Sentence examples for exists a trajectory from inspiring English sources

By the continuity of system (3.3), there exists a trajectory Γ that connects ((a_{2k},0)) and ((b_{2k},0)).

We need to show that there exists a trajectory connecting the two singular points ((a_{2k},0)) and ((b_{2k},0)).

In this section we show that if for any initial point, there exists a trajectory of the dynamical system induced by a nonexpansive set-valued mapping, which converges to an invariant set, then a convergent trajectory also exists for a nonstationary dynamical system induced by approximations of.

From the vector field construction of the phase space of model (2.5), we suppose there exists a trajectory (Pi(C,t_{0})) starting from the initial point (C(S_{C}, mathit{RL} in Sigma_{p_{max}}) such that the line (I=mathit{RL}) tangents to this trajectory at point (D(G(mathit{RL}),mathit{RL})).

We show there that if for any initial point, there exists a trajectory of the dynamical system induced by a nonexpansive set-valued mapping, which converges to a given invariant set, then a convergent trajectory also exists for a nonstationary dynamical system induced by approximations of.

For any point (y_{0}in A), it follows from Definitions 4.1 and 4.2, and [18], Theorem 1.40, that there exists a total trajectory (Y cdot)) with (y(0)=y_{0}) and (y(t)in A) for all (tinmathbb{R}).

Proof of Theorem 5.1 For ε > 0, u ε ∈ A ε, we obtain that there exists a complete bounded trajectory u ˆ ε ( t ) of equation (3.3), with some external force f ˆ ε = f ˆ 0 + ε − ρ f ˆ 1 ∈ H ( f ε ), (5.21).

Then there exists a G-Picard trajectory ({x_{n}}) converging to x a fixed point of F. It is important to understand that if F is a G-contraction then for ((x,y) in E(G)) and (uin F x)), there is (v in F y)) such that there is an 1-directed path from u to v such that (d u,v) lelambda d x,y)).

Then there exists a (G_{m} -Picard trajectory ({x_{n}}) converG_{m} -Picardixed pointrajectory) Arguing as in [12], it can be shown that if (F : X to X) is a multivalued G-contraction, then there exists (alphain,]0,1[) such that, for all (y in[x]_{x_{n}}) and all (u in F(x)), there exists (v in F(y)converging^{m}) such toat (p_{m}(u,v) lealpha p_{m}(x,y)).

The creation of the National Institute of Circus Arts NICAA), which offers a three-year bachelor of circus arts course, is a hothouse for new performers and companies, and there also exists an established Australian trajectory for performers out of circus school.

There exists a connection between speed and trajectory shapes.