In this note, we provide a few sufficient conditions for the invariant subspace problem. Introduction An important open problem in operator theory is the invariant subspace problem. Since the problem is solved for all finite dimensional complex vector spaces of dimension at least 2, H denotes a separable Hilbert space whose dimension is infinite. It is enough to think for a contraction T , that...

In this paper we introduce a new method for solving box-constrained mixed-integer polynomial problems to global optimality. The approach, a specialized branch-and-bound algorithm, is based on the computation of lower bounds provided by the minimization of separable underestimators of the polynomial objective function. The underestimators are the novelty of the approach because the standard appr...

Researchers are often interested in treatment effects on outcomes that only defined conditional a post-treatment event status. For example, study of the effect different cancer treatments quality life at end follow-up, individuals who die during is undefined. In these settings, naive contrast variable not an average causal effect, even randomized experiment. Therefore principal stratum those wo...