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...

Various methods have been discussed in the literature to evaluate the range of values for a risk measure of a function of random variables. The uncertainty with the chosen dependence risk model makes these bounds worth investigating and the tighter the entire spectrum of values is, the more informative the bounds are. It is natural to believe that the individual risk distributions are known; an...

In validated branch and bound algorithms for global optimization, upper bounds on the global optimum are obtained by evaluating the objective at an approximate optimizer; the upper bounds are then used to eliminate subregions of the search space. For constrained optimization, in general, a small region must be constructed within which existence of a feasible point can be proven, and an upper bo...

This paper presents a fast and powerful method for the computation of eigenvalue bounds for Hessian matrices ∇2φ(x) of nonlinear wice continuously differentiable functions φ : U ⊆ R → R on hyperrectangles B ⊂ U . The method is based on a recently proposed procedure [9] for an efficient computation of spectral bounds using extended codelists. Both that approach and the one presented here substan...

Three sources of variation in experimental results for a test are distinguished: trials, persons, and items. Unreliability is defined only in terms of variation over trials. This definition leads to a more complet~ analysis than does the conventional one; Spearman’s contention is verified that the conventional approach--which was formulated by Yule--introduces unnecessary hypotheses. It is emph...

Purpose The purpose of this study is to examine the impact economic growth, trade openness and manufacturing on CO2 emissions in India. Design/methodology/approach employed autoregressive distributive lag (ARDL) bounds test approach uses emissions, trade, GDP per capita relationship using an annual time series data from World Development Indicators during 1971 2016. Findings Results depict that...

We prove that the best constant in the general Brascamp–Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp–Lieb inequality which have arisen recently in harmonic analysis.

where V+ = (|V |+ V )/2 is the positive part of V . Eden and Foias have obtained in [3] a version of a one-dimensional generalised Sobolev inequality which gives best known estimates for the constants in the inequality (2) for 1 ≤ γ < 3/2. The aim of this short article is to extend the method from [3] to a class of matrix-valued potentials. By using ideas from [6] this automatically improves on...

We show that the lower and upper Frechét-Hoeffding copulas, which are singular, can be regularized to absolutely continuous copulas. The method, which is constructive and explicit, states sufficient conditions for when an absolutely continuous copula can be achieved by averaging. A higher degree of regularisation cannot be achieved with the proposed method.