Sentence examples for convergent to zero from inspiring English sources

And we can get that the state error variables are convergent to zero as, and the phase error variables are convergent to zero and as defined by Corollary 3.5, which illustrated that the complex network (4.1) achieves phase synchronization.

Now from the exponential convergence of in system (2.6) and asymptotical convergence of in system (2.8), we obtain that in system (2.7) are asymptotical convergent to zero.

Now we prove the solution convergent to zero firstly.

Then the sequence ( x n ) is weakly convergent to zero.

Some examples of matrix convergent to zero are.

Specifically, the estimation errors are asymptotically convergent to zero using LaSalle-Yoshizawa Theorem. LaSalle-Yoshizawa Theorem

Moreover, since X = L1 [0,T] × R) is a separable Banach space and u ε n x, ρ ε n x are bounded sequences in the dual space X* = L∞([0,T] × R) of X, there are two subsequences of u ε n x, ρ ε n x (still denoted by u ε n x, ρ ε n x ) weak star convergent to two functions U, P ∈ L∞([0,T] × R), respectively.

If x ∈ N θ 0 ( c ˆ, φ, f ), the sequence x is said to be almost lacunary strong φ-convergent to zero with respect to a modulus f.

On the other hand, the sequence is not F Λ Open image in new window-convergent to zero as F ( Λ x k − ℓ, z ; t ) = t t + | Λ x k | = t t + k z 2, if m − [ λ m ] + 1 ≤ k ≤ m ; 1, otherwise.

Thus, from every subsequence, one can extract a convergent one that converges to zero thus, begin{array}{*{20}l} &X_{k,M} z_{1},z_{2} -overline{X}_{k,M}(z_{1},z_{2} -overline{X}_{kto+infty]{M} z_{{a.s.}}0 & qquad forall z_{1},z_{2}} in mathbb{C}backslashmathbb{R}_.

Three sequences ({x_{n}}), ({y_{n}}), and ({z_{n}}) are proved to be strongly convergent to the zero point of the sum of an infinite family of m-accretive mappings and an infinite family of (mu_{i} -inversely strongly accretive mu_{i} -inversely