41. Also, the Cauchy Riemann equations imply that the dot product \ nabla u \ cdot \ nabla v = 0. 42. His 1867 " Elementary Treatise of Quaternions " included extensive treatment of the nabla or del operator ". 43. (A contrary view is that notation is not abused if one does not think of \ nabla as a vector. 44. Covariant derivatives are denoted either by the operator \ nabla _ { i } or by subscripts preceded by a semicolon. 45. For the rest of this section, \ nabla \ phi \, will assumed to be zero unless otherwise specified. 46. Its components are known as "'Beltrami stress functions "'. \ varepsilon is the Nabla operator. 47. However, in the above, we used the chain rule so the existence of \ nabla f would not be sufficient. 48. Where \ scriptstyle \ boldsymbol \ nabla T is the temperature gradient and \ scriptstyle \ mathcal K is the Thomson coefficient. 49. Where \ nabla _ 1 ^ 2 and \ nabla _ 2 ^ 2 refer to particle 1 and particle 2 respectively. 50. Where \ nabla _ 1 ^ 2 and \ nabla _ 2 ^ 2 refer to particle 1 and particle 2 respectively.
