Sentence examples for warping function from inspiring English sources

Also, as W μ = 0, for all W ∈ Γ(D⊥), i.e., the mean curvature vector of N⊥ is parallel and the leaves of D⊥ are extrinsic spheres in M. Hence from a result of Hiepko [10], the submanifold M is locally a warped product semi-invariant submanifold of N T and N⊥ with warping function λ = e μ. ■.

The Lorentzian manifold is the warped product, in the sense of [1, page ], with base, fiber, and warping function.

Recently Atceken [4] studied contact CR-warped product submanifolds in Cosymplectic space-forms and obtained an inequality for second fundamental form in terms of warping function.

This algorithm unifies the nonlinear frequency warping function and speaker variability due to vocal tract length differences in the front-end of the automatic speech recognition and significantly reduces computational complexity.

The nonuniform shear warping distribution is taken into account by employing one independent warping parameter multiplying a shear warping function, which is obtained by solving a corresponding boundary value problem, formulated exploiting the longitudinal local equilibrium equation.

The shear locking is avoided by introducing an interior node to the element and adopting two-node Hermitian interpolation functions for transverse displacements and torsional rotation and three-node Lagrangian interpolation functions for the flexural rotations and warping function.

The nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, respectively, which are obtained by solving the corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation.

Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, which are obtained by solving corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation.

The function f is called the warping function of the warped product [7].

Lemma 3.1 Let M = N 1 × f N 2 be a warped product manifold with the warping function f.

We note that the warping functions w are in the set 𝓜 = { w ∈ C([0, T))|0 ≤ w(t) < L and w(t1) < w(t2), t1 < t2} of continuous, non-negative, and strictly increasing functions bounded by L and defined over the interval [0, T). We then determine a warping function that minimizes the cost function.