Sentence examples for manifold at the from inspiring English sources

Hence, the curvature tensor R provides the complete information of the manifold at the curvature level on g.

Then, the time-varying sliding mode manifold is designed through calculating a series of algebraic equations with fixed final states to make the system trajectories start on the manifold at the initial time.

Further experiments were performed using the HFM manifold at the 1.5″ (3.8 cm) depth and temperatures were varied at 20 °C, 30 °C and 40 °C to determine the effects of temperature on the mass transfer.

If we solve these for (E_{1} ) and (E_{2} ), we compute (W_{20} ( theta )) and (W_{11} ( theta )) from (8), (9), (10) and confirm the following values to investigate the qualities of the bifurcation periodic solution in the center manifold at the critical value (tau_{k} ) (see [9]).

CAPs samples were collected from a sampling manifold at the exposure chamber entry at 3.0 L/min on 47-mm Teflon filters (polytetrafluoroethylene; Gelman, Ann Arbor, MI) throughout each exposure (about 5 hr); samples were analyzed gravimetrically using a Mettler MT5 precision microbalance (Mettler Toledo, Columbus, OH).

It contains, on the one hand, the kinetic parameters that are unknown (r in case that all the rate constants are unknown) and, on the other hand, the degrees of freedom which are needed to define the equilibrium manifold at the two bifurcation points.

The tangent space, at, is the plane tangent to the surface of the manifold at that point.

The model is applicable to a fixed topology of wells that may have been drilled in different reservoirs and are interconnected with manifolds at the surface.

throughout the entire system, from the manifolds at the engine to the exit point.

The key idea is to "grow" the manifold in steps, which consist of finding a new point on the manifold at a prescribed distance from the last point.

The (2 M + N -1) × D matrix A ω0) is the array manifold at ω0, whose columns are the steering vectors corresponding to the sources directions.