Nonlinear maximum principles for dissipative linear nonlocal operators and applications

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.     

Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.     

A Frustrated Phosphane–Borane Lewis Pair and Hydrogen: A Kinetics Study

The energy profile of a frustrated Lewis pair (FLP) dihydrogen splitting system was determined by a combined experimental kinetic and DFT study. A trimethylene‐bridged phosphane–borane FLP was converted into its endothermic H₂‐cleavage product by sequential H⁺/H^? addition. The system could be handled at low temperature, and the kinetics of the H₂ elimination were determined to give a rate constant of k_HH,exp(299 K)=(2.87±0.1)×10^?4 s^?1 in solution. The primary kinetic isotope effects were determined; for example, (k_HH/k_DD)_exp=3.19. The system was accurately analyzed by DFT calculations.     

Cycloaddition Reactions of an Active Cyclic Phosphane/Borane Pair with Alkenes,Alkynes, and Carbon Dioxide

The active six-membered cyclo-FLP 6 undergoes a rapid P/B addition reaction to carbon dioxide. At elevated temperature, the resulting heterobicyclo[2.2.2]octane derived product 7 undergoes ring opening and equilibrates with the cyclotetramer (7)₄ . In the large macrocyclic structure, four monomeric six-membered cyclo-FLP units are connected by four CO₂ molecules to form the supramolecular ring system. The P/B cyclo-FLP 6 undergoes a variety of additional cycloaddition reactions.     

Correction to: convergence rates for Kaczmarz-type algorithms

Numerical Algorithms - We will refer to the paper “Convergence rates for Kaczmarz-type algorithms”, published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar...     

On The Cut-off Parameters in the Bosonization Technique

Jordan's boson representation and cut-off repolarization for the one-dimensional two-fermion model (TFT) is used to get the equivalence of the model with the two-dimensional Coulomb gas and sine-Gordon model. The scaling equations for the coupling constants are thereby obtained up to the third order.