Sentence examples for bounded by a closed from inspiring English sources

The main idea of OpenLR for locations which are bound to the road network (such as line locations or closed line locations, describing an area bounded by a closed path, i.e. a circuit of road segments) is covering the location completely with a concatenation of (several) shortest-paths.

Furthermore, it cannot output accurate closed regions, such as the gray matter region (polygon bounded by a closed yellow curve in Fig. 10 d).

In the OpenLR standard, area locations are two-dimensional parts of the surface of the earth which are bounded by a closed curve.

Let Q ⊂ R 2 be the domain bounded by a closed curve Γ: x 2 = − 2 t ln t, passing through the origin of coordinates and the point { x = 0, t = 1 } and symmetrical with respect to the axis 0t.

The grazing flow of a fully turbulent boundary layer along a perforated plate, which is bounded by a closed cavity on its backside, can give rise to highly coherent, self-sustained oscillations of the shear flow, even in absence of acoustic resonant or fluid elastic effects.

Corollary 5 Let K be a plane domain of area A, bounded by a simple closed curve of length P.

Proposition 2 Let K be a domain of area A, bounded by a simple closed curve of perimeter P in the Euclidean plane R 2. Let r and R be, respectively, the maximum inscribed radius and minimum circumscribed radius of K. Then we have the following Bonnesen's isoperimetric inequality: P 2 − 4 π A ≥ π 2 ( R − r ) 2, (4).

Corollary 3 Let K be a domain of area A, bounded by a simple closed curve of length P in the Euclidean plane R 2. Let r and R be, respectively, the inscribed radius and circumscribed radius of K, then P 2 − 4 π A ≥ π 2 ( R − r ) 2 + [ π ( R + r ) − P ] 2, (20).

Let K be a plane domain of area A and bounded by a simple closed curve of perimeter P. Denote by R and r, respectively, the radius of the minimum circumscribed disc and radius of the maximum inscribed disc of K. Then we have begin{aligned}& pi t^{2}-Pt+Aleq0;quad rleq tleq R, & frac{P-sqrt{P^{2}-4pi A}{2pi}leqq rleq Rleq frac{P+sqrt{P^{2}-4pi A}{2pi}}, & P^{2}-4pi Agepi^{2}(R- r)^{2}.

First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level.

Two algorithms are implemented: the first one for simply connected open surfaces bounded by closed lines, and for closed surface with plane symmetry; and the second for closed surfaces.