We show that the action of universal R-matrix of affine U q sl 2 quantum algebra, when q is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular expression, satisfying Yang-Baxter equation. It reduced to intertwining operators of all representations , corresponding to Chiral Potts, if the parameters of these representations lie on well known algebraic cu...

Let P = f" + (I ,,) , the direct sum of the p x p identity matrix and the negative of the q x q ident ity matrix. The fo llowing theorem is proved. TH EOHEM: If X = cZ where Z is a 4 x 4 P-orthogonal , P-skew-symmetric matrix and Ie I .;;; 2, there exist matrices A an.d B, both of which are P-orthogollal and P-skew-symmetric, sach that X = AB BA. Methods for o btaining certain matrices which sa...

In this paper we present a new method to construct a polynomial u(x) ∈ Z[x] which will make Φk(u(x)) reducible. We construct a finite separable extension of Q(ζk), denoted as E. By primitive element theorem, there exists a primitive element θ ∈ E such that E = Q(θ). We represent the primitive k-th root of unity ζk by θ and get a polynomial u(x) ∈ Q[x] from the representation. The resulting u(x)...

Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integer powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P. Slightly generalizing [H-H], we define a multiparameter deformation Lλ/μVP of the classical skew Schur module. In case R is a field and q is not a root of 1, arguments like t...

A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the min imum distance of a q-ary repeated-root cyclic code C is expressecin terms of the min imum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the ...

Transfer matrix functional relations for the generalized τ 2 (t q) model Abstract The N-state chiral Potts model in lattice statistical mechanics can be obtained as a " descendant " of the six-vertex model, via an intermediate " Q " or " τ 2 (t q) " model. Here we generalize this to obtain a column-inhomogeneous τ 2 (t q) model, and derive the functional relations satisfied by its row-to-row tr...

$^{229}$Th is a promising candidate for developing nuclear optical clock and searching the new physics beyond standard model. Accurate knowledge of properties very important. In this work, we calculate hyperfine-structure constants first four states $^{229}$Th$^{3+}$ using relativistic coupled-cluster method based on Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with lowest-order...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...