Some historical remarks

In the following 20 years, a group of physicists in the Ukraine [2] studied a series of other aromatic crystals spectroscopically. It developed that there are also very characteristic differences from the spectra of free molecules. In the year 1948, A. S. Davydov [3] formulated the basic theoretical explanation for the observable interaction processes in the crystal spectra, between the molecules in electronically excited states within the crystal. He made use of the model of Frenkel excitons [4] and was able in particular to give a quantitative explanation of a characteristic line splitting, the Davydov splitting, as a fundamental property of organic molecular crystals. Fig. 6.1 shows as an example the splitting of the 0,0-transition in the Ti So absorption spectrum of anthracene at room temperature. 

Energy Transfer and Excitons are, as we have already mentioned, perhaps the most interesting and in any case the most characteristic photophysical processes in molecular crystals. The investigation of these processes began in 1934, when A. Winterstein, U. Schon and H. Vetter [5] were able to explain the green fluorescence radiation from anthracene crystals, which had been described as due to the effect of an unknown chrysogen , in terms of sensitised fluorescence. This fluorescence is emitted by tetracene molecules which are present at very low concentration in the anthracene. Pure anthracene fluoresces in the crystalline phase just as in solution with a blue-violet colour. This observation set off a large number of spectroscopic studies of the sensitised emission from mixed crystals. Very soon, J. Franck and E. Teller [6] pointed out in a summary report of this field that there was an important cormection here to the primary processes of photosynthesis and other biophysical processes. 

Perhaps it is not well known that Leontovich (1935) was the first to investigate a stochastic model of chemical reaction. From the beginning and from the end of the nineteen-forties the works of Delbriick (1940) and Siegert (1949) might be mentioned. While the former studied fluctuations in the 

Remark As a practical example, the assumption (4) means the following for the reaction IX - Y. The deterministic model is 

Additionally, it can be seen that for the case of second order reaction the connection between the deterministic rate constant k and the discrete stochastic rate constant k r) is given by 

The two models are equivalent when the infinitesimal transition probabilities are linear in every co-ordinate of the indices. 

Using assumption (4) and adopting the condition that the process is homogeneous in time (i.e transition probability function depends only on t - s and not specifically on / and s) the Kolmogorov equations (5.9) and (5.10) can be reduced to (linear) ordinary differential-difference equation ( differential in time, and difference in state and in accordance with (5.27) we get, for a deterministic initial condition 

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Abstract After some historical remarks we discuss different criteria of dynamical stability of stars and the properties of the critical states where the loss of dynamical stability leads to a collapse with formation of a neutron star or a black hole. At the end some observational and theoretical problems related to quark stars are discussed. 

In this chapter, we provide a general overview of the field of chemometrics. Some historical remarks and relevant literature to this subject make the strong connection to statistics visible. First practical examples (Section 1.5) show typical problems related to chemometrics, and the methods applied will be discussed in detail in subsequent chapters. Basic information on univariate statistics (Section 1.6) might be helpful to understand the concept of randomness that is fundamental in statistics. This section is also useful for making first steps in R. 

Definitions, typical examples for chemical and biochemical sensors, and some historical remarks are given in Chapters 1 and 2. 

Goal. - Probability. - Informatioa -Chance. - Necessity. - Chance and Necessity. - Self-Organizatioa - Physical Systems. - Chemical and Biochemical Systems. - Applications to Biology. - Sociology A Stochastic Model for the Formation of Public Opinion. - Chaos. - Some Historical Remarks and Outlook. 

Some historical remarks. The physical assumption adopted by van Kampen (1976) is that the grand-canonical distribution of the particle number of an ideal mixture is Poissonian. Based on this — strongly restrictive — assumption, and utilising the conservation of the total number of atoms the stationary distribution can be obtained. This stationary distribution can be identified with the stationary solution of the master equation, and it is not Poissonian in general, even for large systems. 

In many respects, this conference has had some historic occasions, more than the previous conferences. In particular, seeing Hans Bethe and Edward Teller, who rarely agree on anything, sitting side by side in the front row was viewed by the participants as a remarkable occurrence. Their presence in this conference greatly increased its visibility. 

Theoretical Quantum Chemistry as Science and Discipline Some Philosophical Remarks on a Historical Issue... 

Section 14.2 presents a description of the TDL technique for temperature measurement, including the theory and basic principles behind the method. Section 14.3 provides a historical overview of the development of this technique to provide a sense of the considerable amount of research that has been performed in this field to date. Section 14.4 provides details of four TDL-based systems capable of temperature measurement in full-scale environments that are thought to be of particular interest to the industrial combustion community. Finally, Section 14.5 contains some concluding remarks about the current state of TDL sensors and possible outcomes of future developments. 

In the following sections, after some preliminary historical remarks and a more precise characterisation of the charge carriers in terms of polarons, we will introduce the more important experimental methods. Afler that, we treat ultrapure crystals (Sect. 8.5) and disordered organic solids (Sect 8.6). 

Anastas closed his remarks by discussing impediments to innovation. He explained that change can come much more slowly than anyone would expect because people do not like to do things differently from the way they have done them before. New ideas and new perspectives often face harsh opposition. He led the audience in considering some amusing historical examples of mistakes made by a few of our greatest scientific leaders ... 

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