Hydrodynamic cavitation is a new technique in wastewater treatment processes. The degradation of Rbodamine B was studied on a 220 liters hydrodynamic cavitation setup using multiple hole orifice plates in this paper. ...Hydrodynamic cavitation is a new technique in wastewater treatment processes. The degradation of Rbodamine B was studied on a 220 liters hydrodynamic cavitation setup using multiple hole orifice plates in this paper. The experimental results showed that Rhodamine B was really decomposed by hydrodynamic cavitation. Some factors influencing degradation effect i.e. geometric parameters and operation conditions also were discussed. It was concluded there was the optimal ratio of total area of holes to crosssectional area of the pipe and the rate constant increased with a reduction in the value of the modified cavitional number.展开更多
In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexa...In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].展开更多
Let M be an n-dimensional complete Riemannian manifold with Ricci curvature n- 1. By developing some new techniques, Colding(1996) proved that the following three conditions are equivalent: 1)dGH(M, S^n) → 0; 2) the ...Let M be an n-dimensional complete Riemannian manifold with Ricci curvature n- 1. By developing some new techniques, Colding(1996) proved that the following three conditions are equivalent: 1)dGH(M, S^n) → 0; 2) the volume of M Vol(M) → Vol(S^n); 3) the radius of M rad(M) →π. By developing a different technique, Petersen(1999) gave the 4th equivalent condition, namely he proved that the n + 1-th eigenvalue of M, λ_(n+1)(M) → n, is also equivalent to the radius of M, rad(M) →π, and hence the other two.In this paper, we use Colding's techniques to give a new proof of Petersen's theorem. We expect our estimates will have further applications.展开更多
It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of ...It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of a continuous Hunt process by the first exitdistribution from any ball.展开更多
文摘Hydrodynamic cavitation is a new technique in wastewater treatment processes. The degradation of Rbodamine B was studied on a 220 liters hydrodynamic cavitation setup using multiple hole orifice plates in this paper. The experimental results showed that Rhodamine B was really decomposed by hydrodynamic cavitation. Some factors influencing degradation effect i.e. geometric parameters and operation conditions also were discussed. It was concluded there was the optimal ratio of total area of holes to crosssectional area of the pipe and the rate constant increased with a reduction in the value of the modified cavitional number.
文摘In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].
基金supported by National Natural Science Foundation of China(Grant No.11171253)
文摘Let M be an n-dimensional complete Riemannian manifold with Ricci curvature n- 1. By developing some new techniques, Colding(1996) proved that the following three conditions are equivalent: 1)dGH(M, S^n) → 0; 2) the volume of M Vol(M) → Vol(S^n); 3) the radius of M rad(M) →π. By developing a different technique, Petersen(1999) gave the 4th equivalent condition, namely he proved that the n + 1-th eigenvalue of M, λ_(n+1)(M) → n, is also equivalent to the radius of M, rad(M) →π, and hence the other two.In this paper, we use Colding's techniques to give a new proof of Petersen's theorem. We expect our estimates will have further applications.
基金Project supported by the National Natural Science Foundation of China (No.10271109)
文摘It is skowed that if the first exit distribution leaving any ball from the center is theuniform distribution on the sphere, then the Levy process is a scaled Brownian motion.The paper also gives a characterization of a continuous Hunt process by the first exitdistribution from any ball.
