An eigenvalue of the adjacency matrix a graph is said to be main if all-ones vector not orthogonal its associated eigenspace. A generalized Bethe tree with $k$ levels rooted in which vertices at same level have degree. Fran\c{c}a and Brondani [On spectrum trees, Linear Algebra Appl., 628 (2021) 56-71] recently conjectured that any has exactly eigenvalues whenever even. We disprove conjecture by...

We investigate the generalized supersymmetric t− J model with boundary impurities in different gradings. All three different gradings: fermion, fermion, boson (FFB), boson, fermion, fermion (BFF) and fermion, boson, fermion (FBF), are studied for the generalized supersymmetric t − J model. Boundary K-matrix operators are found for the different gradings. By using the graded algebraic Bethe ansa...

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model. Specifying the parameters appropriately, we obtain the Bethe ansatz equations of the supersymmetric t-J model, the Hubbard model, or of Yang’s model of elec...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . 1.1 Markov Random Field Models 1 1.2 An Overview of Optimal Estimators and Approximations . . . . . . . 2 1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Goa...

For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free energy approximations with arbitrary count...

An integrable quantum group deformation of the supersymmetric t-J model is introduced. Open boundary conditions lead to an spl q (2; 1) invariant hamiltonian. A general procedure to obtain such invariant models is proposed. To solve the model a generalized nested algebraic Bethe ansatz is constructed and the Bethe ansatz equations are obtained. The quantum supergroup structure of the model is i...

The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.

The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.

The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.