ON THREE-SHEETED POLYNOMIAL MAPPINGS OF ${\mathbf C}^2$

Abstract

In this paper, algebraic expressions for (λ, 0) × (4, 0) reduction Wigner coefficients in the SU 3 ⊃ R 3 physical basis are presented. They are obtained by a building-up process. These tables are useful in studies of nuclear algebraic models, such as the sdg interacting boson model.

On quartic forms associated with cubic transformations of the real plane

“…in ω [2], ω [3], ω [4], and ω [5]. Using the components of the vectors (2.5), we can write ω [1] and ω[6] from (2.3) and (2.4) in terms of their components:…”

“…Similarly, using the components of the vector (2.6), we can write the quartic forms ω [2], ω [3], ω [4], and ω [5] in terms of their components:…”

“…Polynomial mappings f : C 2 → C 2 are of interests from many points of view (see [1][2][3][4][5]) most of which are associated with the Jacobian conjecture (see [6]). Polynomial mappings f : R 2 → R 2 are also considered (see [7], [8]) in connection with the real Jacobian conjecture.…”

The complete solution to Bass Generalized Jacobian Conjecture

“…Let us now assume that S isomorphic C 2 , and let G be an isomorphism from C 2 to S. So, F S • G is an unramified endomorphism of geometric degree 3 of C 2 , contrary to [22], Theorem 1.1. We deduce that S is not isomorphic to C 2 .…”

A rough classification of potentially invertible cubic transformations of the real plane

“…The rational real Jacobian conjecture is its generalization (see [4]). Polynomial mappings f : C 2 → C 2 of the complex plane C 2 were considered in [5][6][7][8][9]. My interest to cubic polynomial transformations of R 2 is due to their application to the perfect cuboid problem (see [10] and [11]).…”