29 citations · 65 across the 9 of their papers we have counts for
9 papers
Polynomials with symmetric zeros
R. S. Vieira
Polynomials whose zeros are symmetric either to the real line or to the unit circle are very important in mathematics and physics. We can classify them into three main classes: the…
How to count the number of zeros that a polynomial has on the unit circle?
R. S. Vieira
The classical problem of counting the number of real zeros of a real polynomial was solved a long time ago by Sturm. The analogous problem of counting the number of zeros that a po…
Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
R. S. Vieira
The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differ…
The algebraic Bethe Ansatz and combinatorial trees
R. S. Vieira, A. Lima-Santos
We present in this paper a comprehensive introduction to the algebraic Bethe Ansatz, taking as examples the six-vertex model with periodic and non-periodic boundary conditions. We…
Reflection matrices with symmetry
R. S. Vieira, A. Lima-Santos
We propose a classification of the reflection -matrices (solutions of the boundary Yang-Baxter equation) for the $U_{q}[\mathrm{osp}^{\left(2\right)}\left(2|2m\right)]=U_{q}[C^{…
On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model
Ricardo S. Vieira, A. Lima-Santos
In this paper we consider families of multiparametric -matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families o…
An Introduction to the Theory of Tachyons
Ricardo S. Vieira
The theory of relativity, which was proposed in the beginning of the 20th century, applies to particles and frames of reference whose velocity is less than the velocity of light. I…
Solving Polynomial Equations from Complex Numbers
Ricardo S. Vieira
We show that a polynomial equation of degree less than 5 and with real parameters can be solved by regarding the variable in which the polynomial depends as a complex variable. For…
A New Algorithm for Evaluating Determinants -- The Reduction Method
Ricardo S. Vieira
We present here a new method for evaluating determinants -- the reduction method. Firstly, in the section 2, we apply it to third-order determinants and after, in the section 3, we…