Sentence examples for as solution of from inspiring English sources
We show that a nonparametric estimator of a regression function, obtained as solution of a specific regularization problem is the best linear unbiased predictor in some nonparametric mixed effect model.
A new model for the thermal spike produced by the nuclear energy loss, as source of transient processes, is derived analytically, for power law dependences of the diffusivity on temperature, as solution of the heat equation.
Finally, we discuss some of their applications to different large-scale problems, such as solution of large-scale systems of equations, eigenvalue problems, computation of the PageRank of the Google matrix, and summation of vector-valued power series.
The design is obtained as solution of a nonlinear optimization problem where the objective function represents the given heat flux manipulation task, and the design variables define the material distribution in the device.
Taking (phi =h(x)), defined in 1.7, the change-point of new Burr hazard function is obtained as solution of equation (frac{d}{mathrm{d}x}log (phi )=0).
Most natural water can be represented as solution of three cationic constituents, viz., Ca2+, Mg2+ and alkaline metals and of three anionic constituents viz., SO42−, Cl− and those contributing to alkalinity, i.e., CO32− and HCO3−.
Dilute solutions of strong acids for example, hydrochloric, sulfuric, and perchloric (HCl, H2SO4, HClO4 in water behave essentially as solutions of the ion H3O+, and their acidity increases in proportion to their concentration.
Therefore, it is natural to seek these solutions as solutions of ordinary differential equations.
By Lemma 2.3, we have the critical points of as solutions of problem (3.19).
One also can see that the generating functions are determined as solutions of (2.23).
