The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity

We establish the Harnack inequality for advection-diffusion equations with divergence-free drifts by adapting the classical Moser technique to parabolic equations with drifts with regularity lower than the scale invariant spaces.     

1-Formyl-2,2-dimethylhydrazine as a new decomposition product of 1,1-dimethylhydrazine

A new decomposition product of 1,1-dimethylhydrazine (UDMH), 1-formyl-2,2-dimethylhydrazine (FDMH), was found in water and soil samples. The formation of FDMH was confirmed by LC-MS and NMR studies. The possibility of FDMH conversion to initial UDMH by alkaline hydrolysis was shown.     

New approach to chemical modification of PIM-1 for gas separation membranes

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Ring Opening of Donor–Acceptor Cyclopropanes with the Azide Ion: A Tool for Construction of N‐Heterocycles

A general method for ring opening of various donor–acceptor cyclopropanes with the azide ion through an S_N2‐like reaction has been developed. This highly regioselective and stereospecific process proceeds through nucleophilic attack on the more‐substituted C2 atom of a cyclopropane with complete inversion of configuration at this center. Results of DFT calculations support the S_N2 mechanism and demonstrate good qualitative correlation between the relative experimental reactivity of cyclopropanes and the calculated energy barriers. The reaction provides a straightforward approach to a variety of polyfunctional azides in up to 91 % yield. The high synthetic utility of these azides and the possibilities of their involvement in diversity‐oriented synthesis were demonstrated by the developed multipath strategy of their transformations into five‐, six‐, and seven‐membered N‐heterocycles, as well as complex annulated compounds, including natural products and medicines such as (?)‐nicotine and atorvastatin.     

Discharge estimation under uncertainty using variational methods with application to the full Saint‐Venant hydraulic network model

Estimating river discharge from in situ and/or remote sensing data is a key issue for evaluation of water balance at local and global scales and for water management. Variational data assimilation (DA) is a powerful approach used in operational weather and ocean forecasting, which can also be used in this context. A distinctive feature of the river discharge estimation problem is the likely presence of significant uncertainty in principal parameters of a hydraulic model, such as bathymetry and friction, which have to be included into the control vector alongside the discharge. However, the conventional variational DA method being used for solving such extended problems often fails. This happens because the control vector iterates (i.e., approximations arising in the course of minimization) result into hydraulic states not supported by the model. In this paper, we suggest a novel version of the variational DA method specially designed for solving estimation‐under‐uncertainty problems, which is based on the ideas of iterative regularization. The method is implemented with SIC², which is a full Saint‐Venant based 1D‐network model. The SIC² software is widely used by research, consultant and industrial communities for modeling river, irrigation canal, and drainage network behavior. The adjoint model required for variational DA is obtained by means of automatic differentiation. This is likely to be the first stable consistent adjoint of the 1D‐network model of a commercial status in existence. The DA problems considered in this paper are offtake/tributary estimation under uncertainty in the cross‐device parameters and inflow discharge estimation under uncertainty in the bathymetry defining parameters and the friction coefficient. Numerical tests have been designed to understand identifiability of discharge given uncertainty in bathymetry and friction. The developed methodology, and software seems useful in the context of the future Surface Water and Ocean Topography satellite mission. Copyright © 2016 John Wiley & Sons, Ltd.