In this paper, we consider a finite-horizon model with the time-additive utility and the time varying discount rate. With the assumption of the concavity of absolute risk tolerance, the concavity of the consumption function has been proved. This result significantly broadens the conclusion of Carroll and Kimball (1996) for the case of the HARA utility function.
Two segments of plasmas with different densities, which are operated as the electron injector and accelerator, respectively, are designed to realize a cascaded laser wakefield accelerator.Particle-in-cell simulations indicate that the further acceleration of the electrons in the second uniform-density plasma relies on the injection and acceleration in the first stage. It is found that electrons trapped in the second wakefield period in the first stage can be seeded into the next stage with an optimized phase for efficient acceleration and reducing in the relative energy spread. And finally a 700 MeV electron beam with a relative rms energy spread about 0.6% and the normalized transverse emittance of 1.4π mm mrad was obtained after a 5.5-mm-long acceleration in a dark-current free cascaded laser wakefield accelerator. Our results demonstrate that, for a given laser energy, choices in laser and plasma parameters strongly affect the output electron beam energy and quality, and that all of these parameters can be controlled.
Treating diethynyl-substituted perylenediimides with ICI successfully induced an annulation reaction and generated a series of coronenediimide derivatives. Instead of the expected iodine-substituted cyclization product, chlorine-substituted analogues were produced. The mechanism of this annulation reaction thus necessarily involved a chlorine addition step prior to the aromatic substitution reaction. With facile subsequent transformations, various tetraaryl coronenediimides could be obtained via the annulated chloro-substituted coronenediimide.