The size of {x: rn′rn ⩾ 1} and lower bounds for ∥e−x − rn∥

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...

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 Estrada Index

Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size

The isolation lemma of Mulmuley et al [MVV87] is an important tool in the design of randomized algorithms and has played an important role in several nontrivial complexity upper bounds. On the other hand, polynomial identity testing is a well-studied algorithmic problem with efficient randomized algorithms and the problem of obtaining efficient deterministic identity tests has received a lot of...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces