Comparison with the data

Only a very brief account of the comparison of quarkonia predictions with the data will be possible and we shall confine ourselves to discussing the situation below threshold, i.e. to bound states. 

A preliminary question is to what extent the non-relativistic scheme is adequate for qq systems. As shown in Table 12.1, this seems quite 

It is amusing that a similar computation for a toponium (Ft) system taking m 130 GeV/c yields over 300 bound states  

Details of the various cc and bb states expected in qum konia schemes are given in Figs. 12.3 and 12.4 respectively. The thresholds stfe shown by the shaded lines. Continuous lines denote states that have been experimentally observed whereas broken lines are theoretical predictions. Numbers above the states denote the principal quantum numbers. 

It must be stressed that only the fine details depend on the specific choice of the potential. The qualitative picture is largely independent of which of the potentials discussed previously one actually uses. 

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Table 5.1 lists some of the atomic properties of the Group 2 elements. Comparison with the data for Group 1 elements (p. 75) shows the substantial increase in the ionization energies this is related to their smaller size and higher nuclear charge, and is particularly notable for Be. Indeed, the ionic radius of Be is purely a notional figure since no compounds are known in which uncoordinated Be has a 2- - charge. In aqueous solutions the reduction potential of... 

These considerations also explain the occurrence of cases of dimorphism involving the sodium chloride and cesium chloride structures. It would be expected that increase in thermal agitation of the ions would smooth out the repulsive forces, that is, would decrease the value of the exponent n. Hence the cesium chloride structure would be expected to be stable in the low temperature region, and the sodium chloride structure in the high-temperature region. This result may be tested by comparison with the data for the ammonium halides, if we assume the ammonium ion to approximate closely to spherical symmetry. The low-temperature form of all three salts, ammonium chloride, bromide and iodide, has the cesium chloride structure, and the high-temperature form the sodium chloride structure. Cesium chloride and bromide are also dimorphous, changing into another form (presumably with the sociium chloride structure) at temperatures of about 500°. 

The results of the experiments we carried out and the comparison with the data arising from homogeneous oxidation chemistry allow us to propose and generalize the following conclusions that in part contrast previous literature findings ... 

The structure of the complexes in solution and in crystals was established using spectral methods and by comparison with the data for initial ligands. This approach made it possible to determine the structure of new ligands formed in the reaction by complexation. 

The H-NMR data of isositsirikine (9, C21H26N203, [a]D —20°), isolated from the stem bark of T. psorocarpa (65) were in agreement with those previously reported by Kan et al. (185) from 16-epiisositsirikine (10). The structure was confirmed through direct comparison with an authentic sample obtained by NaBH4 reduction of geissoschizine (6). The stereochemistry at C-16 of isomeric isositsirikines has been revised by Scott (186), and structure 10 represents the correct C-16 configuration for 16-epiisositsirikine. The proton resonances of 10 are reported in Table III in comparison with the data of isositsirikine. The CMR data of 10 are also available. 

A new amorphous alkaloid has been recently isolated from the Chinese plant T. bufalina (Ervatamia hainanensis) collected on Hainan Island (53). Its mass spectrum showed a molecular ion at m/z 382, corresponding to C23H30N2O3. From the fragmentation pattern, this compound would appear to be a coronaridine derivative in which a C2H50 unit is attached to the aliphatic moiety of the molecule. The structure 111 with (S) configuration at C-3 was determined by a detailed analysis of its H-NMR spectrum (Table IV) in comparison with the data of other ibogan alkaloids. 

AU the medical records of the subject should be available for comparison with the data recorded in the case report form (CRF). In the past, physicians have not allowed medical records to be available for the so-called source verification by non-physicians since they felt that this broke the strict confidentiality of the study subject s medical records. However, frequent mistakes in transferring important clinical data to the CRF, the recruitment of subjects who do not meet the inclusion and exclusion criteria and the occasional blatant fraud has led to an insistence by sponsors and regulatory agencies for sponsor s review of study documentation. Indeed, verification of source data cannot take place without access to the medical records of the study subject by the sponsor s staff. 

The predictor x can be a discrete variable, such as the number of carbon atoms, or a continuous variable, such as pressure. The simplest functional form of correlation is the linear form y = a + bx. This form has two parameters a and b, which are to be determined by comparison with the data. This form becomes even simpler if the intercept a = 0. 

Figure 10 Calculated W values for electrons in water vapor as a function of the initial energy of electrons in comparison with the data of Combecher [197].

On hydrophilic surfaces, such as PVA or poly(HEMA), OH-groups of the materials are incorporated in the network structure of adsorbed water molecules (see Sect. 4.4). In consequence, the absolute value of Wj(3 — Wi1 is considered to become still smaller, where - owing to the stabilization of water molecules on the hydrophilic surface - the water-removing-process (reverse reaction of Eq. (2.6)) proceeds slowly. Many experiments were carried out with water-adsorbed hydrophilic surfaces, the behavior of which was time-dependent. In a similar way, the water removal from the proteins [Eq. (2.9)] is also considered to proceed slowly. Thus, we must be careful in considering experimental results in comparison with the data in Tables 3, 4 and 5. 

In the major isomer, the bipyridinium unit is located inside the cavity of the macrocyclic poly ether and the /7Y//7,v-bis(pyridinium)ethylene unit is positioned alongside, as confirmed by the electrochemical analysis. The cyclic voltammo-gram of the catenane shows four monoelectronic processes that, by a comparison with the data obtained for the free cyclophane, can be attributed as follows the first and third processes to the first and second reductions of the bipyridinium unit, and the second and fourth ones to the first and second reductions of the trans-bis (pyridinium)ethylene unit. The comparison with the tetracationic cyclophane also evidences that all these reductions are shifted toward more negative potential values (Fig. 13.33b). 

As Vickers hardness increases, so does the brittleness of the material (Fig. 5.21). Analysing the curves in comparison with the data in Table 5.5,... 

The formation of strong hydrogen bonds in glycerol leads to a very high viscosity and also a long relaxation time (see Table 1.2) however, a comparison with the data for alcohols with comparable volumes suggests that the relationship between viscosity and relaxation time is not the simple linear one implied by the Debye expression. 

The electrostatic free energy of ionization, as calculated from (11) with ZA = +1 and ZB = — 1, is always positive. The quantity d In D/dT is always negative because thermal motion overcomes the orientation of dipoles in an electric field therefore A8el is always negative. The values of D, AFel, AHa, and ASel for several representative solvents are given in Table 8 (Frost and Pearson, 1961). Comparison with the data in... 

Fig. 4.5. Log-scale distribution of the total momentum in double ionization of helium for Up = 14eV based on the assumption that the returning electron promotes the bound electron into an excited state with energy Eq2 = —0.5, —0.22, —0.125 a.u., for curves (1), (2), and (3), respectively. The calculation is in one dimension only. The curves (4) display, for comparison, the distribution generated by the direct rescattering scenario of (4.1) for contact interactions (4b) was calculated in three dimensions and (4a) in one. The spiky structures of curves (4a) and (la) are due to channel closings, which have a more pronounced effect in one than in three dimensions. Curves (lb), (2), and (3) are smoothed so as to suppress these effects, curve (la) is not. The inset redraws curves (lb), (2), and (3) on a linear scale for easier comparison with the data [3]. From [15]...

Comparison with the data for exchange of indole under the same conditions (Table 8.2) shows the 3-position of indolizine to be 1800 times more reactive than the 3-position of indole. This is a measure of the effect of forming the benzenoid transition state for indolizine exchange. 

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