Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems

We consider a quadratic optimal control problem governed by a nonautonomous affine ordinary differential equation subject to nonnegativity control constraints. For a general class of interior penalty functions, we provide a first order expansion for the penalized states and adjoint states around the state and adjoint state of the original problem. Our main argument relies on the following fact: if the optimal control satisfies strict complementarity conditions for its Hamiltonian except for a set of times with null Lebesgue measure, the functional estimates for the penalized optimal control problem can be derived from the estimates of a related finite dimensional problem. Our results provide several types of efficiency measures of the penalization technique: error estimates of the control for L ^s norms (s in [1, +∞]), error estimates of the state and the adjoint state in Sobolev spaces W ^1,s (s in [1, +∞)) and also error estimates for the value function. For the L ¹ norm and the logarithmic penalty, the sharpest results are given, by establishing an error estimate for the penalized control of order ${O(\varepsilon|\log\epsilon|)}$ where ${\varepsilon >0 }$ is the (small) penalty parameter.     

A multicriteria approach to sustainable energy supply for the rural poor

Despite significant progress in energy technology, about two billion people worldwide, particularly the poor in rural areas of developing countries, have no access to electricity. Decision-making concerning the most appropriate energy technology for supplying these areas has been difficult; existing energy decision-support tools have been useful but are mostly incomplete. Trade-offs, as well as impacts that can be positive or negative, may emerge as a result of implementing modern forms of energy. These can affect both community’s livelihoods as well as the confidence of decision-makers in relation to alternative technologies. The paper discusses a newly designed multicriteria approach and its novel robustness analysis for selecting energy generation systems for the improvement of livelihoods in rural areas. The proposed methodology builds upon a sustainable rural livelihoods framework to address multiple interactions and calculate trade-offs aimed at boosting decision-makers’ confidence in the selected technologies. The methodology is tested via a case study in Colombia.     

The sodium salt of diethyl 1H-pyrazole-3,5-dicarboxylate as an efficient amphiphilic receptor for dopamine and amphetamines. crystal structure and solution studies

The sodium salt of the diethyl 1H-pyrazole-3,5-dicarboxylate (2) of amphiphilic character is able to interact with (+)-amphetamine, (+)-methamphetamine, and dopamine, yielding stable complexes. Crystal structure of 2 with (+)-amphetamine leads to a very nice double helical supramolecular structure.     

Efficient visible light-active N-doped TiO2 photocatalysts by a reproducible and controllable synthetic route

A reproducible and controllable method allows the synthesis of practical quantities of efficient, visible light active TiO(2)(N) photocatalysts in which the nitrogen content may be varied to achieve optimum performance.     

Null controllability of a degenerated reaction–diffusion system in cardiac electro-physiology

This Note is devoted to the analysis of the null controllability of a nonlinear reaction–diffusion system, approximating a parabolic–elliptic system, modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precise estimate with respect to the degenerating parameter and it is done combining Carleman estimates and energy inequalities.     

Markovian description of unbiased polymer translocation

We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general Markovian framework for unbiased three-dimensional polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literature by the present authors.     

Kanamycin A: imine formation in aqueous solution

Imine formation in aqueous solution of kanamycin A with pyridoxal 5'‐phosphate and other aldehydes was studied by potentiometry, NMR spectroscopy and computational chemistry. It was found that imines are formed with yields near 100 % at pH 7 in equimolar reactant ratio. In order to identify the kanamycin amino groups involved in the reaction, a NMR spectroscopic study was conducted. The structures of possible imines formed between kanamycin and FURAN or PLP were optimized by molecular mechanics with the OPLS‐2005 force field. The ¹H NMR spectra were calculated at the DFT‐GIAO B3LYP/6‐31G(d) level of theory for all structures and compared with the experimentally observed spectra. From these results a probable structure of the imines was proposed. The results obtained in this work show that kanamycin has the ability to form imine derivatives in high yields due to its anion recognition properties. Copyright © 2012 John Wiley & Sons, Ltd.