in response to escalating textbook prices, limited competition, and to provide a more efficient system to connect buyers and sellers together, online textbook exchanges were developed. most of today's sites handle buyer and seller payments, and usually deduct a small commission only after the sale is completed. according to textbook author henry l. roediger ( and wadsworth publishing company senior editor vicki knight ), the used textbook market is illegitimate, and entirely to blame for the rising costs of textbooks. as methods of " dealing with this problem ", he recommends making previous editions of textbooks obsolete, binding the textbook with other materials, and passing laws to prevent the sale of used books.


their cost function was adaptive, in that the definition of the cost function depends on the computable approximation of the δ 2 0 { \ displaystyle \ delta _ { 2 } ^ { 0 } } set being built. a cost function construction of a k - trivial computably enumerable noncomputable set first appeared in downey et al. we say a δ 2 0 { \ displaystyle \ delta _ { 2 } ^ { 0 } } set a obeys a cost function c if there exists a computable approximation of a, ⟨ a s : s ∈ ω ⟩ { \ displaystyle \ langle a _ { s } : s \ in \ omega \ rangle } s = σ x, s c ( x, s ) < ∞. { \ displaystyle s = \ sigma _ { x, s } c ( x, s ) [ x


as noted below, minsky ( 1967 ) hints at the problem for a rasp but doesn't offer a solution. elgot and robinson ( 1964 ) proved that their rasp model p0 – it has no indirection capability – cannot compute all " recursive sequential functions " ( ones that have parameters of arbitrary length ) if it does not have the capability of modifying its own instructions, but it can via godel numbers if it does ( p. 395 - 397 ; in particular figure 2 and footnote p.


therefore, some would - be clients are not convinced that they are best - placed to assist in the area of integrity and ethical management, because their parent companies face reputational challenges themselves. specialist integrity management consultancy helps business leaders not only to avoid business practices that represent risk to an industry or economy, but also helps to bring such practices under scrutiny so that they can be brought to a quick end.


the terminology is also applied to indirect measurements — that is, values obtained by a computational procedure from observed data. in addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement. in numerical analysis, accuracy is also the nearness of a calculation to the true value ; while precision is the resolution of the representation, typically defined by the number of decimal or binary digits. in military terms, accuracy refers primarily to the accuracy of fire ( justesse de tir ), the precision of fire expressed by the closeness of a grouping of shots at and around the centre of the target.


it was the first randomized polynomial time pit algorithm to be proven correct. the larger the domain the inputs are drawn from, the less likely schwartz – zippel is to fail. if random bits are in short supply, the chen - kao algorithm ( over the rationals ) or the lewin - vadhan algorithm ( over any field ) require fewer random bits at the cost of more required runtime. a sparse pit has at most m { \ displaystyle m } nonzero monomial terms. a sparse pit can be deterministically solved in polynomial time of the size of the circuit and the number m { \ displaystyle m } of monomials, see also. a low degree pit has an upper bound on the degree of the polynomial. any low degree pit problem can be reduced in subexponential time of the size of the circuit to a pit problem for depth - four circuits ; therefore, pit for circuits of depth - four ( and below ) is intensely studied.


in mathematical modeling of social networks, link - centric preferential attachment is a node's propensity to re - establish links to nodes it has previously been in contact with in time - varying networks. this preferential attachment model relies on nodes keeping memory of previous neighbors up to the current time.


in multi - step jobs, a later step can use a referback instead of specifying in full a file which has already been specified in an earlier step. for example : here, mypr02 uses the file identified as newfile in step mypr01 ( dsn means " dataset name " and specifies the name of the file ; a dsn could not exceed 44 characters ). in jobs which contain a mixture of job - specific jcl and procedure calls, a job - specific step can refer back to a file which was fully specified in a procedure, for example : where dsn = *. step01. mypr01. newfile means " use the file identified as newfile in step mypr01 of the procedure used by step step01 of this job ". using the name of the step which called the procedure rather than the name of the procedure allows a programmer to use the same procedure several times in the same job without confusion about which instance of the procedure is used in the referback.


in mathematics and statistics, sums of powers occur in a number of contexts : sums of squares arise in many contexts. for example, in geometry, the pythagorean theorem involves the sum of two squares ; in number theory, there are legendre's three - square theorem and jacobi's four - square theorem ; and in statistics, the analysis of variance involves summing the squares of quantities. faulhaber's formula expresses 1 k + 2 k + 3 k + + n k { \ displaystyle 1 ^ { k } + 2 ^ { k } + 3 ^ { k } + \ cdots + n ^ { k } } as a polynomial in n, or alternatively in terms of a bernoulli polynomial. fermat's right triangle theorem states that there is no solution in positive integers for a 2 = b 4 + c 4 { \ displaystyle a ^ { 2 } = b ^ { 4 } + c ^ { 4 } } and a 4 = b 4 + c 2 { \ displaystyle a ^ { 4 } = b ^ { 4 } + c ^ { 2 } }.


to distinguish these concepts, subtyping is sometimes referred to as interface inheritance ( without acknowledging that the specialization of type variables also induces a subtyping relation ), whereas inheritance as defined here is known as implementation inheritance or code inheritance. still, inheritance is a commonly used mechanism for establishing subtype relationships. inheritance is contrasted with object composition, where one object contains another object ( or objects of one class contain objects of another class ) ; see composition over inheritance. composition implements a has - a relationship, in contrast to the is - a relationship of subtyping.


for example, in the python interactive repl : however, relying on dynamic name resolution in code is discouraged by the python community. the feature also may be removed in a later version of python. examples of languages that use static name resolution include c, c + +, e, erlang, haskell, java, pascal, scheme, and smalltalk. examples of languages that use dynamic name resolution include some lisp dialects, perl, php, python, rebol, and tcl.


in perhaps the first use of substructural type theory to control resources, john c. reynolds showed how to use an affine type theory to control aliasing and other forms of interference in algol - like programming languages. o'hearn used bunched type theory to extend reynolds'system by allowing interference and non - interference to be more flexibly mixed. this resolved open problems concerning recursion and jumps in reynolds'system.


in mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands ; the result is their sum or total. beside numbers, other types of values can be summed as well : functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted " + " is defined. summations of infinite sequences are called series. they involve the concept of limit, and are not considered in this article.


they also arise in algebraic number theory, due to the relation of the sequence to the roots of a polynomial ; in the analysis of algorithms as the running time of simple recursive functions ; and in formal language theory, where they count strings up to a given length in a regular language. constant - recursive sequences are closed under important mathematical operations such as term - wise addition, term - wise multiplication, and cauchy product. the skolem – mahler – lech theorem states that the zeros of a constant - recursive sequence have a regularly repeating ( eventually periodic ) form. on the other hand, the skolem problem, which asks for an algorithm to determine whether a linear recurrence has at least one zero, is a famous unsolved problem in mathematics.


in real - world exploits there are a variety of challenges which need to be overcome for exploits to operate reliably. these factors include null bytes in addresses, variability in the location of shellcode, differences between environments and various counter - measures in operation.


in mathematics, and in particular linear algebra, the moore – penrose inverse a + { \ displaystyle a ^ { + } } of a matrix a { \ displaystyle a } is the most widely known generalization of the inverse matrix. it was independently described by e. h. moore in 1920, arne bjerhammar in 1951, and roger penrose in 1955. earlier, erik ivar fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. when referring to a matrix, the term pseudoinverse, without further specification, is often used to indicate the moore – penrose inverse.


in semantic parsing, statements in natural languages are converted into logical forms that represent their meanings.


most phone companies sell phones from third - party manufacturers. a subscriber identity module ( sim card ), which is activated by the operator once the billing relationship is established. after activation the card is then programmed with the subscriber's mobile subscriber integrated services digital network number ( msisdn ) ( the telephone number ).


it is often more comfortable to use the notation x i = ( x i, x i − 1, x i − 2,...


in social networks, a link between two players is formed only if both of them decide to do so, however either of them can make the decision to delete a link without the other player ’ s approval. the concept of nash equilibrium has a drawback in this case since it does not take into consideration the fact that the players can discuss their decisions. to model such a situation a stability concept that takes this fact into account is required. a useful stability concept in this case is pairwise stability, which accounts for the mutual approval of both players.


the term isomorphism is mainly used for algebraic structures. in this case, mappings are called homomorphisms, and a homomorphism is an isomorphism if and only if it is bijective. in various areas of mathematics, isomorphisms have received specialized names, depending on the type of structure under consideration.


in terms of the modular s - matrix, the fusion coefficients are given by n λ μ ν = σ s λ σ s μ σ s σ ν ∗ s 0 σ { \ displaystyle n _ { \ lambda \ mu } ^ { \ nu } = \ sum _ { \ sigma } { \ frac { s _ { \ lambda \ sigma } s _ { \ mu \ sigma } s _ { \ sigma \ nu } ^ { * } } { s _ { 0 \ sigma } } } } where s ∗ { \ displaystyle s ^ { * } } is the component - wise complex conjugate of s { \ displaystyle s }.


by using the theory of rapidly mixing markov chains, they show that it takes a polynomial time for the random walk to settle down to being a nearly uniform distribution. by using rejection sampling, it is possible to compare the volumes of two convex bodies, one nested within another, when their volumes are within a small factor of each other.


the algorithm runs in strongly polynomial time if : the number of operations in the arithmetic model of computation is bounded by a polynomial in the number of integers in the input instance ; and the space used by the algorithm is bounded by a polynomial in the size of the input. any algorithm with these two properties can be converted to a polynomial time algorithm by replacing the arithmetic operations by suitable algorithms for performing the arithmetic operations on a turing machine. the second condition is strictly necessary : given the integer 2 n { \ displaystyle 2 ^ { n } } ( which takes up space proportional to n in the turing machine model ), it is possible to compute 2 2 n { \ displaystyle 2 ^ { 2 ^ { n } } } with n multiplications using repeated squaring. however, the space used to represent 2 2 n { \ displaystyle 2 ^ { 2 ^ { n } } } is proportional to 2 n { \ displaystyle 2 ^ { n } }, and thus exponential rather than polynomial in the space used to represent the input.


in some cases, the pieces allocated to the partners must satisfy some geometric constraints, in addition to being fair. the most common constraint is connectivity. in case the " cake " is a 1 - dimensional interval, this translates to the requirement that each piece is also an interval. in case the cake is a 1 - dimensional circle ( " pie " ), this translates to the requirement that each piece be an arc ; see fair pie - cutting.


in some cases, instead of repeating digit sequences we find repeating digit patterns. for instance, the number f 3 ( 49 ) { \ displaystyle { \ sqrt { f _ { 3 } ( 49 ) } } } : 1111111111111111111111111. 1111111111111111111111111111111 01200 202020202020202020202020202020202020202020 11010102 00120012000012001200120012001200120012 0010 21120020211210002112100021121000211210... shows repeating digit patterns in base 3 { \ displaystyle 3 }. numbers that are schizophrenic in base b { \ displaystyle b } are also schizophrenic in base b m { \ displaystyle b ^ { m } } ( up to a certain limit, see toth ). an example is f 3 ( 49 ) { \ displaystyle { \ sqrt { f _ { 3 } ( 49 ) } } } above, which is still schizophrenic in base 9 { \ displaystyle 9 } : 1444444444444. 4444444444 350 666666666666666666666 4112 0505050505050505050 337506 75307530753075307 40552382...


, and the restriction to monadic logic means that the graph property in question may be defined in terms of sets of vertices of the given graph, but not in terms of sets of edges, or sets of tuples of vertices. as an example, the property of a graph being colorable with three colors ( represented by three sets of vertices r { \ displaystyle r }, g { \ displaystyle g }, and b { \ displaystyle b } ) may be defined by the monadic second - order formula with the naming convention that uppercase variables denote sets of vertices and lowercase variables denote individual vertices ( so that an explicit declaration of which is which can be omitted from the formula ). the first part of this formula ensures that the three color classes cover all the vertices of the graph, and the rest ensures that they each form an independent set.


in the above example, vectors are represented as n × 1 matrices ( column vectors ), while covectors are represented as 1 × n matrices ( row covectors ). when using the column vector convention : " upper indices go up to down ; lower indices go left to right. " " covariant tensors are row vectors that have indices that are below ( co - row - below ). " covectors are row vectors : hence the lower index indicates which column you are in. contravariant vectors are column vectors : hence the upper index indicates which row you are in.


in the european union, ( advanced ) electronic signatures on legal documents are commonly performed using digital signatures with accompanying identity certificates. however, only qualified electronic signatures ( which require using a qualified trust service provider and signature creation device ) are given the same power as a physical signature.


in the figure, we can see an example of two packets linearly combined into a new coded packet. in the example, we have two packets, namely packet f { \ displaystyle f } and packet e { \ displaystyle e }. the generation size of our example is two. we know this because each packet has two coding coefficients ( c i j { \ displaystyle c _ { ij } } ) appended.


in terms of skills, software designers were expected to think out database structures in entity relationship models and functional decomposition models, then transform those models into database definitions and modules ( the screens and reports ). software developers were then expected to elaborate the database definitions and modules to create working code. finally the day to day running of the system was expected to be carried out by database administrators, who had detailed knowledge of the database internals.


in the 1990s and early 21st century, mainstream ai achieved commercial success and academic respectability by focusing on specific sub - problems where ai can produce verifiable results and commercial applications, such as artificial neural networks and statistical machine learning. these " applied ai " systems are now used extensively throughout the technology industry, and research in this vein is heavily funded in both academia and industry. as of 2018 development on this field was considered an emerging trend, and a mature stage was expected to happen in more than 10 years. most mainstream ai researchers hope that strong ai can be developed by combining programs that solve various sub - problems.


in certain special cases it is convenient to use representations which transform almost like tensors, but with an additional, nonlinear factor in the transformation. a prototypical example is a matrix representing the cross product ( area of spanned parallelogram ) on r 2. { \ displaystyle \ mathbb { r } ^ { 2 }. }


this allows the procedure to access the actual variable. as a result, the variable's actual value can be changed by the procedure to which it is passed.


in queueing theory, a discipline within the mathematical theory of probability, a retrial queue is a model of a system with finite capacity, where jobs which arrive and find the system busy wait for some time before trying again to enter the system. examples of such systems include making restaurant reservations and packet switching networks. = = references = =


in network science, a gradient network is a directed subnetwork of an undirected " substrate " network where each node has an associated scalar potential and one out - link that points to the node with the smallest ( or largest ) potential in its neighborhood, defined as the union of itself and its neighbors on the substrate network.


in ordinal ranking, all items receive distinct ordinal numbers, including items that compare equal. the assignment of distinct ordinal numbers to items that compare equal can be done at random, or arbitrarily, but it is generally preferable to use a system that is arbitrary but consistent, as this gives stable results if the ranking is done multiple times. an example of an arbitrary but consistent system would be to incorporate other attributes into the ranking order ( such as alphabetical ordering of the competitor's name ) to ensure that no two items exactly match.


in numerical analysis, nested dissection is a divide and conquer heuristic for the solution of sparse symmetric systems of linear equations based on graph partitioning. nested dissection was introduced by george ( 1973 ) ; the name was suggested by garrett birkhoff. nested dissection consists of the following steps : form an undirected graph in which the vertices represent rows and columns of the system of linear equations, and an edge represents a nonzero entry in the sparse matrix representing the system. recursively partition the graph into subgraphs using separators, small subsets of vertices the removal of which allows the graph to be partitioned into subgraphs with at most a constant fraction of the number of vertices.


in probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. this special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. the term exponential class is sometimes used in place of " exponential family ", or the older term koopman – darmois family. the terms " distribution " and " family " are often used loosely : specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter ; however, a parametric family of distributions is often referred to as " a distribution " ( like " the normal distribution ", meaning " the family of normal distributions " ), and the set of all exponential families is sometimes loosely referred to as " the " exponential family.


the ecl circuitry consumed huge amount of current at a very low voltage ; the cabinets of the larger models contained extra rack space which held stacks of 400 - amp power supplies, and heavy - gauge wiring leading to the backplane. in the mid - 1990s, the rsx computer board featured risc processing capabilities and high speed 75 ns static ram design ( essentially an all - cache design ) while maintaining complete binary compatibility with existing programs. gould / sel's " high speed data interface " or hsd was considered an industry standard in the process control industry.


in the 1973 article " flowchart techniques for structured programming " presented at a 1973 sigplan meeting isaac nassi and shneiderman argued : with the advent of structured programming and goto - less programming a method is needed to model computation in simply ordered structures, each representing a complete thought possibly defined in terms of other thoughts as yet undefined. a model is needed which prevents unrestricted transfers of control and has a control structure closer to languages amenable to structured programming. we present an attempt at such a model. the new model technique for structured programming they presented has become known as the nassi – shneiderman diagram ; a graphical representation of the design of structured software.


this is seen when comparing system messages ( natural language - like statements in the user ’ s native language ) vs. ‘ binary ’ storage dumps. partial or full set of system state data : some tools collect a complete system state vs. a partial system state ( user or partial ‘ binary ’ storage dump vs. complete system dump ). raw or analyzed data : some tools display raw data, while others analyze it ( examples storage dump formatters that format data, vs. ‘ intelligent ’ data formatters ( “ analyze ” is a common verb ) that combine product knowledge with analysis of state variables to indicate the ‘ meaning ’ of the data.


in programming languages, name resolution is the resolution of the tokens within program expressions to the intended program components.


in the first systematic study of astroturfing in the united states, oxford professor philip n. howard argued that the internet was making it much easier for powerful lobbyists and political movements to activate small groups of aggrieved citizens to have an exaggerated importance in public policy debates. astroturfed accounts on social media do not always require humans to write their posts ; one january 2021 study detailed a " set of human - looking bot accounts " used to post political content, which was able to operate automatically for fourteen days ( and make 1, 586 posts ) before being detected and suspended by twitter. twitter trends are often targeted by astroturfing as they are used as a proxy for popularity. a study conducted by researchers at epfl reported that 20 % of the global twitter trends in 2019 were fake, created automatically using fake and compromised accounts which tweet in a coordinated way to mimic grassroots organizing of regular twitter users.


in mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property.


these have special analysis methods. in particular linear regression techniques are much more efficient than most non - linear techniques. the model can be deterministic or stochastic ( i. e. containing random components ) depending on its planned use.


in number theory, a pernicious number is a positive integer such that the hamming weight of its binary representation is prime, that is, there is a prime number of 1s when it is written as a binary number.


in number theory, a provable prime is an integer that has been calculated to be prime using a primality - proving algorithm. boot - strapping techniques using pocklington primality test are the most common ways to generate provable primes for cryptography. contrast with probable prime, which is likely ( but not certain ) to be prime, based on the output of a probabilistic primality test. in principle, every prime number can be proved to be prime in polynomial time by using the aks primality test. other methods which guarantee that their result is prime, but which do not work for all primes, are useful for the random generation of provable primes. provable primes have also been generated on embedded devices.


. these formulas are equivalent for a quadratic function, but for nonlinear optimization the preferred formula is a matter of heuristics or taste. a popular choice is β = max { 0, β p r } { \ displaystyle \ displaystyle \ beta = \ max \ { 0, \ beta ^ { pr } \ } }, which provides a direction reset automatically. algorithms based on newton's method potentially converge much faster. there, both step direction and length are computed from the gradient as the solution of a linear system of equations, with the coefficient matrix being the exact hessian matrix ( for newton's method proper ) or an estimate thereof ( in the quasi - newton methods, where the observed change in the gradient during the iterations is used to update the hessian estimate ).


to illustrate this property, we shall see what happens when n = 2 ( i. e. we consider 3 interpolation nodes in which case the property is not trivial ). one can check that each set of ( zero - symmetric ) nodes of type ( −a, 0, a ) is optimal when √8 / 3 ≤ a ≤ 1 ( we consider only nodes in ). if we force the set of nodes to be of the type ( −1, b, 1 ), then b must equal 0 ( look at the lebesgue function, whose maximum is the lebesgue constant ).


in mathematics, in graph theory, the seidel adjacency matrix of a simple undirected graph g is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and + 1 for positions corresponding to non - adjacent vertices. it is also called the seidel matrix or — its original name — the ( −1, 1, 0 ) - adjacency matrix. it can be interpreted as the result of subtracting the adjacency matrix of g from the adjacency matrix of the complement of g. the multiset of eigenvalues of this matrix is called the seidel spectrum. the seidel matrix was introduced by j. h. van lint and johan jacob seidel in 1966 and extensively exploited by seidel and coauthors.


the closure of a subset is the result of a closure operator applied to the subset. the closure of a subset under some operations is the smallest superset that is closed under these operations. it is often called the span ( for example linear span ) or the generated set.


: 38 qualcomm further developed the cdma techniques for commercial use and submitted them to the cellular telephone industries association ( ctia ) in 1989 as an alternative to the time - division multiple access ( tdma ) standard for second - generation cell - phone networks. : 49 a few months later, ctia officially rejected qualcomm's cdma standard in favor of the more established tdma standard developed by ericsson. at the time, cdma wasn't considered viable in high - volume commercial applications due to the near - far field effect, whereby phones closer to a cell tower with a stronger signal drown out callers that are further away and have a weaker signal. : 54 – 55, 62 – 65 qualcomm filed three additional patents in 1989. they were for : a power management system that adjusts the signal strength of each call to adjust for the near - far field effect ; a " soft handoff " methodology for transferring callers from one cell - tower to the next ; and a variable rate encoder, which reduces bandwidth usage when a caller isn't speaking. : 54 – 55, 62 – 65


in scientific notation, numbers are written in the form x = a × 10 b { \ displaystyle x = a \ times 10 ^ { b } }, where a { \ displaystyle a } is the significand and 10 b { \ displaystyle 10 ^ { b } } is the exponential part. addition requires two numbers in scientific notation to be represented using the same exponential part, so that the two significands can simply be added. for example : 2. 34 × 10 − 5 + 5. 67 × 10 − 6 = 2. 34 × 10 − 5 + 0. 567 × 10 − 5 = 2. 907 × 10 − 5 { \ displaystyle 2. 34 \ times 10 ^ { - 5 } + 5. 67 \ times 10 ^ { - 6 } = 2. 34 \ times 10 ^ { - 5 } + 0. 567 \ times 10 ^ { - 5 } = 2. 907 \ times 10 ^ { - 5 } }


principally, and most correctly, it can be thought of as the logical design of the base data structures used to store the data. in the relational model these are the tables and views. in an object database the entities and relationships map directly to object classes and named relationships.


as the tree is balanced, the path from one of the input arrays to the root contains only θ ( log k ) elements. in total, there are n elements that need to be transferred. the resulting total running time is therefore in θ ( n log k ).


historically, homographies ( and projective spaces ) have been introduced to study perspective and projections in euclidean geometry, and the term homography, which, etymologically, roughly means " similar drawing ", dates from this time. at the end of the 19th century, formal definitions of projective spaces were introduced, which differed from extending euclidean or affine spaces by adding points at infinity. the term " projective transformation " originated in these abstract constructions.


a further method for the derivation of a concept hierarchy exists in the usage of several patterns that should indicate a sub - or supersumption relationship. patterns like “ x, that is a y ” or “ x is a y ” indicate that x is a subclass of y. such pattern can be analyzed efficiently, but they often occur too infrequently to extract enough sub - or supersumption relationships. instead, bootstrapping methods are developed, which learn these patterns automatically and therefore ensure broader coverage.


( the expression " a mathematical function of person and item parameters " is analogous to lewin's equation, b = f ( p, e ), which asserts that behavior is a function of the person in their environment. ) the person parameter is construed as ( usually ) a single latent trait or dimension. examples include general intelligence or the strength of an attitude.


in the collection of these 18 problems problem 13 is very special. in it there are 6 unknowns but only 5 equations and so problem 13 is indeterminate and does not have a unique solution. this is the earliest known reference to a system of linear equations in which the number of unknowns exceeds the number of equations. as per a suggestion of jean - claude martzloff, a historian of chinese mathematics, roger hart has named this problem " the well problem. "


and also presume that these tests have identical sensitivity and specificity. in this situation one is carried away by these findings and presume that both the tests are equivalent. however this may not be the case.


in single - linkage clustering, the distance between two clusters is determined by a single pair of elements : those two elements ( one in each cluster ) that are closest to each other. the shortest of these pairwise distances that remain at any step causes the two clusters whose elements are involved to be merged. the method is also known as nearest neighbour clustering. the result of the clustering can be visualized as a dendrogram, which shows the sequence in which clusters were merged and the distance at which each merge took place. mathematically, the linkage function – the distance d ( x, y ) between clusters x and y – is described by the expression d ( x, y ) = min x ∈ x, y ∈ y d ( x, y ), { \ displaystyle d ( x, y ) = \ min _ { x \ in x, y \ in y } d ( x, y ), } where x and y are any two sets of elements considered as clusters, and d ( x, y ) denotes the distance between the two elements x and y.


thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. in mathematical jargon, one says that two objects are the same up to an isomorphism. an automorphism is an isomorphism from a structure to itself. an isomorphism between two structures is a canonical isomorphism ( a canonical map that is an isomorphism ) if there is only one isomorphism between the two structures ( as is the case for solutions of a universal property ), or if the isomorphism is much more natural ( in some sense ) than other isomorphisms.


in particle physics, the hypercharge ( a portmanteau of hyperonic and charge ) y of a particle is a quantum number conserved under the strong interaction. the concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. the hypercharge is useful to classify hadrons ; the similarly named weak hypercharge has an analogous role in the electroweak interaction.


in mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object. a classical example is the problem of enumeration of the vertices of a convex polytope specified by a set of linear inequalities : a x ≤ b { \ displaystyle ax \ leq b } where a is an m×n matrix, x is an n×1 column vector of variables, and b is an m×1 column vector of constants. the inverse ( dual ) problem of finding the bounding inequalities given the vertices is called facet enumeration ( see convex hull algorithms ).


in network theory, collective classification is the simultaneous prediction of the labels for multiple objects, where each label is predicted using information about the object's observed features, the observed features and labels of its neighbors, and the unobserved labels of its neighbors. collective classification problems are defined in terms of networks of random variables, where the network structure determines the relationship between the random variables. inference is performed on multiple random variables simultaneously, typically by propagating information between nodes in the network to perform approximate inference. approaches that use collective classification can make use of relational information when performing inference. examples of collective classification include predicting attributes ( ex. gender, age, political affiliation ) of individuals in a social network, classifying webpages in the world wide web, and inferring the research area of a paper in a scientific publication dataset.


in static timing analysis, the word static alludes to the fact that this timing analysis is carried out in an input - independent manner, and purports to find the worst - case delay of the circuit over all possible input combinations. the computational efficiency ( linear in the number of edges in the graph ) of such an approach has resulted in its widespread use, even though it has some limitations. a method that is commonly referred to as pert is popularly used in sta. however, pert is a misnomer, and the so - called pert method discussed in most of the literature on timing analysis refers to the critical path method ( cpm ) that is widely used in project management. while the cpm - based methods are the dominant ones in use today, other methods for traversing circuit graphs, such as depth - first search, have been used by various timing analyzers.


the numeric processor also incorporated memory management and consequently employed virtual memory concepts. the memory subsystem implemented a 64 way interleaved 4 - port memory. to ensure that there would be no " hot spots " within the memory system, the addresses to the memory were hashed to spread the accesses evenly across the 64 way memory system.


in the autumn of 1884, karoly zipernowsky, otto blathy and miksa deri ( zbd ), three engineers associated with the ganz works of budapest, determined that open - core devices were impractical, as they were incapable of reliably regulating voltage. in their joint 1885 patent applications for novel transformers ( later called zbd transformers ), they described two designs with closed magnetic circuits where copper windings were either wound around a ring core of iron wires or else surrounded by a core of iron wires. in both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air ( see toroidal cores ). the new transformers were 3. 4 times more efficient than the open - core bipolar devices of gaulard and gibbs.


{ \ displaystyle f ^ { - } ( x ) = \ max ( - f ( x ), 0 ) = - \ min ( f ( x ), 0 ) = { \ begin { cases } - f ( x ) & { \ mbox { if } } f ( x ) < 0 \ \ 0 & { \ mbox { otherwise. } } \ end { cases } } } note that both f + and f− are non - negative functions.


in order to support the machine translation service, a mobile device needs to be able to communicate with external computers ( servers ) that receive the user - input text / speech, translate it and send it back to the user. this is usually done via an internet connection ( wap, gprs, edge, umts, wi - fi ) but some earlier applications used sms to communicate with the translation server. mobile translation is not to be confused for the user - editable ( talking ) dictionaries and phrase books that are already widespread and available for many hand - held devices and do not normally require internet connectivity on the mobile device.


in the event calculus, fluents are reified. this means that they are not formalized by means of predicates but by means of functions. a separate predicate holdsat is used to tell which fluents hold at a given time point. for example, h o l d s a t ( o n ( b o x, t a b l e ), t ) { \ displaystyle { \ mathit { holdsat } } ( on ( box, table ), t ) } means that the box is on the table at time t ; in this formula, holdsat is a predicate while on is a function.


this makes the transmission system less susceptible to noise. despite the fact that stibitz described this code before gray, the reflected binary code was later named after gray by others who used it. two different 1953 patent applications use " gray code " as an alternative name for the " reflected binary code " ; one of those also lists " minimum error code " and " cyclic permutation code " among the names. a 1954 patent application refers to " the bell telephone gray code ". other names include " cyclic binary code ", " cyclic progression code ", " cyclic permuting binary " or " cyclic permuted binary " ( cpb ). the gray code is sometimes misattributed to 19th century electrical device inventor elisha gray.


define the amount of elements on the hypersphere s n d { \ displaystyle s _ { n } ^ { d } } within the neighborhood m n n { \ displaystyle m _ { n } ^ { n } } as e { \ displaystyle e }. for a given q → { \ displaystyle { \ vec { q } } }, e { \ displaystyle e } will be equal to the amount of permutations of q → { \ displaystyle { \ vec { q } } } multiplied by the number of orthants. let n j { \ displaystyle n _ { j } } represent the amount of elements in vector q → { \ displaystyle { \ vec { q } } } which take the value j { \ displaystyle j }.


in statistics, the bootstrap error - adjusted single - sample technique ( best or the beast ) is a non - parametric method that is intended to allow an assessment to be made of the validity of a single sample. it is based on estimating a probability distribution representing what can be expected from valid samples. this is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.


in the base ten ( decimal ) number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. for example, 103 = 1000 and 10−4 = 0. 0001. exponentiation with base 10 is used in scientific notation to denote large or small numbers. for instance, 299792458 m / s ( the speed of light in vacuum, in metres per second ) can be written as 2. 99792458×108 m / s and then approximated as 2. 998×108 m / s. si prefixes based on powers of 10 are also used to describe small or large quantities. for example, the prefix kilo means 103 = 1000, so a kilometre is 1000 m.


in the century from 1832 to noether's death in 1935, the field of mathematics – specifically algebra – underwent a profound revolution, whose reverberations are still being felt. mathematicians of previous centuries had worked on practical methods for solving specific types of equations, e. g., cubic, quartic, and quintic equations, as well as on the related problem of constructing regular polygons using compass and straightedge. beginning with carl friedrich gauss's 1832 proof that prime numbers such as five can be factored in gaussian integers, evariste galois's introduction of permutation groups in 1832 ( although, because of his death, his papers were published only in 1846, by liouville ), william rowan hamilton's discovery of quaternions in 1843, and arthur cayley's more modern definition of groups in 1854, research turned to determining the properties of ever - more - abstract systems defined by ever - more - universal rules. noether's most important contributions to mathematics were to the development of this new field, abstract algebra.


in materials science, a matrix is a constituent of a composite material.


in the field of security engineering, a pre - play attack is a cryptographic attack in which an attacker prepares for the attack in advance by carrying out a simulated transaction while pretending to be the device to be attacked, and then repeats the attack a second time with the real device at a time when it is likely to carry out the same series of operations as in the simulation. the technique relies on being able to guess the content of the transaction in advance, something usually made possible by a poor choice of unpredictability within the system. the name is a play on " replay attack ". pre - play attacks are not very effective and chances of success are slim. = = references = =


in parallel computing, all - to - all ( also known as index operation or total exchange ) is a collective operation, where each processor sends an individual message to every other processor. initially, each processor holds p messages of size m each, and the goal is to exchange the i - th message of processor j with the j - th message of processor i. the number of communication rounds and the overall communication volume are measures to evaluate the quality of an all - to - all algorithm. we consider a single - ported full - duplex machine throughout this article.


in 1895, the german physicist wilhelm conrad rontgen discovered and extensively studied x - rays, which were later used in x - ray spectroscopy. one year later, in 1896, french physicist antoine henri becquerel discovered radioactivity, and dutch physicist pieter zeeman observed spectral lines being split by a magnetic field. in 1897, theoretical physicist, joseph larmor explained the splitting of the spectral lines in a magnetic field by the oscillation of electrons. physicist, joseph larmor, created the first solar system model of the atom in 1897. he also postulated the proton, calling it a “ positive electron. ” he said the destruction of this type of atom making up matter “ is an occurrence of infinitely small probability. ”


there are many proposed implementations of programmable matter. scale is one key differentiator between different forms of programmable matter. at one end of the spectrum reconfigurable modular robotics pursues a form of programmable matter where the individual units are in the centimeter size range.


in the first phase, only the melt itself is ejected ; later a depression may form in the center of the hole and gas is discharged together with the melt with a rapid decrease of pressure inside the reactor vessel ; the high temperature of the melt also causes rapid erosion and enlargement of the vessel breach. if the hole is in the center of the bottom, nearly all corium can be ejected. a hole in the side of the vessel may lead to only partial ejection of corium, with a retained portion left inside the reactor vessel.


in russian, both plain and palatalized consonant phonemes are found in words like большои, царь and катя. in hupa, on the other hand, the palatalization is heard as both an onglide and an offglide. in some cases, the realization of palatalization may change without any corresponding phonemic change.


the final form of maxwell's equations was published in 1865 a dynamical theory of the electromagnetic field, in which the theory is formulated in strictly mathematical form. in 1873, maxwell published a treatise on electricity and magnetism as a summary of his work on electromagnetism. in summary, maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics. later, oliver heaviside studied maxwell's a treatise on electricity and magnetism and employed vector calculus to synthesize maxwell's over 20 equations into the 4 recognizable ones which modern physicists use. maxwell's equations also inspired albert einstein in developing the theory of special relativity. the experimental proof of maxwell's equations was demonstrated by heinrich hertz in a series of experiments in the 1890s. after that, maxwell's equations were fully accepted by scientists.


in mathematics, the cycles of a permutation π of a finite set s correspond bijectively to the orbits of the subgroup generated by π acting on s. these orbits are subsets of s that can be written as { c1,..., cn }, such that π ( ci ) = ci + 1 for i = 1,..., n − 1, and π ( cn ) = c1. the corresponding cycle of π is written as ( c1 c2... cn ) ; this expression is not unique since c1 can be chosen to be any element of the orbit. the size n of the orbit is called the length of the corresponding cycle ; when n = 1, the single element in the orbit is called a fixed point of the permutation. a permutation is determined by giving an expression for each of its cycles, and one notation for permutations consist of writing such expressions one after another in some order.


chiu ( 1998 ) and demeza and lockwood ( 1998 ) have extended the model by considering different bargaining games that the parties may play ex post ( which can explain ownership by the less important investor ). oliver williamson ( 2002 ) has criticized the grossman – hart – moore model because it is focused on ex ante investment incentives, while it neglects ex post inefficiencies. schmitz ( 2006 ) has studied a variant of the grossman – hart – moore model in which a party may have or acquire private information about its disagreement payoff, which can explain ex post inefficiencies and ownership by the less important investor. several variants of the grossman – hart – moore model such as the one with private information can also explain joint ownership.


to visualized this theorem and its conclusion, consider the particular case where k { \ displaystyle k } is a convex polygon. in this case, the corners of the polygon ( which are its extreme points ) are all that is needed to recover the polygon shape. the statement of the theorem is false if the polygon is not convex, as then there are many ways of drawing a polygon having given points as corners.


combining these pieces of information gives us this table of conditional probabilities for y : with more than one conditioning variable, the table would still have one row for each potential value of the variable whose conditional probabilities are to be given, and there would be one column for each possible combination of values of the conditioning variables. moreover, the number of columns in the table could be substantially expanded to display the probabilities of the variable of interest conditional on specific values of only some, rather than all, of the other variables. = = references = =


many scada systems have been fielded up to 20 years ago have very little in the way of modern security protections that are instrumented. these types of attacks have the potential to bring a new dynamic forward in the concept of cyber warfare and the potential impact on electrical systems, financial systems, critical infrastructure, and communication systems. though, in reality, these types of attacks may have a closer relation to espionage or idealistically driven attacks, rather than overt warfare.


in removing all non - value activities, you reduce the amount of redundant tasks performed by the bottlenecked machine and hence maximize efficiency. removing the waste operations results in a shorter cycle time hence allowing the machine to complete each process in less time.


in the japanese kantenji braille, the standard 8 - dot braille patterns 578, 1578, 4578, and 14578 are the patterns related to braille pattern dots - 346, since the two additional dots of kantenji patterns 0346, 3467, and 03467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, tarski's plank problem is a question about coverings of convex regions in n - dimensional euclidean space by " planks " : regions between two hyperplanes. tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region. the question was answered affirmatively by thøger bang ( 1950, 1951 ).


the resulting configuration — the number 110 — is the proof. turing's first task had to write a generalized expression using logic symbols to express exactly what his un ( m ) would do. turing's second task is to " godelize " this hugely long string - of - string - of - symbols using godel's technique of assigning primes to the symbols and raising the primes to prime - powers, per godel's method.


in some games such as video poker, blackjack, or caribbean stud poker, it is possible to compute an optimal playing strategy based on the average payoff ( the amount of payoff times the chance of payoff ). because the jackpot of a progressive game constantly grows, it sometimes exceeds the break - even point for players, such that the jackpot wager becomes a " positive expectation bet " for the player, with an average return to player ( rtp ) of greater than 100 %. when the progressive jackpot is less than the break - even point, there is a negative expected value ( house edge ) for all players. in the long run, with optimal strategy, a player can profit by only playing progressive games when their jackpots are above the break - even point, although the " long run " can be quite long, tens of thousands of plays.


in mathematical optimization, cost functions and non - linear components within can be linearized in order to apply a linear solving method such as the simplex algorithm. the optimized result is reached much more efficiently and is deterministic as a global optimum.


the fact that a { \ displaystyle a } is false contradicts this belief, which should therefore be removed from the belief set. the result of revision is therefore { ¬ a } { \ displaystyle \ { \ neg a \ } } in this case. the problem of using deductively closed knowledge bases is that no distinction is made between pieces of knowledge that are known by themselves and pieces of knowledge that are merely consequences of them.


in probability and statistics, a spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. more specifically, a spherical contact distribution function is defined as probability distribution of the radius of a sphere when it first encounters or makes contact with a point in a point process. this function can be contrasted with the nearest neighbour function, which is defined in relation to some point in the point process as being the probability distribution of the distance from that point to its nearest neighbouring point in the same point process. the spherical contact function is also referred to as the contact distribution function, but some authors define the contact distribution function in relation to a more general set, and not simply a sphere as in the case of the spherical contact distribution function. spherical contact distribution functions are used in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.


1 l, an alternative form, for typefaces in which these characters are difficult to distinguish, or the typeface the reader will be using is unknown. a " script l " in various typefaces ( e. g. : 1 l ) has traditionally been used in some countries to prevent confusion ; however, the separate unicode character which represents this, u + 2113 ℓ script small l, is deprecated by the si.


} } \ cdot { \ dfrac { 1 } { i \ left ( r, \ lambda \ right ) } }, \ quad n = 0, 1, 2, \ ldots & { \ text { if } } r \ geq 0 \ \ e ^ { - \ lambda } { \ dfrac { \ lambda ^ { n + r } } { \ left ( n + r \ right )! } } \ cdot { \ dfrac { 1 } { i \ left ( r + s, \ lambda \ right ) } }, \ quad n = s, s + 1, s + 2, \ ldots & { \ text { otherwise } } \ end { cases } } } where λ > 0 { \ displaystyle \ lambda > 0 } and r is a new parameter ; the poisson distribution is recovered at r = 0. here i ( r, λ ) { \ displaystyle i \ left ( r, \ lambda \ right ) } is the pearson's incomplete gamma function : i ( r, λ ) = y = r ∞ e − λ λ y y!


in mathematics, the goormaghtigh conjecture is a conjecture in number theory named for the belgian mathematician rene goormaghtigh. the conjecture is that the only non - trivial integer solutions of the exponential diophantine equation x m − 1 x − 1 = y n − 1 y − 1 { \ displaystyle { \ frac { x ^ { m } - 1 } { x - 1 } } = { \ frac { y ^ { n } - 1 } { y - 1 } } } satisfying x > y > 1 { \ displaystyle x > y > 1 } and n, m > 2 { \ displaystyle n, m > 2 } are 5 3 − 1 5 − 1 = 2 5 − 1 2 − 1 = 31 { \ displaystyle { \ frac { 5 ^ { 3 } - 1 } { 5 - 1 } } = { \ frac { 2 ^ { 5 } - 1 } { 2 - 1 } } = 31 } and 90 3 − 1 90 − 1 = 2 13 − 1 2 − 1 = 8191. { \ displaystyle { \ frac { 90 ^ { 3 } - 1 } { 90 - 1 } } = { \ frac { 2 ^ { 13 } - 1 } { 2 - 1 } } = 8191. }


in modern mapping, a topographic map or topographic sheet is a type of map characterized by large - scale detail and quantitative representation of relief features, usually using contour lines ( connecting points of equal elevation ), but historically using a variety of methods. traditional definitions require a topographic map to show both natural and artificial features. a topographic survey is typically based upon a systematic observation and published as a map series, made up of two or more map sheets that combine to form the whole map.


at that point, all of the other vendors began risc efforts of their own. among these were the dec alpha, amd am29000, intel i860 and i960, motorola 88000, ibm power, and, slightly later, the ibm / apple / motorola powerpc. many of these have since disappeared due to them often offering no competitive advantage over others of the same era.


however, this may not be desirable where the programmer wishes to create closed abstractions. a pitfall of structural typing versus nominative typing is that two separately defined types intended for different purposes, but accidentally holding the same properties ( e. g. both composed of a pair of integers ), could be considered the same type by the type system, simply because they happen to have identical structure. one way this can be avoided is by creating one algebraic data type for each use. in 1990, cook, et al., proved that inheritance is not subtyping in structurally - typed oo languages. checking that two types are compatible, based on structural typing, is a non - trivial operation, e. g., requires maintaining a stack of previous checked types.


in the uk planning laws, applications and restrictions delay flood mitigation work. this can be counteracted by setting up temporary test dams in watercourses that can then be monitored and valued. this does however require the landowners support. ttds have proven to be a great way to get rapid action following a flood event and a way to get communities involved in the defence against future flood events.


in program analysis, a polyvariant or context - sensitive analysis ( as opposed to a monovariant or context - insensitive analysis ) analyzes each function multiple times — typically once at each call site — to improve the precision of the analysis. polyvariance is common in data - flow and pointer analyses. forms of polyvariance include : call - site sensitivity the cartesian product algorithm object sensitivity type sensitivitythe first two are more often used for dataflow analyses, the latter two are more frequently used for pointer analyses.


the norm on the space e { \ displaystyle e } is ‖. ‖ e { \ displaystyle \ |. \ | _ { e } }. the idea to recover the original image is to minimize the following functional for u ∈ h 1 ( ω ) { \ displaystyle u \ in h ^ { 1 } ( \ omega ) } : where c { \ displaystyle c } is a positive definite tensor.


in ontology, the theory of categories concerns itself with the categories of being : the highest genera or kinds of entities according to amie thomasson. to investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities. a distinction between such categories, in making the categories or applying them, is called an ontological distinction. various systems of categories have been proposed, they often include categories for substances, properties, relations, states of affairs or events. a representative question within the theory of categories might articulate itself, for example, in a query like, " are universals prior to particulars? "


in addition, “ hierarchical organization of plans comes from the timing of behavioral sequences. ” the larger the phrase, the longer the response time, which factors into “ decoding ” or “ unpacking ” hierarchical plans. additional evidence is how easy or hard it is to learn a sequence. the mind can create a “ memory for what is about to happen ” as well as a “ memory for what has happened. ” the final evidence for the hierarchical organization of plans is characterized by " chunking ". this skill combines multiple units into larger units.


gotoblas's matrix - matrix multiplication routine, called gemm in blas terms, is highly tuned for the x86 and amd64 processor architectures by means of handcrafted assembly code. it follows a similar decomposition into smaller " kernel " routines that other blas implementations use, but where earlier implementations streamed data from the l1 processor cache, gotoblas uses the l2 cache. the kernel used for gemm is a routine called gebp, for " general block - times - panel multiply ", which was experimentally found to be " inherently superior " over several other kernels that were considered in the design. several other blas routines are, as is customary in blas libraries, implemented in terms of gemm. as of january 2022, the texas advanced computing center website states that goto blas in no more maintained and suggests the use of blis or mkl.


in plant morphology, rolf sattler developed a process morphology ( dynamic morphology ) that overcomes the structure / process ( or structure / function ) dualism that is commonly taken for granted in biology. according to process morphology, structures such as leaves of plants do not have processes, they are processes. in evolution and in development, the nature of the changes of biological objects are considered by many authors to be more radical than in physical systems. in biology, changes are not just changes of state in a pre - given space, instead the space and more generally the mathematical structures required to understand object change over time.


for the sequence to be sociable, the sequence must be cyclic and return to its starting point. the period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. if the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number — for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. a pair of amicable numbers is a set of sociable numbers of order 2. there are no known sociable numbers of order 3, and searches for them have been made up to 5 × 10 7 { \ displaystyle 5 \ times 10 ^ { 7 } } as of 1970. it is an open question whether all numbers end up at either a sociable number or at a prime ( and hence 1 ), or, equivalently, whether there exist numbers whose aliquot sequence never terminates, and hence grows without bound.


in the base −2 representation, a signed number is represented using a number system with base −2. in conventional binary number systems, the base, or radix, is 2 ; thus the rightmost bit represents 20, the next bit represents 21, the next bit 22, and so on. however, a binary number system with base −2 is also possible. the rightmost bit represents ( −2 ) 0 = + 1, the next bit represents ( −2 ) 1 = −2, the next bit ( −2 ) 2 = + 4 and so on, with alternating sign.


minimal algebraic notation is similar to short algebraic notation but omits the indicators for capture ( " x " ), en passant capture ( " e. p. " ), check ( " + " ) and checkmate ( " # " ).


powerful error removal methods exist. " : 5 similarly, davies notes on end - to - end error control, " it is thought that all users of the network will provide themselves with some kind of error control and that without difficulty this could be made to show up a missing packet. because of this, loss of packets, if it is sufficiently rare, can be tolerated.


in mathematics, the term modulo ( " with respect to a modulus of ", the latin ablative of modulus which itself means " a small measure " ) is often used to assert that two distinct mathematical objects can be regarded as equivalent — if their difference is accounted for by an additional factor. it was initially introduced into mathematics in the context of modular arithmetic by carl friedrich gauss in 1801. since then, the term has gained many meanings — some exact and some imprecise ( such as equating " modulo " with " except for " ). for the most part, the term often occurs in statements of the form : a is the same as b modulo cwhich means a and b are the same — except for differences accounted for or explained by c.


these phones can also make voice calls, as well as send sms and e - mail messages, and although this requirement is no longer in force due to minimal use of the textphone feature in these phones, many of these devices remain in service, generally in populated areas. in addition, in the early 2000s bt installed a large number of'multiphones'that provided internet access, on top of voice, sms, and e - mail functionality. these payphones provided these services through the use of a 2 - channel isdn2 connection, a qnx - based operating system, and a touchscreen interface to allow the user to browse websites and receive e - mail messages on a pay - per - minute basis. however, these devices have since been removed due to quickly becoming obsolete, often with the ordinary payphone previously installed in that location taking its place once again.


see also c. hempel, philosophy of natural science 49 ( 1966 ) ( he statements constituting a scientific explanation must be capable of empirical test ) ; k. popper, conjectures and refutations : the growth of scientific knowledge 37 ( 5th ed. 1989 ) ( he criterion of the scientific status of a theory is its falsifiability, or refutability, or testability ) ( emphasis deleted ). david h. kaye said that references to the daubert majority opinion confused falsifiability and falsification and that " inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations. "


in mathematics, a unit vector in a normed vector space is a vector ( often a spatial vector ) of length 1. a unit vector is often denoted by a lowercase letter with a circumflex, or " hat ", as in v ^ { \ displaystyle { \ hat { \ mathbf { v } } } } ( pronounced " v - hat " ). the term direction vector, commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction.


for example, in asl, the signs for " class " and " family " are the same ( a basic sign for'group of people'), except that " class " is signed with a'c'handshape, and " family " with an'f'handshape. in other cases initialization is required for disambiguation, though the signs are not semantically related. for example, in asl, " water " it signed with a'w'handshape touching the mouth, while " dentist " is similar apart from using a'd'handshape. in other cases initialization is not used for disambiguation ; the asl sign for " elevator ", for example, is an'e'handshape moving up and down along the upright index finger of the other hand. the large number of initialized signs in asl and french sign language is partly a legacy of abbe de l'epee's system of methodical sign ( les signes methodiques ), in which the handshapes of most signs were changed to correspond to the initial letter of their translation in the local oral language, and ( in the case of asl ) partly a more recent influence of manually coded english.


relations are intended to represent semantic links between words in every existing language. they can be ontological ( such as " icl " and " iof, " referred to above ), logical ( such as " and " and " or " ), and thematic ( such as " agt " = agent, " ins " = instrument, " tim " = time, " plc " = place, etc. ).


in static strings method, the api caller or client embeds a string as a token in the request. this method is often referred as basic authentication. " from a security point of view, basic authentication is not very satisfactory. it means sending the user's password over the network in clear text for every single page accessed ( unless a secure lower - level protocol, like ssl, is used to encrypt all transactions ). thus the user is very vulnerable to any packet sniffers on the net. "


in object - oriented programming, object copying is creating a copy of an existing object, a unit of data in object - oriented programming. the resulting object is called an object copy or simply copy of the original object. copying is basic but has subtleties and can have significant overhead. there are several ways to copy an object, most commonly by a copy constructor or cloning.


in numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. iterative methods for nonlinear equations and their systems, such as newton's method are usually only locally convergent. an iterative method that converges for an arbitrary initial approximation is called globally convergent. iterative methods for systems of linear equations are usually globally convergent.


in mathematics, the grothendieck group, or group of differences, of a commutative monoid m is a certain abelian group. this abelian group is constructed from m in the most universal way, in the sense that any abelian group containing a homomorphic image of m will also contain a homomorphic image of the grothendieck group of m. the grothendieck group construction takes its name from a specific case in category theory, introduced by alexander grothendieck in his proof of the grothendieck – riemann – roch theorem, which resulted in the development of k - theory. this specific case is the monoid of isomorphism classes of objects of an abelian category, with the direct sum as its operation.


in practice, document clustering often takes the following steps : 1. tokenization tokenization is the process of parsing text data into smaller units ( tokens ) such as words and phrases. commonly used tokenization methods include bag - of - words model and n - gram model. 2.