complexity measures. the measurement and tracking of maintainability are intended to help reduce or reverse a system's tendency toward " code entropy " or degraded integrity, and to indicate when it becomes cheaper and / or less risky to rewrite the code than it is to change it.


in proof theory, the semantic tableau ( ; plural : tableaux, also called truth tree ) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first - order logic. an analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. computation constructs this tree and uses it to prove or refute the whole formula. the tableau method can also determine the satisfiability of finite sets of formulas of various logics. it is the most popular proof procedure for modal logics ( girle 2000 ).


an algorithm is a formal procedure in which each step is clearly defined. it guarantees success if applied correctly. the long multiplication usually taught in school is an example of an algorithm for solving the problem of multiplying big numbers.


in mathematics, a ranked partially ordered set or ranked poset may be either : a graded poset, or a poset with the property that for every element x, all maximal chains among those with x as greatest element have the same finite length, or a poset in which all maximal chains have the same finite length. the second definition differs from the first in that it requires all minimal elements to have the same rank ; for posets with a least element, however, the two requirements are equivalent. the third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank. richard p. stanley defines a graded poset of length n as one in which all maximal chains have length n. = = references = =


many other shock - related changes take place within both impactor and target as the shock wave passes through, and some of these changes can be used as diagnostic tools to determine whether particular geological features were produced by impact cratering. as the shock wave decays, the shocked region decompresses towards more usual pressures and densities. the damage produced by the shock wave raises the temperature of the material. in all but the smallest impacts this increase in temperature is sufficient to melt the impactor, and in larger impacts to vaporize most of it and to melt large volumes of the target. as well as being heated, the target near the impact is accelerated by the shock wave, and it continues moving away from the impact behind the decaying shock wave.


in occupational health and safety, a tagging system is a system of recording and displaying the status of a machine or equipment, enabling staff to view whether it is in working order. it is a product of industry - specific legislation which sets safety standards for a particular piece of equipment, involving inspection, record - keeping, and repair. this sets standardized umbrella terms for equipment and machinery ( e. g. machinery, scaffolding, forklift, cherry picker ) to be deemed'safe to use '.


in some circumstances, the " pre - " in preadaptation can be interpreted as applying, for non - teleological reasons, prior to the adaptation itself, creating a meaning for the term that is distinct from exaptation. for example, future environments ( say, hotter or drier ones ), may resemble those already encountered by a population at one of its current spatial or temporal margins. this is not actual foresight, but rather the luck of having adapted to a climate which later becomes more prominent. cryptic genetic variation may have the most strongly deleterious mutations purged from it, leaving an increased chance of useful adaptations, but this represents selection acting on current genomes with consequences for the future, rather than foresight. function may not always come before form : developed structures could change or alter the primary functions they were intended for due to some structural or historical cause.


{ \ displaystyle n = 1, 2,... }, to converge to a minimum, provided such a minimum exists and p n { \ displaystyle \ mathbf { p } _ { n } } is selected appropriately in each step. for gradient descent, p n { \ displaystyle \ mathbf { p } _ { n } } is selected as − ∇ f ( x n ) { \ displaystyle - \ nabla f ( \ mathbf { x } _ { n } ) }. the value of α j { \ displaystyle \ alpha _ { j } } for the j { \ displaystyle j } that fulfills the armijo – goldstein condition depends on x { \ displaystyle \ mathbf { x } } and p { \ displaystyle \ mathbf { p } }, and is thus denoted below by α ( x, p ) { \ displaystyle \ alpha ( \ mathbf { x }, \ mathbf { p } ) }.


a page table maps virtual memory to physical memory. there may be a single page table, a page table for each process, a page table for each segment, or a hierarchy of page tables, depending on the architecture and the os. the page tables are usually invisible to the process.


in subjective testing, implicit learning occurs when participants who show above chance performance have no knowledge of their judgements. subjects who are theorized to have no knowledge of their judgements generally are convinced that their judgements are guesses and will have an accuracy rate that has little correlation with their ratings of confidence they assigned to each of their judgements. in artificial grammar learning and sequence learning participants showed higher than chance performance. these participants were convinced that they were only making assumptions and had no real knowledge of the subject. results usually showed that in reality, they had gained implicit knowledge throughout the experiment.


in numerical analysis, the schur complement method, named after issai schur, is the basic and the earliest version of non - overlapping domain decomposition method, also called iterative substructuring. a finite element problem is split into non - overlapping subdomains, and the unknowns in the interiors of the subdomains are eliminated. the remaining schur complement system on the unknowns associated with subdomain interfaces is solved by the conjugate gradient method.


in number theory, zsigmondy's theorem, named after karl zsigmondy, states that if a > b > 0 { \ displaystyle a > b > 0 } are coprime integers, then for any integer n ≥ 1 { \ displaystyle n \ geq 1 }, there is a prime number p ( called a primitive prime divisor ) that divides a n − b n { \ displaystyle a ^ { n } - b ^ { n } } and does not divide a k − b k { \ displaystyle a ^ { k } - b ^ { k } } for any positive integer k < n { \ displaystyle k 1 { \ displaystyle n > 1 } and n { \ displaystyle n } is not equal to 6, then 2 n − 1 { \ displaystyle 2 ^ { n } - 1 } has a prime divisor not dividing any 2 k − 1 { \ displaystyle 2 ^ { k } - 1 } with k < n { \ displaystyle k


in mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values. as well as substituting individual objects such as alice, the number 1, the tallest building in london etc. for x, we may substitute both alice and bob, or all the numbers between 0 and 10, or all the buildings in london over 20 stories. the point of the theory is to give first - order logic the power of set theory, but without any " existential commitment " to such objects as sets. the classic expositions are boolos 1984 and lewis 1991.


in post - quantum cryptography, ring learning with errors ( rlwe ) is a computational problem which serves as the foundation of new cryptographic algorithms, such as newhope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. public - key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought.


there are two main approaches. in languages with declaration - site variance annotations ( e. g., c # ), the programmer annotates the definition of a generic type with the intended variance of its type parameters. with use - site variance annotations ( e. g., java ), the programmer instead annotates the places where a generic type is instantiated.


the main reasons for unsuccessful call setups in mobile networks are lack of radio coverage ( either in the downlink or the uplink ), radio interference between different subscribers, imperfections in the functioning of the network ( such as failed call setup redirect procedures ), overload of the different elements of the network ( such as cells ), etc. the call setup success rate is one of the key performance indicators ( kpis ) used by the network operators to assess the performance of their networks. it is assumed to have direct influence on the customer satisfaction with the service provided by the network and its operator. the call setup success rate is usually included, together with other technical parameters of the network, in a key performance indicator known as service accessibility. the operators of telecommunication networks aim at increasing the call setup success rate as much as practical and affordable. in mobile networks this is achieved by improving radio coverage, expanding the capacity of the network and optimising the performance of its elements, all of which may require considerable effort and significant investments on the part of the network operator.


in mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. the points of the order polytope are the monotonic functions from the given set to the unit interval, its vertices correspond to the upper sets of the partial order, and its dimension is the number of elements in the partial order. the order polytope is a distributive polytope, meaning that coordinatewise minima and maxima of pairs of its points remain within the polytope. the order polytope of a partial order should be distinguished from the linear ordering polytope, a polytope defined from a number n { \ displaystyle n } as the convex hull of indicator vectors of the sets of edges of n { \ displaystyle n } - vertex transitive tournaments.


this smaller design, the cell broadband engine or cell / be was fabricated using a 90 nm soi process. in march 2007, ibm announced that the 65 nm version of cell / be is in production at its plant ( at the time, now globalfoundries') in east fishkill, new york, with bandai namco entertainment using the cell / be processor for their 357 arcade board as well as the subsequent 369. in february 2008, ibm announced that it would begin to fabricate cell processors with the 45 nm process. in may 2008, ibm introduced the high - performance double - precision floating - point version of the cell processor, the powerxcell 8i, at the 65 nm feature size. in may 2008, an opteron - and powerxcell 8i - based supercomputer, the ibm roadrunner system, became the world's first system to achieve one petaflops, and was the fastest computer in the world until third quarter 2009. the world's three most energy - efficient supercomputers, as represented by the green500 list, are similarly based on the powerxcell 8i. in august 2009 the 45 nm cell processor was introduced in concert with sony's playstation 3 slim. by november 2009, ibm had discontinued the development of a cell processor with 32 apus but was still developing other cell products.


in more advanced areas of mathematics, when viewing euclidean space as a vector space, its distance is associated with a norm called the euclidean norm, defined as the distance of each vector from the origin. one of the important properties of this norm, relative to other norms, is that it remains unchanged under arbitrary rotations of space around the origin. by dvoretzky's theorem, every finite - dimensional normed vector space has a high - dimensional subspace on which the norm is approximately euclidean ; the euclidean norm is the only norm with this property.


the practice of integrity management consultancy combines numerous disciplines including established knowledge acquisition methodologies, public relations practices, business risk management techniques, corporate social responsibility ( csr ), compliance functions, insider threat detection and financial expertise to help clients make responsible and ethical business decisions. integrity management consultancies offer services such as : identifying potential reputational and ethical threats for clients developing practical recommendations to mitigate these threats making recommendations for, and carrying out due diligence on local professional service suppliers providing advice on accessing a local pool of talent and addressing cultural considerations for building an effective local workforce conducting detailed investigations into proposed local partners and key employees preparing community needs reviews for better targeting of csr programmes and ; administering anti and counter - corruption trainingmany also offer general ethics audits so that companies can obtain independent verification to attest to the high standard of their corporate ethics. of course, this is not an exhaustive list as each consultancy offers different services.


in mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. one of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.


in statistics, the box – cox distribution ( also known as the power - normal distribution ) is the distribution of a random variable x for which the box – cox transformation on x follows a truncated normal distribution. it is a continuous probability distribution having probability density function ( pdf ) given by f ( y ) = 1 ( 1 − i ( f < 0 ) − sgn ( f ) φ ( 0, m, s ) ) 2 π s 2 exp { − 1 2 s 2 ( y f f − m ) 2 } { \ displaystyle f ( y ) = { \ frac { 1 } { \ left ( 1 - i ( f < 0 ) - \ operatorname { sgn } ( f ) \ phi ( 0, m, { \ sqrt { s } } ) \ right ) { \ sqrt { 2 \ pi s ^ { 2 } } } } } \ exp \ left \ { - { \ frac { 1 } { 2s ^ { 2 } } } \ left ( { \ frac { y ^ { f } } { f } } - m \ right ) ^ { 2 } \ right \ } } for y > 0, where m is the location parameter of the distribution, s is the dispersion, ƒ is the family parameter, i is the indicator function, φ is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.


in mathematics, a 2 - valued morphism is a homomorphism that sends a boolean algebra b onto the two - element boolean algebra 2 = { 0, 1 }. it is essentially the same thing as an ultrafilter on b, and, in a different way, also the same things as a maximal ideal of b. 2 - valued morphisms have also been proposed as a tool for unifying the language of physics.


in multithreaded computing, the aba problem occurs during synchronization, when a location is read twice, has the same value for both reads, and the read value being the same twice is used to conclude that nothing has happened in the interim ; however, another thread can execute between the two reads and change the value, do other work, then change the value back, thus fooling the first thread into thinking nothing has changed even though the second thread did work that violates that assumption. the aba problem occurs when multiple threads ( or processes ) accessing shared data interleave. below is a sequence of events that illustrates the aba problem : process p 1 { \ displaystyle p _ { 1 } } reads value a from some shared memory location, p 1 { \ displaystyle p _ { 1 } } is preempted, allowing process p 2 { \ displaystyle p _ { 2 } } to run, p 2 { \ displaystyle p _ { 2 } } writes value b to the shared memory location p 2 { \ displaystyle p _ { 2 } } writes value a to the shared memory location p 2 { \ displaystyle p _ { 2 } } is preempted, allowing process p 1 { \ displaystyle p _ { 1 } } to run, p 1 { \ displaystyle p _ { 1 } } reads value a from the shared memory location, p 1 { \ displaystyle p _ { 1 } } determines that the shared memory value has not changed and continues. although p 1 { \ displaystyle p _ { 1 } } can continue executing, it is possible that the behavior will not be correct due to the " hidden " modification in shared memory.


if that sum of squares is divided by n, the number of observations, the result is the mean of the squared residuals. since this is a biased estimate of the variance of the unobserved errors, the bias is removed by dividing the sum of the squared residuals by df = n − p − 1, instead of n, where df is the number of degrees of freedom ( n minus the number of parameters ( excluding the intercept ) p being estimated - 1 ). this forms an unbiased estimate of the variance of the unobserved errors, and is called the mean squared error. another method to calculate the mean square of error when analyzing the variance of linear regression using a technique like that used in anova ( they are the same because anova is a type of regression ), the sum of squares of the residuals ( aka sum of squares of the error ) is divided by the degrees of freedom ( where the degrees of freedom equal n − p − 1, where p is the number of parameters estimated in the model ( one for each variable in the regression equation, not including the intercept ) ).


if neighborhood searched is limited to just one or a very small number of changes from the current solution, then it can be difficult to escape from local minima, even with additional meta - heuristic techniques such as simulated annealing or tabu search. in large neighborhood search techniques, the possible changes from one solution to its neighbor may allow tens or hundreds of values to change, and this means that the size of the neighborhood may itself be sufficient to allow the search process to avoid or escape local minima, though additional meta - heuristic techniques can still improve performance. = = references = =


an example from linear algebra is the multiplicative monoid of real square matrices of order n ( called the full linear monoid ). the map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law ( ab ) t = btat, which has the same form of interaction with multiplication as taking inverses has in the general linear group ( which is a subgroup of the full linear monoid ). however, for an arbitrary matrix, aat does not equal the identity element ( namely the diagonal matrix ).


for each unit, its duties and responsibilities in response to each command are specified. this is analogous to establishing a work breakdown structure for a development project, or defining an organizational chart for a business or military operation. step 3 specifies the processing that is triggered within each unit upon receipt of an input command.


in military munitions, a fuze ( sometimes fuse ) is the part of the device that initiates function. in some applications, such as torpedoes, a fuze may be identified by function as the exploder. the relative complexity of even the earliest fuze designs can be seen in cutaway diagrams.


are the preconditions each necessary and collectively sufficient to reach the long - term outcomes and ultimate impact? are there gaps in the logic?


in the decision phase the following approaches are usually used : fixed threshold – in this approach, the scores are compared to a threshold which was set previously and if the score is higher than the threshold a cut is declared. adaptive threshold – in this approach, the scores are compared to a threshold which considers various scores in the video to adapt the threshold to the properties of the current video. like in the previous case, if the score is higher than the corresponding threshold a cut is declared. machine learning - machine learning techniques can be applied also to the decision process.


: ch1 four - vectors describe, for instance, position xμ in spacetime modeled as minkowski space, a particle's four - momentum pμ, the amplitude of the electromagnetic four - potential aμ ( x ) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the dirac algebra. the lorentz group may be represented by 4×4 matrices λ. the action of a lorentz transformation on a general contravariant four - vector x ( like the examples above ), regarded as a column vector with cartesian coordinates with respect to an inertial frame in the entries, is given by ( matrix multiplication ) where the components of the primed object refer to the new frame. related to the examples above that are given as contravariant vectors, there are also the corresponding covariant vectors xμ, pμ and aμ ( x ).


in quantum physics, the mathematical notion is usually applied to representations of the gauge group. for example, an su ( 2 ) { \ displaystyle { \ text { su } } ( 2 ) } gauge theory will have multiplets which are fields whose representation of su ( 2 ) { \ displaystyle { \ text { su } } ( 2 ) } is determined by the single half - integer number s = : n / 2 { \ displaystyle s = : n / 2 }, the isospin. since irreducible su ( 2 ) { \ displaystyle { \ text { su } } ( 2 ) } representations are isomorphic to the n { \ displaystyle n } th symmetric power of the fundamental representation, every field has n { \ displaystyle n } symmetrized internal indices. fields also transform under representations of the lorentz group so ( 1, 3 ) { \ displaystyle { \ text { so } } ( 1, 3 ) }, or more generally its spin group spin ( 1, 3 ) { \ displaystyle { \ text { spin } } ( 1, 3 ) } which can be identified with sl ( 2, c ) { \ displaystyle { \ text { sl } } ( 2, \ mathbb { c } ) } due to an exceptional isomorphism.


in order to transmit information, the continuous wave must be turned off and on with a telegraph key to produce the different length pulses, " dots " and " dashes ", that spell out text messages in morse code, so a " continuous wave " radiotelegraphy signal consists of pulses of sine waves with a constant amplitude interspersed with gaps of no signal. in on - off carrier keying, if the carrier wave is turned on or off abruptly, communications theory can show that the bandwidth will be large ; if the carrier turns on and off more gradually, the bandwidth will be smaller. the bandwidth of an on - off keyed signal is related to the data transmission rate as : b n = b k { \ displaystyle b _ { n } = bk } where b n { \ displaystyle b _ { n } } is the necessary bandwidth in hertz, b { \ displaystyle b } is the keying rate in signal changes per second ( baud rate ), and k { \ displaystyle k } is a constant related to the expected radio propagation conditions ; k = 1 is difficult for a human ear to decode, k = 3 or k = 5 is used when fading or multipath propagation is expected. the spurious noise emitted by a transmitter which abruptly switches a carrier on and off is called key clicks.


in mathematics, a group g is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. in abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures ; see the article direct sum of modules for more information. a group which can be expressed as a direct sum of non - trivial subgroups is called decomposable, and if a group cannot be expressed as such a direct sum then it is called indecomposable.


this theorem is one of the main reasons why 1 is not considered a prime number : if 1 were prime, then factorization into primes would not be unique ; for example, 2 = 2 ⋅ 1 = 2 ⋅ 1 ⋅ 1 = … { \ displaystyle 2 = 2 \ cdot 1 = 2 \ cdot 1 \ cdot 1 = \ ldots } the theorem generalizes to other algebraic structures that are called unique factorization domains and include principal ideal domains, euclidean domains, and polynomial rings over a field. however, the theorem does not hold for algebraic integers. this failure of unique factorization is one of the reasons for the difficulty of the proof of fermat's last theorem. the implicit use of unique factorization in rings of algebraic integers is behind the error of many of the numerous false proofs that have been written during the 358 years between fermat's statement and wiles's proof.


common proof rules used are modus ponens and universal instantiation. in contrast, an indirect proof may begin with certain hypothetical scenarios and then proceed to eliminate the uncertainties in each of these scenarios until an inescapable conclusion is forced. for example, instead of showing directly p ⇒ q, one proves its contrapositive ~ q ⇒ ~ p ( one assumes ~ q and shows that it leads to ~ p ). since p ⇒ q and ~ q ⇒ ~ p are equivalent by the principle of transposition ( see law of excluded middle ), p ⇒ q is indirectly proved. proof methods that are not direct include proof by contradiction, including proof by infinite descent. direct proof methods include proof by exhaustion and proof by induction.


in mathematics, a cantor cube is a topological group of the form { 0, 1 } a for some index set a. its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 ( which is itself given the discrete topology ). if a is a countably infinite set, the corresponding cantor cube is a cantor space. cantor cubes are special among compact groups because every compact group is a continuous image of one, although usually not a homomorphic image.


in set theory and boolean algebra, it is often stated as " union and intersection interchange under complementation ", which can be formally expressed as : a ∪ b = a ∩ b, a ∩ b = a ∪ b, { \ displaystyle { \ begin { aligned } { \ overline { a \ cup b } } & = { \ overline { a } } \ cap { \ overline { b } }, \ \ { \ overline { a \ cap b } } & = { \ overline { a } } \ cup { \ overline { b } }, \ end { aligned } } } where : a { \ displaystyle { \ overline { a } } } is the negation of a { \ displaystyle a }, the overline being written above the terms to be negated, ∩ { \ displaystyle \ cap } is the intersection operator ( and ), ∪ { \ displaystyle \ cup } is the union operator ( or ).


in telecommunication, a burst transmission or data burst is the broadcast of a relatively high - bandwidth transmission over a short period. burst transmission can be intentional, broadcasting a compressed message at a very high data signaling rate within a very short transmission time. in the 1980s, the term " data burst " ( and " info burst " ) was used for a technique used by some united kingdom and south african tv programmes to transmit large amounts of primarily textual information.


in mathematics, a multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions. the name is a portmanteau of multiple and mandelbrot set. the same can be applied to the julia set, this being called multijulia set.


for simple patterns, summation of long sequences may be represented with most summands replaced by ellipses. for example, summation of the first 100 natural numbers may be written as 1 + 2 + 3 + 4 + + 99 + 100. otherwise, summation is denoted by using σ notation, where { \ textstyle \ sum } is an enlarged capital greek letter sigma.


of these, the addresses of the 16 general - purpose registers ( r0 - r15 ) are not fixed. instead, the r0 register is located at the address pointed to by the " context pointer " ( cp ) register, and the remaining 15 registers follow sequentially thereafter. register windows also provide an easy upgrade path. since the additional registers are invisible to the programs, additional windows can be added at any time.


near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. near sets offer a framework for solving problems based on human perception that arise in areas such as image processing, computer vision as well as engineering and science problems. near sets have a variety of applications in areas such as topology, pattern detection and classification, abstract algebra, mathematics in computer science, and solving a variety of problems based on human perception that arise in areas such as image analysis, image processing, face recognition, ethology, as well as engineering and science problems.


in the field of selection principles, tsaban devised the method of omission of intervals for establishing covering properties of sets of real numbers that have certain combinatorial structures. in nonabelian cryptology he devised the algebraic span method that solved a number of computational problems that underlie a number of proposals for nonabelian public - key cryptographic schemes ( such as the commutator key exchange ).


this allowed the star to use vectors of length not limited by the length of registers, making it highly flexible. unfortunately, the pipeline had to be very long in order to allow it to have enough instructions in flight to make up for the slow memory. that meant the machine incurred a high cost when switching from processing vectors to performing operations on non - vector operands. additionally, the low scalar performance of the machine meant that after the switch had taken place and the machine was running scalar instructions, the performance was quite poor. the result was rather disappointing real - world performance, something that could, perhaps, have been forecast by amdahl's law.


while it is possible to write computer programs as long lists of numbers ( machine language ) and while this technique was used with many early computers, it is extremely tedious and potentially error - prone to do so in practice, especially for complicated programs. instead, each basic instruction can be given a short name that is indicative of its function and easy to remember – a mnemonic such as add, sub, mult or jump. these mnemonics are collectively known as a computer's assembly language. converting programs written in assembly language into something the computer can actually understand ( machine language ) is usually done by a computer program called an assembler.


in secure computing terms, because access to a resource via a handle is mediated by another system, a handle functions as a capability : it not only identifies an object, but also associates access rights. for example, while a filename is forgeable ( it is just a guessable identifier ), a handle is given to a user by an external system, and thus represents not just identity, but also granted access. for example, if a program wishes to read the system password file ( / etc / passwd ) in read / write mode ( o _ rdwr ), it could try to open the file via the following call : this call asks the operating system to open the specified file with the specified access rights. if the os allows this, then it opens the file ( creates an entry in the per - process file descriptor table ) and returns a handle ( file descriptor, index into this table ) to the user : the actual access is controlled by the os, and the handle is a token of that.


in order - theoretic mathematics, a series - parallel partial order is a partially ordered set built up from smaller series - parallel partial orders by two simple composition operations. the series - parallel partial orders may be characterized as the n - free finite partial orders ; they have order dimension at most two. they include weak orders and the reachability relationship in directed trees and directed series – parallel graphs. the comparability graphs of series - parallel partial orders are cographs. series - parallel partial orders have been applied in job shop scheduling, machine learning of event sequencing in time series data, transmission sequencing of multimedia data, and throughput maximization in dataflow programming. series - parallel partial orders have also been called multitrees ; however, that name is ambiguous : multitrees also refer to partial orders with no four - element diamond suborder and to other structures formed from multiple trees.


it is common in economic models that involve decision - making over time to assume that decision - makers are exponential discounters. exponential discounting posits that the decision maker assigns future utility of any good according to the formula u ( t ) = u ( 0 ) e − ρ t { \ displaystyle u ( t ) = u ( 0 ) e ^ { - \ rho t } } where t = 0 { \ displaystyle t = 0 } is the present, u ( 0 ) { \ displaystyle u ( 0 ) } is the utility assigned to the good if it were consumed immediately, and ρ { \ displaystyle \ rho } is the " discount factor ", which is the same for all goods and constant over time. mathematically, it is the unique continuous function that satisfies the equation u ( t 1 ) / u ( t 2 ) = u ( t 1 + c ) / u ( t 2 + c ) ; { \ displaystyle u ( t _ { 1 } ) / u ( t _ { 2 } ) = u ( t _ { 1 } + c ) / u ( t _ { 2 } + c ) ; } that is, the ratio of utility values for a good at two different moments of time only depends on the interval between these times, but not on their choice.


working in the opposite direction, the second expression asserts that a is false and b is false ( or equivalently that " not a " and " not b " are true ). knowing this, a disjunction of a and b must be false also. the negation of said disjunction must thus be true, and the result is identical to the first claim.


in mathematics, a cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. see : cycle ( graph theory ), a cycle in a graph forest ( graph theory ), an undirected graph with no cycles biconnected graph, an undirected graph in which every edge belongs to a cycle directed acyclic graph, a directed graph with no cycles strongly connected graph, a directed graph in which every edge belongs to a cycle aperiodic graph, a directed graph in which the cycle lengths have no nontrivial common divisor pseudoforest, a directed or undirected graph in which every connected component includes at most one cycle cycle graph, a graph that has the structure of a single cycle pancyclic graph, a graph that has cycles of all possible lengths cycle detection ( graph theory ), the algorithmic problem of finding cycles in graphsother similarly - named concepts include cycle graph ( algebra ), a graph that illustrates the cyclic subgroups of a group circulant graph, a graph with an automorphism which permutes its vertices cyclically.


in the 1890s michelson built a mechanical device called the harmonic analyzer, for computing coefficients of fourier series and drawing graphs of their partial sums. he and s. w. stratton published a paper about this machine in the american journal of science in 1898.


prices of $ 60 for keyboards were achieved, and key tronic rapidly became the largest independent keyboard manufacturer. meanwhile, ibm made their own keyboards, using their own patented technology : keys on older ibm keyboards were made with a " buckling spring " mechanism, in which a coil spring under the key buckles under pressure from the user's finger, triggering a hammer that presses two plastic sheets ( membranes ) with conductive traces together, completing a circuit. this produces a clicking sound and gives physical feedback for the typist, indicating that the key has been depressed. the first electronic keyboards had a typewriter key travel distance of 0. 187 inches ( 4. 75 mm ), keytops were a half - inch ( 12. 7 mm ) high, and keyboards were about two inches ( 5 cm ) thick.


transportation modes are an essential component of transport systems since they are the means by which mobility is supported. geographers consider a wide range of modes that may be grouped into three broad categories based on the medium they exploit : land, water and air. each mode has its own requirements and features, and is adapted to serve the specific demands of freight and passenger traffic.


in the 17th century, european mathematicians isaac barrow, rene descartes, pierre de fermat, blaise pascal, john wallis and others discussed the idea of a derivative. in particular, in methodus ad disquirendam maximam et minima and in de tangentibus linearum curvarum distributed in 1636, fermat introduced the concept of adequality, which represented equality up to an infinitesimal error term. this method could be used to determine the maxima, minima, and tangents to various curves and was closely related to differentiation. isaac newton would later write that his own early ideas about calculus came directly from " fermat's way of drawing tangents. "


in regular expressions, the period (., also called " dot " ) is the wildcard pattern which matches any single character. combined with the asterisk operator. * it will match any number of any characters. in this case, the asterisk is also known as the kleene star.


in telecommunications, falsing is a signaling error condition when a signal decoder detects a valid input although the implied protocol function was not intended. this is also known as a false decode. other forms are referred to as talk - off.


in some computer programming languages, the size in bits of certain data types 16 - bit computing a 16 - bit integer can represent up to 65, 536 values.


declare a new variable in the procedure ( called l for reference ). on each remaining unconnected exit path, add a statement that sets l to the label value on that path. combine the resulting programs into a selection statement that executes the program with the entry path label indicated by l construct a loop that executes this selection statement as long as l is not 0. construct a sequence that initializes l to 1 and executes the loop. note that this construction can be improved by converting some cases of the selection statement into subprocedures.


in mathematics, list edge - coloring is a type of graph coloring that combines list coloring and edge coloring. an instance of a list edge - coloring problem consists of a graph together with a list of allowed colors for each edge. a list edge - coloring is a choice of a color for each edge, from its list of allowed colors ; a coloring is proper if no two adjacent edges receive the same color.


in punctuation, a word divider is a form of glyph which separates written words. in languages which use the latin, cyrillic, and arabic alphabets, as well as other scripts of europe and west asia, the word divider is a blank space, or whitespace. this convention is spreading, along with other aspects of european punctuation, to asia and africa, where words are usually written without word separation. in computing, the word " delimiter " refers to a character that separates two words. in character encoding, word segmentation depends on which characters are defined as word dividers.


in mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities ( the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes ) and allowing " varieties " defined over any commutative ring ( for example, fermat curves are defined over the integers ). scheme theory was introduced by alexander grothendieck in 1960 in his treatise " elements de geometrie algebrique " ; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the weil conjectures ( the last of which was proved by pierre deligne ). strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra.


in the japanese kantenji braille, the standard 8 - dot braille patterns 23578, 123578, 234578, and 1234578 are the patterns related to braille pattern dots - 12346, since the two additional dots of kantenji patterns 012346, 123467, and 0123467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in stream ciphers, ivs are loaded into the keyed internal secret state of the cipher, after which a number of cipher rounds are executed prior to releasing the first bit of output. for performance reasons, designers of stream ciphers try to keep that number of rounds as small as possible, but because determining the minimal secure number of rounds for stream ciphers is not a trivial task, and considering other issues such as entropy loss, unique to each cipher construction, related - ivs and other iv - related attacks are a known security issue for stream ciphers, which makes iv loading in stream ciphers a serious concern and a subject of ongoing research.


where f× is the multiplicative group of f ( that is, f excluding 0 ). these elements are " special " in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation ( since the determinant is polynomial in the entries ). when f is a finite field of order q, the notation sl ( n, q ) is sometimes used.


in mathematics, a primary cyclic group is a group that is both a cyclic group and a p - primary group for some prime number p. that is, it is a cyclic group of order pm, cpm, for some prime number p, and natural number m. every finite abelian group g may be written as a finite direct sum of primary cyclic groups, as stated in the fundamental theorem of finite abelian groups : g = 1 ≤ i ≤ n c p i m i. { \ displaystyle g = \ bigoplus _ { 1 \ leq i \ leq n } \ mathrm { c } _ { { p _ { i } } ^ { m _ { i } } }. } this expression is essentially unique : there is a bijection between the sets of groups in two such expressions, which maps each group to one that is isomorphic.


the question then becomes : on which level of iterated logarithms do to compare two numbers? there is a sense in which one may want to consider 10 10 10 { \ displaystyle 10 ^ { 10 ^ { 10 } } } and 10 10 9 { \ displaystyle 10 ^ { 10 ^ { 9 } } } to be " close in magnitude ". the relative error between these two numbers is large, and the relative error between their logarithms is still large ; however, the relative error in their second - iterated logarithms is small : log 10 ( log 10 ( 10 10 10 ) ) = 10 { \ displaystyle \ log _ { 10 } ( \ log _ { 10 } ( 10 ^ { 10 ^ { 10 } } ) ) = 10 } and log 10 ( log 10 ( 10 10 9 ) ) = 9 { \ displaystyle \ log _ { 10 } ( \ log _ { 10 } ( 10 ^ { 10 ^ { 9 } } ) ) = 9 } such comparisons of iterated logarithms are common, e. g., in analytic number theory.


like for conic sections, a line cuts this oval at, at most, two points. a non - singular plane cubic defines an elliptic curve, over any field k for which it has a point defined. elliptic curves are now normally studied in some variant of weierstrass's elliptic functions, defining a quadratic extension of the field of rational functions made by extracting the square root of a cubic.


column 3 - f = furniture vans, carriages, motor cars, portable engines and machines on wheels. column 4 - l = livestock column 5 - h = horse boxes and prize cattle vans. column 6 - c = carriages and motor cars by passenger or parcels train. = = references = =


in random graphs the sizes of components are given by a random variable, which, in turn, depends on the specific model of how random graphs are chosen. in the g ( n, p ) { \ displaystyle g ( n, p ) } version of the erdos – renyi – gilbert model, a graph on n { \ displaystyle n } vertices is generated by choosing randomly and independently for each pair of vertices whether to include an edge connecting that pair, with probability p { \ displaystyle p } of including an edge and probability 1 − p { \ displaystyle 1 - p } of leaving those two vertices without an edge connecting them. the connectivity of this model depends on p { \ displaystyle p }, and there are three different ranges of p { \ displaystyle p } with very different behavior from each other. in the analysis below, all outcomes occur with high probability, meaning that the probability of the outcome is arbitrarily close to one for sufficiently large values of n { \ displaystyle n }.


in mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. these properties are particularly considered in topology and graph theory, but also in set theory.


in telecommunications, average bitrate ( abr ) refers to the average amount of data transferred per unit of time, usually measured per second, commonly for digital music or video. an mp3 file, for example, that has an average bit rate of 128 kbit / s transfers, on average, 128, 000 bits every second. it can have higher bitrate and lower bitrate parts, and the average bitrate for a certain timeframe is obtained by dividing the number of bits used during the timeframe by the number of seconds in the timeframe. bitrate is not reliable as a standalone measure of audio or video quality, since more efficient compression methods use lower bitrates to encode material at a similar quality.


in number theory, he proved there is no odd perfect number with fewer than four prime factors. in algebra, he was notable for the study of associative algebras. he first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the peirce decomposition. in the philosophy of mathematics, he became known for the statement that " mathematics is the science that draws necessary conclusions ".


in systems theory, it involves the description of a network whose components are compartments that represent a population of elements that are equivalent with respect to the manner in which they process input signals to the compartment. instant homogeneous distribution of materials or energies within a " compartment. " the exchange rate of materials or energies among the compartments is related to the densities of these compartments. usually, it is desirable that the materials do not undergo chemical reactions while transmitting among the compartments. when concentration of the cell is of interest, typically the volume is assumed to be constant over time, though this may not be totally true in reality.


in short, it is a cartesian product and it corresponds to a product in the category of types. most functional programming languages have a primitive notion of product type.


in the cs reconstruction models using constrained ℓ 1 { \ displaystyle \ ell _ { 1 } } minimization, larger coefficients are penalized heavily in the ℓ 1 { \ displaystyle \ ell _ { 1 } } norm. it was proposed to have a weighted formulation of ℓ 1 { \ displaystyle \ ell _ { 1 } } minimization designed to more democratically penalize nonzero coefficients. an iterative algorithm is used for constructing the appropriate weights. each iteration requires solving one ℓ 1 { \ displaystyle \ ell _ { 1 } } minimization problem by finding the local minimum of a concave penalty function that more closely resembles the ℓ 0 { \ displaystyle \ ell _ { 0 } } norm. an additional parameter, usually to avoid any sharp transitions in the penalty function curve, is introduced into the iterative equation to ensure stability and so that a zero estimate in one iteration does not necessarily lead to a zero estimate in the next iteration. the method essentially involves using the current solution for computing the weights to be used in the next iteration.


in order to capture sufficient thermoacoustic data to form an accurate 3d map of electromagnetic absorption, it is necessary to surround the anatomy being imaged with a 2d array of transducers. the world's first 3d thermoacoustic animal scanner ( fig. 8 : left panel ) accomplished this by combining a cylindrical array of 128 transducers ( fig. 8 : center panel ) with rotation of the animal being imaged about the vertical axis. the net result was to capture thermoacoustic data over the surface of a sphere surrounding the animal being imaged ( fig. 8 : right panel ). this device was capable of visualizing structures as small as 1 / 3 millimeter.


applied to a function with one variable, the y combinator usually does not terminate. more interesting results are obtained by applying the y combinator to functions of two or more variables. the additional variables may be used as a counter, or index.


new centers were then chosen to better represent the cluster. this process was repeated until the centers at the start matched the centers at the end. when the cluster centers have not changed, it could be interpreted that this means proper clusters have been chosen.


in the diagrams below, p is used for n ’ s parent, s for the sibling of n, c ( meaning close nephew ) for s ’ s child in the same direction as n, and d ( meaning distant nephew ) for s ’ s other child ( s cannot be a nil node in the first iteration, because it must have black height one, which was the black height of n before its deletion, but c and d may be nil nodes ). the diagrams show the current node n as the left child of its parent p even though it is possible for n to be on either side. the code samples cover both possibilities by means of the side variable dir. at the beginning ( in the first iteration ) of removal, n is the nil node replacing the node to be deleted.


testers debug materials and procedures. the team reviews and revises the project according to feedback. after completing the development of the course material, the designers should conduct an imperative pilot test ; this can be carried out by involving key stakeholders and rehearsing the course material.


in mathematics and computer science, in the field of coding theory, the hamming bound is a limit on the parameters of an arbitrary block code : it is also known as the sphere - packing bound or the volume bound from an interpretation in terms of packing balls in the hamming metric into the space of all possible words. it gives an important limitation on the efficiency with which any error - correcting code can utilize the space in which its code words are embedded. a code that attains the hamming bound is said to be a perfect code.


in mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. preorders are more general than equivalence relations and ( non - strict ) partial orders, both of which are special cases of a preorder : an antisymmetric ( or skeletal ) preorder is a partial order, and a symmetric preorder is an equivalence relation. the name preorder comes from the idea that preorders ( that are not partial orders ) are'almost'( partial ) orders, but not quite ; they are neither necessarily antisymmetric nor asymmetric. because a preorder is a binary relation, the symbol ≤ { \ displaystyle \, \ leq \, } can be used as the notational device for the relation.


whether or not a name is well - formed depends on the type of computer system being used. early computers permitted only a few letters or digits in the name of a file, but modern computers allow long names ( some up to 255 characters ) containing almost any combination of unicode letters or unicode digits, making it easier to understand the purpose of a file at a glance. some computer systems allow file names to contain spaces ; others do not.