An O(n log n) procedure is presented for obtaining facets of the knapsack polytope by lifting the inequalities induced by the extensions of strong minimal covers. The procedure does not require any sequential lifting of the inequalities. In contrast, it utilizes the information from the maximal cliques implied by the knapsack constraint for determining the combination of the lifting coe4cients ...

Abstract The formulation of a discrete-time anti-windup scheme for linear systems with constrained control signals is extended to the sampled-data case. Thus, the control of a continuous-time linear plant via a discrete linear nominal controller and a discrete anti-windup compensator is considered. Stability of the antiwindup compensator is equivalent to the known discrete problem while a hybri...

For a totally positive definite quadratic form over the ring of integers real number field $K$, we show that there are only finitely many extensions $K$ fixed degree which is universal (namely, those have short basis in suitable sense). Along way give general construction rank bounded by $D(\log D)^{d-1}$, where $d$ $\mathbb Q$ and $D$ its discriminant. Furthermore, for any prove (weak) Kitaoka...

Given a complete real-valued field k of residue characteristic zero, we study properties differential form ? on smooth proper k-analytic curve X. In particular, associate to (X,?) natural tropical reduction datum combining data and algebra-geometric over the k˜. We show that this satisfies compatibility condition, prove lifting theorem asserting any compatible lifts an actual pair (X,?). obtain...

This brief note only contains a modest contribution: we just fix some inaccuracies in the proof of the prime level weight 2 case of Serre’s conjecture given in [K], for the case of trivial character. More precisely, the modularity lifting result needed at a crucial step is the one for the case of a deformation corresponding to a p-adic semistable (in the sense of Fontaine) Galois representation...

We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of RC, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality. Our tools include the use of 2-variable weighted...