Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations

AbstractIn this paper, we present a new approach to obtain the comparison theorem of two 1-dimensional SDEs with diffusion and jumps. The two equations is treated as one two-dimensional SDE and the comparison requirement is regarded as to keep the solution (Xt1,Xt2) within the constraint K={(x1,x2);x1⩽x2}. We then apply a new criteria of “viability condition” which is a necessary and sufficient condition to keep the solution to be inside the constraint K

CO preferential oxidation in a novel Au@ZrO₂ flow-through catalytic membrane reactor with high stability and efficiency

CO preferential oxidation (CO-PROX) achieves much interest as a strategy to remove trace CO in reformed gases for hydrogen utilization. Herein, we reported a novel Au@ZrO₂ catalytic membrane reactor by embedding gold nano-particles in ZrO₂ hollow fiber membrane for CO-PROX. The flow-through catalytic membrane exhibited high catalytic activity and oxygen selectivity, which gave a turnover frequency of 4.73 s⁻¹ at 60 °C, 2–3 times higher than conventional catalyst pellets. CO conversion of >95% was achieved over the catalytic membrane, which maintained great operational stability during 500-h operation even CO₂ and H₂O were added in the feed stream. The excellent catalytic performance of the flow-through catalytic membrane makes gold catalyst possible for practical application in the removal of CO from hydrogen

Fixed-bed column adsorption of arsenic(V) by porous composite of magnetite/hematite/carbon with eucalyptus wood microstructure

The fixed-bed column adsorption-desorption of As(V) by the porous composite of iron oxides and carbon with eucalyptus wood hierarchical microstructure (PC-Fe/C) was experimentally studied. The increase in the influent As(V) concentration and the inflow rate resulted in an earlier exhaustion of the column. The breakthrough curves indicated that a larger adsorbent mass, a smaller adsorbent grain size and a lower influent pH prolonged the column life span. The operating temperature had negligible effect. All breakthrough curves could be well fitted with the Thomas and Yoon–Nelson models. Under the condition of the influent flow rate of 5.136 mL/min, the influent As(V) concentration of 20 mg/L, the influent pH of 3, the adsorbent mass of 2 g, the adsorbent grain size of <100 mesh, and the operating temperature of 35 °C, the equilibrium adsorption capacity reached 10.49 mg/g, which was greater than those of natural/synthetic iron oxides adsorbents and iron-oxide-coated adsorbents