Sentence examples for estimate theory from inspiring English sources

Extensions of Smale's point estimate theory for Newton's method on Lie groups were given in [19].

Another important result on Newton's method is Smale's point estimate theory (i.e., α-theory and γ-theory) in [2], where the notions of approximate zeros were introduced and the rules to judge an initial point x 0 to be an approximate zero were established, depending on the information of the analytic nonlinear operator at this initial point and at a solution x ∗, respectively.

The γ-conditions for nonlinear operators in Banach spaces were first introduced and explored by Wang [25, 26] to study Smale's point estimate theory, which was extended in [19] for a map f from a Lie group to its Lie algebra in view of the map d 2 f as given in Definition 5.1 below.

Let L be a positive nondecreasing integrable function on [ 0, R ], where R is a positive number large enough such that ∫ 0 R ( R − s ) L ( s ) d s ≥ R. The notion of Lipschitz condition in the inscribed sphere with the L average for operators from Banach spaces to Banach spaces was first introduced in [23] by Wang for the study of Smale's point estimate theory.

Very recently, the book Convergence Estimates in Approximation Theory written by Gupta and Agarwal (see [8]) introduced some approximation properties of certain complex q-operators in compact disks.

Table 1 summarizes these estimates (theory and simulation) over wide ranges of the parameters typical of in vivo conditions: K M = 10 μM - 1000 μM [ 17], enzyme copy numbers of ten and one hundred per compartment which correspond to enzyme concentrations ranging from 4 μM to 2.5 mM and compartment diameters ranging from 50 nm to 200 nm.

"While this updated estimate in theory gives Congress additional time to complete work on increasing the debt limit, I caution strongly against delaying action," the Treasury secretary, Timothy F. Geithner, wrote Monday to lawmakers.

In this article, the curvature of the columns is estimated from theory.

We emphasize solute chemical potentials in polymers, liquids and their mixtures as they cannot be understood and estimated without theory.

The maximum pressure recovery coefficient (PRC) was estimated in theory and a theoretical equation was obtained with the ideal gas assumption.

The Lennard Jones (LJ) diameter of α-pinene was 6.19129 × 10−8 cm, which differs only 0.95% from one estimated by theory.