This paper gives an explicit method for computing the resultant of any sparse unmixed bivariate system with given support. We construct square matrices whose determinant is exactly the resultant. The matrices constructed are of hybrid Sylvester and Bézout type. The results extend those in [14] by giving a complete combinatorial description of the matrix. Previous work by D’Andrea [5] gave pure ...

An equigenerated monomial ideal $$I$$ in the polynomial ring $$R=k[z_1,\ldots, z_n]$$ is a Freiman if $$\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$$ , where $$\ell(I)$$ analytic spread of and $$\mu(I)$$ number minimal generators . In this paper we classify all simple connected unmixed bipartite graphs whose cover ideals are ideals.

‎in this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of villarreal on bipartite graphs‎. ‎for bipartite graphs two‎ ‎different characterizations were given by ravindra and villarreal‎. ‎we show that these two characterizations imply each other‎.

‎let $i$ denote an ideal of a noetherian ring $r$‎. ‎the purpose of‎ ‎this article is to introduce the concepts of quintasymptotic‎ ‎sequences over $i$ and quintasymptotic cograde of $i$‎, ‎and to show that they play a role analogous to quintessential sequences‎ ‎over $i$ and quintessential cograde of $i$‎. ‎we show that‎, ‎if $r$ is‎ ‎local‎, ‎then the quintasymptotic cograde of $i$ is una...

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det (sI−Φ(X)) and det (I− sΦ(X)∗) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of C. A...

The ideal binary mask is often seen as a goal for time-frequency masking algorithms trying to increase speech intelligibility, but the required availability of the unmixed signals makes it difficult to calculate the ideal binary mask in any real-life applications. In this paper we derive the theory and the requirements to enable calculations of the ideal binary mask using a directional system w...