Sentence examples for be the differential operator from inspiring English sources

Let L be the differential operator defined in (26).

Let be the differential operator and Then the eigenvalue problem (2.1).

Furthermore, let L ( x, t, ∂ x ) be the differential operator (2) with coefficients a i j and a j satisfying the conditions (21) and (22) (with G T instead of D × R ).

end{aligned} (1.5) Let (H 0)) be the differential operator in (L^{2}(0,1]) associated to -varphi +Kvarphi=lambda varphi,qquad lim_{yto0+} bigl varphi' y)U_{0} y)- varphi y)U'_{0} y) bigr)=0,qquad varphi(1)=0.

Let £ ξ be the differential operator £ ξ u = u t t − u x x + c u t − ξ u, acting on functions on ⊤ 2. Following the discussion in [14], we know that if ξ < 0, £ ξ has the resolvent R ξ, R ξ : L 1 ( ⊤ 2 ) → C ( ⊤ 2 ), h i ( t, x ) ↦ u i ( t, x ), where u ( t, x ) is the unique solution of Eq. (2), and the restriction of R ξ on L p ( ⊤ 2 ) ( 1 < p < ∞ ) or C ( ⊤ 2 ) is compact.

where is the differential operator.

We all know that any differential form u can be decomposed as u = d ( T u ) + T ( d u ), where d is the differential operator, and T is the homotopy operator.

In the calculation, s is the differential operator, K is a proportional gain, Qd is the current value of Q, and I(Qd) is the calculation of the inverse kinematics of the parallel links.

(lambda (c_{i})) is continuous at (c_{i}=infty), where (H infty)) is the differential operator associated to -varphi"+alpha ^{2}varphi=lambda varphi quad textit{in } L^{2} -1, 1),qquad varphi -1)=varphi -1=varphi

It follows that the radial part of (D(I_ell )), which is the differential operator corresponding to (D(I_ell )) on (T^+), annihilates the restricted character (I t) = chi _{T^+}^prime (t)).

If I is any element of the universal enveloping algebra (mathsf {U}(mathfrak {g})) and D(I) is the differential operator associated to I by (X mapsto L_X), then begin{aligned} D(I chi (x) = mathrm {STr}, (rho _*(I), rho (x), mathrm {e}^{,sum xi _j, rho _*(F_j)}),.