Investigation of the catalytic activity of a Pd/biphenyl-based phosphine system in the Ullmann homocoupling of aryl bromides

We described Ullmann homocoupling promoted by a Pd/biphenyl-based phosphine system using DMF as solvent. Using Hammett equation it is found that the rate determining step of the reaction depends on the electronic nature of substituents of aryl bromides. Increase the rate of reaction with decreasing the electron donating of the substituent from NH₂ to H suggesting an oxidative addition step as the rate determining step. Decrease the rate of reaction with increasing the electron-withdrawing ability of the substituent from H to NO₂ indicating a reductive elimination step as the rate determining step.     

Complete dynamical analysis of a neuron under magnetic flow effect

In the last decades, many studies have been done about nervous system from the mathematical and computational point of view. Many mathematical models have been proposed to describe neuron. Most of them have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Very recently, according to the Maxwell electromagnetic induction theorem, researchers proposed a new neuron model which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. In this paper, dynamical properties of this new model, such as equilibria and its stability, phase portraits, bifurcation diagram, Lyapunov exponents, and basin of attraction, are investigated. Moreover, an implementation of electronic circuit and FPGA is also done to verify the feasibility of the theoretical model.