  We obtain two series of spectral parameter dependent solutions to the
generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times
N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions
are presented for the inhomogeneous GYBEs. The first series of the solutions
includes as particular cases the $X$-shaped trigonometric braiding matrices.
For construction of the second series the colored and graded permutation
operators are defined, and multi-spectral parameter Yang-Baxterization is
performed. For some examples the corresponding integrable models are discussed.
The unitary solutions existing in these two series can be considered as
generalizations of the multipartite Bell matrices in the quantum information
theory.
