In this paper, we proved the first non-trivial case of the DDVV conjecture. Namely, for all 3 × 3 matrices, the DDVV inequality is valid. We also classified all the minimal submanifolds for which the equality holds.

Though in most data warehousing applications no relevance is given to the time when events are recorded, some domains call for a different behavior. In particular, whenever late registrations of events take place, and particularly when the events registered are subject to further updates, the traditional design solutions fail in preserving accountability and query consistency. In this paper we ...

Though in most data warehousing applications no relevance is given to the time when events are recorded, some domains call for a different behavior. In particular, whenever late measurements of events take place, and particularly when the events registered are subject to further updates, the traditional design solutions fail in preserving accountability and query consistency. In this article, w...

In this paper, we introduce an operation that creates families of facet-defining inequalities for highdimensional infinite group problems using facet-defining inequalities of lower-dimensional group problems. We call this family sequential-merge inequalities because they are produced by applying two group cuts one after the other and because the resultant inequality depends on the order of the ...

This paper analyzes the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n b...

This paper analyses the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n b...

Abstrac t . We consider the acyclic subgraph polytope and define the notion of strength of a relaxation as the maximum improvement obtained by using this relaxation instead of the most trivial relaxation of the problem. We show that the strength of a relaxation is the maximum of the strengths of the relaxations obtained by simply adding to the trivial relaxation each valid inequality separately...

We present a new procedure for generating cutting planes for the max-cut problem. The procedure consists of three steps. First, we generate a violated (or near-violated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the max-cut problem. This can be done by computing the minimum eigenvalue of a certain matrix. Second, we use this linear inequality to constr...