Even modes

An important development in the phase-shift technique is the use of a radiofrequency synthesizer as the driver for the Pockels cell modulator. In this way, the excitation beam can be modulated at any frequency between 1 and 200 MHz [137-139]. This approach allows use of cw lasers such as the He-Cd laser and even mode-locked lasers [139] as the excitation source. If d and M are measured at six to ten suitably spaced frequencies, least-squares curve-fitting techniques can be employed to obtain lifetimes with greatly enhanced precision. Typical data obtained by this multifrequency technique make measurement of decay times as short as 10 ps possible. Gratton and coworkers have developed other curve-fitting procedures to analyze data obtained on a multifrequency phase-shift fluorimeter. These experiments include the construction of time-resolved spectra [140], measurements of ro-... 

Figure 4.3. Top Plucked string. Center Possible sinusoidal modes of vibration of a center-plucked string. Bottom The even modes, which would not be excited by the center-plucked condition.

Application of the theory of coalescence to the observed phase separation anomalies For the even mode of drainage" of the liquid film separating the drop from another drop or from an interface, several models have predicted a physical property group as the controlling group in addition to functions characterizing the drop dimensions and the rupture film thickness. 

In particular, we can concentrate on the middle monomer (which is a typical inner monomer), using cos (np/2) = f for the even modes and 0 for the odd modes, resulting in... 

Note in Eqs. (8.14) and (8.15) that is the terminal relaxation time for block A, and that the summation must be taken over all integer values (for both even and odd modes of the characteristic equation, Eq. (8.11)) for an ABA-type triblock copolymer, and only over even integer values (i.e., only for even modes of the characteristic equation, Eq. (8.11a)) for an AB-type block copolymer. 

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