Multiplication, significant

Tyutyulkov analysed cross-conjugated systems like [14] theoretically, using the Coulson-Rushbrooke theorem and Wannier transformation of the Bloch MO. His results hold multiple significance. First, it was suggested, by taking into account the interaction between the one-dimensional chains of the quasi-one-dimensional polymer, that the critical temperature may reach 10 -10 K (see p. 226). Secondly, the radical centres of hydrocarbons... 

Hochberg Y, Benjamini Y (1990) More powerful procedures for multiple significance testing. Stat... 

Figure Al.6,8 shows the experimental results of Scherer et al of excitation of I2 using pairs of phase locked pulses. By the use of heterodyne detection, those authors were able to measure just the mterference contribution to the total excited-state fluorescence (i.e. the difference in excited-state population from the two units of population which would be prepared if there were no interference). The basic qualitative dependence on time delay and phase is the same as that predicted by the hannonic model significant interference is observed only at multiples of the excited-state vibrational frequency, and the relative phase of the two pulses detennines whether that interference is constructive or destructive.

Quantum mechanics (QM) is the correct mathematical description of the behavior of electrons and thus of chemistry. In theory, QM can predict any property of an individual atom or molecule exactly. In practice, the QM equations have only been solved exactly for one electron systems. A myriad collection of methods has been developed for approximating the solution for multiple electron systems. These approximations can be very useful, but this requires an amount of sophistication on the part of the researcher to know when each approximation is valid and how accurate the results are likely to be. A significant portion of this book addresses these questions. 

Unfortunately, the simple situations just described are often the exception. In many cases, both the sampling variance and method variance are significant, and both multiple samples and replicate analyses of each sample are required. The overall error in this circumstance is given by... 

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