Real , Imaginary

The nature of the solution given by Equation (5-19) depends upon the nature of the roots, r and ri- The behavior of this damped system depends upon whether the root is real, imaginary, or zero. The eritieal damping eoeffieient cy ean now be defined as that whieh makes the radieal zero. Thus,... 

FORMAT FREQUENCY REAL IMAGINARY LOG MODULUS ANGLE ) WR1TE(6,93)... 

Because chemical-shift evolution just rotates the magnetization vector in the x -y (real-imaginary) plane without affecting its magnitude, the phase of the detected 13 C magnetization is not important. So we can live with a simple 1/(2J) delay. 

Figure 6-14 The four types of 2D phase quadrants, corresponding to frequency modes that are real-real (RR), imaginary-real (IR), real-imaginary (RI), and imaginary-imaginary (II). (Reproduced from A. E. Derome, Modern NMR Techniques for Chemistry Research, Pergamon Press, Oxford, UK, 1987, p. 207.)...

The multiplication of a matrix, A, by a constant c (a real, imaginary or complex number) is achieved by simply multiplying each element by the constant, resulting in the elements changing from ,y to ca,y, for all ij. 

This defines the exponential function, which plays a major role in applied mathematics. The very steep growth of the factorials guarantees that the expansion will converge to a finite quantity for any finite value of x, real, imaginary, or complex. The inverse of the exponential function is the natural logarithm, defined in Eq. (3.55) ... 

Before discussing the results of the dimer models, the polarizability spectrum of the monomer model obtained using the perturbation theory (Eq. 5.1) is compared with that calculated by the QME method (Eqs. 5.8, 5.14, 5.17) to confirm the reliability of our results for EIT phenomenon. Figure 5.3 shows the real/imaginary parts of the polarizability spectra (Re[a] and Im[a], respectively) as the functions of the frequency of the probe field ( > ). Im[a] of Fig. 5.3a, b corresponds to the... 

We briefly note from our computational approach the part relevant to electrode contributions. The contact effects due to the electrodes are to renormalize the electronic structure of the device molecule. The self-energy explicitly involves the contact effects on the molecule region due to the electrodes, so it plays a critical role in determining the transport characteristics its real/imaginary parts give rise to shift and broadening of the molecular energy levels. 

Note that the Is function given above is not the only function which satisfies the Schrbdinger equation for E = Ei multiplication of the Is wavefunction by any number c, positive or negative, real, imaginary or complex, yields a new function which is also a solution of the time-independent Schrodinger equation, equation (1.9), with the same energy ... 

Variables and Units handle real, imaginary, and complex numbers with or without associated units. A high-performance calculation engine provides speed and sophisticated memory management to help find solutions faster. 

Fig. 10. Rheological master curve of PI-3(reference temperature Tr =230 K) of the real imaginary parts of the shear modulus.

ReZ/ImZ real/imaginary part of the double layer impedance Ohm cm ... 

Depending on the sign and/or the magnitude of constants A and S, the roots to Equation (6-16) may be real, imaginary, or complex. Let us consider the solutions to the differential equation in each of these cases. 

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