The Periods of States for Markov Chains in a Random Environment

The periods of states for Markov chains in a random environment are introduced and some properties about periods are investigated. An open problem (Orey, 1991; Problem 1.3.3) is studied under the assumption that states have periods.     

On the output function in a Ginsburg’s machine

We give the form of the output function in Ginsburg’s machine in which the input and output dictionaries are abelian groups and the transition function is of a special form.     

Utilizing the Space‐Charge Region of the FeNi‐LDH/CoP p‐n Junction to Promote Performance in Oxygen Evolution Electrocatalysis

The modulation of electron density is an effective option for efficient alternative electrocatalysts. Here, p‐n junctions are constructed in 3D free‐standing FeNi‐LDH/CoP/carbon cloth (CC) electrode (LDH=layered double hydroxide). The positively charged FeNi‐LDH in the space‐charge region can significantly boost oxygen evolution reaction. Therefore, the j at 1.485 V (vs. RHE) of FeNi‐LDH/CoP/CC achieves ca. 10‐fold and ca. 100‐fold increases compared to those of FeNi‐LDH/CC and CoP/CC, respectively. Density functional theory calculation reveals OH^? has a stronger trend to adsorb on the surface of FeNi‐LDH side in the p‐n junction compared to individual FeNi‐LDH further verifying the synergistic effect in the p‐n junction. Additionally, it represents excellent activity toward water splitting. The utilization of heterojunctions would open up an entirely new possibility to purposefully regulate the electronic structure of active sites and promote their catalytic activities.