Tremendous efforts have been devoted to develop low-cost and highly active electrocatalysts for oxygen evolution reaction (OER). Here, we report the synthesis of mesoporous nickel oxide by the template method and its application in the title reaction. The as-prepared mesoporous NiO possesses a large surface area, uniform mesopores, and rich surface electrophilic Ni3+ and O− species. The overpotential of meso-NiO in alkaline medium is 132 mV at 10 mA cm−1 and 410 mV at 50 mA cm−1, which is much smaller than that of the other types of NiO samples. The improvement in the OER activity can be ascribed to the synergy of the large surface area and uniform mesopores for better mass transfer and high density of Ni3+ and O− species favoring the nucleophilic attack by OH− to form a NiOOH intermediate. The reaction process and the role of electrophilic Ni3+ and O− were discussed in detail. This results are more conducive to the electrochemical decomposition of water to produce hydrogen fuel as a clean and renewable energy.

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.

The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated. Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.

We investigate the effects due to anisotropy and magnetic field interaction for a quasi-two-dimensional Boltzmann gas in an elliptical parabolic quantum dot. The specific heat is studied with varying temperature, anisotropy, and magnetic field strength. The cases without and with the inclusion of the spin Zeeman interaction are considered.

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin (FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system. An exact analytical expression is established for the evolution of the eigenstates. This result then provides a general solution to the time-dependent Schrödinger equation.