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By Fan Sh., Han W.

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It is important to note that one or the other (but not both) boundary conditions must be specified over the entire bounding surface and the solution that satisfies the given boundary conditions over this closed surface s is the unique solution. It is further to be noted that for a unique solution, potential must be defined at least at one point on the boundary and the solution must satisfy this boundary condition. The uniqueness theorem1 presented above provides for a set of boundary conditions over closed surfaces.

40 in the Cartesian system of space coordinates. 42c) where the contour c is the edge (or border) of the surface s. 42c reduces to a simpler form as elaborated through the following example. Let the vectors A and B be independent of the z coordinate. 1, with two sides, bc and da, parallel to the Z-axis. Let the vector potential along the side bc be A1 and along ad be A 2. Along the side ab the potential varies from A 2 to A1, while, along cd, it varies from A1 to A 2. 42c, is ϕ = ( A1z − A2z ) where ℓ indicates the length of the side bc (and ad).

Applications for the torch function synthesis method for the solution of eddy current equation are discussed in Chapter 5. 2 Uniqueness Theorem for Vector Magnetic Potentials In general, there are infinite solutions of Laplace and Poisson equations for the vector magnetic potential A. The uniqueness theorem2 reviewed here describes boundary conditions to be satisfied for a unique solution of these equations. 40, given the distribution of magnetic potential in a volume v bounded by the closed surface s.

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0,1 distribution in the highest level sequences of primitive sequences over Z 2e by Fan Sh., Han W.

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