Upper Bounds for ‖A−1Q‖∞

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

Upper bounds for discriminants

Upper bounds for centerlines

In 2008, Bukh, Matoušek, and Nivasch conjectured that for every n-point set S in Rd and every k, 0 ≤ k ≤ d− 1, there exists a k-flat f in Rd (a “centerflat”) that lies at “depth” (k + 1)n/(k + d + 1) − O(1) in S, in the sense that every halfspace that contains f contains at least that many points of S. This claim is true and tight for k = 0 (this is Rado’s centerpoint theorem), as well as for k...

Lower Bounds and Upper Bounds for MaxSAT

This paper presents several ways to compute lower and upper bounds for MaxSAT based on calling a complete SAT solver. Preliminary results indicate that (i) the bounds are of high quality, (ii) the bounds can boost the search of MaxSAT solvers on some benchmarks, and (iii) the upper bounds computed by a Stochastic Local Search procedure (SLS) can be substantially improved when its search is init...