The branch-and-bound algorithm computes the largest simplex by using lower and upper bounds on the radius of the inscribed ball, by which the computation time is reduced by a factor of five in comparison with the brute-force search.
The area within the circular window varied in size from zero to some upper limit (a maximum radius of the circular window set in virtue of the proportion of the whole population) specified by the user, never including > 50% of the total population.
In this paper, some new upper bounds on the spectral radius of the Hadamard product of two nonnegative matrices and some upper and lower bounds on the spectral radius of the iterative matrix of a nonsingular M-matrix are given.
Given a finite set of points on the Euclidean sphere, the worst case quadrature error for functions in Sobolev spaces has recently been shown to provide upper bounds on the covering radius of the point set.
Lemma 3.3 shows that there is an upper limit on the spectral radius of the matrix (mathfrak {A}) given by (34) above which the system cannot be stabilized.
In the paper, some new upper bounds for the spectral radius of the Hadamard product of nonnegative matrices, and the low bounds for the minimum eigenvalue of the Fan product of nonsingular M-matrices are given.
Motivated by [8] and [1 4, 9, 10], in this paper we propose some inequalities on the upper bounds for the spectral radius of the Hadamard product of any k nonnegative matrices.
The buckets used for the trials have the shape of truncated cone and thus the volume of the bucket was calculated using Eq. (3): {text{Volume}} = pi / 3h(R^{ 2} + {text{Rr}} + r^{ 2} ), (3)where h is the height of the bucket, R 2 the radius of the upper surface of the bucket, Rr the radius of the middle of the bucket and r the radius of the bottom of the bucket.
Then λ 1 = p q − k + p 2 q 2 − 6 p q k + 4 p k + 4 q k 2 − 3 k 2 2. We now present an upper bound on the spectral radius of the bipartite graph G. Theorem 1 For positive integers p, q and k satisfying p ≤ q and k < p, let G be a bipartite graph with partite sets U and V having | U | = p and | V | = q, and | E ( G ) | = p q − k.
Moreover, we investigate the enhancement of the Q-factor by tuning the position and radius of the lateral, upper, and lower boundary holes near the cavity edge.
