In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

In this paper, we are interested in extending the classical KolmogorovSmirnov homogeneity test to compare two samples of interval-valued observed measurements. In such a case, the test result is interval-valued, and one major difficulty is to find the bounds of this set. We propose a very efficient computational method for approximating these bounds by using a p-box (pairs of upper and lower cu...

In this paper, we address the problem of deriving bounds for the moments of nearest neighbor distributions. The bounds are formulated for the general case and specifically applied to the problem of noise variance estimation with the Delta test and the Gamma test. For this problem, we focus on the rate of convergence and the bias of the estimators and validate the theoretical achievements with e...

The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.

It is shown that the aliasing probability is bounded above by (1 + E ) / L M 1/L ( E small for large L) for test lengths L less than the period, L,, of the signature polynomial; for test lengths L that are multiples of L,, the aliasing probability is bounded above by 1; and, for test lengths L greater than L, and not a multiple of L,, the aliasing probability is bounded above by 2 / ( L c + 1)....

Extensive reading has for many years been seen as an important and motivating means of improving general language proficiency in a second language. This article argues that while extensive reading per se is an important medium for long-term second language acquisition, extensive reading schemes may not be the most effective means of promoting acquisition. This argument springs from the disappoi...

We consider the following problem: a robot is at an unknown position in an indoor-environment and has to do a complete relocalization, that is, it has to enumerate all positions that it might be located at. This problem occurs when, for example, the robot “wakes up” after a breakdown (e.g., a power failure or maintenance works) and the possibility exists that it has been moved meanwhile. An ide...

Alioscia Hamma,1, 2 Fotini Markopoulou,1,2, 3 Isabeau Prémont-Schwarz,1,2, 3 and Simone Severini4 Perimeter Institute for Theoretical Physics 31 Caroline St. N, N2L 2Y5, Waterloo ON, Canada Massachusetts Institute of Technology, Research Laboratory of Electronics 77 Massachusetts Ave. Cambridge MA 02139 Department of Physics, University of Waterloo Waterloo, Ontario N2L 3G1, Canada Institute fo...