In this paper, we present a method for the fast and accurate computation of the local cross-correlation of 3D vectorial data. Given spherical patches of 3D vector fields, our method computes the full crosscorrelation over all possible rotations and allows an accurate estimation of the rotation offset between two patches. Our approach is based on a novel harmonic representation for 3D vector fie...

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

• (i) G = ZN = Z/NZ = {0, 1, 2, ....., N − 1} with addition modulo N . For 0 ≤ n ≤ N − 1 let γn : G → S, γn(m) = exp(2πimn/N). Then {γ0, ....., γN−1} is a complete list of the characters so that ZN is isomorphic to ZN . An example of a primitive N ’th root of unity is ω := exp 2πi/N . • (ii) G = T = R/Z; for n ∈ Z let γn : G→ S, γn(x) = exp(2πinx). Then G∗ = {γn : n ∈ Z} so that G∗ is isomorphi...

Extending the previous work on the corresponding inverse Dirichlet problem, we present a factorization method for the solution of an inverse Neumann boundary value problem for harmonic vector fields. 2000 Mathematics Subject Classification: 31B10, 31B20, 45A05, 45Q05, 78A30.

This article studies the numerical approximation of harmonic maps into surfaces, i.e., critical points for the Dirichlet energy among weakly differentiable vector fields that are constrained to attain their pointwise values in a given manifold. An iterative algorithm that is based on a linearization of the constraint about the current iterate at the nodes of a triangulation is devised and its g...

We develop a systematic approach to construct the one-loop N = 4 SYM effective action depending on both N = 2 vector multiplet and hypermultiplet background fields. Beginning with the formulation of N = 4 SYM theory in terms of N = 2 harmonic superfields, we construct the one-loop effective action using the covariant N = 2 harmonic supergraphs and calculate it in N = 2 harmonic superfield form ...

A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and theWeinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling constants are normalizations of Lorentz invariantly embedded little groups (spin and polarization) arising in a harmonic analysis of quantum vector fields. It...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...