A critical comparison

The time-independent and the time-dependent approaches are completely equivalent. Equation (4.11) documents this correspondence in the clearest way the time-dependent wavepacket f f(t), which contains the stationary states for all energies, and the time-independent wavefunction tot(Ef), which embraces the entire history of the fragmentation process, are related to each other by a Fourier transformation between the time and the energy domains, 

Both approaches rest upon the Golden Rule expression for the photodissociation cross section and comprise the same basic assumption, namely the weak interaction between the light pulse on one hand and the molecule on the other hand (Henriksen 1988). 

The time-independent and time-dependent approaches merely provide different views of the dissociation process and different numerical tools for the calculation of photodissociation cross sections. The time-independent approach is a boundary value problem, i.e., the stationary wavefunction 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

Which approach offers the better interpretation of the photodissociation dynamics in general and of the dissociation cross sections in particular The answer to this question depends very much on the particular system and cannot be decided in a unique way. There are cases which are better described by the time-independent picture while other systems may be better understood within the time-dependent view. In the course of this monograph we will always attempt to combine both views in order to reveal all facets of a particular system. 

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Union Carbide Corp., Kabelitems Wire and Cables No. 157, A. Critical Comparison ofXEPE andEPR for use as Electrical Insulation on Underground Power Cables, Danbury, Conn. 

There was some argument in the literature over the relative merits and demerits of the JKR and the DMT theories [23-26], but the controversy has now been satisfactorily resolved. A critical comparison of the JKR and DMT theories can be obtained from the literature [23-30]. According to Tabor [23], JKR theory is valid when the dimensionless parameter given by Eq. 25 exceeds a value of about five. 

Chiomatograirilic methods often devdop in a cyclic manner The discovery of a new separation technique naturally stimulates interest concerning the method this attention wanes when another technique appears on the horizon and soon interest is directed at the new technique. There is then a confrontation between the methods and a critical comparison of the advantages and disadvantages of the two m hods. This sometimes leads to a renaissance of the older method, which has been the subject of further development in the meantime. In this context discover-les made in connection with the modem technique are often used to advantage in / the older one... 

The gas chromatograph (GC) resembles the MS in providing both qualitative and quantitative EGA but is significantly slower in operation. The interval between analyses is normally controlled by the retention time of the last component to be eluted from the column such delay may permit the occurrence of secondary reactions between primary products [162]. Several systems and their applications have been described [144,163— 167] sample withdrawal can be achieved [164] without the necessity for performing the reaction in an atmosphere of carrier gas. By suitable choice of separation column or combination of columns [162], it is possible to resolve species which are difficult to measure in a small low-resolution MS, e.g. H20, NH3, CH4, N2 and CO. Wiedemann [168] has made a critical comparison of results obtained by MS and GC techniques and adjudged the quality of data as being about equal. 

Mahdihassan, S. A critical comparison of basic terms in Greek and Chinese systems of alchemy. Studs Hist Med 8, no. 3-4 (1984) 143-152. 

A critical comparison between experiment and theory is hindered by the range of experimental values reported in the literature for each molecule. This reflects the difficulty in the measurement of absolute ionization cross sections and justifies attempts to develop reliable semiempirical methods, such as the polarizability equation, for estimating the molecular ionization cross sections which have not been measured or for which only single values have been reported. The polarizability model predicts a linear relationship between the ionization cross section and the square root of the ratio of the volume polarizability to the ionization potential. Plots of this function against experimental values for ionization cross sections for atoms are shown in Figure 7 and for molecules in Figure 8. The equations determined... 

Resch-Genger U, Grabolle M, Nitschke R, Nann T (2010) Nanocrystals and nanoparticles vs. molecular fluorescent labels as reporters for bioanalysis and the life sciences. A critical comparison. In Demchenko AP (ed) Advanced Fluorescence Reporters in Chemistry and Biology II. Springer Ser Fluoresc 9 3—40... 

Synthesis of 1,2,3-Thiadiazoles and a Critical Comparison of the Various Routes... 

The synthetic utility of the carbonylation of zirconacycles was further enhanced by the development of a pair of selective procedures producing either ketones or alcohols [30] and has been extensively applied to the synthesis of cyclic ketones and alcohols, most extensively by Negishi [22—27,29—33,65,87,131—134], as detailed below in Section I.4.3.3.4. The preparation of unsaturated aldehydes by carbonylation with CO is not very satisfactory. The use of isonitriles in place of CO, however, has provided a useful alternative [135], and this has been applied to the synthesis of curacin A [125]. Another interesting variation is the cyanation of alkenes [136]. Further developments and a critical comparison with carbonylation using CO will be necessary before the isonitrile reaction can become widely useful. The relevant results are shown in Scheme 1.35. 

EW Thulstrup and J Michl, A critical comparison of methods for analysis of linear dichroism of solutes in stretched polymers, J. Phys. Chem., 84 82-93, 1980. 

O Connor D. V., Ware W. R. and Andre J. C. Pouget J., Mugnier J. and Valeur B. (1989) (1979) Deconvolution of Fluorescence Decay Correction of Timing Errors in Multi-Curves. A Critical Comparison of Tech- frequency Phase/Modulation Fluoro-... 

Tsukada Y, Fang J, Erdjument-Bromage H, Warren ME, Borchers CH, Tempst P, Zhang Y (2006) Histone demethylation by a family of JmjC domain-containing proteins. Nature 439 811-816 van Holde K, Yager T (2003) Models for chromatin remodeling a critical comparison. Biochem Cell Biol 81 169-172... 

Kleidernigg, O.P. and Kappe, C.O., Separation of enantiomers of 4-aryldihydropyrimidines by direct enantioselective HPLC. A critical comparison of chiral stationary phases. Tetrahedron Asymmetry, 8, 2057, 1997. 

Kim, J.K., Baillic, C. and Mai, Y.W. (1992). Fnterfacial debonding and fiber pull-out stresses, part F. A critical comparison of existing theories with experiments. J. Mater. Sci. 27, 3143-3154. 

Reuschenbach, P. Pagga, U. Strotmann, U. A critical comparison of respirometric biodegradation tests based on OECD 301 and related test methods. Water Res. 2003, 37, 1571-1582. 

SYNTHESIS OF 1,2,3-THIADIAZOLES AND A CRITICAL COMPARISON OF THE VARIOUS ROUTES AVAILABLE... 

Most of the above membrane-oriented studies were carried out for peptides in multilayer systems that were collapsed or transferred onto a sample cell surface. An alternative and very interesting way to study membrane systems is by IRRAS (infrared reflection absorption spectroscopy) at the air-water interface. In this way, unilamellar systems can be studied as a function of surface pressure and under the influence of various membrane proteins and peptides added. Mendelsohn et al.[136] have studied a model series of peptides, [K2(LA) ] (n = 6, 8, 10, 12), in nonaqueous (solution), multilamellar (lipid), and unilamellar (peptide-IRRAS) conditions. In the multilamellar vesicles these peptides are predominantly helical in conformation, but as peptide only monolayers on a D20 subphase the conformation is (1-sheet like, at least initially. For different lengths, the peptides show variable surface pressure sensitivity to development of some helical component. These authors further use their IR data to hypothesize the existence of the less-usual parallel (i-sheet conformation in these peptides. A critical comparison is available for different secondary structures as detected using the IRRAS data for peptides on H20 and D20 subphasesJ137 ... 

As was noted in CHEC-II(1996), a critical comparison of synthetic routes for this class of compounds is not a useful exercise. 

The relation between the osmotic pressure II and the polymer concentration, referred to as the equation of state for the solution, is often used for a critical comparison between theory and experiment (or simulation). Kubo and Ogino... 

Silymarin is considered the active constituent of the milk thistle seed, but it is not a single compound but a descriptive term for several flavonoli-gnans. Constituent analysis of five milk thistle products identified six constituents (representative amount) taxifolin (3.3%), silichristin (23.6 /o), silidianin (5.3 /o), silybin A (20%i), silybin B (30.7%i), and isosilybin (17.3 /o). The total amounts of silybin A and B in the five different products analyzed ranged from 45.7 /o to 61%i. The biological effect of each constituent is not known hence, spectrophotometric analysis would not provide sufficient information for a critical comparison of these products. 

Nevens F A critical comparison of drug therapies in currently used therapeutic strategies for variceal hemorrhage. Aliment Pharmacol Ther 2004 20(Suppl 3) 18. 

The first section summarizes simply the essential features of the different types of molecular orbital calculations currently used to solve theoretical problems in organometallic chemistry. A critical comparison of these calculations is also given. The second section discusses the bonding in organometallic complexes and draws on recent computational results and develops the chemical and structural implications of bonding models based on perturbation theory arguments. 

A critical comparison of several mass separation systems applied in inorganic mass spectrometry was discussed by Brunnee in 1987 ... 

Davar N, Shah R, Pope DG, Ausburger LL. A critical comparison of Hiestand s tabletting indices and traditional measures of compactibility to predict tabletting behavior. Pharma Res 1995 12 S168. 

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