A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus"[1] and "meta-calculus".[2]
^Jane Grossman, Michael Grossman, Robert Katz. The First Systems of Weighted Differential and Integral Calculus, ISBN 0-9771170-1-4, 1980.
^Jane Grossman.Meta-Calculus: Differential and Integral, ISBN 0-9771170-2-2, 1981.
A weightfunction is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result...
have a weightfunction (i.e., a function which weights each term of the inner product with a value). Explicitly, the inner product of functions u ( x )...
mentioned above, the weightfunction gives the most weight to the data points nearest the point of estimation and the least weight to the data points that...
modular form of level Γ {\displaystyle \Gamma } and weight k {\displaystyle k} is a holomorphic function f : H → C {\displaystyle f:{\mathcal {H}}\to \mathbb...
Laguerre polynomials on ( 0 , ∞ ) {\displaystyle (0,\infty )} the weightfunction is w ( x ) = e − x {\displaystyle w(x)=e^{-x}} . Both physicists and...
numbers) labeling different solutions, the strictly positive function w is called a weightfunction, and δmn is the Kronecker delta. The integration is taken...
Human body weight is a person's mass or weight. Strictly speaking, body weight is the measurement of weight without items located on the person. Practically...
Weight loss, in the context of medicine, health, or physical fitness, refers to a reduction of the total body mass, by a mean loss of fluid, body fat (adipose...
differential equation. The dependent unknown u in the same form as the weightfunction w appearing in the boundary expression is termed a primary variable...
device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, massometers and weight balances. The traditional...
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside...
Vehicle weight is a measurement of wheeled motor vehicles; either an actual measured weight of the vehicle under defined conditions or a gross weight rating...
orthogonal polynomials on the interval [−1,1] with respect to the weightfunction (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials...
x' by looking at the "neighborhood" of the point, formalized by a weightfunction W: y ^ = ∑ i = 1 n W ( x i , x ′ ) y i . {\displaystyle {\hat {y}}=\sum...
sets, A and T, together with a weightfunction C : A × T → R. Find a bijection f : A → T such that the cost function: ∑ a ∈ A C ( a , f ( a ) ) {\displaystyle...
_{n+1}(x)=\left(x-{d \over dx}\right)\psi _{n}(x).} Since these functions contain the square root of the weightfunction and have been scaled appropriately, they are orthonormal:...
and their weights. Nontrivial problems can be solved using only a few nodes if the activation function is nonlinear. Modern activation functions include...
expressed in a slightly more general way by introducing a positive weightfunction ω into the integrand, and allowing an interval other than [−1, 1]....
arranges the network into a hierarchy of groups according to a specified weightfunction. The data can then be represented in a tree structure known as a dendrogram...
Tare weight /ˈtɛər/, sometimes called unladen weight, is the weight of an empty vehicle or container. By subtracting tare weight from gross weight (laden...
the weightfunction is the identity function: therefore an integrable function f {\displaystyle f} is said to be a weighted BV function (of weight φ {\displaystyle...
non-negative function with support on some interval [x1, x2] in the real line (where x1 = −∞ and x2 = ∞ are allowed). Such a W is called a weightfunction. Then...
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming...
cumulative distribution function of the discrete measure on the rational numbers, where a i {\displaystyle a_{i}} is the weight of q i {\displaystyle q_{i}}...
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}...
polynomials are defined as an orthogonal system with respect to the weightfunction w ( x ) = 1 {\displaystyle w(x)=1} over the interval [ − 1 , 1 ] {\displaystyle...
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