Sentence examples for frame of vector from inspiring English sources

Let {X0 = ξ, X1, X2,..., X p, Xp+1= ϕX1,..., X2p= ϕX p } be a local orthonormal frame of vector field on N T and {Z1, Z2,..., Z q } be a local orthonormal frame of vector field on N⊥.

Let {X1, X2,..., X p, Xp+1= ϕX1,..., X2p= ϕX p, X2p+1= ξ} be a local orthonormal frame of vector fields on N T and {Z1, Z2,..., Z q } a local orthonormal frame on N⊥.

Let {X0 = ξ, X1, X2,..., X p, Xp+1= ϕX1,..., X2p= X p } and {Z1, Z2,..., Z q } be a local orthonormal frame of vector fields on N T and N⊥, respectively.

where n is the dimension of M and {e1, e2,..., e n } is a local orthonormal frame of vector fields on M. The squared norm of the second fundamental form is defined as ∥ h ∥ 2 = ∑ i, j = 1 n g ( h ( e i, e j ), h ( e i, e j ) ).

If {e1, e2,..., e n } be a local orthonormal frame of vector fields on M then we define h 2 = ∑ i, j = 1 n g ( h ( e i, e j ), h ( e i, e j ) ), and for differentiable function f on M, the Laplacian Δf of f is defined as Δ f = ∑ j = 1 n { e j ( e j f ) - ∇ e j e j f }. (3.12).

The complete artificial DNA was first cloned into the XhoI– NotI frame of vector pBluescript SK and confirmed by automated DNA sequencing.

The magnetic field vector in the Level-1b CDF files is given both in the NEC coordinate frame and in the VFM frame of the vector magnetometer.

The approximating distance functions (d_epsilon ) can be defined in terms of an extended generating frame of smooth vector fields (X_1^epsilon,ldots,X_p^epsilon ), with (pge n) and (X_i^epsilon =X_i) for (i=1,ldots,m), that converges/collapses uniformly on compact sets to the original family(X_1,ldots,X_m) as (epsilon rightarrow 0).