We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induc...We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.展开更多
Surface roughness of quartz particles was determined by measuring the specific surface area of particles.The wettability characteristics of particles were determined by measuring the flotation rate using a laboratory ...Surface roughness of quartz particles was determined by measuring the specific surface area of particles.The wettability characteristics of particles were determined by measuring the flotation rate using a laboratory flotation cell.Experimental results show that the rod mill product has higher roughness than the ball mill product.For the particles with larger surface roughness,the flotation kinetics constant is also higher.Finally,empirical relationships between surface roughness(r) and the flotation kinetics constant(k) of quartz particles as k=A+Br+Cr0.5lnr+D/lnr+E/r and k=A+Br are presented,in which A,B,C,D and E are constants related to experimental conditions and mineralogical properties of mineral.展开更多
In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional.
文摘We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.
文摘Surface roughness of quartz particles was determined by measuring the specific surface area of particles.The wettability characteristics of particles were determined by measuring the flotation rate using a laboratory flotation cell.Experimental results show that the rod mill product has higher roughness than the ball mill product.For the particles with larger surface roughness,the flotation kinetics constant is also higher.Finally,empirical relationships between surface roughness(r) and the flotation kinetics constant(k) of quartz particles as k=A+Br+Cr0.5lnr+D/lnr+E/r and k=A+Br are presented,in which A,B,C,D and E are constants related to experimental conditions and mineralogical properties of mineral.
文摘In this article, we introduce the concept of entropy functional for continuous systems on compact metric spaces, and prove some of its properties. We also extract the Kolmogorov entropy from the entropy functional.
