‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

To differentiate between the laws of nature and accidental generalizations, we must adopt a view necessity that is capable being realized in relationships existing among natural objects. In neo-Sadraian Islamic philosophy, metaphysical accepted as part cause-effect relationship. This paper compares interpretation necessitarian theories about nature, particularly essentialism universal theory. B...

We propose a fast algorithm to estimate brain tissue concentrations from conventional T1-weighted images based on a Bayesian maximum a posteriori formulation that extends the "mixel" model developed in the 90's. A key observation is the necessity to incorporate additional prior constraints to the "mixel" model for the estimation of plausible concentration maps. Experiments on the ADNI standardi...

Kripke distinguishes necessity and priority as two different categories: is a notion of epistemology, while metaphysics. Based on this fundamental argument, objects to Descriptivism, which takes certain properties the criteria identity across all possible worlds, he argues for legitimacy posteriori necessary truths. also criticizes Russell’s methods dealing with empty descriptions, puts forward...

The dynamics of general relativity is encoded in a set ten differential equations, the so-called Einstein field equations. It usually believed that Einstein's equations represent physical law describing coupling spacetime with material fields. However, just six these actually describe mechanism: remaining four relations known as Bianchi identities. paper discusses role identities play relativit...