Rigor resolution

During the early years of physieal ehemistry, Ostwald did not believe in the existence of atoms... and yet he was somehow ineluded in the wild army of ionists. He was resolute in his scepticism and in the 1890s he sustained an obscure theory of energetics to take the place of the atomic hypothesis. How ions could be formed in a solution containing no atoms was not altogether clear. Finally, in 1905, when Einstein had shown in rigorous detail how the Brownian motion studied by Perrin could be interpreted in terms of the collision of dust motes with moving molecules (Chapter 3, Section 3.1.1), Ostwald relented and publicly embraced the existence of atoms. 

Since the proline residue in peptides facilitates the cyclization, 3 sublibraries each containing 324 compounds were prepared with proline in each randomized position. Resolutions of 1.05 and 2.06 were observed for the CE separation of racemic DNP-glutamic acid using peptides with proline located on the first and second random position, while the peptide mixture with proline preceding the (i-alamine residue did not exhibit any enantioselectivity. Since the c(Arg-Lys-0-Pro-0-(i-Ala) library afforded the best separation, the next deconvolution was aimed at defining the best amino acid at position 3. A rigorous deconvolution process would have required the preparation of 18 libraries with each amino acid residue at this position. 

Once the resolution has been optimized as a function of gradient rate, one can continue to fine-tune the separation, raising flow rate and temperature. In a study of temperature and flowrate variation on the separation of the tryptic peptides from rabbit cytochrome c, column performance doubled while analysis time was reduced by almost half using this strategy.97 Commercially available software has been developed to aid in optimization. As a final note, in an industrial laboratory optimization is not completed until a separation has been shown to be rugged. It is a common experience to optimize a separation on one column, only to find that separation fails on a second column of identical type. Reproducibility and rigorous quality control in column manufacture remains a goal to be attained. 

One often finds that when high resolution separation schemes are utilized, other techniques and disciplines must participate in the scheme of understanding and effectively utilizing the separation with subsequent identification of the resulting zones. A rigorous and often multidimensional detection scheme such as mass spectrometry and/or fluorescence is found both for the life science and industrial polymer applications. Other disciplines including informatics and statistics are often... 

Sensitivity impacts upon the limit of detection and resolution of the device, making it a key performance parameter. Recently, several strategies have been developed in order to provide sensitivity enhancements for optical sensor platforms based on both optical absorption and fluorescence phenomena. These strategies are the result of rigorous theoretical analyses of the relevant systems and, combined with polymer processing technology and planar fabrication protocols, provide a viable route for the development of low-cost, efficient optical sensor platforms. 

Discussions of electrophoretic data handling usually include mention of separation and resolution. Although the two terms are not synonymous, they are often treated as such. In the terminology of separation science, separation refers to the distance between two adjacent band centers. Because bands are seen as being sharply defined with clearly evident blank spaces between adjacent bands, for practical purposes, separation is often taken to be the distance between the top of the faster running of two adjacent bands and the bottom of the slower one. It is the distance between the top of the bottom band and the bottom of the top band. This definition seems preferable to the rigorous one in electrophoresis. 

Nuclear magnetic resonance traditionally has had low sensitivity and spectral resolution. It can provide rigorous quantification of analytes, but not accurate qualitative identification. Individual resonances may be sensitive to the chemical and physical environment of the molecule, which then requires appropriate preparation of samples. The process also has little dynamic range, in contrast to GC-MS. 

More commonly, we are faced with the need for mathematical resolution of components, using their different patterns (or spectra) in the various dimensions. That is, literally, mathematical analysis must supplement the chemical or physical analysis. In this case, we very often initially lack sufficient model information for a rigorous analysis, and a number of methods have evolved to "explore the data", such as principal components and "self-modeling analysis (21), cross correlation (22). Fourier and discrete (Hadamard,. . . ) transforms (23) digital filtering (24), rank annihilation (25), factor analysis (26), and data matrix ratioing (27). 

In general, definitions for TEM resolution are more rigorous than for STEM and it is desirable to find common ground for an objective comparison between STEM and HRTEM resolution. Ultimately, one value of resolution lies in the separation of atom columns at non-periodic lattice sites as shown in Figure 3. ... 

One way to handle this problem, within the framework of the CPMG scheme, is to add proton pulses at judiciously chosen points in the train of the carbon 7r-pulses [42, 43]. An example of such a sequence is given in fig. 4(a). An important issue when setting up experiments of this type is the duration 8 between the pulses. On the one hand, it should be small compared to (l/2)Jis [43]. On the other hand, it should be much longer than the relevant pulse widths. It is difficult to simultaneously fulfill both these requirements rigorously with typical high-resolution equipment, and some compromise has to be settled on. 

Previous sections have detailed phenomena that contribute to the degradation of resolution in optical spectra. Concepts useful in specifying resolution criteria have been established. Although transfer and point-spread functions of varying shape can yield identical numbers when a simple two-point criterion is applied, this many-to-one correspondence does not diminish the criterion s usefulness. More rigorous specification of the transfer function virtually requires graphical presentation for human interpretation. Its use therefore demands far more space in text and more time for study. Frequently, the functional form of the transfer function is well known anyway systems being compared are often of similar type. In these cases, the two-point criterion is entirely adequate. 

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