Lower bounds for incidences with hypersurfaces

Some Lower Bounds for Estrada Index

Lower bounds of heights of points on hypersurfaces

Let us first recall Lehmer’s conjecture [Le] on lower bounds for the height of an algebraic number which was stated in 1933. Let K be an algebraic number field of degree D over Q. For any valuation v we denote Dv = [Kv : Qv], where Kv,Qv are the completions of K,Q with respect to v. For archimedean v we normalise the valuation by |xv| = |x|Dv/D where |.| is the ordinary complex absolute value. ...

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...

Estimating ‎U‎pper and Lower Bounds For Industry Efficiency With Unknown ‎Technology‎

With a brief review of the studies on the industry in Data Envelopment Analysis (DEA) framework, the present paper proposes inner and outer technologies when only some basic information is available about the technology. Furthermore, applying Linear Programming techniques, it also determines lower and upper bounds for directional distance function (DDF) measure, overall and allocative efficienc...