Sylvester conjectured in 1893 and Gallai proved some forty years later that every finite set S of points in the plane includes two points such that the line passing through them includes either no other point of S or all other points of S. There are several ways of extending the notion of lines from Euclidean spaces to arbitrary metric spaces. We present one of them and conjecture that, with li...

In this paper, we consider the fuzzy Sylvester matrix equation AX + XB = C, where A ∈ Rn×n and B ∈ Rm×m are crisp M-matrices, C is an n×m fuzzy matrix and X is unknown. We first transform this system to an (mn)× (mn) fuzzy system of linear equations. Then we investigate the existence and uniqueness of a fuzzy solution to this system. We use the accelerated overrelaxation method to compute an ap...

For k + 1 power series a0(z), . . . , ak(z), we present a new iterative, look-ahead algorithm for numerically computing Padé-Hermite systems and simultaneous Padé systems along a diagonal of the associated Padé tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are wellconditioned. The operati...

The problem of tripeptide loop closure is formulated in terms of the angles { i}i 1 3 describing the orientation of each peptide unit about the virtual axis joining the C atoms. Imposing the constraint that at the junction of two such units the bond angle between the bonds C ON and C OC is fixed at some prescribed value results in a system of three bivariate polynomials in ui : tan i/2 of degre...

Third-generation mobile radio systems use time division-code division multiple access (TD-CDMA) in their time division duplex (TDD) mode. Due to the time division multiple access (TDMA) component of TD-CDMA, joint (or multi-user) detection techniques can be implemented with a reasonable complexity. Therefore, joint detection will already be implemented in the first phase of the system deploymen...

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(ĝln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand–Tsetlin character (or q-character). We also apply the qu...