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this also is a known, computed quantity, and it varies by sample and by out - of - sample test space. in the context of gradient descent algorithms, it is common to introduce a factor of 1 / 2 { \ displaystyle 1 / 2 } to the mse for ease of computation after taking the derivative. so a value which is technically half t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. the irrationality of the square root of 2 is one of the oldest proofs of impossibility. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the arithmetical hierarchy and polynomial hierarchy classify the degree to which problems are respectively computable and computable in polynomial time. for instance, the level Ο 0 0 = Ο 0 0 = Ξ΄ 0 0 { \ displaystyle \ sigma _ { 0 } ^ { 0 } = \ pi _ { 0 } ^ { 0 } = \ delta _ { 0 } ^ { 0 } } of the arithmetical hierarchy... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in number theory, the legendre symbol is a multiplicative function with values 1, β1, 0 that is a quadratic character modulo of an odd prime number p : its value at a ( nonzero ) quadratic residue mod p is 1 and at a non - quadratic residue ( non - residue ) is β1. its value at zero is 0. the legendre symbol was introd... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in systems engineering, dependability is a measure of a system's availability, reliability, maintainability, and in some cases, other characteristics such as durability, safety and security. in real - time computing, dependability is the ability to provide services that can be trusted within a time - period. the servic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
prediction : for every state in s ( k ) of the form ( x β Ξ± β’ y Ξ², j ) ( where j is the origin position as above ), add ( y β β’ Ξ³, k ) to s ( k ) for every production in the grammar with y on the left - hand side ( y β Ξ³ ). scanning : if a is the next symbol in the input stream, for every state in s ( k ) of the form (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
when the true working - correlation is known, consistency does not require mcar. huber - white standard errors improve the efficiency of liang zeger gee in the absence of serial autocorrelation but may remove the marginal interpretation. gee estimates the average response over the population ( " population - averaged "... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in radio systems, tdma is usually used alongside frequency - division multiple access ( fdma ) and frequency - division duplex ( fdd ) ; the combination is referred to as fdma / tdma / fdd. this is the case in both gsm and is - 136 for example. exceptions to this include the dect and personal handy - phone system ( phs... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, effective dimension is a modification of hausdorff dimension and other fractal dimensions that places it in a computability theory setting. there are several variations ( various notions of effective dimension ) of which the most common is effective hausdorff dimension. dimension, in mathematics, is a p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in probability theory, an event is said to happen almost surely ( sometimes abbreviated as a. s. ) if it happens with probability 1 ( or lebesgue measure 1 ). in other words, the set of possible exceptions may be non - empty, but it has probability 0. the concept is analogous to the concept of " almost everywhere " in ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
crashes can be easily identified and might indicate potential vulnerabilities ( e. g., denial of service or arbitrary code execution ). however, the absence of a crash does not indicate the absence of a vulnerability. for instance, a program written in c may or may not crash when an input causes a buffer overflow. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds ( spaces without singularities ) may acquire special, singular points by a number of routes. projection is one way, very obvious in visual terms when three - dimensional objects are project... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in order for a game to be in normal form, we are provided with the following data : there is a finite set i of players, each player is denoted by i. each player i has a finite k number of pure strategies s i = { 1, 2, β¦, k }. { \ displaystyle s _ { i } = \ { 1, 2, \ ldots, k \ }. } a pure strategy profile is an associa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the relationship between the two covariant return types is usually one which allows substitution of the one type with the other, following the liskov substitution principle. this usually implies that the return types of the overriding methods will be subtypes of the return type of the overridden method. the above examp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in some cases, the'cake'to be divided has a negative value. for example, it might be piece of lawn that has to be mowed, or a piece of wasteland that has to be cleaned. then, the cake is a'heterogeneous bad'rather than a'heterogeneous good '. some procedures for envy - free cake - cutting can be adapted to work for a b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in a similar fashion, cross - multiplier 2 states that fpc = ( 1 / 2 ) β while cross - multiplier 3 states that fpd = ( 1 / 2 ). returning to the first multiplier, it can now be seen also to be fpq = ( 1 / 2 ), which, after substituting multipliers 2 and 3, resumes its original form. in much of the following, the grand... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, a fermat number, named after pierre de fermat, the first known to have studied them, is a positive integer of the form f n = 2 2 n + 1, { \ displaystyle f _ { n } = 2 ^ { 2 ^ { n } } + 1, } where n is a non - negative integer. the first few fermat numbers are : 3, 5, 17, 257, 65537, 4294967297, 18446744... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
then it checks if p ( r 1, β¦, r m ) = f k ( r 1, β¦, r m ) { \ displaystyle p ( r _ { 1 }, \ dots, r _ { m } ) = f _ { k } ( r _ { 1 }, \ dots, r _ { m } ) } if they are equal then v accepts, otherwise v rejects. this is the end of the protocol description. if Ο is true then v will accept when p follows the protocol. li... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the pem model, there is no direct communication network between the p processors. the processors have to communicate indirectly over the main memory. if multiple processors try to access the same block in main memory concurrently read / write conflicts occur. like in the pram model, three different variations of thi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
he named them after his advisor wolfgang grobner. in 2007, buchberger received the association for computing machinery's paris kanellakis theory and practice award for this work. however, the russian mathematician nikolai gunther had introduced a similar notion in 1913, published in various russian mathematical journal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
since many users do not have unlimited web space, either as a paid service, or through an isp offering, video hosting services are becoming increasingly popular, especially with the explosion in popularity of blogs, internet forums and other interactive pages. the mass market for camera phones and smartphones has incre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the following, the'1'flag bits indicate the beginning of each segment. 1 2 3 4 5 6 input 1 0 0 1 0 1 flag bits 1 3 6 4 9 6 segmented scan + { \ displaystyle { \ begin { array } { | rrrrrr | l | } 1 & 2 & 3 & 4 & 5 & 6 & { \ text { input } } \ \ \ hline 1 & 0 & 0 & 1 & 0 & 1 & { \ text { flag bits } } \ \ \ hline 1 &... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, a square - difference - free set is a set of natural numbers, no two of which differ by a square number. hillel furstenberg and andras sarkozy proved in the late 1970s the furstenberg β sarkozy theorem of additive number theory showing that, in a certain sense, these sets cannot be very large. in the ga... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
a person intercepting an esn / mdn pair could clone the combination onto a different phone and use it in other areas for making calls without paying. cellular phone cloning became possible with off - the - shelf technology in the 1990s. would - be cloners required three key items : a radio receiver, such as the icom pc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in operating systems, feedback vertex sets play a prominent role in the study of deadlock recovery. in the wait - for graph of an operating system, each directed cycle corresponds to a deadlock situation. in order to resolve all deadlocks, some blocked processes have to be aborted. a minimum feedback vertex set in this... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
it is often denoted hom ( v, k ), or, when the field k is understood, v β { \ displaystyle v ^ { * } } ; other notations are also used, such as v β² { \ displaystyle v'}, v # { \ displaystyle v ^ { \ # } } or v β¨. { \ displaystyle v ^ { \ vee }. } when vectors are represented by column vectors ( as is common when a basi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the prolog syntactical convention a symbol starting with an upper case letter is a variable name ; a symbol that starts with a lowercase letter is a function symbol ; the comma is used as the logical and operator. for mathematical notation, x, y, z are used as variables, f, g as function symbols, and a, b as constan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
with the second method, a service provider sends a personalised otac ( e. g. an enciphered token ) to an authenticated email address ; when the user types the otac into the website, the server authenticates the user. a web application can generate a unique personal identification number ( pin ) that the user can input ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
these identifications are routinely done in mathematics. they can be expressed formally in cartesian coordinates as with basis vectors in the tangent spaces defined by here p and q are any two events and the second basis vector identification is referred to as parallel transport. the first identification is the canonic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
.., β β, m i n d β 1 } { \ displaystyle k _ { min } = \ { - \ infty, min _ { 0 }, - \ infty, min _ { 1 },..., - \ infty, min _ { d - 1 } \ } } k m a x = { m a x 0, + β, m a x 1, + β,. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
decimal megabytes were used for disk capacity by the cdc in 1974. the seagate st - 412, one of several types installed in the ibm pc / xt, had a capacity of 10027008 bytes when formatted as 306 Γ 4 tracks and 32 256 - byte sectors per track, which was quoted as " 10 mb ". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the application of the strahler stream order to hydrology, each segment of a stream or river within a river network is treated as a node in a tree, with the next segment downstream as its parent. when two first - order streams come together, they form a second - order stream. when two second - order streams come tog... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in most computer programming, a programmer keeps a program's intended results in mind and painstakingly constructs a program to achieve those results. inferential programming refers to ( still mostly hypothetical ) techniques and technologies enabling the inverse. this would allow describing an intended result to a com... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. it is the formulation of a system of statements ( i. e. axioms ) that relate a number of primitive terms β in order that a consistent body of propositions may be derived deductively from these statement... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, computer science, telecommunication, information theory, and searching theory, error - correcting codes with feedback are error correcting codes designed to work in the presence of feedback from the receiver to the sender. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
owen, new york : marcel dekker, pp. 149 β 193. see also " confusion over measures of evidence ( p's ) versus errors ( a's ) in classical statistical testing, " raymond hubbard and m. j. bayarri, the american statistician, august 2003, vol. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the context of national or homeland security, law enforcement, or social control policy, trusted systems provide conditional prediction about the behavior of people or objects prior to authorizing access to system resources. for example, trusted systems include the use of " security envelopes " in national security ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in non - canonical mode, data are accumulated in a buffer ( which may or may not be the line editing buffer β some implementations having separate " processed input " and " raw input " queues ) and become " available for reading " according to the values of two input control parameters, the c _ cc and c _ cc members of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
common types of topological spaces include euclidean spaces, metric spaces and manifolds. although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. the study of topological spaces in their own right is called point - set topology or general topolo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the united states, many government regulations simply have categories for " off - highway vehicles " which are loosely defined and often result in suvs ( along with pick - up trucks and minivans ) being classified as light trucks. for example, corporate average fuel economy ( cafe ) regulations previously included "... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in several linux operating systems, the software updater program updates installed software and their associated packages with important software updates for security or with recommended patches. it also informs users when updates are available, listing them in alphabetical order for users to choose which updates to in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
it turns out that one can define simple formulas for p and its inverse ( cate & twigg, 1977 ). first : p ( a ) = { m n β 1 if a = m n β 1, n a mod ( m n β 1 ) otherwise, { \ displaystyle p ( a ) = { \ begin { cases } mn - 1 & { \ text { if } } a = mn - 1, \ \ na { \ bmod { ( } } mn - 1 ) & { \ text { otherwise } }, \ e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the active set at x 0 { \ displaystyle x _ { 0 } } is made up of those constraints g i ( x 0 ) { \ displaystyle g _ { i } ( x _ { 0 } ) } that are active at the current point ( nocedal & wright 2006, p. 308 ). the active set is particularly important in optimization theory, as it determines which constraints will influ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
for example, consider the plaintext : crypto is short for cryptography. " crypto " is a repeated string, and the distance between the occurrences is 20 characters. if we line up the plaintext with a 6 - character keyword " abcdef " ( 6 does not divide into 20 ) : abcdefabcdefabcdefabcdefabcdefabc crypto is short for cr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, the support function ha of a non - empty closed convex set a in r n { \ displaystyle \ mathbb { r } ^ { n } } describes the ( signed ) distances of supporting hyperplanes of a from the origin. the support function is a convex function on r n { \ displaystyle \ mathbb { r } ^ { n } }. any non - empty clo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in protected mode a segment cannot be both writable and executable. therefore, when implementing the tiny memory model the code segment register must point to the same physical address and have the same limit as the data segment register. this defeated one of the features of the 80286, which makes sure data segments ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
an ideal network structure has a vine and cluster structure, providing access to many different clusters and structural holes. networks rich in structural holes are a form of social capital in that they offer information benefits. the main player in a network that bridges structural holes is able to access information ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
less common are unilateral contracts, in which one party makes a promise, but the other side does not promise anything. in these cases, those accepting the offer are not required to communicate their acceptance to the offeror. in a reward contract, for example, a person who has lost a dog could promise a reward if the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
more generally the transition rates are given in form of a finite measure c Ξ» ( Ξ·, d ΞΎ ) { \ displaystyle c _ { \ lambda } ( \ eta, d \ xi ) } on s Ξ» { \ displaystyle s ^ { \ lambda } }. the generator l { \ displaystyle l } of an ips has the following form. first, the domain of l { \ displaystyle l } is a subset of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
there are many key distribution schemes in the literature that are designed to maintain an easy and at the same time secure communication among sensor nodes. the most accepted method of key distribution in wsns is key predistribution, where secret keys are placed in sensor nodes before deployment. when the nodes are de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the following example expressed in c, a program has two variables which are adjacent in memory : an 8 - byte - long string buffer, a, and a two - byte big - endian integer, b. initially, a contains nothing but zero bytes, and b contains the number 1979. now, the program attempts to store the null - terminated string... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
woodall's conjecture, an unsolved problem in this area, states that in any directed graph the minimum number of edges in a dicut ( the unweighted minimum closure ) equals the maximum number of disjoint dijoins that can be found in the graph ( a packing of dijoins ). a fractional weighted version of the conjecture, pose... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by stanisΕaw zaremba and david hilbert around 1900. the method relies on methods of functional analysis and topology. as well as being used to p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the fall of 2004, the exam became computerized ; the mat is now solely a computer - based test ( cbt ). out of the 120 questions, only 100 count in the test - taker's score. the remaining 20 questions are experimental. there is no way for test - takers to identify any of the 20 experimental questions on a given test... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in practice, most failures can be traced back to some type of human error, for example in : management decisions ( e. g. in budgeting, timing, and required tasks ) systems engineering : use studies ( load cases ) systems engineering : requirement analysis / setting systems engineering : configuration control assumption... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
this can be used to handle queries in the following fashion : when we look up cell t for some k, we can check if k is in the range { 1,..., m } : if it is not, then t is uninitialized. otherwise, we check v ], and verify that the first component of this pair is equal to k. if it is not, then t is uninitialized ( and ju... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form lim m β β lim n β β a n, m = lim m β β ( lim n β β a n, m ) { \ displaystyle \ lim _ { m \ to \ infty } \ lim _ { n \ to \ infty } a _ { n, m } = \ lim _ { m \ to \ infty } \ left ( \ lim _ { n \ to \ infty } a _ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the definition of the term named entity is therefore not strict and often has to be explained in the context in which it is used. certain hierarchies of named entity types have been proposed in the literature. bbn categories, proposed in 2002, is used for question answering and consists of 29 types and 64 subtypes. sek... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in more recent years, since the development of the top - down methodologies, ia have been used as a basis for the development of a knowledge audit, which itself in - turn contributes to an organisation's knowledge management strategy. once complete, the ia allows examination into where knowledge is produced, where ther... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in psychology and sociology, a trust metric is a measurement or metric of the degree to which one social actor ( an individual or a group ) trusts another social actor. trust metrics may be abstracted in a manner that can be implemented on computers, making them of interest for the study and engineering of virtual comm... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
now, ΞΈ j = h β 1 ( s, z 1 j, β¦, z m j ) { \ displaystyle { \ breve { \ theta } } _ { j } = h ^ { - 1 } ( s, { \ breve { z } } _ { 1 } ^ { j }, \ ldots, { \ breve { z } } _ { m } ^ { j } ) } is a solution of ( 1 ) with the seed { z 1 j, β¦, z m j } { \ displaystyle \ { { \ breve { z } } _ { 1 } ^ { j }, \ ldots, { \ brev... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, in number theory, gauss composition law is a rule, invented by carl friedrich gauss, for performing a binary operation on integral binary quadratic forms ( ibqfs ). gauss presented this rule in his disquisitiones arithmeticae, a textbook on number theory published in 1801, in articles 234 - 244. gauss c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in other words, if a model defines type colour : : = red | blue | green and some operation uses c of type colour, then by applying this tactic each test class will by divided into three new test classes : one in which c equals red, the other in which c equals blue, and the third where c equals green. proper subset of s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
mood can be bound up with tense, aspect, or both, in particular verb forms. hence, certain languages are sometimes analysed as having a single tense β aspect β mood ( tam ) system, without separate manifestation of the three categories. the term tense, then, particularly in less formal contexts, is sometimes used to de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
storable resources remain available unless depleted by usage, and may be replenished by project tasks that produce them. nonstorable resources must be renewed for each time period, even if not used in previous periods. resource scheduling, availability, and optimisation are considered key to successful project manageme... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the case r = 2, the hypergraph becomes a bipartite graph, and the conjecture becomes Ο ( h ) β€ Ξ½ ( h ) { \ displaystyle \ tau ( h ) \ leq \ nu ( h ) }. this is known to be true by konig's theorem. in the case r = 3, the conjecture has been proved by ron aharoni. the proof uses the aharoni - haxell theorem for matchi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, the entropy influence conjecture is a statement about boolean functions originally conjectured by ehud friedgut and gil kalai in 1996. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, and in particular model theory, a prime model is a model that is as simple as possible. specifically, a model p { \ displaystyle p } is prime if it admits an elementary embedding into any model m { \ displaystyle m } to which it is elementarily equivalent ( that is, into any model m { \ displaystyle m }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
euler's sum of powers conjecture ( disproved ) concerns situations in which the sum of n integers, each a kth power of an integer, equals another kth power. the fermat - catalan conjecture asks whether there are an infinitude of examples in which the sum of two coprime integers, each a power of an integer, with the pow... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
instead, the receiving'client'( object or function ) is provided with its dependencies by external code ( an'injector'), which it is not aware of. dependency injection makes implicit dependencies explicit and helps solve the following problems : how can a class be independent from the creation of the objects it depends... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the record size is stored on a file - by - file basis in special entries in the directory table. sequential access methods for ibm's z / os and z / vse mainframe operating systems : basic sequential access method ( bsam ), basic partitioned access method ( bpam ) and queued sequential access method ( qsam ) ; see acces... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic properties are exposed. when all the theorems of a logic formalised in a structural proof theory have analytic proofs, then the proof the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the dual graph of a directed graph, embedded in the plane, is a graph with a vertex for each face of the given graph, and a dual edge between two dual vertices when the corresponding two faces are separated by an edge. each dual edge crosses one of the original graph edges, turned by 90Β° clockwise. for a dicut in the g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n ; i. e., if there exists an integer x such that : x 2 β‘ q ( mod n ). { \ displaystyle x ^ { 2 } \ equiv q { \ pmod { n } }. } otherwise, q is called a quadratic nonresidue modulo n. originally an abstra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in statistical classification, the bayes classifier minimizes the probability of misclassification. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
there is some centralization ( a general assembly ) and some central decision ( over local decision ) : there is no choice of " each room decision " or " each regulars'community decision ". so it is a central decision. the subsidiarity principle can be applied : there is an " embryonic local governance " connecting the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in statistics, the neyman β pearson lemma was introduced by jerzy neyman and egon pearson in a paper in 1933. the neyman - pearson lemma is part of the neyman - pearson theory of statistical testing, which introduced concepts like errors of the second kind, power function, and inductive behavior. the previous fisherian... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in stack - oriented programming languages ( and concatenative ones, most of which are stack based ), point - free methods are commonly used. for example, a procedure to compute the fibonacci numbers might look like the following in postscript : | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in order to effectively implement variables of such types as array structures ( with indexing done by pointer arithmetic ), many languages restrict the indices to integer data types ( or other types that can be interpreted as integers, such as bytes and enumerated types ), and require that all elements have the same da... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. a more general definition includes all positive rational numbers with this property. the sequence of ( integer ) congruent numbers starts with 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in philosophy, ontological maximalism ( or metaontological maximalism ) is a ontological realist position that asserts, " whatever can exist does in some sense exist ". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, a natural number n is a blum integer if n = p Γ q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. that is, p and q must be of the form 4t + 3, for some integer t. integers of this form are referred to as blum primes. this means that the factors of a blum integer are gau... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
georg cantor, the inventor of set theory, showed in 1874 that there is more than one kind of infinity, specifically that the collection of all natural numbers and the collection of all real numbers, while both infinite, are not equinumerous ( see cantor's first uncountability proof ). in his controversial 1878 paper, c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
this recovers both the inclusion of finite sets in sets ( where a cogenerator is the set of two elements ), and also the inclusion of finite - dimensional vector spaces in vector spaces ( where the cogenerator is the ground field ). sipos showed that the algebras over the codensity monad of the inclusion of finite sets... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
a theory consists of some basis statements called axioms, and some deducing rules ( sometimes included in the axioms ). the theorems of the theory are the statements that can be derived from the axioms by using the deducing rules. this formalization led to proof theory, which allows proving general theorems about theor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
here the matrix completion problem does not obey the restricted isometry property ( rip ). for matrices, the rip would assume that the sampling operator obeys ( 1 β Ξ΄ ) β x β f 2 β€ 1 p β p Ο ( x ) β f 2 β€ ( 1 + Ξ΄ ) β x β f 2 { \ displaystyle ( 1 - \ delta ) \ | x \ | _ { f } ^ { 2 } \ leq { \ frac { 1 } { p } } \ | p _... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in the definitions above, the functions t ( x ), Ξ· ( ΞΈ ), and a ( Ξ· ) were arbitrary. however, these functions have important interpretations in the resulting probability distribution. t ( x ) is a sufficient statistic of the distribution. for exponential families, the sufficient statistic is a function of the data tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
as a byproduct of this latter work, she proved sophie germain's theorem, which verified the first case of fermat's last theorem ( namely, the case in which p { \ displaystyle p } does not divide x y z { \ displaystyle xyz } ) for every odd prime exponent less than 270 { \ displaystyle 270 }, and for all primes p { \ di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
it implies a coarse - grained authentication, given that domains appear on the right part of email addresses, after the at sign. fine - grain authentication, at user level, can be achieved by other means, such as pretty good privacy and s / mime. at present, digital identity needs to be managed by each individual. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in probability theory, a member of the ( a, b, 0 ) class of distributions is any distribution of a discrete random variable n whose values are nonnegative integers whose probability mass function satisfies the recurrence formula p k p k β 1 = a + b k, k = 1, 2, 3, β¦ { \ displaystyle { \ frac { p _ { k } } { p _ { k - 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the n - dimensional parallelotope spanned by the rows of an nΓn hadamard matrix has the maximum possible n - dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. equivalently, a hadamard matrix has maximal determinant among matrices with entries of absolute value ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
an alternative way to compute c x { \ displaystyle { \ textbf { c } } _ { x } }, is by using the n β² Γ m { \ displaystyle n'\ times m } " trajectory matrix " d { \ displaystyle { \ textbf { d } } } that is formed by m { \ displaystyle m } lag - shifted copies of x ( t ) { \ displaystyle { \ it { x ( t ) } } }, which ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in technical applications of 3d computer graphics ( cax ) such as computer - aided design and computer - aided manufacturing, surfaces are one way of representing objects. the other ways are wireframe ( lines and curves ) and solids. point clouds are also sometimes used as temporary ways to represent an object, with th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in non - germanic indo - european languages, past marking is typically combined with a distinction between perfective and imperfective aspect, with the former reserved for single completed actions in the past. french for instance, has an imperfect tense form similar to that of german but used only for past habitual or ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
the discovery of deuterium stood, however. urey and washburn attempted to use electrolysis to create pure heavy water. their technique was sound, but they were beaten to it in 1933 by lewis, who had the resources of the university of california at his disposal. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in software architecture, a service mesh is a dedicated infrastructure layer for facilitating service - to - service communications between services or microservices using a proxy. a dedicated communication layer can provide numerous benefits, such as providing observability into communications, providing secure connec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in number theory, the law of quadratic reciprocity, like the pythagorean theorem, has lent itself to an unusually large number of proofs. several hundred proofs of the law of quadratic reciprocity have been published. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, the bauer β fike theorem is a standard result in the perturbation theory of the eigenvalue of a complex - valued diagonalizable matrix. in its substance, it states an absolute upper bound for the deviation of one perturbed matrix eigenvalue from a properly chosen eigenvalue of the exact matrix. informal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
( gauss'conjecture was proven more than one hundred years later by kurt heegner, alan baker and harold stark. ) however, this was understood ( only ) in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the fermat equation seems not to have been percei... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
in mathematics, linearization is finding the linear approximation to a function at a given point. the linear approximation of a function is the first order taylor expansion around the point of interest. in the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium poin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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