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In the days of text mode computing, Western characters were normally laid out in a grid on the screen, often 80 columns by 24 or 25 lines. Each character was displayed as a small dot matrix, often about 8 pixels wide, and a SBCS (single-byte character set) was generally used to encode characters of Western languages. For aesthetic reasons and readability, it is preferable for Chinese characters to be approximately square-shaped, therefore twice as wide as these fixed-width SBCS characters. As these were typically encoded in a DBCS (double-byte character set), this also meant that their width on screen in a duospaced font was proportional to their byte length.
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Their work, known at the time as the IBM 801, eventually led to the RISC (Reduced Instruction Set Computing) concept. Microcode was removed, and only the most basic versions of any given instruction were put into the CPU. Any more complex code was left to the compiler. The removal of so much circuitry, about 1⁄3 of the transistors in the Motorola 68000 for instance, allowed the CPU to include more registers, which had a direct impact on performance. By the mid-1980s, further developed versions of these basic concepts were delivering performance as much as 10 times that of the fastest CISC designs, in spite of using less-developed fabrication.
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In software, an XML pipeline is formed when XML (Extensible Markup Language) processes, especially XML transformations and XML validations, are connected. For instance, given two transformations T1 and T2, the two can be connected so that an input XML document is transformed by T1 and then the output of T1 is fed as input document to T2. Simple pipelines like the one described above are called linear; a single input document always goes through the same sequence of transformations to produce a single output document.
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In mathematics, the Hutchinson metric otherwise known as Kantorovich metric is a function which measures "the discrepancy between two images for use in fractal image processing" and "can also be applied to describe the similarity between DNA sequences expressed as real or complex genomic signals".
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In the GSM cellular mobile phone standard, timing advance (TA) value corresponds to the length of time a signal takes to reach the base station from a mobile phone. GSM uses TDMA technology in the radio interface to share a single frequency between several users, assigning sequential timeslots to the individual users sharing a frequency. Each user transmits periodically for less than one-eighth of the time within one of the eight timeslots. Since the users are at various distances from the base station and radio waves travel at the finite speed of light, the precise arrival-time within the slot can be used by the base station to determine the distance to the mobile phone.
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In the United States, a common newspaper column measurement is about 11 picas wide —about 1.83 inches (46 mm)—though this measure varies from paper to paper and in other countries. The examples in this article follow this assumption for illustrative purposes only.
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In the context of this article, all graphs will be simple and undirected, unless stated otherwise. This means that the edges of the graph form a set (and not a multiset) and each edge is a pair of distinct vertices. Graphs are assumed to have an implicit representation in which each vertex has a unique identifier or label and in which it is possible to test the adjacency of any two vertices, but for which adjacency testing is the only allowed primitive operation. Informally, a graph property is a property of a graph that is independent of labeling.
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In set theory, the kernel of a function f {\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function f {\displaystyle f} can tell", or the corresponding partition of the domain.An unrelated notion is that of the kernel of a non-empty family of sets B , {\displaystyle {\mathcal {B}},} which by definition is the intersection of all its elements: This definition is used in the theory of filters to classify them as being free or principal.
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For example: the roots of numbers such as 10, 15, 20 which are not squares, the sides of numbers which are not cubes etc." In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational magnitudes: "their sums or differences, or results of their addition to a rational magnitude, or results of subtracting a magnitude of this kind from an irrational one, or of a rational magnitude from it." The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c.
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In programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. If an operand is both preceded and followed by operators (for example, ^ 3 ^), and those operators have equal precedence, then the operand may be used as input to two different operations (i.e. the two operations indicated by the two operators). The choice of which operations to apply the operand to, is determined by the associativity of the operators. Operators may be associative (meaning the operations can be grouped arbitrarily), left-associative (meaning the operations are grouped from the left), right-associative (meaning the operations are grouped from the right) or non-associative (meaning operations cannot be chained, often because the output type is incompatible with the input types).
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While the continuity assumption is usually met, the compactness assumption about the parameter space is often not, as the bounds of the true parameter values might be unknown. In that case, concavity of the likelihood function plays a key role. More specifically, if the likelihood function is twice continuously differentiable on the k-dimensional parameter space Θ {\displaystyle \Theta } assumed to be an open connected subset of R k , {\displaystyle \mathbb {R} ^{k}\,,} there exists a unique maximum θ ^ ∈ Θ {\displaystyle {\hat {\theta }}\in \Theta } if the matrix of second partials is negative definite for every θ ∈ Θ {\displaystyle \,\theta \in \Theta \,} at which the gradient ∇ L ≡ i = 1 n i {\displaystyle \;\nabla L\equiv \left_{i=1}^{n_{\mathrm {i} }}\;} vanishes, and if the likelihood function approaches a constant on the boundary of the parameter space, ∂ Θ , {\displaystyle \;\partial \Theta \;,} i.e., which may include the points at infinity if Θ {\displaystyle \,\Theta \,} is unbounded.
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In the bandwidth-limited regime ( ρ > 2 b / 2 D {\displaystyle \rho >2~b/2D} , i.e. the domain of non-binary signaling), the effective coding gain γ e f f ( A ) {\displaystyle \gamma _{\mathrm {eff} }(A)} of a signal set A {\displaystyle A} at a given target error rate P s ( E ) {\displaystyle P_{s}(E)} is defined as the difference in dB between the S N R n o r m {\displaystyle SNR_{\mathrm {norm} }} required to achieve the target P s ( E ) {\displaystyle P_{s}(E)} with A {\displaystyle A} and the S N R n o r m {\displaystyle SNR_{\mathrm {norm} }} required to achieve the target P s ( E ) {\displaystyle P_{s}(E)} with M-PAM or (M×M)-QAM (i.e. no coding). The nominal coding gain γ c ( A ) {\displaystyle \gamma _{c}(A)} is defined as γ c ( A ) = ( 2 ρ − 1 ) d min 2 ( A ) 6 E s . {\displaystyle \gamma _{c}(A)={(2^{\rho }-1)d_{\min }^{2}(A) \over 6E_{s}}.} This definition is normalized so that γ c ( A ) = 1 {\displaystyle \gamma _{c}(A)=1} for M-PAM or (M×M)-QAM. The UBE becomes P s ( E ) ≈ K s ( A ) Q 3 γ c ( A ) S N R n o r m , {\displaystyle P_{s}(E)\approx K_{s}(A)Q{\sqrt {3\gamma _{c}(A)SNR_{\mathrm {norm} }}},} where K s ( A ) {\displaystyle K_{s}(A)} is the average number of nearest neighbors per two dimensions.
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It follows from ZFC alone that Π 1 1 {\displaystyle {\boldsymbol {\Pi }}_{1}^{1}} and Σ 2 1 {\displaystyle {\boldsymbol {\Sigma }}_{2}^{1}} have the uniformization property. It follows from the existence of sufficient large cardinals that Π 2 n + 1 1 {\displaystyle {\boldsymbol {\Pi }}_{2n+1}^{1}} and Σ 2 n + 2 1 {\displaystyle {\boldsymbol {\Sigma }}_{2n+2}^{1}} have the uniformization property for every natural number n {\displaystyle n} . Therefore, the collection of projective sets has the uniformization property.
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In multiple criteria decision aiding (MCDA), multicriteria classification (or sorting) involves problems where a finite set of alternative actions should be assigned into a predefined set of preferentially ordered categories (classes). For example, credit analysts classify loan applications into risk categories (e.g., acceptable/unacceptable applicants), customers rate products and classify them into attractiveness groups, candidates for a job position are evaluated and their applications are approved or rejected, technical systems are prioritized for inspection on the basis of their failure risk, clinicians classify patients according to the extent to which they have a complex disease or not, etc.
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In some n-ary groups there exists an element e (called an n-ary identity or neutral element) such that any string of n-elements consisting of all e's, apart from one place, is mapped to the element at that place. E.g., in a quaternary group with identity e, eeae = a for every a. An n-ary group containing a neutral element is reducible. Thus, an n-ary group that is not reducible does not contain such elements.
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In telephony, ringdown is a method of signaling an operator in which telephone ringing current is sent over the line to operate a lamp or cause the operation of a self-locking relay known as a drop. Ringdown is used in manual operation, and is distinguished from automatic signaling by dialing a number. The signal consists of a continuous or pulsed alternating current (AC) signal transmitted over the line.
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The process also involves taking geographic coordinates of the ground resolution cell with GPS technology and comparing those with the coordinates of the "pixel" being studied provided by the remote sensing software to understand and analyze the location errors and how it may affect a particular study. Ground truth is important in the initial supervised classification of an image. When the identity and location of land cover types are known through a combination of field work, maps, and personal experience these areas are known as training sites.
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In superscalar designs, the number of execution units is invisible to the instruction set. Each instruction encodes one operation only. For most superscalar designs, the instruction width is 32 bits or fewer. In contrast, one VLIW instruction encodes multiple operations, at least one operation for each execution unit of a device.
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In mathematics, a multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers. If G is any group, then the set Ch(G) of these morphisms forms an abelian group under pointwise multiplication. This group is referred to as the character group of G. Sometimes only unitary characters are considered (characters whose image is in the unit circle); other such homomorphisms are then called quasi-characters.
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In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme). The need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most regular cases (see Dimension of an algebraic variety). A large part of dimension theory consists in studying the conditions under which several dimensions are equal, and many important classes of commutative rings may be defined as the rings such that two dimensions are equal; for example, a regular ring is a commutative ring such that the homological dimension is equal to the Krull dimension. The theory is simpler for commutative rings that are finitely generated algebras over a field, which are also quotient rings of polynomial rings in a finite number of indeterminates over a field.
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In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): P ( A ∣ B ) = P ( A ∩ B ) P ( B ) {\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}}} .For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing.
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In programming languages and type theory, a product of types is another, compounded, type in a structure. The "operands" of the product are types, and the structure of a product type is determined by the fixed order of the operands in the product. An instance of a product type retains the fixed order, but otherwise may contain all possible instances of its primitive data types. The expression of an instance of a product type will be a tuple, and is called a "tuple type" of expression.
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In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism.
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In the context of the Release 8 of 3GPP standards, VCC was replaced by a wider concept that covers all services provided by IMS. This work resulted in the specification of IMS Service Continuity and IMS Centralized Services (ICS), which are meant to be used in particular to provide the continuity of voice calls between LTE and legacy 2G/3G networks.
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In signal processing, signal subspace methods are empirical linear methods for dimensionality reduction and noise reduction. These approaches have attracted significant interest and investigation recently in the context of speech enhancement, speech modeling, and speech classification research. The signal subspace is also used in radio direction finding using the MUSIC (algorithm).Essentially the methods represent the application of a principal components analysis (PCA) approach to ensembles of observed time-series obtained by sampling, for example sampling an audio signal. Such samples can be viewed as vectors in a high-dimensional vector space over the real numbers.
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Multiplication is modulo irreducible polynomial x 8 + x 4 + x 3 + x + 1 {\displaystyle x^{8}+x^{4}+x^{3}+x+1} . If processed bit by bit, then, after shifting, a conditional XOR with 1B16 should be performed if the shifted value is larger than FF16 (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in GF ( 2 8 ) {\displaystyle \operatorname {GF} (2^{8})} .
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The Baire space is defined to be the Cartesian product of countably infinitely many copies of the set of natural numbers, and is given the product topology (where each copy of the set of natural numbers is given the discrete topology). The Baire space is often represented using the tree of finite sequences of natural numbers. The Baire space can be contrasted with Cantor space, the set of infinite sequences of binary digits.
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The buffer pointer is a proxy for the memory address 0xB8000000. Functional programming languages based on lambda-calculus reify the concept of a procedure abstraction and procedure application in the form of the Lambda expression. The Scheme programming language reifies continuations (approximately, the call stack).
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On the song's third week on the chart it reached its peak position of 16, where it remained for three weeks. It has since been certified gold by the Australian Recording Industry Association (ARIA) for sales of 35,000 units.In New Zealand the single entered at number 38 on the New Zealand Singles Chart. The following week, it rose to position 21 and then proceeded to fall off the charts.
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One purpose of XML Metadata Interchange (XMI) is to enable easy interchange of metadata between UML-based modeling tools and MOF-based metadata repositories in distributed heterogeneous environments. XMI is also commonly used as the medium by which models are passed from modeling tools to software generation tools as part of model-driven engineering. Examples of XMI, and lists of the XML tags that make up XMI-formatted files, are available in the version 2.5.1 specification document.
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A stronger notion is that of strongly exposed point of C {\displaystyle C} which is an exposed point x ∈ C {\displaystyle x\in C} such that some exposing functional f {\displaystyle f} of x {\displaystyle x} attains its strong maximum over C {\displaystyle C} at x {\displaystyle x} , i.e. for each sequence ( x n ) ⊂ C {\displaystyle (x_{n})\subset C} we have the following implication: f ( x n ) → max f ( C ) ⟹ ‖ x n − x ‖ → 0 {\displaystyle f(x_{n})\to \max f(C)\Longrightarrow \|x_{n}-x\|\to 0} . The set of all strongly exposed points of C {\displaystyle C} is usually denoted str exp ( C ) {\displaystyle \operatorname {str} \exp(C)} . There are two weaker notions, that of extreme point and that of support point of C {\displaystyle C} .
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In social network theory, social relationships are viewed in terms of nodes and ties. Nodes are the individual actors within the networks, and ties are the relationships between the actors. There can be many kinds of ties between the nodes. In its simplest form, a social network is a map of all of the relevant ties between the nodes being studied.
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In the Japanese kantenji braille, the standard 8-dot Braille patterns 37, 137, 347, and 1347 are the patterns related to Braille pattern dots-23, since the two additional dots of kantenji patterns 023, 237, and 0237 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.
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During batch processing, several different programs were loaded in the computer memory, and the first one began to run. When the first program reached an instruction waiting for a peripheral, the context of this program was stored away, and the second program in memory was given a chance to run. The process continued until all programs finished running.The use of multiprogramming was enhanced by the arrival of virtual memory and virtual machine technology, which enabled individual programs to make use of memory and operating system resources as if other concurrently running programs were, for all practical purposes, nonexistent.Multiprogramming gives no guarantee that a program will run in a timely manner.
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In the Internet protocol suite, the application layer contains the communications protocols and interface methods used in process-to-process communications across an Internet Protocol (IP) computer network. The application layer only standardizes communication and depends upon the underlying transport layer protocols to establish host-to-host data transfer channels and manage the data exchange in a client–server or peer-to-peer networking model. Though the TCP/IP application layer does not describe specific rules or data formats that applications must consider when communicating, the original specification (in RFC 1123) does rely on and recommend the robustness principle for application design.
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In statistics and data mining, affinity propagation (AP) is a clustering algorithm based on the concept of "message passing" between data points. Unlike clustering algorithms such as k-means or k-medoids, affinity propagation does not require the number of clusters to be determined or estimated before running the algorithm. Similar to k-medoids, affinity propagation finds "exemplars," members of the input set that are representative of clusters.
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The C programming language uses an integer type, where relational expressions like i > j and logical expressions connected by && and || are defined to have value 1 if true and 0 if false, whereas the test parts of if, while, for, etc., treat any non-zero value as true. Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (bit), or as a bit string of length one, which can store only two values. The implementation of Booleans in computers are most likely represented as a full word, rather than a bit; this is usually due to the ways computers transfer blocks of information.
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More generally, | Z: n Z | = n {\displaystyle |\mathbb {Z} :n\mathbb {Z} |=n} for any positive integer n. When G is finite, the formula may be written as | G: H | = | G | / | H | {\displaystyle |G:H|=|G|/|H|} , and it implies Lagrange's theorem that | H | {\displaystyle |H|} divides | G | {\displaystyle |G|} . When G is infinite, | G: H | {\displaystyle |G:H|} is a nonzero cardinal number that may be finite or infinite. For example, | Z: 2 Z | = 2 {\displaystyle |\mathbb {Z} :2\mathbb {Z} |=2} , but | R: Z | {\displaystyle |\mathbb {R} :\mathbb {Z} |} is infinite. If N is a normal subgroup of G, then | G: N | {\displaystyle |G:N|} is equal to the order of the quotient group G / N {\displaystyle G/N} , since the underlying set of G / N {\displaystyle G/N} is the set of cosets of N in G.
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Intermediate angles give intermediate correlations in a way that, on careful analysis, proves inconsistent with the idea that each particle has a definite, independent probability of producing the observed measurements (the correlations violate Bell's inequality). This subtle dependence of one measurement on the other holds even when measurements are made simultaneously and a great distance apart, which gives the appearance of a superluminal communication taking place between the two electrons. Put simply, how can Bob's electron "know" what Alice measured on hers, so that it can adjust its own behavior accordingly?
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Comprehensive test procedures which outline the steps, and their expected results clearly identify what is to be seen as a result of performing the step. After the step or set of steps is completed the last step's expected result will call out what has been seen and then identify what requirement or requirements have been verified (identified by number). The requirement number, title and verbiage are tied together in another location in the test document.
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In some cases, the problem may also be simplified by subtracting a point from both sides of the equation and taking the norm of the result. For example, to solvefor ξ 3 {\textstyle \xi _{3}} , where ξ 1 {\textstyle \xi _{1}} and ξ 2 {\textstyle \xi _{2}} intersect at the point q {\textstyle q} , both sides of the equation may be applied to a point p {\textstyle p} that is not on the axis of ξ 3 {\textstyle \xi _{3}} . Subtracting q {\textstyle q} and taking the norm of both sides yields This may be solved using Subproblem 3.
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Therefore, in the case of drawing a red card or a king, drawing any of a red king, a red non-king, or a black king is considered a success. In a standard 52-card deck, there are twenty-six red cards and four kings, two of which are red, so the probability of drawing a red or a king is 26/52 + 4/52 – 2/52 = 28/52. Events are collectively exhaustive if all the possibilities for outcomes are exhausted by those possible events, so at least one of those outcomes must occur.
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In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Laurence Kirby and Jeff Paris showed that it is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic). This was the third example of a true statement that is unprovable in Peano arithmetic, after the examples provided by Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of ε0-induction in Peano arithmetic. The Paris–Harrington theorem gave another example.
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For example, the torus is different from the sphere: the torus has a "hole"; the sphere doesn't. However, since continuity (the basic notion of topology) only deals with the local structure, it can be difficult to formally define the obvious global difference. The homotopy groups, however, carry information about the global structure.
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In the example program only normal calls are used, so all the information will be on a single stack. For asynchronous calls, a separate stack is initiated for each asynchronous process so that the processes share data but run asynchronously.
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In order for virtual memory compression to provide measurable performance improvements, the throughput of the virtual memory system must be improved when compared to the uncompressed equivalent. Thus, the additional amount of processing introduced by the compression must not increase the overall latency. However, in I/O-bound systems or applications with highly compressible data sets, the gains can be substantial.
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In plumbing fittings, the "M" or "F" usually comes at the beginning rather than the end of the abbreviated designation. For example: MIPT denotes male iron pipe thread; FIPT denotes female iron pipe thread.A short length of pipe having an MIP thread at both ends is sometimes called a nipple. A short pipe fitting having an FIP thread at both ends is sometimes called a coupling.
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In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem. Therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal.
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In the following code, neither f nor g functions is reentrant. In the above, f() depends on a non-constant global variable v; thus, if f() is interrupted during execution by an ISR which modifies v, then reentry into f() will return the wrong value of v. The value of v and, therefore, the return value of f, cannot be predicted with confidence: they will vary depending on whether an interrupt modified v during f's execution. Hence, f is not reentrant. Neither is g, because it calls f, which is not reentrant.
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In linear algebra, the n × n {\displaystyle n\times n} identity matrix I {\displaystyle \mathbf {I} } has entries equal to the Kronecker delta: where i {\displaystyle i} and j {\displaystyle j} take the values 1 , 2 , ⋯ , n {\displaystyle 1,2,\cdots ,n} , and the inner product of vectors can be written as Here the Euclidean vectors are defined as n-tuples: a = ( a 1 , a 2 , … , a n ) {\displaystyle \mathbf {a} =(a_{1},a_{2},\dots ,a_{n})} and b = ( b 1 , b 2 , . . . , b n ) {\displaystyle \mathbf {b} =(b_{1},b_{2},...,b_{n})} and the last step is obtained by using the values of the Kronecker delta to reduce the summation over j {\displaystyle j} . It is common for i and j to be restricted to a set of the form {1, 2, ..., n} or {0, 1, ..., n − 1}, but the Kronecker delta can be defined on an arbitrary set.
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In many less-developed countries, such as Spain, Mexico, Brazil, and Egypt, calls were placed at a central office the caller went to, filled out a paper slip, sometimes paid in advance for the call, and then waited for it to be connected. In Spain these were known as locutorios, literally "a place to talk". In towns too small to support a phone office, placing long-distance calls was a sideline for some businesses with telephones, such as pharmacies.
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Internally, the CPU of the computer is built up from a number of separate parts dedicated to a single task, for instance, adding a number, or fetching from memory. Normally, as the instruction flows through the machine, only one part is active at any given time. This means that each sequential step of the entire process must complete before a result can be saved.
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A bijective function is also called a bijection. That is, combining the definitions of injective and surjective, ∀ y ∈ Y , ∃ ! x ∈ X such that y = f ( x ) , {\displaystyle \forall y\in Y,\exists !x\in X{\text{ such that }}y=f(x),} where ∃ !
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, particularly abstract algebra, a binary operation • on a set is flexible if it satisfies the flexible identity: a ∙ ( b ∙ a ) = ( a ∙ b ) ∙ a {\displaystyle a\bullet \left(b\bullet a\right)=\left(a\bullet b\right)\bullet a} for any two elements a and b of the set. A magma (that is, a set equipped with a binary operation) is flexible if the binary operation with which it is equipped is flexible. Similarly, a nonassociative algebra is flexible if its multiplication operator is flexible. Every commutative or associative operation is flexible, so flexibility becomes important for binary operations that are neither commutative nor associative, e.g. for the multiplication of sedenions, which are not even alternative. In 1954, Richard D. Schafer examined the algebras generated by the Cayley–Dickson process over a field and showed that they satisfy the flexible identity.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs). Formally, distributions ƒ(x) and g(x) bear the property if for every x 1 > x 0 , f ( x 1 ) g ( x 1 ) ≥ f ( x 0 ) g ( x 0 ) {\displaystyle {\text{for every }}x_{1}>x_{0},\quad {\frac {f(x_{1})}{g(x_{1})}}\geq {\frac {f(x_{0})}{g(x_{0})}}} that is, if the ratio is nondecreasing in the argument x {\displaystyle x} . If the functions are first-differentiable, the property may sometimes be stated ∂ ∂ x ( f ( x ) g ( x ) ) ≥ 0 {\displaystyle {\frac {\partial }{\partial x}}\left({\frac {f(x)}{g(x)}}\right)\geq 0} For two distributions that satisfy the definition with respect to some argument x, we say they "have the MLRP in x." For a family of distributions that all satisfy the definition with respect to some statistic T(X), we say they "have the MLR in T(X)."
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then without knowing the value of n, we can determine that the remainder of n divided by 105 (the product of 3, 5, and 7) is 23. Importantly, this tells us that if n is a natural number less than 105, then 23 is the only possible value of n. The earliest known statement of the theorem is by the Chinese mathematician Sunzi in the Sunzi Suanjing in the 3rd century CE.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Job j {\displaystyle j} on machine i {\displaystyle i} takes time p j / s i {\displaystyle p_{j}/s_{i}} . R: Unrelated-machines scheduling. There are m {\displaystyle m} parallel machines, and they are unrelated – Job j {\displaystyle j} on machine i {\displaystyle i} takes time p i j {\displaystyle p_{ij}} .These letters might be followed by the number of machines, which is then fixed.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Their specific use as metadata is left to the developer and can cover a wide range of types of information about any given application, classes and members that is not instance-specific. The decision to expose any given attribute as a property is also left to the developer as is the decision to use them as part of a larger application framework. Attributes are implemented as classes that are derived from System.Attribute.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Unlike Peano arithmetic, Skolem arithmetic is a decidable theory. This means it is possible to effectively determine, for any sentence in the language of Skolem arithmetic, whether that sentence is provable from the axioms of Skolem arithmetic. The asymptotic running-time computational complexity of this decision problem is triply exponential.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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The process responds at the next time step by randomly moving into a new state s ′ {\displaystyle s'} , and giving the decision maker a corresponding reward R a ( s , s ′ ) {\displaystyle R_{a}(s,s')} . The probability that the process moves into its new state s ′ {\displaystyle s'} is influenced by the chosen action. Specifically, it is given by the state transition function P a ( s , s ′ ) {\displaystyle P_{a}(s,s')} .
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the SQUOZE encoding, identifiers in the symbol table were represented in a 50-character alphabet, allowing a 36-bit machine word to represent six alphanumeric characters plus two flag bits, thus saving two bits per six characters, because the six bits normally allocated for each character could store up to 64 states rather than only the 50 states needed to represent the 50 letters of the alphabet, and 506 < 234. Using base 50 already saves a single bit every three characters, so it was used in two three-character chunks. The manual has a formula for encoding six characters ABCDEF: ( A ∗ 50 2 + B ∗ 50 + C ) ∗ 2 17 + ( D ∗ 50 2 + E ∗ 50 + F ) {\displaystyle (A*50^{2}+B*50+C)*2^{17}+(D*50^{2}+E*50+F)} For example "SQUOZE", normally 36 bits: 35 33 37 31 44 17(base 8) would be encoded in two 17-bit pieces to fit in the 34 bits as ( 0o220231 << 17 ) | 0o175473 == 0o110114575473. A simpler example of the same logic would be how a three-digit BCD number would take up 12 bits, such as 987: 9 8 7(base 16) 1001 1000 0111(base 2), but any such value could be stored in 10 bits directly, saving two bits, such as 987: 3db(base 16) 11 1101 1011(base 2).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In order to state the hypergraph regularity and counting lemmas formally, we need to define several rather technical terms to formalize appropriate notions of pseudo-randomness (random-likeness) and boundedness, as well as to describe the random-like blocks and partitions. Notation K j ( k ) {\displaystyle K_{j}^{(k)}} denotes a k {\displaystyle k} -uniform clique on j {\displaystyle j} vertices. G ( j ) {\displaystyle {\mathcal {G}}^{(j)}} is an l {\displaystyle l} -partite j {\displaystyle j} -graph on vertex partition G ( 1 ) = V 1 ⊔ … ⊔ V l {\displaystyle {\mathcal {G}}^{(1)}=V_{1}\sqcup \ldots \sqcup V_{l}} . K j ( G ( i ) ) {\displaystyle {\mathcal {K}}_{j}({\mathcal {G}}^{(i)})} is the family of all j {\displaystyle j} -element vertex sets that span the clique K j ( i ) {\displaystyle K_{j}^{(i)}} in G ( i ) {\displaystyle {\mathcal {G}}^{(i)}} .
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In most cases, we want to find out the relationships between social data and another event or we want to get interesting results from social data analyses to predict some events. There are some outstanding articles in this field, including Twitter Mood Predicts The Stock Market, Predicting The Present With Google Trends etc. In order to accomplish these goals, we need the appropriate methods to do the analyses. Usually, we use statistic methods, methods of machine learning or methods of data mining to do the analyses. Universities all over the world are opening graduate program in Social Data Analysis.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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The client decides which commands to execute at which points. To execute a command, it passes the command object to the invoker object.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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, y 1 ) . {\displaystyle P(y_{i}|x_{i},x_{i-1},x_{i-2},...,x_{1},y_{i-1},y_{i-2},...,y_{1}).} .
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of p-values departs from a uniform distribution and becomes a right-skewed unimodal distribution, especially for small p-values. This leads to a large Type I error rate.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In set theory, the notation Y X {\displaystyle Y^{X}} is used to denote the set of functions from the set X {\displaystyle X} to the set Y {\displaystyle Y} . Currying is the natural bijection between the set A B × C {\displaystyle A^{B\times C}} of functions from B × C {\displaystyle B\times C} to A {\displaystyle A} , and the set ( A C ) B {\displaystyle (A^{C})^{B}} of functions from B {\displaystyle B} to the set of functions from C {\displaystyle C} to A {\displaystyle A} . In symbols: A B × C ≅ ( A C ) B {\displaystyle A^{B\times C}\cong (A^{C})^{B}} Indeed, it is this natural bijection that justifies the exponential notation for the set of functions. As is the case in all instances of currying, the formula above describes an adjoint pair of functors: for every fixed set C {\displaystyle C} , the functor B ↦ B × C {\displaystyle B\mapsto B\times C} is left adjoint to the functor A ↦ A C {\displaystyle A\mapsto A^{C}} . In the category of sets, the object Y X {\displaystyle Y^{X}} is called the exponential object.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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The various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two-dimensional space, meaning that a path could be of any shape. Similar cost optimization problems can also arise in a constrained space, especially a one-dimensional linear network such as a road or telecommunications network. Although they are similar in principle, the problems in network space require very different (usually simpler) algorithms to solve, largely adopted from graph theory. The collection of GIS tools for solving these problems are called network analysis.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In modulus 12, one can assert that: 38 ≡ 14 ( mod 12 ) {\displaystyle 38\equiv 14{\pmod {12}}} because 38 − 14 = 24, which is a multiple of 12. Another way to express this is to say that both 38 and 14 have the same remainder 2, when divided by 12. The definition of congruence also applies to negative values. For example: 2 ≡ − 3 ( mod 5 ) − 8 ≡ 7 ( mod 5 ) − 3 ≡ − 8 ( mod 5 ) . {\displaystyle {\begin{aligned}2&\equiv -3{\pmod {5}}\\-8&\equiv 7{\pmod {5}}\\-3&\equiv -8{\pmod {5}}.\end{aligned}}}
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2023, only special cases of the conjecture have been proven.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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gxf5 14. Nxf7 Kxf7 15. Bd2 Nd7 16.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Renaming truth as a product of the will cannot help it solve the problems of the intellect, according to Bittle. Bittle cited what he saw as contradictions in pragmatism, such as using objective facts to prove that truth does not emerge from objective fact; this reveals that pragmatists do recognize truth as objective fact, and not, as they claim, what is useful. Bittle argued there are also some statements that cannot be judged on human welfare at all.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the Japanese kantenji braille, the standard 8-dot Braille patterns 2, 12, 24, and 124 are the 8-dot braille patterns related to Braille pattern dots-1, since the two additional dots of kantenji patterns 01, 17, and 017 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, quantales are certain partially ordered algebraic structures that generalize locales (point free topologies) as well as various multiplicative lattices of ideals from ring theory and functional analysis (C*-algebras, von Neumann algebras). Quantales are sometimes referred to as complete residuated semigroups.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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This can be significantly faster, as setjmp and longjmp must conservatively store all registers which may be in use according to the ABI, whereas the clobber method allows the compiler to store (by spilling to the stack) only what it knows is actually in use. Due to the lack of direct language support, many authors have written their own libraries for coroutines which hide the above details.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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For example, 29/30 could be written as 1 2 4 2 3 5 {\displaystyle {\tfrac {1\,\,2\,\,4}{2\,\,3\,\,5}}} , representing the value 4 5 + 2 3 × 5 + 1 2 × 3 × 5 {\displaystyle {\tfrac {4}{5}}+{\tfrac {2}{3\times 5}}+{\tfrac {1}{2\times 3\times 5}}} . This can be viewed as a form of mixed radix notation, and was very convenient for dealing with traditional systems of weights, measures, and currency. For instance, for units of length, a foot is 1/3 of a yard, and an inch is 1/12 of a foot, so a quantity of 5 yards, 2 feet, and 7 3 4 {\displaystyle 7{\tfrac {3}{4}}} inches could be represented as a composite fraction: 3 7 2 4 12 3 5 {\displaystyle {\tfrac {3\ \,7\,\,2}{4\,\,12\,\,3}}\,5} yards.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In statistics, factor analysis of mixed data or factorial analysis of mixed data (FAMD, in the French original: AFDM or Analyse Factorielle de Données Mixtes), is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory methods developed by the French school called Analyse des données (data analysis) founded by Jean-Paul Benzécri. The term mixed refers to the use of both quantitative and qualitative variables. Roughly, we can say that FAMD works as a principal components analysis (PCA) for quantitative variables and as a multiple correspondence analysis (MCA) for qualitative variables.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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With stack machines, in contrast, results can be stored in one of two ways. Firstly, results can be stored using a temporary variable in memory. Storing and subsequent retrievals cost additional instructions and additional data cache cycles.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Around 2007, LSTM trained by Connectionist Temporal Classification (CTC) started to outperform traditional speech recognition in certain applications. In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49% through CTC-trained LSTM, which is now available through Google Voice to all smartphone users. Transformers, a type of neural network based on solely on attention, have been widely adopted in computer vision and language modeling, sparking the interest of adapting such models to new domains, including speech recognition.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In programming languages that have non-hygienic macro systems, it is possible for existing variable bindings to be hidden from a macro by variable bindings that are created during its expansion. In C, this problem can be illustrated by the following fragment: Running the above through the C preprocessor produces: The variable a declared in the top scope is shadowed by the a variable in the macro, which introduces a new scope. As a result, a is never altered by the execution of the program, as the output of the compiled program shows: a is now 4, b is now 9
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In parallel France and Germany signed a joint development agreement in 1984 and were joined by Italy and the UK in 1986. In 1986, the MTS and European Commission proposed reserving the 900 MHz spectrum band for GSM. It was long believed that the former Finnish prime minister Harri Holkeri made the world's first GSM call on 1 July 1991, MTS calling Kaarina Suonio (deputy mayor of the city of Tampere) using a network built by Nokia and Siemens and operated by Radiolinja. In 2021 a former Nokia engineer Pekka Lonka revealed to Helsingin Sanomat making a test call just a couple of hours earlier.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mutual authentication schemes that require a user's input password as part of the verification process, there is a higher vulnerability to hackers because the password is human-made rather than a computer-generated certificate. While applications could simply require users to use a computer-generated password, it is inconvenient for people to remember. User-made passwords and the ability to change one's password are important for making an application user-friendly, so many schemes work to accommodate the characteristic.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation. It can take different forms, namely either a spoken language or a sign language. Natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Second, synchronization in many concurrent programs in a finite state, and therefore can be adequately described by regular expressions. For precisely the same reasons, path expressions are useful for controlling the behavior of complicated asynchronous circuits. In fact, the finite state assumption may be even more reasonable at the hardware level than at the monitor level. Path expressions provide a high level of descriptive synchronization that aids in the prevention and detection of design errors in complex systems and overcomes some of the dangers, such as certain forms of coding errors.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In paging the memory address space or segment is divided into equal-sized blocks called pages. Using virtual memory hardware, each page can reside in any location at a suitable boundary of the computer's physical memory, or be flagged as being protected. Virtual memory makes it possible to have a linear virtual memory address space and to use it to access blocks fragmented over physical memory address space. Most computer architectures which support paging also use pages as the basis for memory protection.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the above example, the RLI mark (right-to-left isolate) forces the following text to be interpreted in the reverse order: the triple-quote is first (ending the string), followed by a semicolon (starting a new line), and finally with the premature return (returning None and ignoring any code below it). The new line terminates the RLI mark, preventing it from flowing into the below code. Because of the Bidi character, some source code editors and IDEs rearrange the code for display without any visual indication that the code has been rearranged, so a human code reviewer would not normally detect them.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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If we remove the vertex v, we can four-color the remaining vertices. We can set the colors as (in clockwise order) red, yellow, blue, and green. In this situation, there can be a Kempe chain joining the red and blue neighbors or a Kempe chain joining the green and yellow neighbors, but not both, since these two paths would necessarily intersect, and the vertex where they intersect cannot be colored.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that axa = a. Regular semigroups are one of the most-studied classes of semigroups, and their structure is particularly amenable to study via Green's relations.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Infinity can also be used to describe infinite series, as follows: ∑ i = 0 ∞ f ( i ) = a {\displaystyle \sum _{i=0}^{\infty }f(i)=a} means that the sum of the infinite series converges to some real value a . {\displaystyle a.}
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Although languages that are described as having imperfective and perfective aspects agree in most cases in their use of these aspects, they may not agree in every situation. For example: Some languages have additional grammatical aspects. Spanish and Ancient Greek, for example, have a perfect (not the same as the perfective), which refers to a state resulting from a previous action (also described as a previous action with relevance to a particular time, or a previous action viewed from the perspective of a later time).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In order to get 128 bits of security for hash based signatures to sign 1 million messages using the fractal Merkle tree method of Naor Shenhav and Wool the public and private key sizes are roughly 36,000 bits in length.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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y-axis ( ↑ {\displaystyle \uparrow } ): terms that can bind types, corresponding to polymorphism. z-axis ( ↗ {\displaystyle \nearrow } ): types that can bind types, corresponding to (binding) type operators.The different ways to combine these three dimensions yield the 8 vertices of the cube, each corresponding to a different kind of typed system. The λ-cube can be generalized into the concept of a pure type system.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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(This bound is tight, as a sequence of m − 1 {\displaystyle m-1} zeroes and m − 1 {\displaystyle m-1} ones cannot have any subset of size m {\displaystyle m} summing to zero.) There are known proofs of this result using the Cauchy-Davenport theorem, Fermat's little theorem, or the Chevalley–Warning theorem.Generalizing this result, one can define for any abelian group G the minimum quantity E G Z ( G ) {\displaystyle EGZ(G)} of elements of G such that there must be a subsequence of o ( G ) {\displaystyle o(G)} elements (where o ( G ) {\displaystyle o(G)} is the order of the group) which adds to zero. It is known that E G Z ( G ) ≤ 2 o ( G ) − 1 {\displaystyle EGZ(G)\leq 2o(G)-1} , and that this bound is strict if and only if G = Z m {\displaystyle G=\mathbb {Z} _{m}} .
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the United States, common telephone lines are designed to transmit frequencies between 300 and 3400 Hz. Since electric power in the United States is distributed at 60 Hz, it normally does not interfere with telephone communications because its frequency is too low.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically contingent.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In marketing, contact center telephony is the communication and collaboration system used by businesses to either manage high volumes of inbound queries or outbound telephone calls keeping their workforce or agents productive and in control to serve or acquire customers. This business communication system is an extension of computer telephony integration (CTI).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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{\displaystyle f\circ g_{1}=f\circ g_{2}\implies g_{1}=g_{2}.} Monomorphisms are a categorical generalization of injective functions (also called "one-to-one functions"); in some categories the notions coincide, but monomorphisms are more general, as in the examples below. In the setting of posets intersections are idempotent: the intersection of anything with itself is itself.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mistrustful cryptography the participating parties do not trust each other. For example, Alice and Bob collaborate to perform some computation where both parties enter some private inputs. But Alice does not trust Bob and Bob does not trust Alice. Thus, a secure implementation of a cryptographic task requires that after completing the computation, Alice can be guaranteed that Bob has not cheated and Bob can be guaranteed that Alice has not cheated either.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Derived from the causal order is the differential structure and the conformal metric of a manifold. A probability is assigned to a causal set becoming embedded in a manifold; thus there can be a transition from a discrete Planck scale fundamental unit of volume to a classical large scale continuous space.Random graphs by Antonsen Spacetime is described by dynamical graphs with points (associated with vertices) and links (of unit length) that are created or annihilated according to probability calculations. The parameterization of graphs in a metaspace gives rise to time.Bootstrap universe by Cahill and Klinger An iterative map composed of monads and the relations between them becomes a tree-graph of nodes and links.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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