the lrn removes the need for the public telephone number to identify the local exchange carrier. if a subscriber changes to another telephone service provider, the current telephone number can be retained, and only the lrn needs to be changed. in addition to supporting service provider telephone number portability, an lrn also supports the possibility of two other types of number portability : service portability ( for example, ordinary service to isdn ) and geographic portability.


in order to define a custom structure type using oracle database one could use statements such as these : such structure type can be then used to create a table that would also hold all columns defined in person _ type : custom structure types support inheritance, which means that one can create another type that inherits from previous. not final statement must be however included in a base structure type definition in order to allow for creation of any other subtypes. student _ type then could be used in order to create a student _ table which will include all columns defined in person _ type as well. primary key and constraints should be defined during or after creation of table and cannot be defined inside structure type itself. each custom structure type can also contain other types in order to support more complex structures :


in the 19th century, sir william thomson made a hypothesis that the chemical elements were based upon knotted vortices in the aether. in an attempt to make a periodic table of the elements, p. g. tait, c. n. little and others started to attempt to count all possible knots. because their work predated the invention of the digital computer, all work had to be done by hand.


voip systems are based on internet standards and technology which have not previously attempted to satisfy such complex and demanding requirements as those that specify call control. an alternative name often used is call processing. in a voip network, call control is one of three major categories of communications traffic, the other two being call signaling and media communications. call control uses q. 931, a connection protocol for digital networks, especially voip systems. messages are transmitted as octets as specified in itu h. 245, which resolves the type of call media to be used ( for example, conventional call, videoconferencing, or voip ), and then manages the connection after it has been established. call control functions include, but are not limited to, the determination of master / slave status for the endpoints, monitoring of the status of the endpoints, modification of the parameters of a connection, termination of a connection, and restarting a terminated or failed connection.


these critics suggest that direct parameters would be better placed on the operational uses of data in general. opponents of regulatory reform say this would, perhaps unintentionally, drastically inhibit businesses ability to utilize the data for positive measures. furthermore, because singular data points may be used across a large array of industries, sector - specific legislation may prove fruitless.


in pseudocode the algorithm can be stated as : begin 1 ) objective function : f ( x ), x = ( x 1, x 2,...


an example is the assignment of the code eur to the euro. iso 4217 amendment 94, which created this code, states " the code element'eu'has been reserved by the iso 3166 maintenance agency for use within iso 4217 where'r'has been appended to make an acceptable mnemonic code. " here the r comes from the third letter in the word " euro ".


the conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. it is commonly attributed to magnus hestenes and eduard stiefel, who programmed it on the z4, and extensively researched it. the biconjugate gradient method provides a generalization to non - symmetric matrices. various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems.


when an item in the left column is related to an item across the top, a mark is placed in the intersecting cell. the number of relationships are added up for each row and each column.


thus, metaheuristics usually allow to meet the resolution delays imposed in the industrial field as well as they allow to study general problem classes instead that particular problem instances. in general, many of the best performing techniques in precision and effort to solve complex and real - world problems are metaheuristics. their fields of application range from combinatorial optimization, bioinformatics, and telecommunications to economics, software engineering, etc. these fields are full of many tasks needing fast solutions of high quality.


in probability theory and machine learning, the multi - armed bandit problem ( sometimes called the k - or n - armed bandit problem ) is a problem in which a fixed limited set of resources must be allocated between competing ( alternative ) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. this is a classic reinforcement learning problem that exemplifies the exploration – exploitation tradeoff dilemma. the name comes from imagining a gambler at a row of slot machines ( sometimes known as " one - armed bandits " ), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. the multi - armed bandit problem also falls into the broad category of stochastic scheduling.


in test - driven development ( tdd ), which is frequently used in both extreme programming and scrum, unit tests are created before the code itself is written. when the tests pass, that code is considered complete. the same unit tests are run against that function frequently as the larger code base is developed either as the code is changed or via an automated process with the build. if the unit tests fail, it is considered to be a bug either in the changed code or the tests themselves. the unit tests then allow the location of the fault or failure to be easily traced. since the unit tests alert the development team of the problem before handing the code off to testers or clients, potential problems are caught early in the development process.


in the 1970s, there was a two - player game made by tri - ang toys & games called check lines, in which the board consisted of eleven holes arranged in a geometrical pattern of twelve straight lines each containing three of the holes. each player had exactly five tokens and played in turn placing one token in any of the holes. the winner was the first player whose tokens were arranged in two lines of three ( which by definition were intersecting lines ). if neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.


in optimal control theory, the evolution of n state variables through time depends at any time on their own values and on the values of k control variables. with linear evolution, matrices of coefficients appear in the state equation ( equation of evolution ). in some problems the values of the parameters in these matrices are not known with certainty, in which case there are random matrices in the state equation and the problem is known as one of stochastic control. : ch. 13 a key result in the case of linear - quadratic control with stochastic matrices is that the certainty equivalence principle does not apply : while in the absence of multiplier uncertainty ( that is, with only additive uncertainty ) the optimal policy with a quadratic loss function coincides with what would be decided if the uncertainty were ignored, the optimal policy may differ if the state equation contains random coefficients.


the position of an element in a sequence is its rank or index ; it is the natural number for which the element is the image. the first element has index 0 or 1, depending on the context or a specific convention. in mathematical analysis, a sequence is often denoted by letters in the form of a n { \ displaystyle a _ { n } }, b n { \ displaystyle b _ { n } } and c n { \ displaystyle c _ { n } }, where the subscript n refers to the nth element of the sequence ; for example, the nth element of the fibonacci sequence f { \ displaystyle f } is generally denoted as f n { \ displaystyle f _ { n } }. in computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory ; infinite sequences are called streams. the empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.


in most languages that provide this feature, a procedural parameter f of a subroutine p can be called inside the body of p as if it were an ordinary procedure : procedure p ( f ) : return f ( 6, 3 ) * f ( 2, 1 ) when calling the subroutine p, one must give it one argument, that must be some previously defined function compatible with the way p uses its parameter f. for example, if we define procedure plus ( x, y ) : return x + y then we may call p ( plus ), and the result will be plus ( 6, 3 ) * plus ( 2, 1 ) = ( 6 + 3 ) * ( 2 + 1 ) = 27. on the other hand, if we define procedure quot ( u, v ) : return u / v then the call p ( quot ) will return quot ( 6, 3 ) * quot ( 2, 1 ) = ( 6 / 3 ) * ( 2 / 1 ) = 4. finally, if we define procedure evil ( z ) return z + 100 then the call p ( evil ) will not make much sense, and may be flagged as an error.


in number theory, a branch of mathematics, a mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of fermat's last theorem. since the theorem has now been proven, these are now of mainly historical significance, though the mirimanoff polynomials are interesting in their own right. the theorem is due to dmitry mirimanoff.


in mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. for example, 0 is an identity element of the addition of real numbers. this concept is used in algebraic structures such as groups and rings. the term identity element is often shortened to identity ( as in the case of additive identity and multiplicative identity ) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.


in probability theory and statistics, the hermite distribution, named after charles hermite, is a discrete probability distribution used to model count data with more than one parameter. this distribution is flexible in terms of its ability to allow a moderate over - dispersion in the data. the authors kemp and kemp have called it " hermite distribution " from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of ( modified ) hermite polynomials.


the typical metric used in this case the lee distance. there exist a gray isometry between z 2 2 m { \ displaystyle \ mathbb { z } _ { 2 } ^ { 2m } } ( i. e. gf ( 22m ) ) with the hamming distance and z 4 m { \ displaystyle \ mathbb { z } _ { 4 } ^ { m } } ( also denoted as gr ( 4, m ) ) with the lee distance. = = references = =


in mathematical logic, proof compression by splitting is an algorithm that operates as a post - process on resolution proofs. it was proposed by scott cotton in his paper " two techniques for minimizing resolution proof ". the splitting algorithm is based on the following observation : given a proof of unsatisfiability π { \ displaystyle \ pi } and a variable x { \ displaystyle x }, it is easy to re - arrange ( split ) the proof in a proof of x { \ displaystyle x } and a proof of ¬ x { \ displaystyle \ neg x } and the recombination of these two proofs ( by an additional resolution step ) may result in a proof smaller than the original. note that applying splitting in a proof π { \ displaystyle \ pi } using a variable x { \ displaystyle x } does not invalidates a latter application of the algorithm using a differente variable y { \ displaystyle y }. actually, the method proposed by cotton generates a sequence of proofs π 1 π 2 … { \ displaystyle \ pi _ { 1 } \ pi _ { 2 } \ ldots }, where each proof π i + 1 { \ displaystyle \ pi _ { i + 1 } } is the result of applying splitting to π i { \ displaystyle \ pi _ { i } }.


in political science, the policy cycle is a tool used for analyzing the development of a policy. it can also be referred to as a " stages model " or " stages heuristic ". it is thus a rule of thumb rather than the actual reality of how policy is created, but has been influential in how political scientists looked at policy in general. it was developed as a theory from harold lasswell's work.


this is primarily because adding another opteron processor increases memory bandwidth, while that is not always the case for xeon systems, and the fact that the opterons use a switched fabric, rather than a shared bus. in particular, the opteron's integrated memory controller allows the cpu to access local ram very quickly. in contrast, multiprocessor xeon system cpus share only two common buses for both processor - processor and processor - memory communication. as the number of cpus increases in a typical xeon system, contention for the shared bus causes computing efficiency to drop. intel migrated to a memory architecture similar to the opteron's for the intel core i7 family of processors and their xeon derivatives.


then, they consider the above lp with one additional constraint : the additional constraint guarantees that the " vacant space " in the bins can be filled by the small items. the dual of this lp is more complex and cannot be solved by a simple knapsack - problem separation oracle. csirik, johnson and kenyon present a different method to solve it approximately in time exponential in 1 / epsilon. jansen and solis - oba present an improved method to solve it approximately in time exponential in 1 / epsilon.


in mathematics, especially group theory, the centralizer ( also called commutant ) of a subset s in a group g is the set c g ( s ) { \ displaystyle \ operatorname { c } _ { g } ( s ) } of elements of g that commute with every element of s, or equivalently, such that conjugation by g { \ displaystyle g } leaves each element of s fixed. the normalizer of s in g is the set of elements n g ( s ) { \ displaystyle \ mathrm { n } _ { g } ( s ) } of g that satisfy the weaker condition of leaving the set s ⊆ g { \ displaystyle s \ subseteq g } fixed under conjugation. the centralizer and normalizer of s are subgroups of g. many techniques in group theory are based on studying the centralizers and normalizers of suitable subsets s. suitably formulated, the definitions also apply to semigroups.


in mathematics, the mertens conjecture is the statement that the mertens function m ( n ) { \ displaystyle m ( n ) } is bounded by ± n { \ displaystyle \ pm { \ sqrt { n } } }. although now disproven, it had been shown to imply the riemann hypothesis. it was conjectured by thomas joannes stieltjes, in an 1885 letter to charles hermite ( reprinted in stieltjes ( 1905 ) ), and again in print by franz mertens ( 1897 ), and disproved by andrew odlyzko and herman te riele ( 1985 ). it is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor.


relation algebra to specify information systems.


in the japanese kantenji braille, the standard 8 - dot braille patterns 58, 158, 458, and 1458 are the patterns related to braille pattern dots - 46, since the two additional dots of kantenji patterns 046, 467, and 0467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


let ℓ { \ displaystyle \ ell } be the single literal of the unit clause of η ′ { \ displaystyle \ eta ^ { \ prime } }. then any occurrence of ℓ { \ displaystyle { \ overline { \ ell } } } in the subproof above η { \ displaystyle \ eta } will not be cancelled by resolution inferences with η ′ { \ displaystyle \ eta ^ { \ prime } } anymore. consequently, ℓ { \ displaystyle { \ overline { \ ell } } } will be propagated downwards when the proof is fixed and will appear in the clause of η { \ displaystyle \ eta }.


in some texts, especially in random matrix theory, authors have found it more convenient to use a matrix argument in the jack function. the connection is simple. if x { \ displaystyle x } is a matrix with eigenvalues x 1, x 2, …, x m { \ displaystyle x _ { 1 }, x _ { 2 }, \ ldots, x _ { m } }, then j κ ( α ) ( x ) = j κ ( α ) ( x 1, x 2, …, x m ). { \ displaystyle j _ { \ kappa } ^ { ( \ alpha ) } ( x ) = j _ { \ kappa } ^ { ( \ alpha ) } ( x _ { 1 }, x _ { 2 }, \ ldots, x _ { m } ). }


in some cases, fpus may be specialized, and divided between simpler floating - point operations ( mainly addition and multiplication ) and more complicated operations, like division. in some cases, only the simple operations may be implemented in hardware or microcode, while the more complex operations are implemented as software. in some current architectures, the fpu functionality is combined with simd units to perform simd computation ; an example of this is the augmentation of the x87 instructions set with sse instruction set in the x86 - 64 architecture used in newer intel and amd processors.


in some older virtual memory operating systems, space in swap backing store is reserved when programs allocate memory for runtime data. operating system vendors typically issue guidelines about how much swap space should be allocated.


in most legal proceedings, one party has a burden of proof, which requires it to present prima facie evidence for all of the essential facts in its case. if it cannot, its claim may be dismissed without any need for a response by other parties. a prima facie case might not stand or fall on its own ; if an opposing party introduces other evidence or asserts an affirmative defense, it can be reconciled only with a full trial.


and by stanley p. frankel in 1950 for the purpose of automatically solving linear systems on digital computers. over - relaxation methods had been used before the work of young and frankel. an example is the method of lewis fry richardson, and the methods developed by r. v. southwell. however, these methods were designed for computation by human calculators, requiring some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. these aspects are discussed in the thesis of david m. young jr.


in mathematics, in the field of algebraic number theory, a modulus ( plural moduli ) ( or cycle, or extended ideal ) is a formal product of places of a global field ( i. e. an algebraic number field or a global function field ). it is used to encode ramification data for abelian extensions of a global field.


in the 1993 book " information coordination : the management of information models, systems, and organizations " veryard gives a snapshot of the state of the art around these subjects. " maximizing the value of corporate data depends upon being able to manage information models both within and between businesses. a centralized information model is not appropriate for many organizations, " veryard explains. his book " takes the approach that multiple information models exist and the differences and links between them have to be managed. coordination is currently an area of both intensive theoretical speculation and of practical research and development. information coordination explains practical guidelines for information management, both from on - going research and from recent field experience with case tools and methods ".


only call packets from or destined to a phone serviced by the concentrator actually are processed by the concentrator — nonlocal phones'time slots just pass through the concentrator unchanged. if the concentrator malfunctions, a fail - safe relay connects the " in " wires to the " out " wires, and nonlocal phones detect no difference. the central switch periodically counts concentrators, and schedules maintenance, probably before users notice the failure. concentrators for several hundred customers can be threaded on this loop like pearls. the interface between remote concentrators and their parent telephone switches has been standardised by etsi as the v5 interface.


considering even the simple case of exponentiation as a primitive recursive function, and that the composition of primitive recursive functions is primitive recursive, one can begin to see how quickly a primitive recursive function can grow. and any function that can be computed by a turing machine in a running time bounded by a primitive recursive function is itself primitive recursive. so it is difficult to imagine a practical use for full μ - recursion where primitive recursion will not do, especially since the former can be simulated by the latter up to exceedingly long running times. and in any case, kurt godel's first incompleteness theorem and the halting problem imply that there are while loops that always terminate but cannot be proven to do so ; thus it is unavoidable that any requirement for a formal proof of termination must reduce the expressive power of a programming language. while we have shown that every loop that terminates has a variant, this does not mean that the well - foundedness of the loop iteration can be proven.


abstract datatypes are structures of concrete datatypes, with a new name assigned. for example, a list of integers could be called integer _ list. in object - oriented jargon, abstract datatypes are called classes.


even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence without an outside argument. the values of the loadings l { \ displaystyle l }, the averages μ { \ displaystyle \ mu }, and the variances of the " errors " ε { \ displaystyle \ varepsilon } must be estimated given the observed data x { \ displaystyle x } and f { \ displaystyle f } ( the assumption about the levels of the factors is fixed for a given f { \ displaystyle f } ). the " fundamental theorem " may be derived from the above conditions : i z a i z b i = j ℓ a j ℓ b j + i ε a i ε b i { \ displaystyle \ sum _ { i } z _ { ai } z _ { bi } = \ sum _ { j } \ ell _ { aj } \ ell _ { bj } + \ sum _ { i } \ varepsilon _ { ai } \ varepsilon _ { bi } } the term on the left is the ( a, b ) { \ displaystyle ( a, b ) } - term of the correlation matrix ( a p × p { \ displaystyle p \ times p } matrix derived as the product of the p × n { \ displaystyle p \ times n } matrix of standardized observations with its transpose ) of the observed data, and its p { \ displaystyle p } diagonal elements will be 1 { \ displaystyle 1 } s. the second term on the right will be a diagonal matrix with terms less than unity.


the equivalence class of a set a under this relation, then, consists of all those sets which have the same cardinality as a. there are two ways to define the " cardinality of a set " : the cardinality of a set a is defined as its equivalence class under equinumerosity. a representative set is designated for each equivalence class.


in mathematics, a minimum bottleneck spanning tree ( mbst ) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. a bottleneck edge is the highest weighted edge in a spanning tree. a spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. for a directed graph, a similar problem is known as minimum bottleneck spanning arborescence ( mbsa ).


in telephony, a service switching point ( ssp ) is the telephone exchange that initially responds, when a telephone caller dials a number, by sending a query to a central database called a service control point ( scp ) so that the call can be handled. the service switching point uses the signalling system no. 7 ( ss7 ) protocols which are responsible for the call setup, management, and termination with other service switching points.


in mathematics and statistics, the arithmetic mean ( arr - ith - met - ik ), arithmetic average, or just the mean or average ( when the context is clear ) is the sum of a collection of numbers divided by the count of numbers in the collection. the collection is often a set of results from an experiment, an observational study, or a survey. the term " arithmetic mean " is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic. in addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent.


clustering of machines and parts is one of the most popular production flow analysis methods. the algorithms for machine part grouping include rank order clustering, modified rank order clustering, and similarity coefficients. there are also a number of mathematical models and algorithms to aid in planning a cellular manufacturing center, which take into account a variety of important variables such as, " multiple plant locations, multi - market allocations with production planning and various part mix. " once these variables are determined with a given level of uncertainty, optimizations can be performed to minimize factors such as, " total cost of holding, inter - cell material handling, external transportation, fixed cost for producing each part in each plant, machine and labor salaries. "


in some data exfiltration scenarios, a large amount of aggregated data may be exfiltrated. however, in these and other scenarios, it is likely that certain types of data may be targeted. types of data that are targeted includes : usernames, associated passwords, and other system authentication related information information associated with strategic decisions cryptographic keys personal financial information social security numbers and other personally identifiable information ( pii ) mailing addresses united states national security agency hacking tools


in the 1960s, theoretical research in computer science on regular expressions and finite automata led to the discovery that context - free grammars are equivalent to nondeterministic pushdown automata. these grammars were thought to capture the syntax of computer programming languages. the first high - level computer programming languages were under development at the time ( see history of programming languages ) and writing compilers was difficult. but using context - free grammars to help automate the parsing part of the compiler simplified the task.


in mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. a very simple example is the subgroup of invertible 2 × 2 integer matrices of determinant 1 in which the off - diagonal entries are even. more generally, the notion of congruence subgroup can be defined for arithmetic subgroups of algebraic groups ; that is, those for which we have a notion of'integral structure'and can define reduction maps modulo an integer. the existence of congruence subgroups in an arithmetic group provides it with a wealth of subgroups, in particular it shows that the group is residually finite. an important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. congruence subgroups of 2×2 matrices are fundamental objects in the classical theory of modular forms ; the modern theory of automorphic forms makes a similar use of congruence subgroups in more general arithmetic groups.


in mathematics, a self - descriptive number is an integer m that in a given base b is b digits long in which each digit d at position n ( the most significant digit being at position 0 and the least significant at position b−1 ) counts how many instances of digit n are in m.


in music theory, an inversion is a type of change to intervals, chords, voices ( in counterpoint ), and melodies. in each of these cases, " inversion " has a distinct but related meaning. the concept of inversion also plays an important role in musical set theory.


it is not a cogent and simple way. it is claimed to be precise, but precise for what purpose?


in software engineering, a software development process is a process of planning and managing software development. it typically involves dividing software development work into smaller, parallel, or sequential steps or sub - processes to improve design and / or product management. it is also known as a software development life cycle ( sdlc ).


in software, a stack buffer overflow or stack buffer overrun occurs when a program writes to a memory address on the program's call stack outside of the intended data structure, which is usually a fixed - length buffer. stack buffer overflow bugs are caused when a program writes more data to a buffer located on the stack than what is actually allocated for that buffer. this almost always results in corruption of adjacent data on the stack, and in cases where the overflow was triggered by mistake, will often cause the program to crash or operate incorrectly. stack buffer overflow is a type of the more general programming malfunction known as buffer overflow ( or buffer overrun ).


in order to formulate a classical field theory, the following structures are needed :


the classes in a class diagram represent both the main elements, interactions in the application, and the classes to be programmed. in the diagram, classes are represented with boxes that contain three compartments : the top compartment contains the name of the class. it is printed in bold and centered, and the first letter is capitalized.


the algorithm performs a series of iterations, each consisting of two basic steps : authority update : update each node's authority score to be equal to the sum of the hub scores of each node that points to it. that is, a node is given a high authority score by being linked from pages that are recognized as hubs for information. hub update : update each node's hub score to be equal to the sum of the authority scores of each node that it points to.


the term generalized inverse is sometimes used as a synonym for pseudoinverse. a common use of the pseudoinverse is to compute a " best fit " ( least squares ) solution to a system of linear equations that lacks a solution ( see below under § applications ). another use is to find the minimum ( euclidean ) norm solution to a system of linear equations with multiple solutions.


in the absence of interference, there are two factors at play when recalling a list of items : the recency and the primacy effects. the recency effect occurs when the short - term memory is used to remember the most recent items, and the primacy effect occurs when the long - term memory has encoded the earlier items. the recency effect can be eliminated if there is a period of interference between the input and the output of information extending longer than the holding time of short - term memory ( 15 – 30 seconds ). this occurs when a person is given subsequent information to recall preceding the recall of the initial information.


the trade secret law varies from country to country, unlike the case for patents, trademarks and copyright for which there are formal conventions through which subscribing countries grant the same protection to the property as the others ; examples of which are the paris convention for the protection of industrial property and the world intellectual property organization ( wipo ), under united nations, a supportive organization designed " to encourage creative activity, to promote the protection of intellectual property throughout the world ". the world trade organization defined a trade secret by the following criteria : natural and legal persons shall have the possibility of preventing information lawfully within their control from being disclosed to, acquired by, or used by others without their consent in a manner contrary to honest commercial practices ( 10 ) so long as such information : ( a ) is secret in the sense that it is not, as a body or in the precise configuration and assembly of its components, generally known among or readily accessible to persons within the circles that normally deal with the kind of information in question ; ( b ) has commercial value because it is secret ; and ( c ) has been subject to reasonable steps under the circumstances, by the person lawfully in control of the information, to keep it secret. for purposes of illustration, the following may be a provision in a license agreement serving to define know - how : - know - how shall mean technical data, formulas, standards, technical information, specifications, processes, methods, codebooks, raw materials, as well as all information, knowledge, assistance, trade practices and secrets, and improvements thereto, divulged, disclosed, or in any way communicated to the licensee under this agreement, unless such information was, at the time of disclosure, or thereafter becomes part of the general knowledge or literature which is generally available for public use from other lawful sources. the burden of proving that any information disclosed hereunder is not confidential information shall rest on the licensee.


moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems. in mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them. in this context, statements become well - formed formulas of some formal language.


rack ( 1984 and 2013 ), for the case n = 3, the explicit values of the optimal ( unique and zero - symmetric ) 4 interpolation nodes and the explicit value of the minimal lebesgue constant are known. all arbitrary optimal sets of 4 interpolation nodes in when n = 3 have been explicitly determined, in two different but equivalent fashions, by h. - j. rack and r. vajda ( 2015 ). the padua points provide another set of nodes with slow growth ( although not as slow as the chebyshev nodes ) and with the additional property of being a unisolvent point set.


while principles of operation discusses the tlb in general terms, the details are not part of the architecture and vary from model to model. starting with the 3031, 3032, and 3033 processor complexes, ibm offered a feature called dual - address space : 5 - 13 – 5 - 17, dual - address - space control : 5 - 17 – 5 - 20, das authorization mechanisms : 5 - 21 – 5 - 24, pc - number translation ( das ), which allows a program to switch between the translation tables for two address spaces, referred to as primary address space ( cr1 ) and secondary address space ( cr7 ), and to move data between the address spaces subject to protection key. das supports a translation table to convert a 16 - bit address space number ( asn ) to an std, with privileged instructions to load the std into cr1 ( primary ) or cr7 ( secondary ).


10 consecutive 0 bits followed by a 1 bit provide frame synchronization. one frame is sent at the desired sample rate, for a bit rate of 256×48 khz = 12. 288 mbit / s. this is twice the baud rate used by s / pdif ( 3. 072 mbit / s, doubled by biphase coding to 6. 144 mbd ), but still within the specified 15 mbaud capacity of the popular totx147 / torx147 toslink transceivers. user data bit allocations : user bit 0 is designated for timecode transport user bit 1 is designated for midi data transport user bit 2 is designated for s / mux indication ( 96 khz sample rate mode ) user bit 3 is reserved and set to 0the transmission speed of the user bits is equal to the sampling rate ( e. g. 48, 000 bits per second )


in mathematics texts it is customary to denote permutations using lowercase greek letters. commonly, either α { \ displaystyle \ alpha } and β, { \ displaystyle \ beta, } or σ, τ { \ displaystyle \ sigma, \ tau } and π { \ displaystyle \ pi } are used. permutations can be defined as bijections from a set s onto itself. all permutations of a set with n elements form a symmetric group, denoted s n { \ displaystyle s _ { n } }, where the group operation is function composition. thus for two permutations, π { \ displaystyle \ pi } and σ { \ displaystyle \ sigma } in the group s n { \ displaystyle s _ { n } }, the four group axioms hold : closure : if π { \ displaystyle \ pi } and σ { \ displaystyle \ sigma } are in s n { \ displaystyle s _ { n } } then so is π σ.


in the following example, the vector p does not escape into g, so it can be allocated on the stack and then removed from the stack before calling g. if, however, we had then either p would need to be allocated on the heap or ( if g is known to the compiler when f is compiled, and behaves well ) allocated on the stack in such a fashion that it can remain in place when g is called. if continuations are used to implement exception - like control structures, escape analysis can often detect this to avoid having to actually allocate a continuation and copy the call stack into it. for example, in escape analysis will determine that the continuation captured by call / cc doesn't escape, so no continuation structure needs to be allocated, and invoking the continuation by calling continuation can be implemented by unwinding the stack.


in subtyping systems, the bottom type is a subtype of all types. it is dual to the top type, which spans all possible values in a system. if a type system is sound, the bottom type is uninhabited and a term of bottom type represents a logical contradiction. in such systems, typically no distinction is drawn between the bottom type and the empty type, and the terms may be used interchangeably.


in number theory, brun's theorem states that the sum of the reciprocals of the twin primes ( pairs of prime numbers which differ by 2 ) converges to a finite value known as brun's constant, usually denoted by b2 ( sequence a065421 in the oeis ). brun's theorem was proved by viggo brun in 1919, and it has historical importance in the introduction of sieve methods.


that provides a clear and structured approach to the description of shared data and the coordination and communication between concurrent processes. this method is flexible in its ability to express timing, and can be used in different ways. in addition, path expressions are useful for process synchronization for two reasons : first, the close relationship between stream expressions and regular expressions that simplify the task of writing and reasoning about programs that use this synchronization mechanism.


in the bantu languages, attributive verbs are formed by the addition of the " pre - prefix " ( or " initial vowel " ). for example, in luganda : abasajja batambula " the men walk " ( predicative ) abasajja abatambula " the men who walk " ( attributive ) this is similar to the behaviour of attributive adjectives : abasajja bagagga " the men are rich " ( predicative ) abasajja abagagga " the men who are rich " ( i. e " the rich men " ) ( attributive ) the attributive verb formation is the usual way of forming relatives in luganda when the antecedent is the subject of the subordinate verb, and is sometimes called the " subject relative ". relative pronouns do exist, but they are only used for " object relatives ", i. e. relative clauses where the antecedent is the object of the subordinate verb.


in metadata, a synonym ring or synset, is a group of data elements that are considered semantically equivalent for the purposes of information retrieval. these data elements are frequently found in different metadata registries. although a group of terms can be considered equivalent, metadata registries store the synonyms at a central location called the preferred data element. according to wordnet, a synset or synonym set is defined as a set of one or more synonyms that are interchangeable in some context without changing the truth value of the proposition in which they are embedded.


in mathematics, a schur - convex function, also known as s - convex, isotonic function and order - preserving function is a function f : r d → r { \ displaystyle f : \ mathbb { r } ^ { d } \ rightarrow \ mathbb { r } } that for all x, y ∈ r d { \ displaystyle x, y \ in \ mathbb { r } ^ { d } } such that x { \ displaystyle x } is majorized by y { \ displaystyle y }, one has that f ( x ) ≤ f ( y ) { \ displaystyle f ( x ) \ leq f ( y ) }. named after issai schur, schur - convex functions are used in the study of majorization. every function that is convex and symmetric is also schur - convex. the opposite implication is not true, but all schur - convex functions are symmetric ( under permutations of the arguments ).


in upsr, the data is transmitted in both directions, clock and counter clock wise, at the source adm. at the destination then, both signals are compared and the best one of the two is selected. if a failure occurs then the destination just needs to switch to the unaffected path.


in telecommunication, a basic exchange telecommunications radio service ( betrs ) is a commercial service that can extend telephone service to rural areas by replacing the local loop with radio communications. in the betrs, non - government ultra high frequency ( uhf ) and very high frequency ( vhf ) common carrier and the private radio service frequencies are shared.


convergence is usually non - monotone, that is, neither the objective function nor the residual or gradient magnitude necessarily decrease with each iteration along a successful convergence toward the solution. if f { \ displaystyle f } is a quadratic function with hessian a { \ displaystyle a }, 1 / α l o n g { \ displaystyle 1 / \ alpha ^ { long } } is the rayleigh quotient of a { \ displaystyle a } by vector δ x { \ displaystyle \ delta x }, and 1 / α s h o r t { \ displaystyle 1 / \ alpha ^ { short } } is the rayleigh quotient of a { \ displaystyle a } by vector a δ x { \ displaystyle { \ sqrt { a } } \ delta x } ( here taking a { \ displaystyle { \ sqrt { a } } } as a solution to ( a ) t a = a { \ displaystyle ( { \ sqrt { a } } ) ^ { t } { \ sqrt { a } } = a }, more at definite matrix ). fletcher compared its computational performance to conjugate gradient ( cg ) methods, finding cg tending faster for linear problems, but bb often faster for non - linear problems versus applicable cg - based methods. bb has low storage requirements, suitable for large systems with millions of elements in x { \ displaystyle x }. α s h o r t α l o n g = c o s 2 ( { \ displaystyle { \ frac { \ alpha ^ { short } } { \ alpha ^ { long } } } = cos ^ { 2 } ( } angle between δ x { \ displaystyle \ delta x } and δ g ) { \ displaystyle \ delta g ) }.


the cp decomposition has found some applications in linguistics and chemometrics. the cp rank was introduced by frank lauren hitchcock in 1927 and later rediscovered several times, notably in psychometrics. the cp decomposition is referred to as candecomp, parafac, or candecomp / parafac ( cp ). parafac2 rank decomposition is yet to explore. another popular generalization of the matrix svd known as the higher - order singular value decomposition computes orthonormal mode matrices and has found applications in econometrics, signal processing, computer vision, computer graphics, psychometrics.


{ \ displaystyle \ left ( \ pm a ^ { \ frac { p + 1 } { 4 } } \ right ) ^ { 2 } = a ^ { \ frac { p + 1 } { 2 } } = a \ cdot a ^ { \ frac { p - 1 } { 2 } } \ equiv a \ left ( { \ frac { a } { p } } \ right ) = a { \ bmod { p } }. } this formula only works if it is known in advance that a { \ displaystyle a } is a quadratic residue, which can be checked using the law of quadratic reciprocity. the quadratic reciprocity theorem was conjectured by euler and legendre and first proved by gauss, who referred to it as the " fundamental theorem " in his disquisitiones arithmeticae and his papers, writing the fundamental theorem must certainly be regarded as one of the most elegant of its type.


in numerical mathematics, artificial precision is a source of error that occurs when a numerical value or semantic is expressed with more precision than was initially provided from measurement or user input. for example, a person enters their birthday as the date 1984 - 01 - 01 but it is stored in a database as 1984 - 01 - 01t00 : 00 : 00z which introduces the artificial precision of the hour, minute, and second they were born, and may even affect the date, depending on the user's actual place of birth. this is also an example of false precision, which is artificial precision specifically of numerical quantities or measures.


bob proceeds to generate a string of random bits b ′ { \ displaystyle b'} of the same length as b { \ displaystyle b } and then measures the qubits he has received from alice, obtaining a bit string a ′ { \ displaystyle a'}. at this point, bob announces publicly that he has received alice's transmission. alice then knows she can now safely announce b { \ displaystyle b }, i. e., the bases in which the qubits were prepared.


in practice, we can construct one specific rank factorization as follows : we can compute b { \ textstyle b }, the reduced row echelon form of a { \ textstyle a }. then c { \ textstyle c } is obtained by removing from a { \ textstyle a } all non - pivot columns ( which can be determined by looking for columns in b { \ textstyle b } which do not contain a pivot ), and f { \ textstyle f } is obtained by eliminating any all - zero rows of b { \ textstyle b }. note : for a full - rank square matrix ( i. e. when n = m = r { \ textstyle n = m = r } ), this procedure will yield the trivial result c = a { \ textstyle c = a } and f = b = i n { \ textstyle f = b = i _ { n } } ( the n × n { \ textstyle n \ times n } identity matrix ).


in the unicode standard, a plane is a continuous group of 65, 536 ( 216 ) code points. there are 17 planes, identified by the numbers 0 to 16, which corresponds with the possible values 00 – 1016 of the first two positions in six position hexadecimal format ( u + hhhhhh ). plane 0 is the basic multilingual plane ( bmp ), which contains most commonly used characters.


the network does this by utilising the authentication center and is accomplished without transmitting the key directly. every gsm phone contains a unique identifier ( different from the phone number ), called the international mobile equipment identity ( imei ). this can be found by dialing * # 06 #. when a phone contacts the network, its imei may be checked against the equipment identity register to locate stolen phones and facilitate monitoring.


concretely, in a linear regression where the errors are identically distributed, the variability of residuals of inputs in the middle of the domain will be higher than the variability of residuals at the ends of the domain : linear regressions fit endpoints better than the middle. this is also reflected in the influence functions of various data points on the regression coefficients : endpoints have more influence. thus to compare residuals at different inputs, one needs to adjust the residuals by the expected variability of residuals, which is called studentizing. this is particularly important in the case of detecting outliers, where the case in question is somehow different from the others in a dataset. for example, a large residual may be expected in the middle of the domain, but considered an outlier at the end of the domain.


these are set on objects by the higher - level storage systems that use the osd for persistent storage. for example, attributes might be used to classify objects, or to capture relationships among different objects stored on different osds. a list command returns a list of identifiers for objects within a partition, optionally filtered by matches against their attribute values.


in the following, we have n kinds of items, a 1 { \ displaystyle a _ { 1 } } through a n { \ displaystyle a _ { n } } and m kinds of bins b 1 { \ displaystyle b _ { 1 } } through b m { \ displaystyle b _ { m } }. each bin b i { \ displaystyle b _ { i } } is associated with a budget t i { \ displaystyle t _ { i } }. for a bin b i { \ displaystyle b _ { i } }, each item a j { \ displaystyle a _ { j } } has a profit p i j { \ displaystyle p _ { ij } } and a weight w i j { \ displaystyle w _ { ij } }. a solution is an assignment from items to bins.


opensocial markup language ( osml markup ) is a new set of standardized tags to accomplish common tasks or safely perform normally unsafe operations within templates. osml is extensible. developers can create a library of their own custom tags.


there are two ways to give consent : explicit consent or implied consent. explicit consent is when a patient clearly communicates to a healthcare worker, verbally or in writing or in some other way, that relevant confidential information can be shared. implied consent, means that a patient's consent to share personal confidential information is assumed.


subsequences can contain consecutive elements which were not consecutive in the original sequence. a subsequence which consists of a consecutive run of elements from the original sequence, such as ⟨ b, c, d ⟩, { \ displaystyle \ langle b, c, d \ rangle, } from ⟨ a, b, c, d, e, f ⟩, { \ displaystyle \ langle a, b, c, d, e, f \ rangle, } is a substring. the substring is a refinement of the subsequence. the list of all subsequences for the word " apple " would be " a ", " ap ", " al ", " ae ", " app ", " apl ", " ape ", " ale ", " appl ", " appe ", " aple ", " apple ", " p ", " pp ", " pl ", " pe ", " ppl ", " ppe ", " ple ", " pple ", " l ", " le ", " e ", " " ( empty string ).


in the case of integrating supplemental data source, kg ( knowledge graph ) formally represents the meaning involved in information by describing concepts, relationships between things, and categories of things. these embedded semantics with the data offer significant advantages such as reasoning over data and dealing with heterogeneous data sources. the rules can be applied on kg more efficiently using graph query.


in number theory, the chinese hypothesis is a disproven conjecture stating that an integer n is prime if and only if it satisfies the condition that 2 n − 2 { \ displaystyle 2 ^ { n } - 2 } is divisible by n — in other words, that an integer n is prime if and only if 2 n ≡ 2 mod n { \ displaystyle 2 ^ { n } \ equiv 2 { \ bmod { n } } }. it is true that if n is prime, then 2 n ≡ 2 mod n { \ displaystyle 2 ^ { n } \ equiv 2 { \ bmod { n } } } ( this is a special case of fermat's little theorem ), however the converse ( if 2 n ≡ 2 mod n { \ displaystyle 2 ^ { n } \ equiv 2 { \ bmod { n } } } then n is prime ) is false, and therefore the hypothesis as a whole is false. the smallest counterexample is n = 341 = 11×31. composite numbers n for which 2 n − 2 { \ displaystyle 2 ^ { n } - 2 } is divisible by n are called poulet numbers. they are a special class of fermat pseudoprimes.


now if the domain is a set, the function comprehension principle, also called axiom of unique choice or non - choice, says that a function as a set, with some codomain, exists well. ( and this principle is valid in a theory like c z f { \ displaystyle { \ mathsf { czf } } }. also compare with the replacement axiom. )


in 1912, british engineer arthur pollen developed the first electrically powered mechanical analogue computer ( called at the time the argo clock ). it was used by the imperial russian navy in world war i. the alternative dreyer table fire control system was fitted to british capital ships by mid - 1916. mechanical devices were also used to aid the accuracy of aerial bombing.


in robot motion planning, a pfaffian constraint is a set of k linearly independent constraints linear in velocity, i. e., of the form one source of pfaffian constraints is rolling without slipping in wheeled robots. = = references = =


in mathematics, a relative scalar ( of weight w ) is a scalar - valued function whose transform under a coordinate transform, on an n - dimensional manifold obeys the following equation where that is, the determinant of the jacobian of the transformation. a scalar density refers to the w = 1 { \ displaystyle w = 1 } case. relative scalars are an important special case of the more general concept of a relative tensor.


in 1969 frank deremer invented the lalr and simple lr parsers, both based on the lr parser and having greatly reduced memory requirements at the cost of less language recognition power. the lalr parser was the stronger alternative. these two parsers have since been widely used in compilers of many computer languages. recent research has identified methods by which canonical lr parsers may be implemented with dramatically reduced table requirements over knuth's table - building algorithm.


branching processes can also be used to model other systems with similar dynamics, e. g., the spread of surnames in genealogy or the propagation of neutrons in a nuclear reactor. a central question in the theory of branching processes is the probability of ultimate extinction, where no individuals exist after some finite number of generations. using wald's equation, it can be shown that starting with one individual in generation zero, the expected size of generation n equals μn where μ is the expected number of children of each individual.


in mathematics, a translation plane is a projective plane which admits a certain group of symmetries ( described below ). along with the hughes planes and the figueroa planes, translation planes are among the most well - studied of the known non - desarguesian planes, and the vast majority of known non - desarguesian planes are either translation planes, or can be obtained from a translation plane via successive iterations of dualization and / or derivation. in a projective plane, let p represent a point, and l represent a line. a central collineation with center p and axis l is a collineation fixing every point on l and every line through p. it is called an elation if p is on l, otherwise it is called a homology. the central collineations with center p and axis l form a group.


in mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. for example, currying a function f { \ displaystyle f } that takes three arguments creates a nested unary function g { \ displaystyle g }, so that the code let x = f ( a, b, c ) { \ displaystyle { \ text { let } } x = f ( a, b, c ) } gives x { \ displaystyle x } the same value as the code let h = g ( a ) let i = h ( b ) let x = i ( c ), { \ displaystyle { \ begin { aligned } { \ text { let } } h = g ( a ) \ \ { \ text { let } } i = h ( b ) \ \ { \ text { let } } x = i ( c ), \ end { aligned } } } or called in sequence, let x = g ( a ) ( b ) ( c ). { \ displaystyle { \ text { let } } x = g ( a ) ( b ) ( c ). } in a more mathematical language, a function that takes two arguments, one from x { \ displaystyle x } and one from y { \ displaystyle y }, and produces outputs in z, { \ displaystyle z, } by currying is translated into a function that takes a single argument from x { \ displaystyle x } and produces as outputs functions from y { \ displaystyle y } to z.


in mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function. known generically as extremum, they may be defined either within a given range ( the local or relative extrema ) or on the entire domain ( the global or absolute extrema ) of a function. pierre de fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.


in socio - hydrology, it is often assumed that societies build flood memory after extreme events. flood memory is considered as a primary mechanism explaining the emergence of levee effects. it is hyphosised to be built after flooding and proportional to associated losses. flood memory does decay over time. it is very difficult to observe, so proxy variable such as flood insurance coverage are used.


., k − 1 { \ displaystyle 1, 2,..., k - 1 }, find the best cover that does not violate the budget. call this cover h 1 { \ displaystyle h _ { 1 } }.


in quantum mechanics, different possibilities can cancel. in probability theory with a finite number of states, the probabilities can always be multiplied by a positive number to make their sum equal to one.


in the germanic languages, a strong verb is a verb that marks its past tense by means of changes to the stem vowel. the majority of the remaining verbs form the past tense by means of a dental suffix, and are known as weak verbs. in modern english, strong verbs include sing ( present i sing, past i sang, past participle i have sung ) and drive ( present i drive, past i drove, past participle i have driven ), as opposed to weak verbs such as open ( present i open, past i opened, past participle i have opened ). not all verbs with a change in the stem vowel are strong verbs, however ; they may also be irregular weak verbs such as bring, brought, brought or keep, kept, kept.


next is that the errors in behavior suggest internal plans for what will be done later. also, the time to initiate a movement sequence can increase with the length or complexity of the sequence. the next line is the properties of movements occurring early in a sequence can anticipate later features.


in mathematics, especially in order theory, a maximal element of a subset s of some preordered set is an element of s that is not smaller than any other element in s. a minimal element of a subset s of some preordered set is defined dually as an element of s that is not greater than any other element in s. the notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum. the maximum of a subset s { \ displaystyle s } of a preordered set is an element of s { \ displaystyle s } which is greater than or equal to any other element of s, { \ displaystyle s, } and the minimum of s { \ displaystyle s } is again defined dually. in the particular case of a partially ordered set, while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements. specializing further to totally ordered sets, the notions of maximal element and maximum coincide, and the notions of minimal element and minimum coincide.


in music theory, the scale degree is the position of a particular note on a scale relative to the tonic — the first and main note of the scale from which each octave is assumed to begin. degrees are useful for indicating the size of intervals and chords and whether an interval is major or minor. in the most general sense, the scale degree is the number given to each step of the scale, usually starting with 1 for tonic. defining it like this implies that a tonic is specified.


in mathematics, informally speaking, euclid's orchard is an array of one - dimensional " trees " of unit height planted at the lattice points in one quadrant of a square lattice. more formally, euclid's orchard is the set of line segments from ( x, y, 0 ) to ( x, y, 1 ), where x and y are positive integers. the trees visible from the origin are those at lattice points ( x, y, 0 ), where x and y are coprime, i. e., where the fraction x / y is in reduced form. the name euclid's orchard is derived from the euclidean algorithm.


for this problem : auletta, de prisco, penna and persiano presented a 4 - approximation monotone algorithm, which runs in polytime when the number of machines is fixed. ambrosio and auletta proved that the longest processing time algorithm is monotone whenever the machine speeds are powers of some c ≥ 2, but not when c ≤ 1. 78. in contrast, list scheduling is not monotone for c > 2. andelman, azar and sorani presented a 5 - approximation monotone algorithm, which runs in polytime even when the number of machines is variable. kovacz presented a 3 - approximation monotone algorithm.


in the first and second editions of a dictionary of modern english usage fowler uses the heading false scent to explain writing that causes the reader to second - guess : because the writer knows what is coming ahead, he may forget that his reader does not, and unwittingly " lay false scent " by writing something ambiguous that can only be disambiguated later in the text ( for example " i looked at the man with the telescope, and watched him put the telescope away " ). the reader, once he realises he has been distracted, must go back and rescan the sentence or paragraph to understand the writer's intended meaning. = = references = =


this can be compared with the classical discrete fourier transform, which takes o ( n 2 n ) { \ displaystyle o ( n2 ^ { n } ) } gates ( where n { \ displaystyle n } is the number of bits ), which is exponentially more than o ( n 2 ) { \ displaystyle o ( n ^ { 2 } ) }. the quantum fourier transform acts on a quantum state vector ( a quantum register ), and the classical fourier transform acts on a vector. both types of vectors can be written as lists of complex numbers.


in order for the conditions for atomic broadcast to be satisfied, the participants must effectively " agree " on the order of receipt of the messages. participants recovering from failure, after the other participants have " agreed " an order and started to receive the messages, must be able to learn and comply with the agreed order. such considerations indicate that in systems with crash failures, atomic broadcast and consensus are equivalent problems. a value can be proposed by a process for consensus by atomically broadcasting it, and a process can decide a value by selecting the value of the first message which it atomically receives. thus, consensus can be reduced to atomic broadcast.


in mathematical finite group theory, a group of gf ( 2 ) - type is a group with an involution centralizer whose generalized fitting subgroup is a group of symplectic type ( gorenstein 1982, definition 1. 45 ). as the name suggests, many of the groups of lie type over the field with 2 elements are groups of gf ( 2 ) - type. also 16 of the 26 sporadic groups are of gf ( 2 ) - type, suggesting that in some sense sporadic groups are somehow related to special properties of the field with 2 elements. timmesfeld ( 1978 ) showed roughly that groups of gf ( 2 ) - type can be subdivided into 8 types.


in mathematical optimization, the cutting - plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. such procedures are commonly used to find integer solutions to mixed integer linear programming ( milp ) problems, as well as to solve general, not necessarily differentiable convex optimization problems. the use of cutting planes to solve milp was introduced by ralph e. gomory. cutting plane methods for milp work by solving a non - integer linear program, the linear relaxation of the given integer program.


in probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. if a { \ displaystyle a } is the hypothesis, and b { \ displaystyle b } and c { \ displaystyle c } are observations, conditional independence can be stated as an equality : p ( a b, c ) = p ( a c ) { \ displaystyle p ( a \ mid b, c ) = p ( a \ mid c ) } where p ( a b, c ) { \ displaystyle p ( a \ mid b, c ) } is the probability of a { \ displaystyle a } given both b { \ displaystyle b } and c { \ displaystyle c }. since the probability of a { \ displaystyle a } given c { \ displaystyle c } is the same as the probability of a { \ displaystyle a } given both b { \ displaystyle b } and c { \ displaystyle c }, this equality expresses that b { \ displaystyle b } contributes nothing to the certainty of a { \ displaystyle a }.


in queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation ( sometimes heavy traffic limit theorem or diffusion approximation ) is the matching of a queueing model with a diffusion process under some limiting conditions on the model's parameters. the first such result was published by john kingman who showed that when the utilisation parameter of an m / m / 1 queue is near 1 a scaled version of the queue length process can be accurately approximated by a reflected brownian motion.


in the basic sip specification, only requests and final responses ( i. e. 2xx response codes ) are transmitted reliably, this is, they are retransmitted by the sender until the acknowledge message arrives ( i. e. the corresponding response code to a request, or the ack request corresponding to a 2xx response code ). this mechanism is necessary since sip can run not only over reliable transport protocols ( tcp ) that assure that the message is delivered, but also over unreliable ones ( udp ) that offer no delivery guarantees, and it is even possible that both kinds of protocols are present in different parts of the transport network. however, in such an scenario as the ims framework, it is necessary to extend this reliability to provisional responses to invite requests ( for session establishment, this is, to start a call ). the reliability of provisional responses extension provides a mechanism to confirm that provisional responses such as the 180 ringing response code, that lets the caller know that the callee is being alerted, are successfully received.


two regularization parameters are used in this framework : λ { \ displaystyle \ lambda } for the estimation of c ^ y x π, c ^ x x π = υ d υ t { \ displaystyle { \ widehat { \ mathcal { c } } } _ { yx } ^ { \ pi }, { \ widehat { \ mathcal { c } } } _ { xx } ^ { \ pi } = { \ boldsymbol { \ upsilon } } \ mathbf { d } { \ boldsymbol { \ upsilon } } ^ { t } } and λ ~ { \ displaystyle { \ widetilde { \ lambda } } } for the estimation of the final conditional embedding operator c ^ y x π = c ^ y x π ( ( c ^ x x π ) 2 + λ ~ i ) − 1 c ^ x x π. { \ displaystyle { \ widehat { \ mathcal { c } } } _ { y \ mid x } ^ { \ pi } = { \ widehat { \ mathcal { c } } } _ { yx } ^ { \ pi } \ left ( \ left ( { \ widehat { \ mathcal { c } } } _ { xx } ^ { \ pi } \ right ) ^ { 2 } + { \ widetilde { \ lambda } } \ mathbf { i } \ right ) ^ { - 1 } { \ widehat { \ mathcal { c } } } _ { xx } ^ { \ pi }. } the latter regularization is done on square of c ^ x x π { \ displaystyle { \ widehat { \ mathcal { c } } } _ { xx } ^ { \ pi } } because d { \ displaystyle d } may not be positive definite.


on the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. these functors, and certain variants of them, are essential parts of sheaf theory. due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry.


as an example, the greatest common divisor of 15 and 69 is 3, and 3 can be written as a combination of 15 and 69 as 3 = 15 × ( −9 ) + 69 × 2, with bezout coefficients −9 and 2. many other theorems in elementary number theory, such as euclid's lemma or the chinese remainder theorem, result from bezout's identity. a bezout domain is an integral domain in which bezout's identity holds. in particular, bezout's identity holds in principal ideal domains. every theorem that results from bezout's identity is thus true in all principal ideal domains.


in other words, each quantifier is a family of properties on dom ( a ), so each is called a monadic quantifier. any quantifier defined as an n > 0 - ary relation between properties on dom ( a ) is called monadic. lindstrom introduced polyadic ones that are n > 0 - ary relations between relations on domains of structures.


in mathematics in general, a characterization theorem says that a particular object – a function, a space, etc. – is the only one that possesses properties specified in the theorem. a characterization of a probability distribution accordingly states that it is the only probability distribution that satisfies specified conditions. more precisely, the model of characterization of probability distribution was described by v. m. zolotarev in such manner.


while this allows non - standard interpretations of symbols such as + { \ displaystyle + }, one can restrict their meaning by providing additional axioms. the satisfiability modulo theories problem considers satisfiability of a formula with respect to a formal theory, which is a ( finite or infinite ) set of axioms.


in non - relational systems, hierarchical databases, the distant counterpart of a table is a structured file, representing the rows of a table in each row of the file and each column in a row. this structure implies that a row can have repeating information, generally in the child data segments. data are stored in sequence of physical records.


in the field of retrieval systems, established approaches include : data retrieval systems, such as database management systems, are well suitable for the storage and retrieval of structured data. information retrieval systems, such as web search engines, are very effective in finding the relevant documents or web pages. both approaches require a user to read and analyze often long lists of data sets or documents in order to extract meaning. the goal of knowledge retrieval systems is to reduce the burden of those processes by improved search and representation. this improvement is needed to leverage the increasing data volumes available on the internet.


most such devices include a tiny postage - stamp - sized lcd screen for viewing simplified ladder logic ( only a very small portion of the program being visible at a given time ) and status of i / o points, and typically these screens are accompanied by a 4 - way rocker push - button plus four more separate push - buttons, similar to the key buttons on a vcr remote control, and used to navigate and edit the logic. most have a small plug for connecting via rs - 232 or rs - 485 to a personal computer so that programmers can use simple applications in general - purpose os like ms windows, macos or linux, that have user - friendly ( g ) uis, for programming instead of being forced to use the tiny lcd and push - button set for this purpose. unlike regular plcs that are usually modular and greatly expandable, the plrs are usually not modular or expandable, but their price can be two orders of magnitude less than a plc, and they still offer robust design and deterministic execution of the logic.


in mathematics and geographic information science, a shortest - path graph is an undirected graph defined from a set of points in the euclidean plane. the shortest - path graph is proposed with the idea of inferring edges between a point set such that the shortest path taken over the inferred edges will roughly align with the shortest path taken over the imprecise region represented by the point set. the edge set of the shortest - path graph varies based on a single parameter t ≥ 1. when the weight of an edge is defined as its euclidean length raised to the power of the parameter t ≥ 1, the edge is present in the shortest - path graph if and only if it is the least weight path between its endpoints.


there are also examples for which the minimal number of cells is doubly exponential, showing that every general algorithm for cylindrical algebraic decomposition has a double exponential complexity. cad provides an effective version of quantifier elimination over the reals that has a much better computational complexity than that resulting from the original proof of tarski – seidenberg theorem. it is efficient enough to be implemented on a computer. it is one of the most important algorithms of computational real algebraic geometry. searching to improve collins'algorithm, or to provide algorithms that have a better complexity for subproblems of general interest, is an active field of research.


{ \ displaystyle \ textstyle { \ frac { n! } { k! ( n - k )! } } } whenever k ≤ n { \ displaystyle k \ leq n }, and which is zero when k > n { \ displaystyle k > n }. this formula can be derived from the fact that each k - combination of a set s of n members has k!


in practice, wilson's theorem is useless as a primality test because computing ( n − 1 )! modulo n for large n is computationally complex, and much faster primality tests are known ( indeed, even trial division is considerably more efficient ). used in the other direction, to determine the primality of the successors of large factorials, it is indeed a very fast and effective method. this is of limited utility, however.


in mathematics, and in particular game theory, sion's minimax theorem is a generalization of john von neumann's minimax theorem, named after maurice sion. it states : let x { \ displaystyle x } be a compact convex subset of a linear topological space and y { \ displaystyle y } a convex subset of a linear topological space. if f { \ displaystyle f } is a real - valued function on x × y { \ displaystyle x \ times y } with f ( x, ⋅ ) { \ displaystyle f ( x, \ cdot ) } upper semicontinuous and quasi - concave on y { \ displaystyle y }, x ∈ x { \ displaystyle \ forall x \ in x }, and f ( ⋅, y ) { \ displaystyle f ( \ cdot, y ) } lower semicontinuous and quasi - convex on x { \ displaystyle x }, y ∈ y { \ displaystyle \ forall y \ in y } then, min x ∈ x sup y ∈ y f ( x, y ) = sup y ∈ y min x ∈ x f ( x, y ). { \ displaystyle \ min _ { x \ in x } \ sup _ { y \ in y } f ( x, y ) = \ sup _ { y \ in y } \ min _ { x \ in x } f ( x, y ). }


in set theory, # s is one possible notation for the cardinality or size of the set s, instead of | s | { \ displaystyle | s | }. that is, for a set s = { s 1, s 2, s 3, …, s n } { \ displaystyle s = \ { s _ { 1 }, s _ { 2 }, s _ { 3 }, \ dots, s _ { n } \ } }, in which all s i { \ displaystyle s _ { i } } are mutually distinct, # s = n = | s |. { \ displaystyle \ # s = n = | s |. }


the same argument repeated ( by symmetry of the problem ) is valid when ω { \ displaystyle \ omega } starts with a negative rotation about the z axis, or a rotation about the x axis. this shows that if ω { \ displaystyle \ omega } is given by a non - trivial word in a and b, then ω = e { \ displaystyle \ omega \ neq e }. therefore, the group h is a free group, isomorphic to f2.


in numerical analysis, different decompositions are used to implement efficient matrix algorithms. for instance, when solving a system of linear equations a x = b { \ displaystyle a \ mathbf { x } = \ mathbf { b } }, the matrix a can be decomposed via the lu decomposition. the lu decomposition factorizes a matrix into a lower triangular matrix l and an upper triangular matrix u. the systems l ( u x ) = b { \ displaystyle l ( u \ mathbf { x } ) = \ mathbf { b } } and u x = l − 1 b { \ displaystyle u \ mathbf { x } = l ^ { - 1 } \ mathbf { b } } require fewer additions and multiplications to solve, compared with the original system a x = b { \ displaystyle a \ mathbf { x } = \ mathbf { b } }, though one might require significantly more digits in inexact arithmetic such as floating point. similarly, the qr decomposition expresses a as qr with q an orthogonal matrix and r an upper triangular matrix. the system q ( rx ) = b is solved by rx = qtb = c, and the system rx = c is solved by'back substitution '. the number of additions and multiplications required is about twice that of using the lu solver, but no more digits are required in inexact arithmetic because the qr decomposition is numerically stable.


in the context of network theory a scale - free ideal network is a random network with a degree distribution following the scale - free ideal gas density distribution. these networks are able to reproduce city - size distributions and electoral results by unraveling the size distribution of social groups with information theory on complex networks when a competitive cluster growth process is applied to the network. in models of scale - free ideal networks it is possible to demonstrate that dunbar's number is the cause of the phenomenon known as the'six degrees of separation '.


in mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. in propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.


due to this superposition, measurement of the qubit will " collapse " it into one of its basis states with a given probability. because of the entanglement, measurement of one qubit will " collapse " the other qubit to a state whose measurement will yield one of two possible values, where the value depends on which bell's state the two qubits are in initially. bell's states can be generalized to certain quantum states of multi - qubit systems, such as the ghz state for 3 or more subsystems. understanding of bell's states is useful in analysis of quantum communication, such as superdense coding and quantum teleportation. the no - communication theorem prevents this behavior from transmitting information faster than the speed of light.


in contrast to the steady incremental improvements of the past few decades, the application of deep learning decreased word error rate by 30 %. this innovation was quickly adopted across the field.


in metric graph theory, a convex subgraph of an undirected graph g is a subgraph that includes every shortest path in g between two of its vertices. thus, it is analogous to the definition of a convex set in geometry, a set that contains the line segment between every pair of its points. convex subgraphs play an important role in the theory of partial cubes and median graphs. in particular, in median graphs, the convex subgraphs have the helly property : if a family of convex subgraphs has the property that all pairwise intersections are nonempty, then the whole family has a nonempty intersection.


in principle, a 64 - bit microprocessor can address 16 eib ( 16 × 10246 = 264 = 18, 446, 744, 073, 709, 551, 616 bytes, or about 18. 4 exabytes ) of memory. however, not all instruction sets, and not all processors implementing those instruction sets, support a full 64 - bit virtual or physical address space. the x86 - 64 architecture ( as of 2016 ) allows 48 bits for virtual memory and, for any given processor, up to 52 bits for physical memory. these limits allow memory sizes of 256 tib ( 256 × 10244 bytes ) and 4 pib ( 4 × 10245 bytes ), respectively.


in mathematics, pentation ( or hyper - 5 ) is the next hyperoperation after tetration and before hexation. it is defined as iterated ( repeated ) tetration ( assuming right - associativity ), just as tetration is iterated right - associative exponentiation. it is a binary operation defined with two numbers a and b, where a is tetrated to itself b - 1 times. for instance, using hyperoperation notation for pentation and tetration, 2 3 { \ displaystyle 23 } means tetrating 2 to itself 2 times, or 2 ( 2 2 ) { \ displaystyle 2 ( 22 ) }. this can then be reduced to 2 ( 2 2 ) = 2 4 = 2 2 2 2 = 2 2 4 = 2 16 = 65, 536. { \ displaystyle 2 ( 2 ^ { 2 } ) = 24 = 2 ^ { 2 ^ { 2 ^ { 2 } } } = 2 ^ { 2 ^ { 4 } } = 2 ^ { 16 } = 65, 536. }


in sociology, command hierarchy is seen as the most visible element of a " power network. " in this model, social capital is viewed as being mobilized in response to orders that move through the hierarchy leading to the phrase " command and control ".


later it was demonstrated that all basic mathematical structures either are some kinds of named sets or are built of named sets. according to anellis, burgin & kaloujnine introduced set - theoretical named sets in 1983 and burgin introduced named sets in the most general form in 1990. since then burgin continued to develop this theory in a series of papers and a book. in 2011, zellweger applied the theory of named sets to model data relations in the relational database for an end - user interface.


two sets have the same cardinality if, and only if, there is a one - to - one correspondence ( bijection ) between the elements of the two sets. in the case of finite sets, this agrees with the intuitive notion of number of elements. in the case of infinite sets, the behavior is more complex.


in the area of modern algebra known as group theory, the suzuki groups, denoted by sz ( 22n + 1 ), 2b2 ( 22n + 1 ), suz ( 22n + 1 ), or g ( 22n + 1 ), form an infinite family of groups of lie type found by suzuki ( 1960 ), that are simple for n ≥ 1. these simple groups are the only finite non - abelian ones with orders not divisible by 3.


this eliminates noncredible threats, which are threats that a player would not carry out if they were ever called upon to do so. for example, consider a dynamic game with an incumbent firm and a potential entrant to the industry. the incumbent has a monopoly and wants to maintain its market share.


in nonstandard analysis, a branch of mathematics, overspill ( referred to as overflow by goldblatt ( 1998, p. 129 ) ) is a widely used proof technique. it is based on the fact that the set of standard natural numbers n is not an internal subset of the internal set * n of hypernatural numbers. by applying the induction principle for the standard integers n and the transfer principle we get the principle of internal induction : for any internal subset a of * n, if 1 is an element of a, and for every element n of a, n + 1 also belongs to a, then a = * nif n were an internal set, then instantiating the internal induction principle with n, it would follow n = * n which is known not to be the case.


in this case, the voting circuit can output the correct result, and discard the erroneous version. after this, the internal state of the erroneous replication is assumed to be different from that of the other two, and the voting circuit can switch to a dmr mode. this model can be applied to any larger number of replications.


in statistics, binary data is a statistical data type consisting of categorical data that can take exactly two possible values, such as " a " and " b ", or " heads " and " tails ". it is also called dichotomous data, and an older term is quantal data. the two values are often referred to generically as " success " and " failure ". as a form of categorical data, binary data is nominal data, meaning the values are qualitatively different and cannot be compared numerically.


in network theory, the wiener connector is a means of maximizing efficiency in connecting specified " query vertices " in a network. given a connected, undirected graph and a set of query vertices in a graph, the minimum wiener connector is an induced subgraph that connects the query vertices and minimizes the sum of shortest path distances among all pairs of vertices in the subgraph. in combinatorial optimization, the minimum wiener connector problem is the problem of finding the minimum wiener connector. it can be thought of as a version of the classic steiner tree problem ( one of karp's 21 np - complete problems ), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph. the minimum wiener connector was first presented by ruchansky et al. in 2015. the minimum wiener connector has applications in many domains where there is a graph structure and an interest in learning about connections between sets of individuals.


early scrambling or encryption methods required a hard line for authorization of receive sites. today, a digital cellular telephone is sufficient for most situations. c - band transportable service remains a prevalent source of long - haul transmission because of its immunity to the " rain fade " that ku band experiences in significant rainstorms.


in principle, there can be more than one such code for a given word length, but the term gray code was first applied to a particular binary code for non - negative integers, the binary - reflected gray code, or brgc. bell labs researcher george r. stibitz described such a code in a 1941 patent application, granted in 1943. frank gray introduced the term reflected binary code in his 1947 patent application, remarking that the code had " as yet no recognized name ". he derived the name from the fact that it " may be built up from the conventional binary code by a sort of reflection process ".


in mathematics, a surjective function ( also known as surjection, or onto function ) is a function f such that every element y can be mapped from some element x such that f ( x ) = y. in other words, every element of the function's codomain is the image of at least one element of its domain. it is not required that x be unique ; the function f may map one or more elements of x to the same element of y. the term surjective and the related terms injective and bijective were introduced by nicolas bourbaki, a group of mainly french 20th - century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. the french word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. any function induces a surjection by restricting its codomain to the image of its domain.


.., n } → { 0, 1 } { \ displaystyle f : \ { 0, 1,..., n \ } \ rightarrow \ { 0, 1 \ } }. symmetric boolean functions are used to classify boolean satisfiability problems.


in mathematics, in the areas of group theory and combinatorics, hall words provide a unique monoid factorisation of the free monoid. they are also totally ordered, and thus provide a total order on the monoid. this is analogous to the better - known case of lyndon words ; in fact, the lyndon words are a special case, and almost all properties possessed by lyndon words carry over to hall words. hall words are in one - to - one correspondence with hall trees.


as told by hardy : i remember once going to see him when he was lying ill at putney. i had ridden in taxi - cab no. 1729, and remarked that the number seemed to be rather a dull one, and that i hoped it was not an unfavourable omen. " no, " he replied, " it is a very interesting number ; it is the smallest number expressible as the sum of two cubes in two different ways. "


in physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties ( usually mass, charge, or size ) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system. the concept of a test particle often simplifies problems, and can provide a good approximation for physical phenomena. in addition to its uses in the simplification of the dynamics of a system in particular limits, it is also used as a diagnostic in computer simulations of physical processes.


kernel adaptive filters implement a nonlinear transfer function using kernel methods. in these methods, the signal is mapped to a high - dimensional linear feature space and a nonlinear function is approximated as a sum over kernels, whose domain is the feature space. if this is done in a reproducing kernel hilbert space, a kernel method can be a universal approximator for a nonlinear function.


a semigroup without an identity element can be easily turned into a monoid by just adding an identity element. consequently, monoids are studied in the theory of semigroups rather than in group theory. semigroups should not be confused with quasigroups, which are a generalization of groups in a different direction ; the operation in a quasigroup need not be associative but quasigroups preserve from groups a notion of division.


in mathematics, probabilistic metric spaces are a generalization of metric spaces where the distance no longer takes values in the non - negative real numbers r ≥ 0, but in distribution functions. let d + be the set of all probability distribution functions f such that f ( 0 ) = 0 ( f is a nondecreasing, left continuous mapping from r into such that max ( f ) = 1 ). then given a non - empty set s and a function f : s × s → d + where we denote f ( p, q ) by fp, q for every ( p, q ) ∈ s × s, the ordered pair ( s, f ) is said to be a probabilistic metric space if : for all u and v in s, u = v if and only if fu, v ( x ) = 1 for all x > 0. for all u and v in s, fu, v = fv, u. for all u, v and w in s, fu, v ( x ) = 1 and fv, w ( y ) = 1 ⇒ fu, w ( x + y ) = 1 for x, y > 0.


in modern news, social media has become a major source of amateur reporting. the arab spring is believed to have been aided by citizen journalism that was reported using and disseminated by facebook and twitter. the top 15 most popular social media sites range from 15 million users to 900 million users, and as their user base grows stronger, amateur reporting's base expands as well.


in particular, this problem arises when we attempt to build a so - called rasp, a " universal machine " ( see more at universal turing machine ) that uses its finite - state machine to interpret a " program of instructions " located in its registers – i. e. we are building what is nowadays called a computer with the von neumann architecture. observe that the counter machine's finite state machine must call out a register explicitly ( directly ) by its name / number : inc ( 65, 356 ) calls out register number " 65, 365 " explicitly. if the number of registers exceeds the capability of the finite state machine to address them, then registers outside the bounds will be unreachable. for example, if the finite state machine can only reach 65, 536 = 216 registers then how can it reach the 65, 537th? so how do we address a register beyond the bounds of the finite state machine?


in order to achieve a precise and effective typestate analysis, it is necessary to address the problem of aliasing. aliasing occurs when an object has more than one reference or pointer that points to it. for the analysis to be correct, state changes to a given object must be reflected in all references that point to that object, but in general it is a difficult problem to track all such references. this becomes especially hard if the analysis needs to be modular, that is, applicable to each part of a large program separately without taking the rest of the program into account.


the coordinating committee admitted that they " wrestled with articulating a business case for implementing rda ", nevertheless the report recommended that rda be adopted by the three national libraries, contingent on several improvements being made. the earliest possible date for implementation was given as january 2013, as the consensus emerging from the analysis of the test data showed that while there were discernible benefits to implementing rda, these benefits would not be realized without further changes to current cataloging practices, including developing a successor to the marc format. several other institutions were involved in the rda test. many of these institutions documented their findings in a special issue of cataloging & classification quarterly.


in supervised learning, a random sub - sample of all records is taken and manually classified as either'fraudulent'or'non - fraudulent'( task can be decomposed on more classes to meet algorithm requirements ). relatively rare events such as fraud may need to be over sampled to get a big enough sample size. these manually classified records are then used to train a supervised machine learning algorithm. after building a model using this training data, the algorithm should be able to classify new records as either fraudulent or non - fraudulent.


in the cellular phone industry, mobile phones and their networks sometimes support concatenated short message service ( or concatenated sms ) to overcome the limitation on the number of characters that can be sent in a single sms text message transmission ( which is usually 160 ). using this method, long messages are split into smaller messages by the sending device and recombined at the receiving end. each message is then billed separately.


in set theory, functions are identified with their function graphs. using set builder notation, a collection of pairs may be characterized, f : = { ⟨ x, y ⟩ x ∈ a ∧ ψ ( x, y ) }. { \ displaystyle f : = { \ big \ { } \ langle x, y \ rangle \ mid x \ in a \ land \ psi ( x, y ) { \ big \ } }. } the axiom of replacement in zermelo – fraenkel set theory implies that this is actually a set and a function in the above sense.


this notation has been retained in operating systems that were directly or indirectly derived from cp / m, including dr - dos, ms - dos, os / 2 and windows. on linux systems, the command hexcat produces this classic output format too.


in the fields of databases and transaction processing ( transaction management ), a schedule ( or history ) of a system is an abstract model to describe execution of transactions running in the system. often it is a list of operations ( actions ) ordered by time, performed by a set of transactions that are executed together in the system. if the order in time between certain operations is not determined by the system, then a partial order is used. examples of such operations are requesting a read operation, reading, writing, aborting, committing, requesting a lock, locking, etc. not all transaction operation types should be included in a schedule, and typically only selected operation types ( e. g., data access operations ) are included, as needed to reason about and describe certain phenomena. schedules and schedule properties are fundamental concepts in database concurrency control theory.


in order of increasing strength, i. e., decreasing sets of pairs, three of the possible partial orders on the cartesian product of two partially ordered sets are ( see fig. 4 ) : the lexicographical order : ( a, b ) ≤ ( c, d ) if a < c or ( a = c and b ≤ d ) ; the product order : ( a, b ) ≤ ( c, d ) if a ≤ c and b ≤ d ; the reflexive closure of the direct product of the corresponding strict orders : ( a, b ) ≤ ( c, d ) if ( a < c and b < d ) or ( a = c and b = d ). all three can similarly be defined for the cartesian product of more than two sets. applied to ordered vector spaces over the same field, the result is in each case also an ordered vector space. see also orders on the cartesian product of totally ordered sets.


in mathematics, particularly in functional analysis and topology, closed graph is a property of functions. a function f : x → y between topological spaces has a closed graph if its graph is a closed subset of the product space x × y. a related property is open graph. this property is studied because there are many theorems, known as closed graph theorems, giving conditions under which a function with a closed graph is necessarily continuous. one particularly well - known class of closed graph theorems are the closed graph theorems in functional analysis.


attack - an attempt by a player to win a point by hitting the ball over the net. attack line - in indoor volleyball, a line three metres from the net which marks the limit for where a back - row player may advance to hit a ball from above the net. back - row player - in indoor volleyball, any of three players positioned at the back of the court.


army used in for tactical group messaging in its force battle command brigade and below ( fbcb2 ) system. several other approaches to reliable multicast were being developed at approximately the same time, and in april 1999, the ietf chartered the reliable multicast transport working group ( rmtwg ) to standardize reliable multicast transport. the rmtwg pursued the strategy of developing building blocks and protocol instantiations. this strategy avoided a " one size fits all " protocol, which in turn could accommodate the large number of applications and types of applications that reliable multicast could support. building blocks were defined as “ a set of easily - separable coarse - grained modular components that are common to multiple protocols along with abstract apis that define a building block's access methods and their arguments. ” initial building blocks included negative acknowledgments, forward error correction, a generic signaling mechanism for router assist, and transport protection protocol instantiations were defined as “ specifications that define the necessary gluing logic and minimal additional functionality required to realize a working protocol from one or more building blocks. ” those specifications would also include an abstract api that defined the interface between the protocol implementation and an application. two protocol instantiations were chosen : a nack - based protocol an asynchronous layered coding protocolin july 2005 the nack - based protocol building blocks and protocol instantiation were submitted as “ experimental ” in rfc 3940, and in november 2009 “ nack - oriented reliable multicast ( norm ) transport protocol ” was approved in rfc 5740. the rmtwg was disestablished in september 2013.


in probability and statistics, student's t - distribution ( or simply the t - distribution ) t ν { \ displaystyle t _ { \ nu } } is a continuous probability distribution that generalizes the standard normal distribution. like the latter, it is symmetric around zero and bell - shaped. however, t ν { \ displaystyle t _ { \ nu } } has heavier tails and the amount of probability mass in the tails is controlled by the parameter ν { \ displaystyle \ nu }.