In this paper, we give the general crossing relation for boundary reflection matrix R(β) ,which is the extension of the work given by Ghoshal and Zamolodchikov .We also use the first non-trivial extended crossing relation to determine the scaler factor of R(β) which is the rational diagonal solution to the boundary Yang-Baxter equation in the case of l=2 and n=3.

In [Lem2003b] we have sketched the historical development of problems related to Legendre’s equations ar−bs = 1 and the associated Pell equation x−dy = 1 with d = ab. In [Lem2003c] we discussed certain “non-standard” ideas to solve the Pell equation. Now we move from the historical to the modern part: below we will describe the theory of the first 2-descent on Pell conics and explain its connec...

This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation , 2 , 1 , 0 , 3 , 2 3 , 2 , , = ≥ + = − − m n w w w n m n m m n m , with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the...

In this article, we generalize the well-known Gauss Pell numbers and refer to them as generalized k-Pell numbers. There are relationships discovered between class of typical Also, known polynomials, call such polynomials polynomials. We obtain relations Furthermore, provide matrices for novel generalizations these After that, Cassini’s identities