Sentence examples for bounded together with from inspiring English sources
Since is bounded together with being demicompact, there exists a subsequence of which converges strongly to some.
Proof Since q is of bounded variation for t ≥ 0, all solutions of (3) are bounded together with their derivatives, see e.g. [[18], Theorem 2].
An infinitely differentiable function φ ( x ) of the continuous argument x ∈ R n that is continuous and bounded together with all its derivatives is said to be smooth.
An infinitely differentiable function of the continuous argument (yin mathbb{R}^{n-1}) that is continuous and bounded together with all its derivatives is said to be smooth.
We shall show that the sequence of modified problems (17) is such that each problem has a unique solution, which is uniformly bounded, together with its first and second order derivatives.
System (3.2) is said to be reducible (or reducible to zero), if there exists which is bounded together with its inverse on such that is a constant (or zero) matrix on.
Since W is continuous, thus, W is bounded on bounded sets, together with that | Ω − Ω ν | → 0 as ν → ∞, we then have the last integral in the right hand side of (3.4) converges to zero as ν → ∞.
Finally, such bounds together with the input sequence are used for bounding the parameters of the linear model.
The two fundamental developments in this work are (1) a method to explicitly compute upper bounds on failure probability based on solving an optimization problem, and (2) a hybrid method, utilizing the upper bounds together with conditional sampling, to achieve highly accurate estimates of failure probabilities.
On the basis of the estimate of tire longitudinal forces we estimate the range of lateral forces which the tire can exert; these bounds, together with the rate limiter of the braking system, represent the hard constraints of MPC controller and the saturations of LQR controller.
Finally, collecting all these bounds together with ε being small enough, we have bigl| u^-u_{h}^bigr| _{L^{2}(Omega)} le C h biggl[ bigl| u^bigr| _{H^{1}(Omega)} +sum_{v=y,z tau=sigma,omega} bigl(bigl| v^ bigr| _{H^{2}(Omega)}+bigl| tau ^bigr| _{H^{1}(Omega)^{d}} bigr) biggr].
