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.

Attacks that exploit out-of-bounds errors in C and C++ programs are still prevalent despite many years of research on bounds checking. Previous backwards compatible bounds checking techniques, which can be applied to unmodified C and C++ programs, maintain a data structure with the bounds for each allocated object and perform lookups in this data structure to check if pointers remain within bou...

Objective To find lower and upper bounds of HIV prevalence in Malawi under mild and intuitive assumptions to assess the importance of the refusal issue in the estimation of HIV prevalence. Methods We derive bounds based on the following two key assumptions: (i) Among those who have never taken an HIV test before, those who refuse to take an HIV test (hereafter “refusers”) have at least as much ...

This paper gives identification and estimation results for quantile and average effects in nonseparable panel models, when the distribution of period specific disturbances does not vary over time. Bounds are given for interesting effects with discrete regressors that are strictly exogenous or predetermined. We allow for location and scale time effects and show how monotonicity can be used to sh...

The problem of providing lower confidence bounds for the mean improvements of p ≥ 2 test treatments over a control treatment is considered. The expected average and expected maximum allowances are two criteria for comparing different systems of confidence intervals or bounds. In this paper, lower bounds are derived for the expected average allowance and the expected maximum allowance of Dunnett...

The Life and Strange Surprizing Adventures of Robinson Crusoe by Daniel Defoe, first published in 1719, is almost a universal title. Its reach extends so far and wide that even those who are not English native speakers and have not read the novel have some knowledge of the titular character and his desolate island ordeal. The figure of the man with the goat skin clothes starring at the beach, h...