When the reward factor [theta] is 0.20 and the penalty factor [sigma] is 0.60 in the simulation experiments, we randomly tag the nodes whose initial expectation value
This approach can be extended to the expectation values
of the current density  and then to the calculation within the Floquet scheme of nonlinear optical properties under intense laser fields (high harmonic generation  and saturable absorption [36, 37]) of graphene.
The key to obtain the correct expectation values
of the potential is to first find out <0[absolute value of ([phi][phi])]0>.
The customer total consumption and the service expectation value
are very high so this kind of customers value is high.
An essential point in this process is the expansion in an auxiliary orthonormal basis, which allows all occurrent expectation values
to be written either in terms of the coefficients of the transverse dynamic spin susceptibility itself or in terms of other observables that can be obtained independently.
Because Z[??] is the interval grey linguistic variables, we can get the ranking alternatives by the expectation value
If h is even, then the expectation value
can be reduced to <hf, f> = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], but
Next, as an independent measure of a possible psi effect, one calculates the expectation value
and the variance of Pot for the specific observed N value.
Using the mass expectation values
in the marble-sized regions A and B calculated in Appendix A, we obtain
(12) This expectation value
is referred to in the United States as the "option privilege." (13) In many cases the amount of the expectation value
can be agreed to in advance with the Dutch tax authorities.
So, we obtain the expectation value
<([PI] + Y[PHI])(x)([PI] + Y[PHI])(x')> = [[gamma].sup.2][[beta].sup.-1.sub.1(x, x').
The PES associated with the IBM Hamiltonian of equation (1) is given by its expectation value
in the coherent state and can be written as: