Nabla

Finally, 3 " (j)[f (x )] is a short symbol expressing the m-th order partial derivative operators, acting first over the function f (x) and then, the resultant function, evaluated at the point x . The differential operators can be defined in the same manner as the terms present in equation (9), but using as second argument the nabla vector ... 

Equation (44) suggests that a vector operator V or nabla (called del") be defined in Cartesian coordinates by... 

The V operator may be used to define further quantities, such as V20 (nabla squared 0) defined as the scalar product... 

Instead of the dot product the vector product of the nabla operator can also be formed to produce a function called curl or rot,... 

The divergence of a vector v with components vt,v2. .., v is the scalar number noted either dive or, with the nabla notation V t, defined as ... 

The vectorial operator gradient (with symbol nabla V) allows the passage from scalar to vectorial fields. For scalar the vector V4> (gradient of (fi) is given by... 

The notation 8/8R designates the gradient operator, also called nabla (V j). We thus finally obtain from Eqs. 2.35 and 2.36 [296]... 

J. Escobar. Algebra lineal para principiantes. Serie Nabla-Delta, Medellin, Colombia, 1990. 

We shall assume that our system is spherically symmetric so with the nabla operator in spherical coordinates, the diffusion equation may be written... 

The recurring vectorial operator V, known as del or nabla, is a differential operator that, in rectangular coordination is defined as ... 

V - nabla operator, Vt]a = (Vtjai> Vt uA), H - a field conjugate to the parameter tp. In Eq. 5 the dependence of order parameters on coordinates is used implicitly. 

In noncubic materials, A must be replaced by the 3x3 exchange-stiffness tensor A v, and the energy is X J A v dM/dxy dM/dxv dV. Here the indices ju and v denote the spatial coordinates x, y, and z of the bonds. The energy is anisotropic with respect to the nabla operator = d/d (bond anisotropy) but isotropic with respect to the magnetization M. By contrast, the relativistic anisotropic exchange Xa i Ha(i VMa VMP dV is isotropic with respect to V but anisotropic with respect to M. 

The mathematical operator V, called Nabla or del, appearing in Eq. (7-6) has the structure ... 

Ski Slopes," "Hernias", and Curls. In Cartesian space the "del" (or nabla = Assyrian harp or atled = "backwards delta") operator or function V is given by... 

Fock 18, 19 hamiltonian 16 kinetic energy 16 Laplacian 85 logical 86 mathematical 84 matrix element of 16 momentum 16 nabla 85 symmetry 27, 38 optical rotation 33 optical rotatory power 33 orbital energy 18 order of reaction 55 order of reflection 36 order parameters 36 oscillator strength 33 osmole 51... 

Differentiation of a tensor with respect to a scalar does not change its rank. The spatial differentiation of a tensor raises its rank by unity, and identical to multiplication by the vector V, called del or Hamiltonian operator or the nabla... 

The relativistic correction of the mass variation with velocity depends essentially on the fourth power of the nabla operator [68b]. In fact one can write the involved integral as ... 

Another vector that we need to discuss is the nabla, V. This vector may be decomposed in the cartesian coordinates as follows ... 

Usi g these new-found formulas, we evaluate the dot product of nabla and the... 

Here the first term with V the Nabla operator is the kinetic energy, the second is the potential energy due to the nuclear charge, and the last term is the total electrostatic interaction energy over all pairs of electrons. 

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