Regular behaviour

As follows from the above treatment for higher values of the scaled energy e which includes both the energy and magnetic field strength the behaviour of the system becomes more chaotic, while for the smaller values regular behaviour is observed. 

Only the measurements of Bengtson are available for the 3p 2 ) 5s-3p ( P) 5p fine structure transitions in 5r/(Table 3). No comparative data from other sources have been found in the literature for fine structure transitions in //(Table 4), and thus we have made use of the regular behaviour of the oscillator strengths for analysing /-value data. 

Therefore, we have attempted to assess the correctness of our results by analysing their possible regular behaviour along the group. As an example, we have collected in Table 4 the RQDO oscillator strengths for a few multiplets that cor-... 

The practice to keep the total concentration of the counterion constant by adding varying amount of the neutral salt leads to a more regular behaviour of the RP-IPC system and is therefore to be recommended [386]. 

An Empirical Relationship between the Electrical Conductivity of Mercury and Temperature over its Entire Liquid Range, also its thermal Conductivity and the Latter s Regular Behaviour. J. Inorg. Nucl. Chem. 28, 803—811 (1966). 

If l) t) shows regular behaviour, for instance periodicities, then 6 t) shows an oscillating behaviour. If 0 t) decays, this would be an indication that l) t) develops complicated structures by looking less and less like its starting configuration. For the wave function (1.4.3) it is easy to calculate 0 t). The result is ... 

The slopes of these lines provide partial molar enthalpies of solution of 97.5 4.7 and 89.2 2.6 kJ mol1 for NaBr and Nal, respectively, where the thermodynamic reference state is the solid halide. The solvation enthalpies derived from these values are —265.6 9.9 and —225.0 7.9 kJ mol-1 for bromide and iodide ion, respectively. The salts are considered to dissolve in the metal as the dissociated ions, solvated by liquid metal, and the solutions show large deviations from ideal but small deviations from regular behaviour.16 The solubilities of potassium chloride in liquid potassium and in... 

We are beginning to understand chaotic structure in a way not seen before. Numerical methods of measuring chaotic and regular behaviour such as Fast Liapunov Indicators, sup-maps, twist-angles, Frequency Map Analysis, fourier spectal analysis are providing lucid maps of the global dynamical behaviour of multidimensional systems. Fourier spectral analysis of orbits looks to be a powerful tool for the study of Nekhoroshev type stability. Identification of the main resonances and measures of the diffusion of trajectories can be found easily and quickly. Applied to the full N-body problem without simplification, use of these tools is beginning to explain the observed behaviour of real physical systems. 

Yet another possibility is that part of the cells within a continuously stirred suspension would oscillate in a chaotic manner if left on their own, while the remaining cells would oscillate periodically in the absence of the chaotic population. The coupling of the two populations within the same suspension could well suppress any manifestation of chaos by conferring upon the coupled system a global, regular behaviour. 

Behavioural experiments testing out predictions using regular behavioural homework assignments that gather evidence to support or reject particular beliefs (Enright 1997)... 

The regular behaviour shown in Fig. 60 is in marked contrast to the energies of the excited states in even-odd nuclei which can take much lower values. In even-even nuclei, as we have seen, low values obtain in the heaviest elements but they vary continuously and systematically from one nucleus to another. Preiswerk and Stahelin noting this difference have pointed out that the levels of even-even nuclei do not show the continuous displacement with mass number... 

Alii ), especially for the members of Series II (Fig.3). The dependence of AUm and A Hi on the composition of polymer (Fig.3 and 4) shows a regular behaviour within the Series revealing a minima for approximately equimolar content of amide and ketone groups incorporated into the rigid part of the macromolecules ( with the exception for AHm of Series I, in which minimum reaches 75 mol% of DHBP-A in the macromolecule). 

We have also attempted to determine the superstructure of the scattering elements in the melt. SALTS investigations revealed four-clover type scattering patterns of different sizes and intensities for all members of both series, however any regular behaviour could not be detected. These results can suggest then, that the scattering elements of the mesomorphic melts were generally spherulitic in shape. 

Most time series exhibit some regular behaviour, but it is useful to decompose them into following components ... 

It is often mentioned that the stationary distribution of chemical reactions is generally the Poisson distribution (Prigogine, 1978). However, the significance of the Poisson distribution is rather limited other unimodal distributions can also reflect the regular behaviour of the fluctuating chemical sytems. Multimodality of the stationary distribution might be associated, at least loosely speaking, with multistationarity of deterministic... 

The first part of the theorem means that within the class of zero deficiency mechanisms weak reversibility is enough to ensure regular behaviour. 

As the V-graph of a weakly reversible mechanism is cyclic (Exercise 4 below), the regular behaviour of a mechanism cannot be inferred from both zero deficiency theorem and by Vol pert s theorem at the same time at most one of them can be used. 

As the FHJ-graph and the V-graph of a compartmental system may be considered to be identical, for compartmental systems it is literally true that regular behaviour can be assured when there are either no or many cycles. 

Show that all the reactions with three short complexes and with a single linkage class show regular behaviour, either by proving the equality of the deficiency to zero, or by directly verifying the properties needed for quasithermodynamic behaviour. 

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