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Residual
A residual is generally a quantity left over at the end of a process. It may refer to: Business * Residual (entertainment industry), in business, one of an ongoing stream of royalties for rerunning or reusing motion pictures, television shows or commercials * Profit (accounting), residuals that shareholders, partners or other owners are entitled to, after debtors are covered **Residual in the bankruptcy of insolvent businesses, moneys that are left after all assets are sold and all creditors paid, to be divided among ''residual claimants'' * Residual (or balloon) in finance, a lump sum owed to the financier at the end of a loan's term; for example Balloon payment mortgage Mathematics, statistics and econometrics * Residual (statistics) ** Studentized residual * Residual time, in the theory of renewal processes * Residual (numerical analysis) ** Minimal residual method ** Generalized minimal residual method * Residual set, the complement of a meager set * Residual property (m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residual (entertainment Industry)
Residuals are financial compensations that are paid to the actors, film or television directors, and others involved in making TV shows and movies in cases of reruns, syndication, DVD release, or online streaming release. Residuals are calculated and administered by industry trade unions like SAG-AFTRA, the Directors Guild of America, and the Writers Guild of America. The word is typically used in the plural form. History Technological advances gave rise to residual payments, and their evolution can be traced in terms of those technologies. Radio Residuals were established in U.S. network radio. Live radio programs with nationwide audiences were generally performed either two or three times to account for different time zones between the east and west coasts of the United States. The performers were paid for each performance. After audio "transcription disc" technology became widely available in the late 1930s, it was initially used to make recordings to send to radio stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studentized Residual
In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's ''t''-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym ''Student''. Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing. Motivation The key reason for studentizing is that, in regression analysis of a multivariate distribution, the variances of the ''residuals'' at different input variable values may differ, even if the variances of the ''errors'' at these different input variable values are equal. The issue is the difference between errors and residuals in statistics, particularly the behavior of residuals in regressions. Consider the simple linear regression model : Y = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residual (statistics)
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its " true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the '' estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solow Residual
The Solow residual is a number describing empirical productivity growth in an economy from year to year and decade to decade. Robert Solow, the Nobel Memorial Prize in Economic Sciences-winning economist, defined rising productivity as rising output with constant capital and labor input. It is a " residual" because it is the part of growth that is not accounted for by measures of capital accumulation or increased labor input. Increased physical throughput – i.e. environmental resources – is specifically excluded from the calculation; thus some portion of the residual can be ascribed to increased physical throughput. The example used is for the intracapital substitution of aluminium fixtures for steel during which the inputs do not alter. This differs in almost every other economic circumstance in which there are many other variables. The Solow residual is procyclical and measures of it are now called the rate of growth of multifactor productivity or total factor productivity, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residually Finite Group
{{unsourced, date=September 2022 In the mathematical field of group theory, a group ''G'' is residually finite or finitely approximable if for every element ''g'' that is not the identity in ''G'' there is a homomorphism ''h'' from ''G'' to a finite group, such that :h(g) \neq 1.\, There are a number of equivalent definitions: *A group is residually finite if for each non-identity element in the group, there is a normal subgroup of finite index not containing that element. *A group is residually finite if and only if the intersection of all its subgroups of finite index is trivial. *A group is residually finite if and only if the intersection of all its normal subgroups of finite index is trivial. *A group is residually finite if and only if it can be embedded inside the direct product of a family of finite groups. Examples Examples of groups that are residually finite are finite groups, free groups, finitely generated nilpotent groups, polycyclic-by-finite groups, fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Residual Method
In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector. The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986. It is a generalization and improvement of the MINRES method due to Paige and Saunders in 1975. The MINRES method requires that the matrix is symmetric, but has the advantage that it only requires handling of three vectors. GMRES is a special case of the DIIS method developed by Peter Pulay in 1980. DIIS is applicable to non-linear systems. The method Denote the Euclidean norm of any vector v by \, v\, . Denote the (square) system of linear equations to be solved by : Ax = b. \, The matrix ''A'' is assumed to be invertible of size ''m''-by-''m''. Furthermore, it is assumed that b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residuated Lattice
In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice ''x'' ≤ ''y'' and a monoid ''x''•''y'' which admits operations ''x''\''z'' and ''z''/''y'', loosely analogous to division or implication, when ''x''•''y'' is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, these operations coincide when the monoid is commutative. The general concept was introduced by Morgan Ward and Robert P. Dilworth in 1939. Examples, some of which existed prior to the general concept, include Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation ∧, for example Kleene algebras and action algebras. Definition In mathematics, a residuated lattice is an algebraic structure L = (''L'', ≤, •, I) such that : (i) (''L'', ≤) is a lattice. : (ii) (''L'', •, I) is a monoid. :(iii) For all ''z'' ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residual (numerical Analysis)
Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find ''x'' such that : f(x)=b. Given an approximation ''x''0 of ''x'', the residual is : b - f(x_0) that is, "what is left of the right hand side" after subtracting ''f''(''x''0)" (thus, the name "residual": what is left, the rest). On the other hand, the error is : x - x_0 If the exact value of ''x'' is not known, the residual can be computed, whereas the error cannot. Residual of the approximation of a function Similar terminology is used dealing with differential, integral and functional equations. For the approximation f_\text of the solution f of the equation : T(f)(x)=g(x) \, , the residual can either be the function : ~g(x)~ - ~T(f_\text)(x) or can be said to be the maximum of the norm of this difference : \max_ , g(x)-T(f_\text)(x), over the domain \mathcal X, where the function f_\text is expected to approximate the solution f , or some integral of a function of the differe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residual Time
In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between any given time t and the next epoch of the renewal process under consideration. In the context of random walks, it is also known as overshoot. Another way to phrase residual time is "how much more time is there to wait?". The residual time is very important in most of the practical applications of renewal processes: * In queueing theory, it determines the remaining time, that a newly arriving customer to a non-empty queue has to wait until being served. * In wireless networking, it determines, for example, the remaining lifetime of a wireless link on arrival of a new packet. * In dependability studies, it models the remaining lifetime of a component. * etc. Formal definition Consider a renewal process \, with ''holding times'' S_ and ''jump times'' (or renewal epochs) J_, and i\in\mathbb. The holding times S_ are non-negativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lung Volumes
Lung volumes and lung capacities refer to the volume of air in the lungs at different phases of the respiratory cycle. The average total lung capacity of an adult human male is about 6 litres of air. Tidal breathing is normal, resting breathing; the tidal volume is the volume of air that is inhaled or exhaled in only a single such breath. The average human respiratory rate is 30–60 breaths per minute at birth, decreasing to 12–20 breaths per minute in adults. Factors affecting volumes Several factors affect lung volumes; some can be controlled, and some cannot be controlled. Lung volumes vary with different people as follows: A person who is born and lives at sea level will develop a slightly smaller lung capacity than a person who spends their life at a high altitude. This is because the partial pressure of oxygen is lower at higher altitude which, as a result means that oxygen less readily diffuses into the bloodstream. In response to higher altitude, the body's dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residuated Mapping
In mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. It refines the concept of a monotone function. If ''A'', ''B'' are posets, a function ''f'': ''A'' → ''B'' is defined to be monotone if it is order-preserving: that is, if ''x'' ≤ ''y'' implies ''f''(''x'') ≤ ''f''(''y''). This is equivalent to the condition that the preimage under ''f'' of every down-set of ''B'' is a down-set of ''A''. We define a principal down-set to be one of the form ↓ = . In general the preimage under ''f'' of a principal down-set need not be a principal down-set. If it is, ''f'' is called residuated. The notion of residuated map can be generalized to a binary operator (or any higher arity) via component-wise residuation. This approach gives rise to notions of left and right division in a partially ordered magma, additionally endowing it with a quasigroup structure. (One speaks only of residuated algebra for higher arities). A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
