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...

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose Newton polytopes are scaled copies of one polytope, thus taking a step towards systems with arbitrary supports. First, we specify matrices whose determinant equa...

Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. For cases when this cannot be done, an upper bound on the degree of the extraneous factor in the projection operator can be determined a priori, thus resulting in quick identification of the extraneous factor in the projection operator. (Fo...

Let C be a clutter with a perfect matching e1, . . . , eg of König type and let ∆C be the Stanley-Reisner complex of the edge ideal of C. If all c-minors of C have a free vertex and C is unmixed, we show that ∆C is pure shellable. We are able to describe in combinatorial terms when ∆C is pure. If C has no cycles of length 3 or 4, then it is shown that ∆C is pure if and only if ∆C is pure shella...

We give a new and simple proof that unmixed local rings having Hilbert-Kunz multiplicity equal to 1 must be regular.

Let A be an integral matrix whose set of column vectors is A = {v1, . . . , vq} and let A(P ) be the Ehrhart ring of P = conv(A). We are able to show that if A is the incidence matrix of a d-uniform unmixed clutter with covering number g and the system x ≥ 0;xA ≥ 1 is TDI, then the Castelnuovo-Mumford regularity of A(P ) is sharply bounded by (d − 1)(g − 1). Let R = K[x1, . . . , xn] be a polyn...