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wiki_12500_chunk_0 | Simpson's Rule | Points inside the integration range are given alternating weights 4/3 and 2/3. Simpson's 3/8 rule, also called Simpson's second rule, requires one more function evaluation inside the integration range and gives lower error bounds, but does not improve on order of the error. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12501_chunk_0 | MISER algorithm | In numerical integration, methods such as the trapezoidal rule use a deterministic approach. Monte Carlo integration, on the other hand, employs a non-deterministic approach: each realization provides a different outcome. In Monte Carlo, the final outcome is an approximation of the correct value with respective error b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12502_chunk_0 | MISER algorithm | V a r ( f ) ≡ σ N 2 = 1 N − 1 ∑ i = 1 N ( f ( x ¯ i ) − ⟨ f ⟩ ) 2 . {\displaystyle \mathrm {Var} (f)\equiv \sigma _{N}^{2}={\frac {1}{N-1}}\sum _{i=1}^{N}\left(f({\overline {\mathbf {x} }}_{i})-\langle f\rangle \right)^{2}.} which leads to V a r ( Q N ) = V 2 N 2 ∑ i = 1 N V a r ( f ) = V 2 V a r ( f ) N = V 2 σ N 2 N ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12503_chunk_0 | MISER algorithm | The estimation of the error of QN is thus δ Q N ≈ V a r ( Q N ) = V σ N N , {\displaystyle \delta Q_{N}\approx {\sqrt {\mathrm {Var} (Q_{N})}}=V{\frac {\sigma _{N}}{\sqrt {N}}},} which decreases as 1 N {\displaystyle {\tfrac {1}{\sqrt {N}}}} . This is standard error of the mean multiplied with V {\displaystyle V} . Thi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12504_chunk_0 | MISER algorithm | It is important to notice that, unlike in deterministic methods, the estimate of the error is not a strict error bound; random sampling may not uncover all the important features of the integrand that can result in an underestimate of the error. While the naive Monte Carlo works for simple examples, an improvement over... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12505_chunk_0 | Givens rotation | In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. Givens rotations are named after Wallace Givens, who introduced them to numerical analysts in the 1950s while he was working at Argonne National Laboratory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12506_chunk_0 | Jacobi rotation | In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A, when applied as a similarity transformation: A ↦ Q k ℓ T A Q k ℓ = A ′ . {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12507_chunk_0 | Jacobi rotation | {\displaystyle {\begin{bmatrix}{*}&&&\cdots &&&*\\&\ddots &&&&&\\&&a_{kk}&\cdots &a_{k\ell }&&\\\vdots &&\vdots &\ddots &\vdots &&\vdots \\&&a_{\ell k}&\cdots &a_{\ell \ell }&&\\&&&&&\ddots &\\{*}&&&\cdots &&&*\end{bmatrix}}\to {\begin{bmatrix}{*}&&&\cdots &&&*\\&\ddots &&&&&\\&&a'_{kk}&\cdots &0&&\\\vdots &&\vdots &\d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12508_chunk_0 | Jacobi rotation | Also, an explicit matrix for Qkℓ is rarely computed; instead, auxiliary values are computed and A is updated in an efficient and numerically stable way. However, for reference, we may write the matrix as Q k ℓ = . {\displaystyle Q_{k\ell }={\begin{bmatrix}1&&&&&&\\&\ddots &&&&0&\\&&c&\cdots &s&&\\&&\vdots &\ddots &\vd... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12509_chunk_0 | Jacobi rotation | That is, Qkℓ is an identity matrix except for four entries, two on the diagonal (qkk and qℓℓ, both equal to c) and two symmetrically placed off the diagonal (qkℓ and qℓk, equal to s and −s, respectively). Here c = cos θ and s = sin θ for some angle θ; but to apply the rotation, the angle itself is not required. Using K... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12510_chunk_0 | Incomplete LU factorization | In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12511_chunk_0 | Bartels–Stewart algorithm | In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12512_chunk_0 | Bartels–Stewart algorithm | Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system that can then be... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12513_chunk_0 | Cuthill–McKee algorithm | In numerical linear algebra, the Cuthill–McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth. The reverse Cuthill–McKee algorithm (RCM) due to Alan George and Joseph Liu is th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12514_chunk_0 | Cuthill–McKee algorithm | It starts with a peripheral node and then generates levels R i {\displaystyle R_{i}} for i = 1 , 2 , . . {\displaystyle i=1,2,..} until all nodes are exhausted. The set R i + 1 {\displaystyle R_{i+1}} is created from set R i {\displaystyle R_{i}} by listing all vertices adjacent to all nodes in R i {\displaystyle R_{i}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12515_chunk_0 | Gauss–Seidel method | In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacob... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12516_chunk_0 | Jacobi eigenvalue algorithm | In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). It is named after Carl Gustav Jacob Jacobi, who first proposed the method in 1846, but only became widely used in t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12517_chunk_0 | Jacobi method | In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12518_chunk_0 | Jacobi method | The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12519_chunk_0 | QR algorithm | In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was developed in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya, working independently. The basic idea is to perfo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12520_chunk_0 | Rayleigh–Ritz method | In numerical linear algebra, the Rayleigh–Ritz method is commonly applied to approximate an eigenvalue problem for the matrix A ∈ C N × N {\displaystyle A\in \mathbb {C} ^{N\times N}} of size N {\displaystyle N} using a projected matrix of a smaller size m < N {\displaystyle m | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12521_chunk_0 | Alternating direction implicit method | In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12522_chunk_0 | Biconjugate gradient stabilized method | In numerical linear algebra, the biconjugate gradient stabilized method, often abbreviated as BiCGSTAB, is an iterative method developed by H. A. van der Vorst for the numerical solution of nonsymmetric linear systems. It is a variant of the biconjugate gradient method (BiCG) and has faster and smoother convergence tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12523_chunk_0 | Derivation of the conjugate gradient method | In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system A x = b {\displaystyle {\boldsymbol {Ax}}={\boldsymbol {b}}} where A {\displaystyle {\boldsymbol {A}}} is symmetric positive-definite. The conjugate gradient method can be derived from several dif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12524_chunk_0 | Successive over-relaxation | In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process. It was devised simultaneously by David M. Young Jr. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12525_chunk_0 | Successive over-relaxation | and by Stanley P. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers. Over-relaxation methods had been used before the work of Young and Frankel. An example is the method of Lewis Fry Richardson, and the methods developed by R. V. Southwell. However, these methods were designed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12526_chunk_0 | Thomas algorithm | In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as a i x i − 1 + b i x i + c i x i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12527_chunk_0 | Thomas algorithm | For such systems, the solution can be obtained in O ( n ) {\displaystyle O(n)} operations instead of O ( n 3 ) {\displaystyle O(n^{3})} required by Gaussian elimination. A first sweep eliminates the a i {\displaystyle a_{i}} 's, and then an (abbreviated) backward substitution produces the solution. Examples of such mat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12528_chunk_0 | Beam and Warming scheme | In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, is a second order accurate implicit scheme, mainly used for solving non-linear hyperbolic equations. It is not used much nowadays. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12529_chunk_0 | Artificial precision | In numerical mathematics, artificial precision is a source of error that occurs when a numerical value or semantic is expressed with more precision than was initially provided from measurement or user input. For example, a person enters their birthday as the date 1984-01-01 but it is stored in a database as 1984-01-01T... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12530_chunk_0 | Hierarchical matrix | In numerical mathematics, hierarchical matrices (H-matrices) are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension n {\displaystyle n} can be represented efficiently in O ( n ) {\displaystyle O(n)} units of storage by storing only its non-zero entries, a non-sparse matrix wou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12531_chunk_0 | Hierarchical matrix | In typical applications, e.g., when discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional to log ( 1 / ϵ ) γ {\displaystyle \log(1/\epsilon )^{\gamma }} with a small constant γ {\displaystyle \gamma } is suff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12532_chunk_0 | Relaxation (iterative method) | In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations. They are also used for the solution of l... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12533_chunk_0 | Relaxation (iterative method) | Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation, it resembles repeated application of a loc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12534_chunk_0 | Uzawa iteration | In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. It is named after Hirofumi Uzawa and was originally introduced in the context of concave programming. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12535_chunk_0 | Boundary knot method | In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent decades have witnessed a research boom on the meshfree numerical PDE techniques since the construction of a mesh in the standard finite element method and boundary e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12536_chunk_0 | Constant strain triangle element | In numerical mathematics, the constant strain triangle element, also known as the CST element or T3 element, is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. The name of this element reflects how ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12537_chunk_0 | Gradient discretization method | For linear problems, stationary or transient, error estimates can be established based on three indicators specific to the GDM (the quantities C D {\displaystyle C_{D}} , S D {\displaystyle S_{D}} and W D {\displaystyle W_{D}} , see below). For non-linear problems, the proofs are based on compactness techniques and do ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12538_chunk_0 | Regularized meshless method | In numerical mathematics, the regularized meshless method (RMM), also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method designed to solve certain partial differential equations whose fundamental solution is explicitly known. The RMM is a strong-form collo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12539_chunk_0 | Markov chain approximation method | In numerical methods for stochastic differential equations, the Markov chain approximation method (MCAM) belongs to the several numerical (schemes) approaches used in stochastic control theory. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as the Runge–Kutta me... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12540_chunk_0 | Markov chain approximation method | for numerical and other approximations problems in stochastic processes. They represent counterparts from deterministic control theory such as optimal control theory.The basic idea of the MCAM is to approximate the original controlled process by a chosen controlled markov process on a finite state space. In case of nee... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12541_chunk_0 | Total variation diminishing | In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12542_chunk_0 | Numerical modeling (geology) | In numerical models and mathematical models, there are two different approaches to describe the motion of matter: Eulerian and Lagrangian. In geology, both approaches are commonly used to model fluid flow like mantle convection, where an Eulerian grid is used for computation and Lagrangian markers are used to visualize... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12543_chunk_0 | Meta-optimization | In numerical optimization, meta-optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson for finding optimal parameter settings of a genetic algorithm. Meta-optimization and related concept... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12544_chunk_0 | BFGS method | In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12545_chunk_0 | Nonlinear conjugate gradient | In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2 , {\displaystyle \displaystyle f(x)=\|Ax-b\|^{2},} the minimum of f {\displaystyle f} is obt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12546_chunk_0 | Nonlinear conjugate gradient | The algorithm stops when it finds the minimum, determined when no progress is made after a direction reset (i.e. in the steepest descent direction), or when some tolerance criterion is reached. Within a linear approximation, the parameters α {\displaystyle \displaystyle \alpha } and β {\displaystyle \displaystyle \beta... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12547_chunk_0 | Nonlinear conjugate gradient | .These formulas are equivalent for a quadratic function, but for nonlinear optimization the preferred formula is a matter of heuristics or taste. A popular choice is β = max { 0 , β P R } {\displaystyle \displaystyle \beta =\max\{0,\beta ^{PR}\}} , which provides a direction reset automatically.Algorithms based on Newt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12548_chunk_0 | Nonlinear conjugate gradient | For high-dimensional problems, the exact computation of the Hessian is usually prohibitively expensive, and even its storage can be problematic, requiring O ( N 2 ) {\displaystyle O(N^{2})} memory (but see the limited-memory L-BFGS quasi-Newton method). The conjugate gradient method can also be derived using optimal co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12549_chunk_0 | Numerov's method | In numerical physics the method is used to find solutions of the unidimensional Schrödinger equation for arbitrary potentials. An example of which is solving the radial equation for a spherically symmetric potential. In this example, after separating the variables and analytically solving the angular equation, we are l... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12550_chunk_0 | Numerov's method | {\displaystyle V_{\text{eff}}(r)=V(r)+{\frac {\hbar ^{2}}{2m}}{\frac {l(l+1)}{r^{2}}}=V(r)+{\frac {L^{2}}{2mr^{2}}},\quad L^{2}=l(l+1)\hbar ^{2}.} This equation we can proceed to solve the same way we would have solved the one-dimensional Schrödinger equation. We can rewrite the equation a little bit differently and th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12551_chunk_0 | Error analysis (mathematics) | In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean. For instance, in a system modeled as a function of two variables z = f ( x , y ) . {\displaystyle z\,=\,f(x,y).} Error analysis deals with the pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12552_chunk_0 | Conjugate Gradient method | In numerically challenging applications, sophisticated preconditioners are used, which may lead to variable preconditioning, changing between iterations. Even if the preconditioner is symmetric positive-definite on every iteration, the fact that it may change makes the arguments above invalid, and in practical tests le... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12553_chunk_0 | Conjugate Gradient method | The flexible version is also shown to be robust even if the preconditioner is not symmetric positive definite (SPD). The implementation of the flexible version requires storing an extra vector. For a fixed SPD preconditioner, r k + 1 T z k = 0 , {\displaystyle \mathbf {r} _{k+1}^{\mathsf {T}}\mathbf {z} _{k}=0,} so bot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12554_chunk_0 | Happy ending | In the 1961 film made on its base she finally accepts the love he offers her and the film ends with their warmly embracing, oblivious of a pouring rain. Hans Christian Andersen's fairy tale The Little Mermaid ends with the protagonist mermaid making a noble sacrifice, resigned to seeing her beloved prince marrying anot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12555_chunk_0 | Frieza | In numerous filler episodes of the anime and Dragon Ball GT, Frieza makes numerous cameo appearances, usually as comic relief, causing trouble in Hell, having somehow been permitted to keep his body despite his wrongdoings. In Hell, he is defeated and sent to prison by Goku and Pikkon along with Cell, his father and th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12556_chunk_0 | Frieza | Using a joint attack, Frieza and Cell send Goku to a lower level where he is frozen by a witch, but the two villains end up frozen themselves when they foolishly venture downwards to gloat at Goku. Goku accidentally breaks the ice holding Frieza and Cell and it shatters to pieces, implying that Frieza and Cell have bee... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12557_chunk_0 | Frieza | The song was the source of reference used by Toriyama for the title of the film Fukkatsu no F and is featured in the movie. Seikima-II frontman Demon Kakka wrote and performed the song "Tada Kogoeru Elegy ~The Theme of Frieza~" (ただ凍える挽歌(Elegy)〜The Theme Of FREEZER〜) that appeared in two episodes of Dragon Ball Kai and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12558_chunk_0 | Bayesian experimental design | In numerous publications on Bayesian experimental design, it is (often implicitly) assumed that all posterior probabilities will be approximately normal. This allows for the expected utility to be calculated using linear theory, averaging over the space of model parameters. Caution must however be taken when applying t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12559_chunk_0 | Matrix (numismatics) | In numismatics, a matrix is an intermediate mould used in the process of manufacturing coins. The use of a matrix lengthens the production of dies, but makes for a gain in consistency. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12560_chunk_0 | Reeded edge | In numismatics, reeded edges are often referred to as "ridged" or "grooved" (American usage), or "milled" (British usage). Some coins, such as United States quarters and dimes, 1 euro, Australian 5, 10, 20 cents, 1 and 2 dollars, as well many other current coins, have reeded edges. One reason for having reeded edges wa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12561_chunk_0 | Constantinian bronzes | In numismatics, the term Constantinian bronzes denotes the series of bronze coins issued in the Roman Empire in the middle of the 4th century. The specific denominations are unclear and debated by historians and numismatists. They are referred to as AE1, AE2, AE3, and AE4, with the former being the largest (near 27 mm)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12562_chunk_0 | Dietary fat | In nutrition, biology, and chemistry, fat usually means any ester of fatty acids, or a mixture of such compounds, most commonly those that occur in living beings or in food.The term often refers specifically to triglycerides (triple esters of glycerol), that are the main components of vegetable oils and of fatty tissue... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12563_chunk_0 | Dietary fat | They are a major and dense source of food energy for many animals and play important structural and metabolic functions, in most living beings, including energy storage, waterproofing, and thermal insulation. The human body can produce the fat it requires from other food ingredients, except for a few essential fatty ac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12564_chunk_0 | Bioavailability | In nutritional science, which covers the intake of nutrients and non-drug dietary ingredients, the concept of bioavailability lacks the well-defined standards associated with the pharmaceutical industry. The pharmacological definition cannot apply to these substances because utilization and absorption is a function of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12565_chunk_0 | Type soundness | In object oriented languages type safety is usually intrinsic in the fact that a type system is in place. This is expressed in terms of class definitions. A class essentially defines the structure of the objects derived from it and an API as a contract for handling these objects. Each time a new object is created it wi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12566_chunk_0 | Viscosity (programming) | In object oriented programming, viscosity refers to the ease at which a developer can add design-preserving code to a system. If it is easier to add a hack than it is to add code that fits into the program's design, then the system has high viscosity. If it is easy to add new code to the program while maintaining the d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12567_chunk_0 | Immutable object | In object-oriented and functional programming, an immutable object (unchangeable object) is an object whose state cannot be modified after it is created. This is in contrast to a mutable object (changeable object), which can be modified after it is created. In some cases, an object is considered immutable even if some ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12568_chunk_0 | Immutable object | For example, an object that uses memoization to cache the results of expensive computations could still be considered an immutable object. Strings and other concrete objects are typically expressed as immutable objects to improve readability and runtime efficiency in object-oriented programming. Immutable objects are a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12569_chunk_0 | Null Object pattern | In object-oriented computer programming, a null object is an object with no referenced value or with defined neutral (null) behavior. The null object design pattern, which describes the uses of such objects and their behavior (or lack thereof), was first published as "Void Value" and later in the Pattern Languages of P... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12570_chunk_0 | Extension methods | In object-oriented computer programming, an extension method is a method added to an object after the original object was compiled. The modified object is often a class, a prototype or a type. Extension methods are features of some object-oriented programming languages. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12571_chunk_0 | Chain-of-responsibility pattern | In object-oriented design, the chain-of-responsibility pattern is a behavioral design pattern consisting of a source of command objects and a series of processing objects. Each processing object contains logic that defines the types of command objects that it can handle; the rest are passed to the next processing objec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12572_chunk_0 | Chain-of-responsibility pattern | In some cases, this can occur recursively, with processing objects calling higher-up processing objects with commands that attempt to solve some smaller part of the problem; in this case recursion continues until the command is processed, or the entire tree has been explored. An XML interpreter might work in this manne... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12573_chunk_0 | Dependency inversion principle | In object-oriented design, the dependency inversion principle is a specific methodology for loosely coupled software modules. When following this principle, the conventional dependency relationships established from high-level, policy-setting modules to low-level, dependency modules are reversed, thus rendering high-le... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12574_chunk_0 | Inner class | In object-oriented programming (OOP), an inner class or nested class is a class declared entirely within the body of another class or interface. It is distinguished from a subclass. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12575_chunk_0 | Class instance | In object-oriented programming (OOP), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program. Formally, "instance" is synonymous with "object" as they are each a particular value (realization), and these may be called an instance object; "instance" emphasizes the d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12576_chunk_0 | Class instance | Each realized variation of that object is an instance of its class. That is, it is a member of a given class that has specified values rather than variables. In a non-programming context, you could think of "dog" as a type and your particular dog as an instance of that class.In class-based programming, objects are crea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12577_chunk_0 | Class instance | Object instantiation is known as construction. Not all classes can be instantiated – abstract classes cannot be instantiated, while classes that can be instantiated are called concrete classes. In prototype-based programming, instantiation is instead done by copying (cloning) a prototype instance. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12578_chunk_0 | Multiple inheritance | In object-oriented programming (OOP), inheritance describes a relationship between two classes in which one class (the child class) subclasses the parent class. The child inherits methods and attributes of the parent, allowing for shared functionality. For example, one might create a variable class Mammal with features... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12579_chunk_0 | Object creation | In object-oriented programming (OOP), the object lifetime (or life cycle) of an object is the time between an object's creation and its destruction. Rules for object lifetime vary significantly between languages, in some cases between implementations of a given language, and lifetime of a particular object may vary fro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12580_chunk_0 | Higher order function | In object-oriented programming languages that do not support higher-order functions, objects can be an effective substitute. An object's methods act in essence like functions, and a method may accept objects as parameters and produce objects as return values. Objects often carry added run-time overhead compared to pure... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12581_chunk_0 | Function table | In object-oriented programming languages that support virtual methods, the compiler will automatically create a dispatch table for each object of a class containing virtual methods. This table is called a virtual method table or vtable, and every call to a virtual method is dispatched through the vtable. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12582_chunk_0 | Module pattern | In object-oriented programming languages where namespaces are incompletely supported, the singleton pattern may be used instead of static members within a non-instantiable class. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12583_chunk_0 | Object resurrection | In object-oriented programming languages with garbage collection, object resurrection is when an object comes back to life during the process of object destruction, as a side effect of a finalizer being executed. Object resurrection causes a number of problems, particularly that the possibility of object resurrection –... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12584_chunk_0 | Encapsulation (object-oriented programming) | In object-oriented programming languages, and other related fields, encapsulation refers to one of two related but distinct notions, and sometimes to the combination thereof: A language mechanism for restricting direct access to some of the object's components. A language construct that facilitates the bundling of data... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12585_chunk_0 | Escape analysis | In object-oriented programming languages, dynamic compilers are particularly good candidates for performing escape analysis. In traditional static compilation, method overriding can make escape analysis impossible, as any called method might be overridden by a version that allows a pointer to escape. Dynamic compilers ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12586_chunk_0 | Named parameters | In object-oriented programming languages, it is possible to use method chaining to simulate named parameters, as a form of fluent interface. Each named-parameter argument is replaced with a method on an "arguments" object that modifies and then returns the object. In C++, this is termed the named parameter idiom. The o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12587_chunk_0 | Data abstraction | In object-oriented programming theory, abstraction involves the facility to define objects that represent abstract "actors" that can perform work, report on and change their state, and "communicate" with other objects in the system. The term encapsulation refers to the hiding of state details, but extending the concept... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12588_chunk_0 | Data abstraction | Various object-oriented programming languages offer similar facilities for abstraction, all to support a general strategy of polymorphism in object-oriented programming, which includes the substitution of one type for another in the same or similar role. Although not as generally supported, a configuration or image or ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12589_chunk_0 | Data abstraction | Although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code – all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes. Consider for example a sample Java f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12590_chunk_0 | Data Clump (Code Smell) | In object-oriented programming, "data clump" is a name given to any group of variables which are passed around together (in a clump) throughout various parts of the program. A data clump, like other code smells, can indicate deeper problems with the program design or implementation. The group of variables that typicall... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12591_chunk_0 | Method body | In object-oriented programming, a class implementation file is often used to contain the implementation code for the method(s) of a class. Programming languages like C and C++ make use of these implementation files so as to separate the interface and implementation of these methods. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12592_chunk_0 | Partial classes | In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12593_chunk_0 | Nullary constructor | In object-oriented programming, a constructor is code that is run when an object is created. Default constructors of objects are usually nullary. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12594_chunk_0 | Covariant return type | In object-oriented programming, a covariant return type of a method is one that can be replaced by a "narrower" type when the method is overridden in a subclass. A notable language in which this is a fairly common paradigm is C++. C# supports return type covariance as of version 9.0. Covariant return types have been (p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12595_chunk_0 | Factory object | In object-oriented programming, a factory is an object for creating other objects; formally, it is a function or method that returns objects of a varying prototype or class from some method call, which is assumed to be "new". More broadly, a subroutine that returns a "new" object may be referred to as a "factory", as i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12596_chunk_0 | Friend function | In object-oriented programming, a friend function, that is a "friend" of a given class, is a function that is given the same access as methods to private and protected data.A friend function is declared by the class that is granting access, so friend functions are part of the class interface, like methods. Friend funct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12597_chunk_0 | God object | In object-oriented programming, a god object (sometimes also called an omniscient or all-knowing object) is an object that references a large number of distinct types, has too many unrelated or uncategorized methods, or some combination of both. The god object is an example of an anti-pattern and a code smell. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12598_chunk_0 | Helper class | In object-oriented programming, a helper class is used to assist in providing some functionality, which isn't the main goal of the application or class in which it is used. An instance of a helper class is called a helper object (for example, in the delegation pattern). Helper classes are often created in introductory ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_12599_chunk_0 | Member variable | In object-oriented programming, a member variable (sometimes called a member field) is a variable that is associated with a specific object, and accessible for all its methods (member functions). In class-based programming languages, these are distinguished into two types: class variables (also called static member var... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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