in mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties : a simple base case ( or cases ) — a terminating scenario that does not use recursion to produce an answer a recursive step — a set of rules that reduces all successive cases toward the base case. for example, the following is a recursive definition of a person's ancestor. one's ancestor is either : one's parent ( base case ), or one's parent's ancestor ( recursive step ). the fibonacci sequence is another classic example of recursion : fib ( 0 ) = 0 as base case 1, fib ( 1 ) = 1 as base case 2, for all integers n > 1, fib ( n ) = fib ( n − 1 ) + fib ( n − 2 ). many mathematical axioms are based upon recursive rules. for example, the formal definition of the natural numbers by the peano axioms can be described as : " zero is a natural number, and each natural number has a successor, which is also a natural number. "


in the early 2000s, scholars noted a lack of theory and conceptual frameworks to inform and guide research and teacher preparation in technology integration. the classic definition of pck proposed by shulman included one dynamic and complex relationship between two different knowledge bodies : content knowledge and pedagogical knowledge. shulman defined pck as the blend between content and pedagogy, highlighting the teacher's comprehension of how specific topics are organized, adapted, and represented according to students'diverse interests and capabilities. for five years, mishra & koehler participated in a design experiment whose focus was to understand p - 20 educators ’ professional development of rich technology uses as well as helping them develop their teaching with technology.


in the 1970s and early 1980s, the cost of making a phone call decreased and more business communication was done by phone. as corporations grew and labor rates increased, the ratio of secretaries to employees decreased. the initial solution to the phone communication problem for businesses was the “ message center. ” a message center or “ message desk ” was a centralized, manual answering service inside a company manned by a few people answering everyone's phones.


in planar graphs, the maximum independent set may be approximated to within any approximation ratio c < 1 in polynomial time ; similar polynomial - time approximation schemes exist in any family of graphs closed under taking minors.


in order to fully specify the bayesian network and thus fully represent the joint probability distribution, it is necessary to specify for each node x the probability distribution for x conditional upon x's parents. the distribution of x conditional upon its parents may have any form. it is common to work with discrete or gaussian distributions since that simplifies calculations.


in other parts of the world, similar concepts have been created to define standards for electronic signatures. in switzerland, the digital signing standard zertes has comparable standards that address the conformity and regulation of trust service providers who product digital certificates. in the united states, the nist digital signature standard ( dss ) does not provide a comparable standard for regulating qualified certificates that would address non - repudiation of a signatory's qualified certificate. an amendment to nist dss is currently being discussed that would be more in - line with how eidas and zertes handle trusted services.


in the 17th century, european mathematicians started using infinite numbers and infinite expressions in a systematic fashion. in 1655, john wallis first used the notation ∞ { \ displaystyle \ infty } for such a number in his de sectionibus conicis, and exploited it in area calculations by dividing the region into infinitesimal strips of width on the order of 1 ∞. { \ displaystyle { \ tfrac { 1 } { \ infty } }. }


in the eqp phase of slqp, the search direction d k { \ displaystyle d _ { k } } of the step is obtained by solving the following equality - constrained quadratic program : min d f ( x k ) + ∇ f ( x k ) t d + 1 2 d t ∇ x x 2 l ( x k, λ k, σ k ) d s. t. b a k ( x k ) + ∇ b a k ( x k ) t d = 0 c a k ( x k ) + ∇ c a k ( x k ) t d = 0. { \ displaystyle { \ begin { array } { rl } \ min \ limits _ { d } & f ( x _ { k } ) + \ nabla f ( x _ { k } ) ^ { t } d + { \ tfrac { 1 } { 2 } } d ^ { t } \ nabla _ { xx } ^ { 2 } { \ mathcal { l } } ( x _ { k }, \ lambda _ { k }, \ sigma _ { k } ) d \ \ \ mathrm { s. t. } & b _ { { \ cal { a } } _ { k } } ( x _ { k } ) + \ nabla b _ { { \ cal { a } } _ { k } } ( x _ { k } ) ^ { t } d = 0 \ \ & c _ { { \ cal { a } } _ { k } } ( x _ { k } ) + \ nabla c _ { { \ cal { a } } _ { k } } ( x _ { k } ) ^ { t } d = 0. \ end { array } } } note that the term f ( x k ) { \ displaystyle f ( x _ { k } ) } in the objective functions above may be left out for the minimization problems, since it is constant.


each element of the queue is a pair of symbols ( terminals or previously defined pairs ) that occur consecutively in the sequence. the priority of a pair is given by the number of occurrences of the pair in the remaining sequence. each time a new pair is created, the priority queue is updated.


in symmetric case, what we want is equal bitrate for the two sources : 5 bits each with separate encoder and joint decoder. we still use linear codes for this system, as we used for asymmetric case. the basic idea is similar, but in this case, we need to do coset partition for both sources, while for a pair of received syndromes ( corresponds to one coset ), only one pair of input variables are possible given the correlation between two sources. suppose we have a pair of linear code c 1 { \ displaystyle \ mathbf { c _ { 1 } } } and c 2 { \ displaystyle \ mathbf { c _ { 2 } } } and an encoder - decoder pair based on linear codes which can achieve symmetric coding.


in the case of its application to a disjunction, consider the following claim : " it is false that either of a or b is true ", which is written as : ¬ ( a ∨ b ). { \ displaystyle \ neg ( a \ lor b ). } in that it has been established that neither a nor b is true, then it must follow that both a is not true and b is not true, which may be written directly as : ( ¬ a ) ∧ ( ¬ b ).


selecting the references can be done manually ( φ 1, φ 2, φ 5,...


( see also the a - theory and the b - theory of time. ) chalmers also considers negative facts. for example, a statement like " there do not exist nonphysical angels. " if in fact true, it does not seem that this logically follows from any of the physical facts by themselves ; but, he argues, it would follow if one added a " that is all " statement at the end of the list of all the physical facts.


in statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. the term " mode " in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. if there is a single mode, the distribution function is called " unimodal ". if it has more modes it is " bimodal " ( 2 ), " trimodal " ( 3 ), etc., or in general, " multimodal ".


in scores for sporting events, in particular tennis and association football, the number 0 has the very specialized names " love " and " nil ". this can cause difficulty for radio and television newsreaders, because the reader must be aware of which name to use, when the score is often written as the digit " 0 " in the script. ( mcleish recommends to readers that they write the number out on the script in words if necessary. ) in cricket, a batsman who is out without scoring is said to have scored " a duck ", but " duck " is not used as a synonym for zero in the same way that " love " or " nil " are : it is always accompanied by the indefinite article and is not usually used in a formal reading of a team's scoresheet.


in nonlinear programming, the constraints are not necessarily linear. nonetheless, many of the same principles apply. to ensure that the global maximum of a non - linear problem can be identified easily, the problem formulation often requires that the functions be convex and have compact lower level sets. this is the significance of the karush – kuhn – tucker conditions.


in the united states, film classification is a voluntary process with the ratings issued by the motion picture association ( mpa ) via the classification and rating administration ( cara ). the system was established in 1968, but the version listed below is the most recent revision, having been in effect since 1990. an unrated film is often informally denoted by " nr " in newspapers and so forth. g ( general audiences ) – all ages admitted.


are : write performance increases linearly with the number of connected devices in the cluster. while the storage cluster is partitioned, all parts remain responsive. there is a risk of conflicting updates.


since the method employs a selector variable ( a factor introduced for each element to permit a counting procedure ) the method is also known as the darwin – fowler method of selector variables. note that a distribution function is not the same as the probability – cf. maxwell – boltzmann distribution, bose – einstein distribution, fermi – dirac distribution. also note that the distribution function f i { \ displaystyle f _ { i } } which is a measure of the fraction of those states which are actually occupied by elements, is given by f i = n i / g i { \ displaystyle f _ { i } = n _ { i } / g _ { i } } or n i = f i g i { \ displaystyle n _ { i } = f _ { i } g _ { i } }, where g i { \ displaystyle g _ { i } } is the degeneracy of energy level i { \ displaystyle i } of energy ε i { \ displaystyle \ varepsilon _ { i } } and n i { \ displaystyle n _ { i } } is the number of elements occupying this level ( e. g. in fermi – dirac statistics 0 or 1 ).


folders can be named just as files can ( except for the root folder, which often does not have a name ). the use of folders makes it easier to organize files in a logical way. when a computer allows the use of folders, each file and folder has not only a name of its own, but also a path, which identifies the folder or folders in which a file or folder resides.


in the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition : semimodular law a ∧ b < : a implies b < : a ∨ b. the notation a < : b means that b covers a, i. e. a < b and there is no element c such that a < c < b. an atomistic semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to ( simple ) matroids. an atomistic semimodular bounded lattice of finite length is called a geometric lattice and corresponds to a matroid of finite rank. semimodular lattices are also known as upper semimodular lattices ; the dual notion is that of a lower semimodular lattice. a finite lattice is modular if and only if it is both upper and lower semimodular. a finite lattice, or more generally a lattice satisfying the ascending chain condition or the descending chain condition, is semimodular if and only if it is m - symmetric. some authors refer to m - symmetric lattices as semimodular lattices. a semimodular lattice is one kind of algebraic lattice.


all the nodes on average are the same in degree therefore attacking one shouldn't cause anymore damage than attacking another. as the number of attacks go up and more nodes are removed, we observe that s decreases non - linearly and acts as if a threshold exists when a fraction of the nodes ( f ) has been removed, ( f≈. 28 ). at this point, s goes to zero. the average size of the isolated clusters behaves opposite, increasing exponentially to = 2, also approaching the threshold line f≈. 28, except decreases back to 1 after. this model was tested for a large range of nodes and proven to maintain the same pattern.


in telecommunication, effective data transfer rate is the average number of units of data, such as bits, characters, blocks, or frames, transferred per unit time from a source and accepted as valid by a sink. note : the effective data transfer rate is usually expressed in bits, characters, blocks, or frames per second. the effective data transfer rate may be averaged over a period of seconds, minutes, or hours.


the amount of parallelism that can be extracted in superscalar designs is limited by the number of instructions that the scheduler can examine for interdependencies. examining a greater number of instructions can improve the chance of finding an instruction that can be run in parallel, but only at the cost of increasing the complexity of the scheduler itself. despite massive efforts, cpu designs using classic risc or cisc isa's have plateaued at about three or four functional units.


the anode is specially designed to dissipate the heat and wear resulting from this intense focused barrage of electrons. the anode is precisely angled at 1 - 20 degrees off perpendicular to the electron current so as to allow the escape of some of the x - ray photons which are emitted perpendicular to the direction of the electron current. the anode is usually made out of tungsten or molybdenum. the tube has a window designed for escape of the generated x - ray photons. the power of a coolidge tube usually ranges from 0. 1 to 18 kw.


idle wait is instead not convenient in case of a kernel critical section for device management, present in monolithic kernels only. a microkernel instead falls on just the first two of the above cases. in a multiprocessor system, most of the conflicts are kernel - level conflicts, due to the access to the kernel level critical sections, and thus the idle wait periods generated by them have a major impact in performance degradation. this idle wait time increases the average number of idle processors and thus decreases scalability and relative efficiency.


in reality, radio propagation changes along with the weather and tropospheric ducting, and occasionally along with other upper - atmospheric phenomena like sunspots and even meteor showers. thus, while a broadcasting authority might fix the range to an area with exact boundaries ( defined as a series of vectors ), this is rarely if ever true. when a broadcast reaches well outside of its intended range due to unusual conditions, dxing is possible. the local terrain can also play a major role in limiting broadcast range.


programmable tools vs. ‘ fixed function ’ tools. some tools can be altered to get varying amounts of data, at varying times. some tools have only a fixed function.


in talent scheduling problem, we can prove that is np - hard by a reduction from the optimal linear arrangement ( ola ) problem. and in this problem, even we restrict each actor is needed for just two days and all actors'salaries are 1, it's still polynomially reducible to the ola problem. thus, this problem is unlikely to have pseudo - polynomial algorithm.


the radiographer ( also known as a radiologic technologist ) is usually responsible for acquiring medical images of diagnostic quality ; although other professionals may train in this area, notably some radiological interventions performed by radiologists are done so without a radiographer. as a field of scientific investigation, medical imaging constitutes a sub - discipline of biomedical engineering, medical physics or medicine depending on the context : research and development in the area of instrumentation, image acquisition ( e. g., radiography ), modeling and quantification are usually the preserve of biomedical engineering, medical physics, and computer science ; research into the application and interpretation of medical images is usually the preserve of radiology and the medical sub - discipline relevant to medical condition or area of medical science ( neuroscience, cardiology, psychiatry, psychology, etc. ) under investigation. many of the techniques developed for medical imaging also have scientific and industrial applications.


the physical addresses are 32 - bit on the 386, but can be larger on newer processors which support physical address extension. the 80386 also introduced two new general - purpose data segment registers, fs and gs, to the original set of four segment registers ( cs, ds, es, and ss ). a 386 cpu can be put back into real mode by clearing a bit in the cr0 control register, however this is a privileged operation in order to enforce security and robustness. by way of comparison, a 286 could only be returned to real mode by forcing a processor reset, e. g. by a triple fault or using external hardware.


in the united kingdom, the financial conduct authority functions as the national competent authority for the regulation of financial markets ; the definition in its handbook of the term " security " applies only to equities, debentures, alternative debentures, government and public securities, warrants, certificates representing certain securities, units, stakeholder pension schemes, personal pension schemes, rights to or interests in investments, and anything that may be admitted to the official list. in the united states, a " security " is a tradable financial asset of any kind. securities can be broadly categorized into : debt securities ( e. g., banknotes, bonds, and debentures ) equity securities ( e. g., common stocks ) derivatives ( e. g., forwards, futures, options, and swaps ). the company or other entity issuing the security is called the issuer.


developing enough shared vocabulary to communicate can often take a while. the same knowledge can be included in different domain knowledge. knowledge which may be applicable across a number of domains is called domain - independent knowledge, for example logics and mathematics. operations on domain knowledge are performed by meta - knowledge.


the high - order byte of the instruction specifies the operation. bits 9 through 15 are the op - code, and bit 8 is the value of the condition code calculation which results in the branch being taken. the low - order byte is a signed word offset relative to the current location of the program counter.


in programming language syntax, spaces are frequently used to explicitly separate tokens. in most languages multiple whitespace characters are treated the same as a single whitespace character ( outside of quoted strings ) ; such languages are called free - form. in a few languages, including haskell, occam, abc, and python, whitespace and indentation are used for syntactical purposes. in the satirical language called whitespace, whitespace characters are the only valid characters for programming, while any other characters are ignored.


in the 1970s, most real - time applications did not use operating systems because the latter were perceived as adding too much overhead. typical computers of the time had barely enough computing power to handle the tasks at hand. moreover, most software of this type was written in assembly language. as a consequence, real - time systems were classic examples of spaghetti code : complex masses of assembly language software using all sorts of machine - dependent tricks to achieve maximum performance.


one of the processor actually controls the exchange, but other is synchronized with the former but does not participate in the exchange control. if a fault is detected by the comparator the processors are decoupled and a check - out program is run independently to find faulty processor. this process runs without disturbing the call processing which is suspended temporarily.


in order to use dantzig – wolfe decomposition, the constraint matrix of the linear program must have a specific form. a set of constraints must be identified as " connecting ", " coupling ", or " complicating " constraints wherein many of the variables contained in the constraints have non - zero coefficients. the remaining constraints need to be grouped into independent submatrices such that if a variable has a non - zero coefficient within one submatrix, it will not have a non - zero coefficient in another submatrix. this description is visualized below : the d matrix represents the coupling constraints and each fi represents the independent submatrices. note that it is possible to run the algorithm when there is only one f submatrix.


in telecommunications, 6b / 8b is a line code that expands 6 - bit codes to 8 - bit symbols for the purposes of maintaining dc - balance in a communications system. the 6b / 8b encoding is a balanced code - - each 8 - bit output symbol contains 4 zero bits and 4 one bits. so the code can, like a parity bit, detect all single - bit errors. the number of 8 - bit patterns with 4 bits set is the binomial coefficient ( 8 4 ) { \ displaystyle { \ tbinom { 8 } { 4 } } } = 70. further excluding the patterns 11110000 and 00001111, this allows 68 coded patterns : 64 data codes, plus 4 additional control codes.


thus it can be expressed as the vector ⟨ x 11, x 22, x 12 ⟩ { \ displaystyle \ langle x _ { 11 }, x _ { 22 }, x _ { 12 } \ rangle }. as another example : the stress tensor ( in matrix notation ) is given as σ =. { \ displaystyle { \ boldsymbol { \ sigma } } = \ left. } in voigt notation it is simplified to a 6 - dimensional vector : σ ~ = ( σ x x, σ y y, σ z z, σ y z, σ x z, σ x y ) ≡ ( σ 1, σ 2, σ 3, σ 4, σ 5, σ 6 ).


in the universal mobile telecommunications system ( umts ) and 3gpp long term evolution ( lte ), user equipment ( ue ) is any device used directly by an end - user to communicate. it can be a hand - held telephone, a laptop computer equipped with a mobile broadband adapter, or any other device. it connects to the base station node b / enodeb as specified in the etsi 125 / 136 - series and 3gpp 25 / 36 - series of specifications. it roughly corresponds to the mobile station ( ms ) in gsm systems. the radio interface between the ue and the node b is called uu.


in software engineering, dependency injection is a programming technique in which an object or function receives other objects or functions that it requires, as opposed to creating them internally. dependency injection aims to separate the concerns of constructing objects and using them, leading to loosely coupled programs. the pattern ensures that an object or function which wants to use a given service should not have to know how to construct those services.


the geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures : values of the human population or interest rates of a financial investment over time. it also applies to benchmarking, where it is particularly useful for computing means of speedup ratios : since the mean of 0. 5x ( half as fast ) and 2x ( twice as fast ) will be 1 ( i. e., no speedup overall ). the geometric mean can be understood in terms of geometry.


similarly, a high - priority task has a high priority because it is more likely to be subject to strict time constraints — it may be providing data to an interactive user, or acting subject to real - time response guarantees. because priority inversion results in the execution of a lower - priority task blocking the high - priority task, it can lead to reduced system responsiveness or even the violation of response time guarantees. a similar problem called deadline interchange can occur within earliest deadline first scheduling ( edf ).


in the alpha architecture, a byte is defined as an 8 - bit datum ( octet ), a word as a 16 - bit datum, a longword as a 32 - bit datum, a quadword as a 64 - bit datum, and an octaword as a 128 - bit datum. the alpha architecture originally defined six data types : quadword ( 64 - bit ) integer longword ( 32 - bit ) integer ieee t - floating - point ( double precision, 64 - bit ) ieee s - floating - point ( single precision, 32 - bit ) to maintain a level of compatibility with the vax, the 32 - bit architecture that preceded the alpha, two other floating - point data types are included : vax g - floating point ( double precision, 64 - bit ) vax f - floating point ( single precision, 32 - bit ) vax h - floating point ( quad precision, 128 - bit ) was not supported, but another 128 - bit floating - point option, x - floating point, is available on alpha, but not vax. h and x have been described as similar, but not identical. software emulation for h - floating is available from dec, as is a source - code level converter named decmigrate.


for instance, the typeface " bauer bodoni " ( sample shown here ) includes fonts " roman " ( or " regular " ), " bold " and " italic " ; each of these exists in a variety of sizes. the term " font " is correctly applied to any one of these alone but may be seen used loosely to refer to the whole typeface. when used in computers, each style is in a separate digital " font file ". in both traditional typesetting and computing, the word " font " refers to the delivery mechanism of the typeface. in traditional typesetting, the font would be made from metal or wood type : to compose a page may require multiple fonts or even multiple typefaces.


perhaps the simplest model of distributed computing is a synchronous system where all nodes operate in a lockstep fashion. this model is commonly known as the local model. during each communication round, all nodes in parallel ( 1 ) receive the latest messages from their neighbours, ( 2 ) perform arbitrary local computation, and ( 3 ) send new messages to their neighbors.


for example, when viewing content on the internet ( the channel ), a web browser ( a communicating party ) would use the http ( the communication protocol ) to request a web page from the server ( another communicating party ), and then render the returned data into its visual form. this is how the request – response messaging pattern operates. alternatively, in computer networking, we have the udp network protocol. it is used with the one - way messaging pattern, where the sending party is not interested whether the message arrives to any receiving party, nor it expects any of the receiving parties to produce an " answering " message.


in probability theory and statistics, the levy distribution, named after paul levy, is a continuous probability distribution for a non - negative random variable. in spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der waals profile. it is a special case of the inverse - gamma distribution. it is a stable distribution.


in most telecommunications organizations, a virtual channel is a method of remapping the program number as used in h. 222 program association tables and program mapping tables to a channel number that can be entered as digits on a receiver's remote control. often, virtual channels are implemented in digital television to help users to go to channels easily and in general to ease the transition from analogue to digital broadcasting. assigning virtual channels is most common in parts of the world where tv stations were colloquially named after the rf channel they were transmitting on ( " channel 6 springfield " ), as was common in north america during the analogue tv era. in other parts of the world, such as europe, virtual channels are rarely used or needed, because tv stations there identify themselves by name, not by rf channel or callsign.


in numerical mathematics, the uzawa iteration is an algorithm for solving saddle point problems. it is named after hirofumi uzawa and was originally introduced in the context of concave programming.


annotea is part of the w3c semantic web efforts. an example implementation of annotea is w3c's amaya editor / browser. the current amaya user interface for annotations is presented in the amaya documentation. other projects consists of plugins for firefox / mozilla or annotatio client which interacts with most browsers per javascript.


in the expressions in this article, is the standard normal probability density function, is the corresponding cumulative distribution function ( where erf is the error function ), and is owen's t function. owen has an extensive list of gaussian - type integrals ; only a subset is given below.


they are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. for instance, a strictly convex function on an open set has no more than one minimum. even in infinite - dimensional spaces, under suitable additional hypotheses, convex functions continue to satisfy such properties and as a result, they are the most well - understood functionals in the calculus of variations. in probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. this result, known as jensen's inequality, can be used to deduce inequalities such as the arithmetic – geometric mean inequality and holder's inequality.


the definition of theorems as sentences of a formal language is useful within proof theory, which is a branch of mathematics that studies the structure of formal proofs and the structure of provable formulas. it is also important in model theory, which is concerned with the relationship between formal theories and structures that are able to provide a semantics for them through interpretation. although theorems may be uninterpreted sentences, in practice mathematicians are more interested in the meanings of the sentences, i. e. in the propositions they express.


in mathematics and computer science, the probabilistic automaton ( pa ) is a generalization of the nondeterministic finite automaton ; it includes the probability of a given transition into the transition function, turning it into a transition matrix. thus, the probabilistic automaton also generalizes the concepts of a markov chain and of a subshift of finite type. the languages recognized by probabilistic automata are called stochastic languages ; these include the regular languages as a subset.


in modular programming, modularity refers to the compartmentalization and interrelation of the parts of a software package. in software design, modularity refers to a logical partitioning of the " software design " that allows complex software to be manageable for the purpose of implementation and maintenance. the logic of partitioning may be based on related functions, implementation considerations, data links, or other criteria. in self - reconfiguring modular robotics, modularity refers to the ability of the robotic system to automatically achieve different morphologies to execute the task at hand.


the limit of 17 planes is due to utf - 16, which can encode 220 code points ( 16 planes ) as pairs of words, plus the bmp as a single word. utf - 8 was designed with a much larger limit of 231 ( 2, 147, 483, 648 ) code points ( 32, 768 planes ), and would still be able to encode 221 ( 2, 097, 152 ) code points ( 32 planes ) even under the current limit of 4 bytes. the 17 planes can accommodate 1, 114, 112 code points. of these, 2, 048 are surrogates ( used to make the pairs in utf - 16 ), 66 are non - characters, and 137, 468 are reserved for private use, leaving 974, 530 for public assignment.


after receiving alice's qubit, operating on the pair and measuring both, bob obtains two classical bits of information. it is worth stressing that if alice and bob do not pre - share entanglement, then the superdense protocol is impossible, as this would violate holevo's theorem. superdense coding is the underlying principle of secure quantum secret coding. the necessity of having both qubits to decode the information being sent eliminates the risk of eavesdroppers intercepting messages.


a black box algorithm is one which uses only these oracles. hence, straight - line programs for black box groups are black box algorithms. explicit straight - line programs are given for a wealth of finite simple groups in the online atlas of finite groups.


in recent years, however, confusion of the term " dollar cost averaging " with what vanguard call a systematic implementation plan has arisen. the term " dollar cost averaging " is used to describe a delayed and staged investment strategy used in the situation where the investor has a windfall gain such as an insurance payout or inheritance, as opposed to the immediate investment of the entire sum. the delayed, staged strategy seems preferable for the investor who is concerned with avoiding timing risk ( the risk of missing out in beneficial movements in price due to an error in market timing ) then instead of investing the entire sum immediately, or waiting for the ( mythical ) ideal time to invest the entire sum, the investor spreads their investment of the windfall sum into the market over time in a staged way, which appears similar to dollar cost averaging. this behaviour is driven by the fear that volatility in the market could cause a significant drop in the value of the investment immediately after the investment is made.


functional programming languages often allow the subtyping of records. consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in which a useful notion of subtyping may be defined and studied. because the resulting calculus allows terms to have more than one type, it is no longer a " simple " type theory.


in probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed ; every one of n values has equal probability 1 / n. another way of saying " discrete uniform distribution " would be " a known, finite number of outcomes equally likely to happen ". a simple example of the discrete uniform distribution is throwing a fair die. the possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1 / 6.


substituting into the first equation relating p ( s 1 ), p ( s 2 ) { \ displaystyle p ( s _ { 1 } ), \ ; p ( s _ { 2 } ) } : p ( s 1 ) p ( s 2 ) = e − e ( s 1 ) / k t e − e ( s 2 ) / k t, { \ displaystyle { \ frac { p ( s _ { 1 } ) } { p ( s _ { 2 } ) } } = { \ frac { e ^ { - e ( s _ { 1 } ) / kt } } { e ^ { - e ( s _ { 2 } ) / kt } } }, } which implies, for any state s of the system p ( s ) = 1 z e − e ( s ) / k t, { \ displaystyle p ( s ) = { \ frac { 1 } { z } } e ^ { - e ( s ) / kt }, } where z is an appropriately chosen " constant " to make total probability 1. ( z is constant provided that the temperature t is invariant. ) z = s e − e ( s ) / k t, { \ displaystyle z = \ sum _ { s } e ^ { - e ( s ) / kt }, } where the index s runs through all microstates of the system.


in order to get more stable results and use all valuable data for training, a data set can be repeatedly split into several training and a validation datasets. this is known as cross - validation. to confirm the model's performance, an additional test data set held out from cross - validation is normally used.


in packed pixel or chunky framebuffer organization, the bits defining each pixel are clustered and stored consecutively. for example, if there are 16 bits per pixel, each pixel is represented in two consecutive ( contiguous ) 8 - bit bytes in the framebuffer. if there are 4 bits per pixel, each framebuffer byte defines two pixels, one in each nibble. the latter example is as opposed to storing a single 4 - bit pixel in a byte, leaving 4 bits of the byte unused.


modularity — the ability to define boundaries around specific domains and problem spaces — is essential for these languages because as stated by tom gruber, " every ontology is a treaty - a social agreement among people with common motive in sharing. " there are always many competing and differing views that make any general - purpose ontology impossible. a general - purpose ontology would have to be applicable in any domain and different areas of knowledge need to be unified. there is a long history of work attempting to build ontologies for a variety of task domains, e. g., an ontology for liquids, the lumped element model widely used in representing electronic circuits ( e. g., ), as well as ontologies for time, belief, and even programming itself.


in mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. the two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. because there are infinitely many prime numbers, there are also infinitely many semiprimes. semiprimes are also called biprimes.


in standard multiple regression, each predictor is multiplied by a number that is called the beta weight, regression weight or weighted regression coefficients ( denoted βw or bw ). the prediction is obtained by adding these products along with a constant. when the weights are chosen to give the best prediction by some criterion, the model referred to as a proper linear model. therefore, multiple regression is a proper linear model. by contrast, unit - weighted regression is called an improper linear model.


all matrices are assumed to have coefficients in the complex numbers. for the equation to make sense, the matrices must have appropriate sizes, for example they could all be square matrices of the same size. but more generally, a and b must be square matrices of sizes n and m respectively, and then x and c both have n rows and m columns.


in some settings it is natural to consider primitive recursive functions that take as inputs tuples that mix numbers with truth values ( that is t for true and f for false ), or that produce truth values as outputs. this can be accomplished by identifying the truth values with numbers in any fixed manner. for example, it is common to identify the truth value t with the number 1 and the truth value f with the number 0. once this identification has been made, the characteristic function of a set a, which always returns 1 or 0, can be viewed as a predicate that tells whether a number is in the set a. such an identification of predicates with numeric functions will be assumed for the remainder of this article.


this is used in order to create input at exactly a specific time, seen as how one can find a particular moment simply by checking every frame at one's leisure. glitch an unintentional feature in a game — usually considered an error.


related to the diatonic modes are the eight church modes or gregorian modes, in which authentic and plagal forms of scales are distinguished by ambitus and tenor or reciting tone. although both diatonic and gregorian modes borrow terminology from ancient greece, the greek tonoi do not otherwise resemble their mediaeval / modern counterparts. in the middle ages the term modus was used to describe both intervals and rhythm.


in the united states, anonymous work is legally defined as " a work on the copies or phonorecords of which no natural person is identified as author. "


in one rearrangement proof, two squares are used whose sides have a measure of a + b { \ displaystyle a + b } and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. in the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. each outer square has an area of ( a + b ) 2 { \ displaystyle ( a + b ) ^ { 2 } } as well as 2 a b + c 2 { \ displaystyle 2ab + c ^ { 2 } }, with 2 a b { \ displaystyle 2ab } representing the total area of the four triangles. within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. these rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom - left corner, and another square of side length b formed in the top - right corner. in this new position, this left side now has a square of area ( a + b ) 2 { \ displaystyle ( a + b ) ^ { 2 } } as well as 2 a b + a 2 + b 2 { \ displaystyle 2ab + a ^ { 2 } + b ^ { 2 } }. since both squares have the area of ( a + b ) 2 { \ displaystyle ( a + b ) ^ { 2 } } it follows that the other measure of the square area also equal each other such that 2 a b + c 2 { \ displaystyle 2ab + c ^ { 2 } } = 2 a b + a 2 + b 2 { \ displaystyle 2ab + a ^ { 2 } + b ^ { 2 } }.


{ \ displaystyle ~ \ operatorname { \ mathbb { p } } \ left ( \ mathbf { x } \ right ) _ { 0 } = n! \, \ prod _ { i = 1 } ^ { k } { \ frac { \ pi _ { i } ^ { x _ { i } } } { x _ { i }! } } ~. } the significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true. using an exact test, this is calculated as p = y : p ( y ) ≤ p ( x ) 0 p ( y ) { \ displaystyle ~ p _ { \ mathcal { } } = \ sum _ { \ mathbf { y } \, : \ ; \ operatorname { \ mathbb { p } } \ left ( \ mathbf { y } \ right ) \, \ leq \, \ operatorname { \ mathbb { p } } \ left ( \ mathbf { x } \ right ) _ { 0 } } \ operatorname { \ mathbb { p } } \ left ( \ mathbf { y } \ right ) ~ } where the sum ranges over all outcomes as likely as, or less likely than, that observed.


in this way, the tester determines whether the particular device under test meets the device specifications. while packaged as a wafer, automatic test equipment ( ate ) can connect to the individual units using a set of microscopic needles. once the chips are sawn apart and packaged, test equipment can connect to the chips using zif sockets ( sometimes called contactors ).


these maximal hypotheses essentially constitute a ( optimistic ) claim that the true concept is defined just by the negative data already observed : thus, if a novel ( never - before - seen ) data point is observed, it should be assumed to be positive. ( i. e., if data has not previously been ruled out, then it's ruled in. ) thus, during learning, the version space ( which itself is a set – possibly infinite – containing all consistent hypotheses ) can be represented by just its lower and upper bounds ( maximally general and maximally specific hypothesis sets ), and learning operations can be performed just on these representative sets. after learning, classification can be performed on unseen examples by testing the hypothesis learned by the algorithm. if the example is consistent with multiple hypotheses, a majority vote rule can be applied.


in mathematics, a filter or order filter is a special subset of a partially ordered set ( poset ), describing " large " or " eventual " elements. filters appear in order and lattice theory, but also topology, whence they originate. the notion dual to a filter is an order ideal. special cases of filters include ultrafilters, which are filters that cannot be enlarged, and describe nonconstructive techniques in mathematical logic.


in older literature on mathematical logic, the period glyph used to indicate how expressions should be bracketed ( see glossary of principia mathematica ).


it was characteristic of logical positivism to consider a scientific theory to be nothing more than a set of sentences, subdivided into the class of theoretical sentences, the class of observational sentences, and the class of mixed sentences. the first class contains terms which refer to theoretical entities, that is to entities not directly observable such as electrons, atoms and molecules ; the second class contains terms which denote quantities or observable entities, and the third class consists of precisely the coordinative definitions which contain both types of terms because they connect the theoretical terms with empirical procedures of measurement or with observable entities. for example, the interpretation of " the geodesic between two points " as correspondent to " the path of a light ray in a vacuum " provides a coordinative definition.


the deterministic behavior is desired and expected in compiling programming languages. in natural language processing, it was thought for a long time that deterministic parsing is impossible due to ambiguity inherent in natural languages ( many sentences have more than one plausible parse ). thus, non - deterministic approaches such as the chart parser had to be applied. however, mitch marcus proposed in 1978 the parsifal parser that was able to deal with ambiguities while still keeping the deterministic behavior.


for example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well - posed in that the solution is highly sensitive to changes in the final data. continuum models must often be discretized in order to obtain a numerical solution. while solutions may be continuous with respect to the initial conditions, they may suffer from numerical instability when solved with finite precision, or with errors in the data.


in plain english, a hierarchy can be thought of as a set in which : no element is superior to itself, and one element, the ( apex or hierarch ), is superior to all of the other elements in the set. the first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects is always transitive. the second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.


in predicate logic, existential instantiation ( also called existential elimination ) is a rule of inference which says that, given a formula of the form ( x ) ( x ) { \ displaystyle ( \ exists x ) \ phi ( x ) }, one may infer ( c ) { \ displaystyle \ phi ( c ) } for a new constant symbol c. the rule has the restrictions that the constant c introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. it is also necessary that every instance of x { \ displaystyle x } which is bound to x { \ displaystyle \ exists x } must be uniformly replaced by c. this is implied by the notation p ( a ) { \ displaystyle p \ left ( { a } \ right ) }, but its explicit statement is often left out of explanations. in one formal notation, the rule may be denoted by x p ( x ) p ( a ) { \ displaystyle \ exists xp \ left ( { x } \ right ) \ implies p \ left ( { a } \ right ) } where a is a new constant symbol that has not appeared in the proof.


in the mixcolumns step, the four bytes of each column of the state are combined using an invertible linear transformation. the mixcolumns function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes. together with shiftrows, mixcolumns provides diffusion in the cipher.


in mathematical optimization and decision theory, a loss function or cost function ( sometimes also called an error function ) is a function that maps an event or values of one or more variables onto a real number intuitively representing some " cost " associated with the event. an optimization problem seeks to minimize a loss function. an objective function is either a loss function or its opposite ( in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc. ), in which case it is to be maximized.


in predicate calculus, a henkin witness for a sentence x φ ( x ) { \ displaystyle \ exists x \, \ varphi ( x ) } in a theory t is a term c such that t proves φ ( c ) ( hinman 2005 : 196 ). the use of such witnesses is a key technique in the proof of godel's completeness theorem presented by leon henkin in 1949.


moreover, it's worth mentioning that if we carry forward the same line of thinking, something fascinating emerges. when we take infinity and divide it by a regular number like 10, the result still holds true : it's infinity. this adds another layer of insight to our mathematical journey, underscoring the depth of what we're uncovering here.


thus the total demand for page file - backed virtual memory must exceed 250 % of the computer's physical memory before the page file will expand. the fragmentation of the page file that occurs when it expands is temporary. as soon as the expanded regions are no longer in use ( at the next reboot, if not sooner ) the additional disk space allocations are freed and the page file is back to its original state.


in fact, a stronger result is true : the number of permutations of length n with major index k and i inversions is the same as the number of permutations of length n with major index i and k inversions, that is, the two statistics are equidistributed. for example, the number of permutations of length 4 with given major index and number of inversions is given in the table below. 0 1 2 3 4 5 6 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 2 0 1 2 1 1 0 0 3 0 1 1 2 1 1 0 4 0 0 1 1 2 1 0 5 0 0 0 1 1 1 0 6 0 0 0 0 0 0 1 { \ displaystyle { \ begin { array } { c | ccccccc } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \ \ \ hline 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \ \ 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \ \ 2 & 0 & 1 & 2 & 1 & 1 & 0 & 0 \ \ 3 & 0 & 1 & 1 & 2 & 1 & 1 & 0 \ \ 4 & 0 & 0 & 1 & 1 & 2 & 1 & 0 \ \ 5 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \ \ 6 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \ end { array } } }


in social psychology, signed graphs have been used to model social situations, with positive edges representing friendships and negative edges enmities between nodes, which represent people. then, for example, a positive 3 - cycle is either three mutual friends, or two friends with a common enemy ; while a negative 3 - cycle is either three mutual enemies, or two enemies who share a mutual friend. according to balance theory, positive cycles are balanced and supposed to be stable social situations, whereas negative cycles are unbalanced and supposed to be unstable. according to the theory, in the case of three mutual enemies, this is because sharing a common enemy is likely to cause two of the enemies to become friends.


in the context of networks, social capital exists where people have an advantage because of their location in a network. contacts in a network provide information, opportunities and perspectives that can be beneficial to the central player in the network. most social structures tend to be characterized by dense clusters of strong connections. information within these clusters tends to be rather homogeneous and redundant.


in social cataloging much like social bookmarking, this software is aimed towards academics. it allows the user to post a citation for an article found on the internet or a website, online database like academic search premier or lexisnexis academic university, a book found in a library catalog and so on. these citations can be organized into predefined categories, or a new category defined by the user through the use of tags. this method allows academics researching or interested in similar areas to connect and share resources.


the wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. the set of all m by n matrices over some field is a metric space with respect to the rank distance d ( a, b ) = r a n k ( b − a ) { \ displaystyle d ( a, b ) = \ mathrm { rank } ( b - a ) }. the helly metric in game theory measures the difference between strategies in a game.


from this definition the following standard definition of a let expression, as used in a functional language may be derived. x ∈ fv ( y ) ( let x : x = y in z ) = z = ( λ x. z ) y { \ displaystyle x \ not \ in \ operatorname { fv } ( y ) \ implies ( \ operatorname { let } x : x = y \ operatorname { in } z ) = z = ( \ lambda x. z ) \ y } for simplicity the marker specifying the existential variable, x : { \ displaystyle x : }, will be omitted from the expression where it is clear from the context. x ∈ fv ( y ) ( let x = y in z ) = z = ( λ x. z ) y { \ displaystyle x \ not \ in \ operatorname { fv } ( y ) \ implies ( \ operatorname { let } x = y \ operatorname { in } z ) = z = ( \ lambda x. z ) \ y }


investigations into home primes make up a minor side issue in number theory. its questions have served as test fields for the implementation of efficient algorithms for factoring composite numbers, but the subject is really one in recreational mathematics. the outstanding computational problem as of 2016 is whether hp ( 49 ) = hp ( 77 ) can be calculated in practice.


line 2 : second matrix - valued set of conditional probabilities. by definition p ( y i | c k ) = j p ( y i | x j ) p ( x j | c k ) = j p ( y i | x j ) p ( x j, c k ) / p ( c k ) = j p ( y i | x j ) p ( c k | x j ) p ( x j ) / p ( c k ) { \ displaystyle { \ begin { aligned } p ( y _ { i } | c _ { k } ) & = \ sum _ { j } p ( y _ { i } | x _ { j } ) p ( x _ { j } | c _ { k } ) \ \ & = \ sum _ { j } p ( y _ { i } | x _ { j } ) p ( x _ { j }, c _ { k } ) { \ big / } p ( c _ { k } ) \ \ & = \ sum _ { j } p ( y _ { i } | x _ { j } ) p ( c _ { k } | x _ { j } ) p ( x _ { j } ) { \ big / } p ( c _ { k } ) \ \ \ end { aligned } } } where the bayes identities p ( a, b ) = p ( a | b ) p ( b ) = p ( b | a ) p ( a ) { \ displaystyle p ( a, b ) = p ( a | b ) p ( b ) = p ( b | a ) p ( a ) \, } are used. line 3 : this line finds the marginal distribution of the clusters c { \ displaystyle c \, } p ( c i ) = j p ( c i, x j ) = j p ( c i | x j ) p ( x j ) { \ displaystyle { \ begin { aligned } p ( c _ { i } ) & = \ sum _ { j } p ( c _ { i }, x _ { j } ) & = \ sum _ { j } p ( c _ { i } | x _ { j } ) p ( x _ { j } ) \ end { aligned } } } this is a standard result.


traditional single - dispatch oo languages make it trivial to add new datatypes but not new functions ; traditional functional languages tend to have the opposite effect, and multiple dispatch, if implemented correctly, allows both. it is desirable for an implementation of multiple dispatch to have the following properties : it is possible to define different " cases " of a multi - method from within different packages without modifying the source of a base package. inclusion of another package in the program should not change the behavior of a given multi - method call, when the call does not use any datatypes defined in the package. conversely, if a datatype is defined in a given package, and a multi - method extension using that type is also defined in the same package, and a value of that type is passed ( through a base type reference or into a generic function ) into another package with no dependency on that package, and then the multi - method is invoked with that value as an argument, the multi - method case defined in the package which includes the type should be employed. to put it another way - - within a given program, the same multi - method invoked with the same set of arguments should resolve to the same implementation, regardless of the location of the call site, and whether or not a given definition is " in scope " or " visible " at the point of the method call.


an examination of the development in artificial intelligence that has followed reveals that the learning machine did take the abstract path suggested by turing as in the case of deep blue, a chess playing computer developed by ibm and one which defeated the world champion garry kasparov ( though, this too is controversial ) and the numerous computer chess games which can outplay most amateurs. as for the second suggestion turing makes, it has been likened by some authors as a call to finding a simulacrum of human cognitive development. and such attempts at finding the underlying algorithms by which children learn of the features of the world around them are only beginning to be made.


in mathematics, the johnson – lindenstrauss lemma is a result named after william b. johnson and joram lindenstrauss concerning low - distortion embeddings of points from high - dimensional into low - dimensional euclidean space. the lemma states that a set of points in a high - dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. the map used for the embedding is at least lipschitz, and can even be taken to be an orthogonal projection. the lemma has applications in compressed sensing, manifold learning, dimensionality reduction, and graph embedding.


in the c, c + +, and d programming languages, a type qualifier is a keyword that is applied to a type, resulting in a qualified type. for example, const int is a qualified type representing a constant integer, while int is the corresponding unqualified type, simply an integer. in d these are known as type constructors, by analogy with constructors in object - oriented programming. type qualifiers are a way of expressing additional information about a value through the type system, and ensuring correctness in the use of the data. type qualifiers are not generally used outside the c / c + + family of languages : many languages have a notation of constants, but express this by the name binding being constant ( a " variable that doesn't vary " ), rather than through the type system ; see alternatives, below.


in some contexts one considers the more general notion of order - indiscernibles, and the term sequence of indiscernibles often refers implicitly to this weaker notion. in our example of binary formulas, to say that the triple ( a, b, c ) of distinct elements is a sequence of indiscernibles implies ( ∨ ) ∧ ( ∨ ). { \ displaystyle ( \ lor ) \ land ( \ lor ) \,. }


this is because models which depend linearly on their unknown parameters are easier to fit than models which are non - linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. linear regression has many practical uses. most applications fall into one of the following two broad categories : if the goal is error reduction in prediction or forecasting, linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables.


the improved coloring with colorsort algorithm takes in consideration the above observation. each vertex is assigned to a color class ck. if k < | qmax | − | q | + 1 the vertex is moved to r ( behind the last vertex in r ).


the fastest 3g - based standard in the umts family is the hspa + standard, which has been commercially available since 2009 and offers 21 mbit / s downstream ( 11 mbit / s upstream ) without mimo, i. e. with only one antenna, and in 2011 accelerated up to 42 mbit / s peak bit rate downstream using either dc - hspa + ( simultaneous use of two 5 mhz umts carriers ) or 2x2 mimo. in theory speeds up to 672 mbit / s are possible, but have not been deployed yet. the fastest 3g - based standard in the cdma2000 family is the ev - do rev. b, which is available since 2010 and offers 15. 67 mbit / s downstream.


in mathematics, a square root of a number x is a number y such that y 2 = x { \ displaystyle y ^ { 2 } = x } ; in other words, a number y whose square ( the result of multiplying the number by itself, or y ⋅ y { \ displaystyle y \ cdot y } ) is x. for example, 4 and −4 are square roots of 16 because 4 2 = ( − 4 ) 2 = 16 { \ displaystyle 4 ^ { 2 } = ( - 4 ) ^ { 2 } = 16 }. every nonnegative real number x has a unique nonnegative square root, called the principal square root or simply the square root ( with a definite article, see below ), which is denoted by x, { \ displaystyle { \ sqrt { x } }, } where the symbol " { \ displaystyle { \ sqrt { ~ ^ { ~ } } } } " is called the radical sign or radix. for example, to express the fact that the principal square root of 9 is 3, we write 9 = 3 { \ displaystyle { \ sqrt { 9 } } = 3 }. the term ( or number ) whose square root is being considered is known as the radicand.


in mathematics, a binary operation is commutative if changing the order of the operands does not change the result. it is a fundamental property of many binary operations, and many mathematical proofs depend on it. most familiar as the name of the property that says something like " 3 + 4 = 4 + 3 " or " 2 × 5 = 5 × 2 ", the property can also be used in more advanced settings. the name is needed because there are operations, such as division and subtraction, that do not have it ( for example, " 3 − 5 = 5 − 3 " ) ; such operations are not commutative, and so are referred to as noncommutative operations.


the above results may be summarized in the following table. each cell represents a subshell, and lists the values of m ℓ { \ displaystyle m _ { \ ell } } available in that subshell. empty cells represent subshells that do not exist.


teamwork offers different perspectives, and each member may have a different way of handling the project. by sharing ideas, teams can produce better quality work than if the project was done by an individual.


such a combination of proteins is also called a light - harvesting complex. although all cells in the green parts of a plant have chloroplasts, the majority of those are found in specially adapted structures called leaves. certain species adapted to conditions of strong sunlight and aridity, such as many euphorbia and cactus species, have their main photosynthetic organs in their stems. the cells in the interior tissues of a leaf, called the mesophyll, can contain between 450, 000 and 800, 000 chloroplasts for every square millimeter of leaf. the surface of the leaf is coated with a water - resistant waxy cuticle that protects the leaf from excessive evaporation of water and decreases the absorption of ultraviolet or blue light to minimize heating. the transparent epidermis layer allows light to pass through to the palisade mesophyll cells where most of the photosynthesis takes place.


in mathematical logic, the scott – curry theorem is a result in lambda calculus stating that if two non - empty sets of lambda terms a and b are closed under beta - convertibility then they are recursively inseparable.


in the 1990s, noam elkies, followed by a. o. l. atkin, devised improvements to schoof's basic algorithm by restricting the set of primes s = { l 1, …, l s } { \ displaystyle s = \ { l _ { 1 }, \ ldots, l _ { s } \ } } considered before to primes of a certain kind. these came to be called elkies primes and atkin primes respectively. a prime l { \ displaystyle l } is called an elkies prime if the characteristic equation : 2 − t + q = 0 { \ displaystyle \ phi ^ { 2 } - t \ phi + q = 0 } splits over f l { \ displaystyle \ mathbb { f } _ { l } }, while an atkin prime is a prime that is not an elkies prime. atkin showed how to combine information obtained from the atkin primes with the information obtained from elkies primes to produce an efficient algorithm, which came to be known as the schoof – elkies – atkin algorithm.


in mathematics — specifically, in riemannian geometry — geodesic convexity is a natural generalization of convexity for sets and functions to riemannian manifolds. it is common to drop the prefix " geodesic " and refer simply to " convexity " of a set or function.


finally, supervenience claims typically involve some modal force, however, the way that modal force is specified depends on which more specific variety of supervenience one decides upon ( see below ). ( 1 ) and ( 2 ) are sometimes called " schemata " because they do not correspond to actual supervenience relations until the sets of properties a and b, the domain of entities to which those properties apply, and a modal force have been specified. for modal forms of supervenience, the modal strength of the relation is usually taken to be a parameter ( that is, the possible worlds appealed to may be physically possible, logically possible, etc. ). also, note that in the early literature properties were not always central, and there remain some who prefer to frame the relation in terms of predicates, facts, or entities instead, for example.


this was the beginning of a new field of mathematics now called analysis. though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable : finding tangent lines to odd curves, and finding areas enclosed by those curves. the methods of calculus reduced these problems mostly to straightforward matters of computation.


in the united states, there are five levels of flooding.


in some cultures of the south pacific, life is believed to leave a person's body when they are sick or asleep, making for multiple " deaths " in the span of one lifetime.


in media where italicization is not possible, alternatives are used as substitutes : in typewritten or handwritten text, underlining is typically used. in plain - text computer files, including e - mail communication, italicised words are often indicated by surrounding them with slashes or other matched delimiters. for example : i was / really / annoyed.


in particular, it must be relatively prime to the order of the group, if the group is finite. if the group is abelian, any powering index works. if the powering index 2 or - 1 works, then the group is abelian. the group of power automorphisms commutes with the group of inner automorphisms when viewed as subgroups of the automorphism group. thus, in particular, power automorphisms that are also inner must arise as conjugations by elements in the second group of the upper central series.


in statistics, mean absolute error ( mae ) is a measure of errors between paired observations expressing the same phenomenon. examples of y versus x include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. mae is calculated as the sum of absolute errors divided by the sample size : it is thus an arithmetic average of the absolute errors | e i | = | y i − x i | { \ displaystyle | e _ { i } | = | y _ { i } - x _ { i } | }, where y i { \ displaystyle y _ { i } } is the prediction and x i { \ displaystyle x _ { i } } the true value.


many x10 protocol charts represent this start code as " 1110 ", but it is important to realize that is in terms of zero crossings, not data bits. immediately after the start code, a 4 - bit house code ( normally represented by the letters a to p on interface units ) appears, and after the house code comes a 5 - bit function code. function codes may specify a unit number code ( 1 – 16 ) or a command code.


finally, eight registers ( g0 through g7 ) are globally visible to all procedure levels. the amd 29000 improved the design by allowing the windows to be of variable size, which helps utilization in the common case where fewer than eight registers are needed for a call. it also separated the registers into a global set of 64, and an additional 128 for the windows.


in the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. the precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method. the field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision : bias is the amount of inaccuracy and variability is the amount of imprecision.


for two groups with general monotone valuations, there always exists a 1 / 2 - democratic envy - free - except - 1 allocation, and it can be found by an efficient algorithm. for three or more groups with binary additive valuations, there always exists a 1 / k - democratic envy - free - except - 1 allocation ; with general monotone valuations, there always exists a 1 / k - democratic envy - free - except - 2 allocation. the factor 1 / k is tight for envy - free - except - c allocation for any constant c. if envy - freeness is relaxed to proportionality or maximin - share, then similar guarantees can be attained using a polynomial - time algorithm. for groups with additive valuations, a variant of round - robin item allocation can be used to find a 1 / 3 - democratic 1 - out - of - best - k allocation.


in the japanese kantenji braille, the standard 8 - dot braille patterns 7, 17, 47, and 147 are the patterns related to braille pattern dots - 3, since the two additional dots of kantenji patterns 03, 37, and 037 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in six - dimensional geometry, a uniform 6 - polytope is a six - dimensional uniform polytope. a uniform polypeton is vertex - transitive, and all facets are uniform 5 - polytopes. the complete set of convex uniform 6 - polytopes has not been determined, but most can be made as wythoff constructions from a small set of symmetry groups. these construction operations are represented by the permutations of rings of the coxeter - dynkin diagrams. each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6 - polytope. the simplest uniform polypeta are regular polytopes : the 6 - simplex { 3, 3, 3, 3, 3 }, the 6 - cube ( hexeract ) { 4, 3, 3, 3, 3 }, and the 6 - orthoplex ( hexacross ) { 3, 3, 3, 3, 4 }.


more precisely, if you start at any node in the network and form the set of all nodes at distance d { \ displaystyle d } or less from that starting node, the set will, with probability tending to 1 as n → ∞, take the form of a tree. in tree - like structures, the number of second neighbors averaged over the whole network, c 2 { \ displaystyle c _ { 2 } }, is : c 2 = ⟨ k 2 ⟩ − ⟨ k ⟩. { \ displaystyle c _ { 2 } = \ langle k ^ { 2 } \ rangle - \ langle k \ rangle. }


in statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample ( termed sample for short ) of individuals from within a statistical population to estimate characteristics of the whole population. statisticians attempt to collect samples that are representative of the population. sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population. each observation measures one or more properties ( such as weight, location, colour or mass ) of independent objects or individuals.


in the context of coding theory, d kl ( p q ) { \ displaystyle d _ { \ text { kl } } ( p \ parallel q ) } can be constructed by measuring the expected number of extra bits required to code samples from p { \ displaystyle p } using a code optimized for q { \ displaystyle q } rather than the code optimized for p { \ displaystyle p }.


in supervised learning, one is given a set of training examples x 1 … x n { \ displaystyle x _ { 1 } \ ldots x _ { n } } with labels y 1 … y n { \ displaystyle y _ { 1 } \ ldots y _ { n } }, and wishes to predict y n + 1 { \ displaystyle y _ { n + 1 } } given x n + 1 { \ displaystyle x _ { n + 1 } }. to do so one forms a hypothesis, f { \ displaystyle f }, such that f ( x n + 1 ) { \ displaystyle f ( x _ { n + 1 } ) } is a " good " approximation of y n + 1 { \ displaystyle y _ { n + 1 } }. a " good " approximation is usually defined with the help of a loss function, ℓ ( y, z ) { \ displaystyle \ ell ( y, z ) }, which characterizes how bad z { \ displaystyle z } is as a prediction of y { \ displaystyle y }.


in statistics, welch's t - test, or unequal variances t - test, is a two - sample location test which is used to test the ( null ) hypothesis that two populations have equal means. it is named for its creator, bernard lewis welch, is an adaptation of student's t - test, and is more reliable when the two samples have unequal variances and possibly unequal sample sizes. these tests are often referred to as " unpaired " or " independent samples " t - tests, as they are typically applied when the statistical units underlying the two samples being compared are non - overlapping. given that welch's t - test has been less popular than student's t - test and may be less familiar to readers, a more informative name is " welch's unequal variances t - test " — or " unequal variances t - test " for brevity.


in robotics, the manipulability ellipsoid is the geometric interpretation of the scaled eigenvectors resulting from the singular value decomposition of the jacobian that describes a robot's motion.


in programming, instrumentation means : profiling : measuring dynamic program behaviors during a training run with a representative input. this is useful for properties of a program that cannot be analyzed statically with sufficient precision, such as alias analysis. inserting timers into functions. logging major events such as crashes.


in mathematics, an integral polytope has an associated ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. the theory of ehrhart polynomials can be seen as a higher - dimensional generalization of pick's theorem in the euclidean plane. these polynomials are named after eugene ehrhart who studied them in the 1960s.


remote call forwarding is also a means for a suburban business to obtain a city - centre local number ( with its full large - city coverage area ) for inbound calls ; while cheaper than a foreign exchange line, this can reduce long - distance telephony costs in markets where local calls are flat - rated but trunk calls are expensive. one alternative to rcf is caller redirect whereby callers simply hear an intercept message notifying them that the number has changed. another alternative is to port the existing number to a voice over ip carrier, which is not tied to a single physical location as the subscriber may be anywhere on broadband internet. however, not all phone numbers can be ported.


for example, on the system / 370 model 158, the keyboard sequence 0 - 7 - x ( zero, seven and x, in that order ) results in an ipl from the device address which was keyed into the input area. the amdahl 470v / 6 and related cpus supported four hexadecimal digits on those cpus which had the optional second channel unit installed, for a total of 32 channels.


a formal language begins with different types of symbols. these types can include variables, operators, function symbols, predicate ( or relation ) symbols, quantifiers, and propositional constants. ( grouping symbols such as delimiters are often added for convenience in using the language, but do not play a logical role. )


in prose writing, twelve, being the last single - syllable numeral, is sometimes taken as the last number to be written as a word, and 13 the first to be written using digits. this is not a binding rule, and in english language tradition, it is sometimes recommended to spell out numbers up to and including either nine, ten or twelve, or even ninety - nine or one hundred. another system spells out all numbers written in one or two words ( sixteen, twenty - seven, fifteen thousand, but 372 or 15, 001 ). in german orthography, there used to be the widely followed ( but unofficial ) rule of spelling out numbers up to twelve ( zwolf ). the duden ( the german standard dictionary ) mentions this rule as outdated.


this random tree has several equivalent definitions and constructions : using sub - trees generated by finitely many leaves, using a brownian excursion, poisson separating a straight line or as a limit of galton - watson trees. intuitively, the brownian tree is a binary tree whose nodes ( or branching points ) are dense in the tree ; which is to say that for any distinct two points of the tree, there will always exist a node between them. it is a fractal object which can be approximated with computers or by physical processes with dendritic structures.


researchers note that a password based protocol with mutual authentication is important because user identities and passwords are still protected, as the messages are only readable to the two parties involved. however, a negative aspect about password - based authentication is that password tables can take up a lot of memory space. one way around using a lot of memory during a password - based authentication scheme is to implement one - time passwords ( otp ), which is a password sent to the user via sms or email. otps are time - sensitive, which means that they will expire after a certain amount of time and that memory does not need to be stored.


this would give a model perplexity of 2190 per sentence. however, it is more common to normalize for sentence length. thus, if the test sample's sentences comprised a total of 1, 000 words, and could be coded using 7. 95 bits per word, one could report a model perplexity of 27. 95 = 247 per word. in other words, the model is as confused on test data as if it had to choose uniformly and independently among 247 possibilities for each word.


in the case of deconvolution of seismic data, the original unknown signal is made of spikes hence is possible to characterize with sparsity constraints or regularizations such as l1 norm / l2 norm norm ratios, suggested by w. c. gray in 1978.


the spectral characteristics of these areas are used to train the remote sensing software using decision rules for classifying the rest of the image. these decision rules such as maximum likelihood classification, parallelopiped classification, and minimum distance classification offer different techniques to classify an image. additional ground truth sites allow the remote sensor to establish an error matrix that validates the accuracy of the classification method used.


the general linear groups pgl ( 2, q ) are imperfect for q an odd prime power. for any group h, the wreath product h wr sym2 of h with the symmetric group on two points is imperfect. in particular, every group can be embedded as a two - step subnormal subgroup of an imperfect group of roughly the same cardinality ( 2 | h | 2 ).


in order to substantiate an athlete's or team's improvements, progress must be monitored. during the monitoring step feedback is provided and the necessary adjustments follow thereafter. it is important to remember this is a feedback loop and operates in a manner that the feedback feeds into adjustments made and vice versa.


due to the nature of our value function ’ s different slopes for gains and losses, our utility is maximized in different ways, depending on how we code the four kinds of transactions x { \ displaystyle x } and y { \ displaystyle y } ( as gains or as losses ) : 1 ) multiple gains : x { \ displaystyle x } and y { \ displaystyle y } are both considered gains. here, we see that v a l u e ( x ) + v a l u e ( y ) > v a l u e ( x + y ) { \ displaystyle value ( x ) + value ( y ) > value ( x + y ) }. thus, we want to segregate multiple gains.


in one sense, drt offers a variation of first - order predicate calculus — its forms are pairs of first - order formulae and the free variables that occur in them. in traditional natural language semantics, only individual sentences are examined, but the context of a dialogue plays a role in meaning as well. for example, anaphoric pronouns such as he and she rely upon previously introduced individual constants in order to have meaning. drt uses variables for every individual constant in order to account for this problem.


in mathematics and computer science, the entscheidungsproblem ( german for'decision problem'; pronounced ) is a challenge posed by david hilbert and wilhelm ackermann in 1928. the problem asks for an algorithm that considers, as input, a statement and answers " yes " or " no " according to whether the statement is universally valid, i. e., valid in every structure satisfying the axioms.


subscribing organisations are expected to provide relevant data to maintain the common data pool. credit reference agencies are bound by the data protection act 2018, which requires that data relating to identifiable individuals must be accurate, relevant, held for a proper purpose and not out - of - date, and gives individuals the legal right to access data held on them. credit agencies are therefore required under law to provide an individual with a copy of their consumer credit report upon request. most agencies also provide online services for ongoing access to reports.


this is one case where they go beyond merely ensuring integrity, and with some reactive security mechanisms, may actually prevent the malicious activity, e. g. by dropping all packets containing the honeytoken at the router. however, such mechanisms have pitfalls because it might cause serious problems if the honeytoken was poorly chosen and appeared in otherwise legitimate network traffic, which was then dropped. the term was first coined by augusto paes de barros in 2003.


the " topics " produced by topic modeling techniques are clusters of similar words. a topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is. topic models are also referred to as probabilistic topic models, which refers to statistical algorithms for discovering the latent semantic structures of an extensive text body.


in mathematics, a cayley graph, also known as a cayley color graph, cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. its definition is suggested by cayley's theorem ( named after arthur cayley ), and uses a specified set of generators for the group. it is a central tool in combinatorial and geometric group theory. the structure and symmetry of cayley graphs makes them particularly good candidates for constructing families of expander graphs.


in mathematics, a closure operator on a set s is a function cl : p ( s ) → p ( s ) { \ displaystyle \ operatorname { cl } : { \ mathcal { p } } ( s ) \ rightarrow { \ mathcal { p } } ( s ) } from the power set of s to itself that satisfies the following conditions for all sets x, y ⊆ s { \ displaystyle x, y \ subseteq s } closure operators are determined by their closed sets, i. e., by the sets of the form cl ( x ), since the closure cl ( x ) of a set x is the smallest closed set containing x. such families of " closed sets " are sometimes called closure systems or " moore families ". a set together with a closure operator on it is sometimes called a closure space. closure operators are also called " hull operators ", which prevents confusion with the " closure operators " studied in topology.


numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. more generally, if p { \ displaystyle p } is a positive definite matrix, then p k = − p ∇ f ( x k ) { \ displaystyle p _ { k } = - p \ nabla f ( x _ { k } ) } is a descent direction at x k { \ displaystyle x _ { k } }. this generality is used in preconditioned gradient descent methods.


in scrum, the term developer or team member refers to anyone who plays a role in the development and support of the product and can include researchers, architects, designers, programmers, etc.


for example, a realizer for the proposition " a implies b " is a computable function that takes a realizer for a, and uses it to compute a realizer for b. realizability models characterize realizers for propositions in terms of their visible behavior, and not in terms of their internal structure. girard shows that for second - order affine linear logic, given a computational system with nontermination and error stops as effects, realizability and focalization give the same meaning to types. ludics was proposed by the logician jean - yves girard.


in the efforts - expended method, the share of effort consumed to date is compared to the total effort expected for the project. for example, the completion percentage may be established on direct work hours, machine hours, or quantities of material.


, which at least chooses a minimum - expected - loss action δ ( x ) { \ displaystyle \ delta ( x ) \! \, } for those x { \ displaystyle x \, \! } for which a finite - expected - loss action does exist. in addition, a generalized bayes rule may be desirable because it must choose a minimum - expected - loss action δ ( x ) { \ displaystyle \ delta ( x ) \, \! }


however, descriptions of the elements of a smart television can be found in public discourse from the beginning of the 1980s, if not earlier, with the introduction of videotex services, particularly teletext information for reception by television sets, leading commentators to consider that televisions and accessories would evolve to encompass a range of related activities. in the words of one commentator : " in the long run, this machine is likely to develop into a multi - purpose receiver, for electronic mail, dealing with the bank, calculations, remote information - and'not the nine o'clock news'or'casablanca'on video. " the mass acceptance of digital television in the mid - late 2000s and early 2010s greatly improved smart tvs.


in modern gaelic, person inflections have almost disappeared, but the negative and interrogative are marked by distinctive forms. in irish, particularly in the south, person inflections are still very common for the ta / bhi series.


a similar system, known as emergency alert, is used in australia to notify the public of impending disasters through both sms and landline phone calls. these messages can be sent based on either the location of the phone or the address to which the handset is registered. in the early 2020s, device manufacturers have begun to integrate satellite messaging connectivity and satellite emergency services into conventional mobile phones for use in remote regions, where there is no reliable terrestrial cellular network.


the purpose of this directive is to prevent the production of waste electronics and also to encourage reuse and recycling of such waste. the directive requires the member states to encourage design and production methods that take into account the future dismantling and recovery of their products. these take - back programs have been adopted in nearly every oecd country. in the united states, most of these policies have been implemented at the state level.


the motive behind the project was to provide the utility of a smartphone in a simplistic and less dynamic delivery. moreover, other projects have focused on building second phones with less functionality, or putting human nature and design above technology. some critics disagree with google's approach to the digital detox phenomenon, however, and instead argue that harmony between technology use and well - being can be achieved. additionally, these critics suggest that the best way to digitally detox is to be mindful of the amount of time that is being spent on a digital device.


in order to prove the hsw coding theorem, we really just need a few basic things from quantum mechanics. first, a quantum state is a unit trace, positive operator known as a density operator. usually, we denote it by ρ { \ displaystyle \ rho }, σ { \ displaystyle \ sigma }, ω { \ displaystyle \ omega }, etc. the simplest model for a quantum channel is known as a classical - quantum channel : the meaning of the above notation is that inputting the classical letter x { \ displaystyle x } at the transmitting end leads to a quantum state ρ x { \ displaystyle \ rho _ { x } } at the receiving end. it is the task of the receiver to perform a measurement to determine the input of the sender.


in mathematics, more precisely in formal language theory, the profinite words are a generalization of the notion of finite words into a complete topological space. this notion allows the use of topology to study languages and finite semigroups. for example, profinite words are used to give an alternative characterization of the algebraic notion of a variety of finite semigroups.


in mathematical statistics, a random variable x is standardized by subtracting its expected value e { \ displaystyle \ operatorname { e } } and dividing the difference by its standard deviation σ ( x ) = var ( x ) : { \ displaystyle \ sigma ( x ) = { \ sqrt { \ operatorname { var } ( x ) } } : } z = x − e σ ( x ) { \ displaystyle z = { x - \ operatorname { e } \ over \ sigma ( x ) } } if the random variable under consideration is the sample mean of a random sample x 1, …, x n { \ displaystyle \ x _ { 1 }, \ dots, x _ { n } } of x : x = 1 n i = 1 n x i { \ displaystyle { \ bar { x } } = { 1 \ over n } \ sum _ { i = 1 } ^ { n } x _ { i } } then the standardized version is z = x − e σ ( x ) / n. { \ displaystyle z = { \ frac { { \ bar { x } } - \ operatorname { e } } { \ sigma ( x ) / { \ sqrt { n } } } }. }


sometimes it is enough to prove negligence, while in other cases a more serious fault is required. thus, anyone who unlawfully interferes, intentionally or through recklessness, with the life, body, health, freedom or property of others is liable to others to repair the resulting damage. on the other hand, less protection is granted in the event of damage to purely intangible interests, nicht - gegenstandliche interessen, that is to say when the victim only suffers purely economic or moral damage.


when the learner knows the conditional probability, then one solution is : c ^ b ( x ) = arg max k ∈ { 1... k } p ( c k | x = x ) { \ displaystyle { \ hat { c } } _ { b } ( x ) = \ arg \ max _ { k \ in \ { 1... k \ } } p ( c _ { k } | x = x ) } this solution is known as the bayes classifier. the corresponding expected prediction error is called the bayes error rate : b e = e x = e x = e x { \ displaystyle be = e _ { x } = e _ { x } = e _ { x } }, where the sum can be omitted in the last step due to considering the counter event. by the definition of the bayes classifier, it maximizes p ( c ^ b ( x ) | x ) { \ displaystyle p ( { \ hat { c } } _ { b } ( x ) | x ) } and, therefore, minimizes the bayes error be. the bayes error is non - zero if the classification labels are not deterministic, i. e., there is a non - zero probability of a given instance belonging to more than one class.. in a regression context with squared error, the bayes error is equal to the noise variance.


in quantum mechanics, the kochen – specker ( ks ) theorem, also known as the bell – kochen – specker theorem, is a " no - go " theorem proved by john s. bell in 1966 and by simon b. kochen and ernst specker in 1967. it places certain constraints on the permissible types of hidden - variable theories, which try to explain the predictions of quantum mechanics in a context - independent way. the version of the theorem proved by kochen and specker also gave an explicit example for this constraint in terms of a finite number of state vectors. the theorem is a complement to bell's theorem ( to be distinguished from the ( bell – ) kochen – specker theorem of this article ).


in number theory, an equidigital number is a natural number in a given number base that has the same number of digits as the number of digits in its prime factorization in the given number base, including exponents but excluding exponents equal to 1. for example, in base 10, 1, 2, 3, 5, 7, and 10 ( 2 × 5 ) are equidigital numbers ( sequence a046758 in the oeis ). all prime numbers are equidigital numbers in any base. a number that is either equidigital or frugal is said to be economical.


some versions of coordinate descent randomly pick a different coordinate direction each iteration. random - restart hill climbing is a meta - algorithm built on top of the hill climbing algorithm. it is also known as shotgun hill climbing.


in social network analysis and mathematical sociology, interpersonal ties are defined as information - carrying connections between people. interpersonal ties, generally, come in three varieties : strong, weak or absent. weak social ties, it is argued, are responsible for the majority of the embeddedness and structure of social networks in society as well as the transmission of information through these networks. specifically, more novel information flows to individuals through weak rather than strong ties.


in political / economic theory, notably socialist, marxist, and many anarchist philosophies, the distinction between private and personal property is an important one. in capitalism private and personal property are considered to be of equal importance and significance without the need for making a distinction. personal property, or possessions, includes " items intended for personal use " ( e. g., one's toothbrush, clothes, and vehicles, and rarely money ). it must be gained in a " fair " manner according to socialist doctrine.


in number theory, bonse's inequality, named after h. bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization. it states that if p1,..., pn, pn + 1 are the smallest n + 1 prime numbers and n ≥ 4, then p n # = p 1 p n > p n + 1 2. { \ displaystyle p _ { n } \ # = p _ { 1 } \ cdots p _ { n } > p _ { n + 1 } ^ { 2 }. } ( the middle product is short - hand for the primorial p n # { \ displaystyle p _ { n } \ # } of pn ) mathematician denis hanson showed an upper bound where n # ≤ 3 n { \ displaystyle n \ # \ leq 3 ^ { n } }.


it is an example of an algorithm, a step - by - step procedure for performing a calculation according to well - defined rules, and is one of the oldest algorithms in common use. it can be used to reduce fractions to their simplest form, and is a part of many other number - theoretic and cryptographic calculations. the euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.


in mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. it is alternately denoted by the symbol o { \ displaystyle o }. some examples of zero matrices are 0 1, 1 =, 0 2, 2 =, 0 2, 3 =, { \ displaystyle 0 _ { 1, 1 } = { \ begin { bmatrix } 0 \ end { bmatrix } }, \ 0 _ { 2, 2 } = { \ begin { bmatrix } 0 & 0 \ \ 0 & 0 \ end { bmatrix } }, \ 0 _ { 2, 3 } = { \ begin { bmatrix } 0 & 0 & 0 \ \ 0 & 0 & 0 \ end { bmatrix } }, \ } the set of m × n matrices with entries in a ring k forms a module k m, n { \ displaystyle k _ { m, n } }. the zero matrix 0 k m, n { \ displaystyle 0 _ { k _ { m, n } } } in k m, n { \ displaystyle k _ { m, n } } is the matrix with all entries equal to 0 k { \ displaystyle 0 _ { k } }, where 0 k { \ displaystyle 0 _ { k } } is the additive identity in k.


in mathematics and statistics, skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well - behaved can be represented as the distribution / law of a pointwise convergent sequence of random variables defined on a common probability space. it is named for the soviet mathematician a. v. skorokhod.


neumann ( 1935 ), g. a. miller ( 1935 ), and j. a. de seguier ( 1904 ).


in either case, the pc would display an error message and halt. some later pc clones used an nmi to conceal the hardware differences from that of a standard pc. on such computers, an nmi would be generated when a program attempted to access incompatible hardware.


in practice, the tests are run once or twice per week during the entire development cycle, using three to five test subjects per round, and with the results delivered within 24 hours to the designers. the number of users actually tested over the course of the project can thus easily reach 50 to 100 people. research shows that user testing conducted by organisations most commonly involves the recruitment of 5 - 10 participants. in the early stage, when users are most likely to immediately encounter problems that stop them in their tracks, almost anyone of normal intelligence can be used as a test subject.


in mathematics, an index set is a set whose members label ( or index ) members of another set. for instance, if the elements of a set a may be indexed or labeled by means of the elements of a set j, then j is an index set. the indexing consists of a surjective function from j onto a, and the indexed collection is typically called an indexed family, often written as { aj } j∈j.


some examples of algorithms used are filterbank, adjacent orientation vector ( aov ) system, and correlation - filter. filterbank requires whole fingerprints and cannot identify just the tips of the finger since it uses both the local and overall structure. the algorithm works by selecting a region of interest and dividing it into sectors.


in mathematics, topology ( from the greek words τοπος,'place, location ', and λογος,'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending ; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. a topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. the deformations that are considered in topology are homeomorphisms and homotopies.


categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. more specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observations of quantitative data grouped within given intervals. often, purely categorical data are summarised in the form of a contingency table.


" surveys in the academic community have shown nlp to be widely discredited among scientists. among the reasons for considering nlp a pseudoscience are that evidence in favor of it is limited to anecdotes and personal testimony, that it is not informed by scientific understanding of neuroscience and linguistics, and that the name " neuro - linguistic programming " uses jargon words to impress readers and obfuscate ideas, whereas nlp itself does not relate any phenomena to neural structures and has nothing in common with linguistics or programming. in fact, in education, nlp has been used as a key example of pseudoscience.