Sentence examples for planar end from inspiring English sources

The planar end E m is located between the two catenoidal ends.

The planar end E m, τ of the surface M k, τ can be parametrized by X m, τ ( x ) : = ( τ x | x | 2, τ u m ( x ) ) ∈ R 3, (4).

The Jacobi operator of M k, τ, up to a multiplicative factor, is asymptotic, respectively, to the operators | x | 4 Δ 0 and L C at the planar end and the catenoidal end.

It has one planar end E m asymptotic to the horizontal plane x 3 = 0, one top end E t and one bottom end E b that are, respectively, asymptotic to the upper end and to the lower end of a catenoid having the x 3 -axis as axis of rotation.

Proof We recall that the Jacobi operator associated to M k, τ, is asymptotic (up to a multiplication by 1 / τ 2 ) to the Jacobi operator of the catenoid (respectively, of the plane) plane at the catenoidal ends (respectively, at the planar end).

s = − s τ ); we recall that n c ( ± s τ, ⋅ ) are the unit normal vectors to the translated copy of the halves catenoid parametrized by X c, τ ± σ τ e 3 along the curves Γ t, Γ b ; at the middle planar end, the vertical vector field e 3 for ρ in a small neighborhood of ρ = ρ τ ; the normal vector field n τ on the remaining part of the surface.

A typical push- pull chromophore consists of a polar A-π-D system with a planar π-system end-capped by a strong electron donor (D) and a strong electron acceptor (A).

The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.

We found continuous planar monolayers of end-grafted FG repeat domains (Fig 1A) to be suitable for this goal.

A detailed analysis is performed for starlike polymers end-tethered to planar surface by terminal monomer of one of their branches.

Howard I, Ingram J, Wolpert D: A modular planar robotic manipulandum with end-point torque control.