Sentence examples for by the univariate functions from inspiring English sources
Let x, s ∈ V. Then λ min ( x ) − ∥ s ∥ F ≤ λ min ( x + s ) ≤ λ max ( x + s ) ≤ λ max ( x ) + ∥ s ∥ F. Before ending this section, we need to consider the separable spectral functions induced by the univariate functions.
Then the parametric variance-based sensitivity index can be firstly expressed as the moments of the FPF, and the FPF is approximated by a product of the univariate functions of the distribution parameters, on which the moments of the FPF approximated by the univariate functions can be easily evaluated by the Gaussian integration using the values of the FPF at the Gaussian nodes.
Takacs (see [8]) has studied the strong law of large numbers for the univariate functions of finite Markov chains indexed by an infinite tree with uniformly bounded degree.
Takacs [1] studied the strong law of large numbers for the univariate functions of finite Markov chains indexed by an infinite tree with uniformly bounded degree.
Taking use of Legendre orthogonal polynomials, the univariate functions of random and interval variables are constructed by the least square fitting method and the univariate contribution bounds of interval variables are derived afterwards.
The method involves novel decomposition at the most probable point that facilitates a univariate approximation of a general multivariate function, response surface generation of the univariate function, and Monte Carlo simulation.
We quantified the degree of aggregation of the point pattern (i.e. the cells present on a given picture of a cell count chamber) by the univariate pair-correlation function g(d), which gives the expected number of points at distance d (called scale) from an arbitrary point, divided by the intensity λ of the pattern.
Firstly, the continuous univariate function Fn is defined by the solution of the corresponding parametrized least squares problem.
As in the univariate case, functions on (mathbb T ^q) can be considered as functions on (mathbb{R }^q), (2pi )-periodic in each variable.
On the other hand, radial basis functions are univariate functions which depend only on the distance between points and they are attractive to high dimensional differential equations.
where λ > 0 and ν are constants, ϕ is the level set function [40], δ is the univariate Dirac function, Ω∈ℜ2, H is the Heaviside function, and the first term ∫ Ω 1 2 − 1 | 2 ) dxdy is a metric or penalizing energy to characterize how close a function ϕ is to a signed distance function in Ω, this penalization is controlled by the parameter μ.
