Quantization conditions Subject

The generalized coordinate q and its conjugate momentum p vary periodically, and the line integral is evaluated over one cycle. (A similar quantization condition on angular momentum led to the famous Bohr postulate L = nh for the hydrogen atom in the old quantum theory [16].) For vibrational motion subject to a potential U K) in a diatomic, the classical energy is E = p llp -f- U R). The integral in (4.80) then translates into... 

Summarizing this section, we have found that the informity rule and the quantization condition Eq. 1.55 lead to entropic growth as the system in a well-defined quantum state with the entropy 5 = 0, will increase to 5 = fcgln n in the CDS structure without any subjective approximations as e.g. statistical deductions based on the pre-assumed level of descriptions being invoked. Still, we have not derived or even explained the origin of time irreversibility. 

The main goal of this report is to present a phenomenon of highly general nature manifested in various dynamical systems. We present the occurrence of peculiar quantization by the parameter of intensity of the excited oscillations and we show that given unchanging conditions it is possible to excite oscillations with a strictly defined discrete set of amplitudes the rest of the amplitudes being forbidden . The realization of oscillations with a specific amplitude from the permitted discrete set of amplitudes is determined by the initial conditions. The occurrence of this unusual property is predetermined by the new general initial conditions, i.e. the nonlinear action of the external excited force with respect to the coordinate of the system subjected to excitation. 

Instead of p[y we can as well introduce as one of the angle momenta the linear expression A. From the principle mentioned in section 2, that the momenta entering into the expression of the Hamiltonian fimction are subject to quantization, we conclude that we have to add to condition (10) a second quantum relation... 

The robustness to sensor drift of the method under study was evaluated using a simple synthetic drift model. A gain for each of the 60 sensors was initiated to 1 after which the gain factor was subject for over 100 random-walk steps taken from a Gaussian distribution with = 0.01. In the on-line learning condition while testing drift robustness, the last unsupervised vector quantization step was run continuously. 

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