If additionally A∗A dμ⩽I and B∗B dμ⩽I, then I−A∗A dμ XI−B∗B dμ∈|||·|||(H) andI−A∗A dμI−B∗B dμ⩽AB .Applications include Young's and arithmetic geometric logarithmic means inequalities for operators and the mean value theorem for operator monotone functions.
The measurements were averaged by the monitor system and displayed as the mean value to the operator.
Mean values for all operator and operation characteristics were statistically different between the two groups with the exception of operator age (t-tests, 95%).
Open image in new window Figure 5 Mean value of particle number operator vs. normalized temperature.
We use the mean value of a single operator to measure the distance between the final state and the ideal ground state.
First, instead of studying the evolution of the eigenstates and their corresponding probability amplitudes, the mean value of a Hermitian operator is defined as a measure of the error.
where E q is the internal energy, ϵ i denotes the energy eigenvalues of the energy operator Ĥ Open image in new window, N q is the quantum mean value of the particle number operator N ̂ Open image in new window, and n i is the eigenvalue of this last operator.
Indicating with n i the number of vehicles counted by the i-th operator, the mean value for each class is given by: Open image in new window (8 where n is the number of operators.
Lastly, in Figure 5, the thermal mean value of the particle number operator vs. the normalized temperature, i.e., N q vs. T t, with q= 1.0, 1.4, 1.7, 1.7 and 2.0, is presented.
