Mild and efficient nickel-catalyzed Heck reactions with electron-rich olefins

A new efficient protocol for the nickel-catalyzed Heck reaction of aryl triflates with vinyl ethers is presented. Mild reaction conditions that equal those of the corresponding palladium-catalyzed Heck reaction are applied, representing a practical and more sustainable alternative to the conventional regioselective arylation of vinyl ethers. A catalytic system comprised of Ni(COD)(2) and 1,1'-bis(diphenylphosphino)ferrocene (DPPF) in combination with the tertiary amine Cy(2)NMe proved effective in the olefination of a wide range of aryl triflates. Both electron-deficient and electron-rich arenes proved compatible, and the corresponding aryl methyl ketone could be secured after hydrolysis in yields approaching quantitative. Good functional group tolerance was observed matching the characteristics of the analogous Pd-catalyzed Heck reaction. The high levels of catalytic activity were explained by the intermediacy of a cationic nickel(II) complex potentially responsible for the successive β-hydride elimination and base promoted catalyst regeneration. Although these elementary reactions are normally considered challenging, DFT calculations suggested this pathway to be favorable under the applied reaction conditions.     

Stability of the μ-Camassa–Holm Peakons

The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the μCH equation are orbitally stable.     

Simplex optimization of electrokinetic injection of DNA in capillary electrophoresis using dilute polymer solution

In DNA analysis by capillary electrophoresis with polymer solutions there are many variables that can be optimized. However, electric field strength, polymer solution concentration and temperature of analysis are the most relevant ones. These are the variables most responsible for the fragment resolution and analysis time. Optimization of such parameters can be obtained simultaneously using chemometric techniques, reaching the optimum working conditions with few experiments. In this work, we have studied the influence of the sample composition and electrokinetic injection conditions in the reproducibility and the quality of the DNA separation results. A simplex optimization has been carried out and the optimum condition was reached with nine experiments.     

Characterization of polyacrylamide based monolithic columns

Supermacroporous monolithic polyacrylamide (pAAm)-based columns have been prepared by radical cryo-copolymerization (copolymerization in the moderately frozen system) of acrylamide with functional co-monomer, allyl glycidyl ether (AGE), and cross-linker N,N'-methylene-bis-acrylamide (MBAAm) directly in glass columns (ID 10 mm). The monolithic columns have uniform supermacroporous sponge-like structure with interconnected supermacropores of pore size 5-100 microm. The monoliths can be dried and stored in the dry state. High mechanical stability of the monoliths allowed sterilization by autoclaving. Column-to-column reproducibility of pAAm-monoliths was demonstrated on 5 monolithic columns from different batches prepared under the same cryostructuration conditions.     

Exact Solution of a Neumann Boundary Value Problem for the Stationary Axisymmetric Einstein Equations

Journal of Nonlinear Science - For a stationary and axisymmetric spacetime, the vacuum Einstein field equations reduce to a single nonlinear PDE in two dimensions called the Ernst equation. By...     

Traveling wave solutions of the Camassa-Holm equation

All weak traveling wave solutions of the Camassa-Holm equation are classified. We show that, in addition to smooth solutions, there are a multitude of traveling waves with singularities: peakons, cuspons, stumpons, and composite waves.     

Far Red-Shifted CdTe Quantum Dots for Multicolour Stimulated Emission Depletion Nanoscopy

Stimulated emission depletion (STED) nanoscopy is a widely used nanoscopy technique. Two-colour STED imaging in fixed and living cells is standardised today utilising both fluorescent dyes and fluorescent proteins. Solutions to image additional colours have been demonstrated using spectral unmixing, photobleaching steps, or long-Stokes-shift dyes. However, these approaches often compromise speed, spatial resolution, and image quality, and increase complexity. Here, we present multicolour STED nanoscopy with far red-shifted semiconductor CdTe quantum dots (QDs). STED imaging of the QDs is optimized to minimize blinking effects and maximize the number of detected photons. The far-red and compact emission spectra of the investigated QDs free spectral space for the simultaneous use of fluorescent dyes, enabling straightforward three-colour STED imaging with a single depletion beam. We use our method to study the internalization of QDs in cells, opening up the way for future super-resolution studies of particle uptake and internalization.     

Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation, which was first derived by means of bi-Hamiltonian methods in [ 1 ]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as a model for nonlinear pulse propagation in monomode optical fibers when certain higher-order nonlinear effects are taken into account; (b) We show that the equation is equivalent, up to a simple change of variables, to the first negative member of the integrable hierarchy associated with the derivative NLS equation; (c) We analyze traveling-wave solutions.