Lower bounds for Schrödinger equations

Some Lower Bounds for Estrada Index

Equations for Lower Bounds on Border Rank

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

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 ...

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

Lower bounds for random 3-SAT via differential equations

It is widely believed that the probability of satis"ability for random k-SAT formulae exhibits a sharp threshold as a function of their clauses-to-variables ratio. For the most studied case, k = 3, there have been a number of results during the last decade providing upper and lower bounds for the threshold’s potential location. All lower bounds in this vein have been algorithmic, i.e., in each ...