We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The transformation is then identified with sequence four mutations. As an application the new formalism we show how to construct integrable system spectral curve arbitrary symmetric Newton polygon. Finally, embed this into double Bruhat cel...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

This chapter presents two fuzzy adaptive variable structure controllers for a class of uncertain multiinput multi-output nonlinear systems with actuator nonlinearities (i.e. with sector nonlinearities and dead-zones). The design of the first controller concerns systems with symmetric and positive definite control-gain matrix, while the design of the second one is extended to the case of non-sym...

The lgrade of a n × n matrix A is the largest rank of any subdiagonal block of a symmetric partition of A. A number of algebraic results on lgrade are given. When A has lgrade d, it can be be approximately decomposed as A = U + V , where U is an upper triangular matrix and V has rank d. If A satisfies GA = N with G and N have lower bandwidths dG and dN , then the decomposition is exact: A = U +...

the fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. a linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. in contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstr...

We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras, we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-hereditary s...

The m-th root of the diagonal of the upper triangular matrix Rm in the QR decomposition of AXB = QmRm converges and the limit is given by the moduli of the eigenvalues of X with some ordering, where A,B,X ∈ Cn×n are nonsingular. The asymptotic behavior of the strictly upper triangular part of Rm is discussed. Some computational experiments are discussed.

Ž Ž . Nq 1. q z s x, t g R , where the principal part is uniformly elliptic on R , q F N, and the constant matrix B is upper triangular and such that the operator obtained by freezing the coefficients a at any point z g R Nq 1 is hypoelliptic. We prove i j 0 p Ž . local L -estimates for the derivatives ­ u i, j s 1, . . . , q of a solution to the x x i j equation Lu s f , under the assumption t...

We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our experiments show that, for difficult input systems, the computing time for removing redundant components can be reduced to a small portion of the total time needed for solving these syst...