Sentence examples for bounds of the solution from inspiring English sources
Also, the results yield the upper bounds of the solution to the stated problem.
In this paper a new discretization concept is proposed which generates uniform lower and upper bounds of the solution of the Thomas-Fermi equation.
The conditions for the existence of at least one positive solution are established together with the estimates of the lower and upper bounds of the solution at any instant of time.
The proof of the method which is based on the construction of some bounds of the solution together with global continuous theorem and fixed point index is of independent interest, and is different from the other papers.
Finally, our main result is applied to an estimation of the bounds of the solutions of a partial differential equation with impulsive terms.
The lower and upper bounds of the solutions can be calculated, respectively, as check{mathbf{x}} = (0.2, 0.3, 0)^{T}, qquadhat{mathbf{x}} = (0.9, 1, 0.8)^{T}.
In view of Theorems 1 and 2 and Corollaries 1 and 2, any result on the existence of lower and upper bounds of the solutions of (1) yields some global asymptotic stability result for the unique equilibrium of (1).
In other words, (check{mathbf{x}}) and (hat{mathbf{x}}) are the lower and upper bounds of the solutions to (A^circmathbf{x} vee A^ circnegmathbf{x} = mathbf{b}), respectively.
Bounds for the mean-square performance are established on the basis of upper bounds for the solution of the relevant Riccati equation.
