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Brill [Color Res Appl 2006;31:142-145] and Brill and S€ usstrunk [Color Res Appl 2008;33:424-426] found that CIECAM02 has the yellow-blue and purple problems and gave partial solutions to them. In this article we model the optimum solution to the yellow-blue and purple problems simultaneously as a constrained non-linear optimization problem. An optimum solution resulting in a new CAT02 matrix is numerically obtained. This new matrix satisfies the nesting rule and performs better than the Hunt-Pointer-Est evez (HPE) matrix in predicting both corresponding colours and colour appearance data sets. Specifically, it was found that the new and HPE matrices performed significantly different on nine (out of 21) corresponding colour data sets and on all corresponding colours data sets as a whole.

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In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of this Hexp map. We also describe a Hom-Lie group action on a smooth manifold. Subsequently, we give the notion of an adjoint representation of a Hom-Lie group on its Hom-Lie algebra. At last, we integrate the Hom-Lie algebra (gl(V),[.,.],Ad), and the derivation Hom-Lie algebra of a Hom-Lie algebra.