Sentence examples similar to e respect from inspiring English sources

The partial orderings ⪯, ≺, and ≪ on E with respect to P are defined as follows, respectively.

The square operator s ↦ s ⋄ s is an automorphism of E with respect to ⋄ and ⋆.

Note that (E^*) coincides with the Steiner symmetral of E with respect to the line ({x^prime =0}).

where the integrals are over the set E with respect to the channel distribution m h (h).

The reverse numerical differentiation of the direct shapes N(E) with respect to energy E facilitates an analytical consideration (Fig. 5b).

Since (m(E subset C_{alpha}), we see that (C_{alpha}) is an essential sets of (F_{s}(E)) with respect to (rho_{s}^{u}).

The partial ordering in E with respect to P is given by x ≲ y ⟺ x i ≤ y i, 1 ≤ i ≤ n, then E is a lattice.

For every (Einmathcal{E} ), if the minimum essential set of (F_{s}(E)) with respect to (rho_{s}^{u}) is connected, then it is a stable set.

Then τ ˜ is clearly an endomorphism of E with respect to ⋆. Therefore the corollary follows immediately from Theorem 2 with δ = 0. □.

While more investigation is required, such changes should result in the complicated behaviors of H E with respect to wavelength, shown in Figure 4b.

The least square procedure is to take the partial derivative of (E) with respect to each element in ({mathbf{m}}) and set the resulting equations to zero.