# Applied Quaternionic Analysis by Kravchenko V. V. PDF

By Kravchenko V. V.

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Example text

F (x) also decreases when R ! 14) ix ! f =o jxj 1 jxj ; when jxj ! 7) is of the type O ! 1 jxj when jxj ! , and in this case f ! 9) taken over the sphere in…nity also. 1. 4) div B = 0: The notation used in these equations is explained in the following table. Notation Physical quantity Units in the mks system volume charge density coulomb/m3 j current density amper/m2 E electric …eld intensity volt/m H magnetic …eld intensity amper/m D electric induction vector coulomb/m2 B magnetic induction vector tesla=volt sec/m2 51 52 3.

1: commute with P taken over the sphere In the case when R we obtain that the integral K! f (x) also decreases when R ! 14) ix ! f =o jxj 1 jxj ; when jxj ! 7) is of the type O ! 1 jxj when jxj ! , and in this case f ! 9) taken over the sphere in…nity also. 1. 4) div B = 0: The notation used in these equations is explained in the following table. Notation Physical quantity Units in the mks system volume charge density coulomb/m3 j current density amper/m2 E electric …eld intensity volt/m H magnetic …eld intensity amper/m D electric induction vector coulomb/m2 B magnetic induction vector tesla=volt sec/m2 51 52 3.

The quantity is called the wave number. 8) ! D E = i! 2. TIME-HARMONIC MAXWELL’S EQUATIONS ! 9) 59 ! " E + j : We now explain a simple procedure for the diagonalization of Maxwell’s equations which was proposed for the …rst time in [44] (see also [58]). We introduce the following pair of purely vectorial biquaternionic functions ! ' := ! " E + H and ! ! " E + H : We apply the operator D to ! 9): D! ' = ! "D E + D H = 2! ! " E + j = ! ' +i! + j : H +i! Thus, ! 10) (D Analogously, ! )! ' = div ~j + ~j: satis…es the equation !