In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A m...In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.展开更多
The effects of soil texture, initial water content and bulk density on diesel oil infiltration in fine sand and silty clay loam materials were evaluated. Three physical and two empirical equations express diesel oil i...The effects of soil texture, initial water content and bulk density on diesel oil infiltration in fine sand and silty clay loam materials were evaluated. Three physical and two empirical equations express diesel oil infiltration through soils with time, with coefficients of determination greater than 0.99. Diesel oil infiltrates more quickly in the fine sand than in the silty clay loam material. Diesel oil infiltration rates are found to decrease with increasing initial water content and bulk density for the silty clay loam material. The infiltration rate of diesel oil in the fine sand material increases slightly with increasing initial water content. The diesel oil saturated conductivity(Kdiesel) decreases with increasing bulk density for the silty clay loam column. Diesel oil sorptivity(S) decreases linearly with increased initial water content and bulk density of the silty clay loam material. Changes in empirical parameters relative to initial water content and bulk density are similar to the parameter S.展开更多
文摘In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.
基金Projects(40272108,41402208)supported by the National Natural Science Foundation of ChinaProjects(ZR2012DL05,ZR2015EL044)supported by Shandong Provincial Natural Science Foundation,China+1 种基金Project(4072-114017)supported by Young Teachers’ Development of Shandong University of Technology,ChinaProject(J12LC51)supported by Shandong Province Higher Educational Science and Technology Program,China
文摘The effects of soil texture, initial water content and bulk density on diesel oil infiltration in fine sand and silty clay loam materials were evaluated. Three physical and two empirical equations express diesel oil infiltration through soils with time, with coefficients of determination greater than 0.99. Diesel oil infiltrates more quickly in the fine sand than in the silty clay loam material. Diesel oil infiltration rates are found to decrease with increasing initial water content and bulk density for the silty clay loam material. The infiltration rate of diesel oil in the fine sand material increases slightly with increasing initial water content. The diesel oil saturated conductivity(Kdiesel) decreases with increasing bulk density for the silty clay loam column. Diesel oil sorptivity(S) decreases linearly with increased initial water content and bulk density of the silty clay loam material. Changes in empirical parameters relative to initial water content and bulk density are similar to the parameter S.
