Topological resolution

Pictures of high resolution appear crisp, whereas pictures of low resolution appear fuzzy. A decrease of resolution is accompanied by an increase of fuzziness. Consequently, similarity measures based on the minimum level of resolution required to distinguish objects can be formulated in terms of the maximum level of fuzziness at which the objects are distinguishable. Similarity can be regarded as fuzzy equivalence. This principle provides an alternative mathematical basis for using the methods of topological resolution [262] in similarity analysis the theory of fuzzy sets [382-385]. 

With this cycloaddition we report the first example of topological resolution. In this case there is no knowledge of the reaction rates which may be very similar indeed if not even identical. Both enantiomers do in principle add to the diene but the one in the exo-fashion while the other one, also in order to keep the bulky isopropyl group away from the diene substituents, prefers the endo-route. 

This way the stereochemical results obtained from steroids triggered a complete line of research that did eventually lead to the quite useful process of topological resolution. 

Resolution-based similarity measures Similarity expressed by the geometrical or topological resolution required to distinguish objects. 

The physical techniques used in IC analysis all employ some type of primary analytical beam to irradiate a substrate and interact with the substrate s physical or chemical properties, producing a secondary effect that is measured and interpreted. The three most commonly used analytical beams are electron, ion, and photon x-ray beams. Each combination of primary irradiation and secondary effect defines a specific analytical technique. The IC substrate properties that are most frequendy analyzed include size, elemental and compositional identification, topology, morphology, lateral and depth resolution of surface features or implantation profiles, and film thickness and conformance. A summary of commonly used analytical techniques for VLSI technology can be found in Table 3. 

Figure 2.11 Beta sheets are usuaiiy represented simply by arrows in topology diagrams that show both the direction of each (3 strand and the way the strands are connected to each other along the polypeptide chain. Such topology diagrams are here compared with more elaborate schematic diagrams for different types of (3 sheets, (a) Four strands. Antiparallel (3 sheet in one domain of the enzyme aspartate transcarbamoylase. The structure of this enzyme has been determined to 2.8 A resolution in the laboratory of William Lipscomb, Harvard University, (b) Five strands. Parallel (3 sheet in the redox protein flavodoxin, the structure of which has been determined to 1.8 A resolution in the laboratory of Martha Ludwig, University of Michigan, (c) Eight strands. Antiparallel barrel in the electron carrier plastocyanln. This Is a closed barrel where the sheet is folded such that (3 strands 2 and 8 are adjacent. The structure has been determined to 1.6 A resolution in the laboratory of Hans Freeman in Sydney, Australia. (Adapted from J. Richardson.)...

Lebioda, L., Stec, B., Brewer, J.M. The structure of yeast enolase at 2.5 A resolution. An 8-fold p + a barrel with a novel ppoa(pa)6 topology. /. Biol. Chem. 

The structures of many different plant, insect, and animal spherical viruses have now been determined to high resolution, and in most of them the subunit structures have the same jelly roll topology. However, a very different fold of the subunit was found in bacteriophage MS2, whose structure was determined to 3 A resolution by Karin Valegard in the laboratory of Lars Liljas, Uppsala. 

The chemical nature of the packing has the largest influence on the retention of molecules and a big impact on the efficiency of the separation itself. The chemical and physical properties of the sorbent are determined by the choice of the comonomers for the copolymerization. The type of the copolymerization process employed by the synthetic chemist introduces the macroporous structure into the sorbent and determines the surface topology (accessibility, resolution) and the surface chemistry of the packing (4). 

High resolution Sorbent topology, packing process... 

Dedicated SEM instruments have a resolution of about 5 nm. The main difference between SEM and TEM is that SEM sees contrast due to the topology and composition of a surface, whereas the electron beam in TEM projects all information on the mass it encounters in a two-dimensional image, which, however, is of subnanometer resolution. 

All three proteins were analyzed at 3.0 A resolution. Experiments were performed on a portion of the relative density map containing an entire connected protein. In order to discern effects of topological features just outside the boundaries of this volume, our analysis was extended 5.0 A outside the boundaries on all sides of this volume. 

The possibility to resolve the two enantiomers of 27a (or 26) by crystalline complexa-tion with optically active 26 (or 27a) is mainly due to differences in topological complementarity between the H-bonded chains of host and guest molecules. In this respect, the spatial relationships which affect optical resolution in the above described coordination-assisted clathrates are similar to those characterizing some optically resolved molecular complexes S4). This should encourage additional applications of the lattice inclusion phenomena to problems of chiral recognition. 

In this study we use electron microscopy (EM) to study xanthan strandedness and topology both in the ordered and disordered conformation. Correlation of data obtained from electron micrographs to physical properties of dilute aqueous solution on the same sample will be used to provide a working hypothesis of the solution configuration of xanthan. Electron micrographs obtained from xanthan of different origins will be compared to assess similarities and differences in secondary structure at the level of resolution in the used EM technique. 

With respect to the intensity resolution relationship of NSE, PEB-2 [essentially PE with one ethyl branch every 50 main chain bonds the sample is obtained by saturating 1-4 polybutadiene, the residual 1-2 groups (7%) cause the ethyl branches Mw = 73200 g/mol Mw/Mn = 1.02] has two advantages compared to PEP (1) the Rouse rate W/4 of PEB-2 is more than two times faster than that of PEP at a given temperature [W/pEP (500 K) = 3.3 x 1013 A4s 1 W/pEB (509 K) = 7 x 1013A4s-1] (2) at the same time, the topological constraints are stronger. 

Some racemates (Figure 3.23) are more efficiently resolved on the bonded-type CSP than the coated-type CSP by using chloroform as a component of the eluent. On the bonded-type CSP of 24n, topologically interesting catenanes and molecular knots are successfully resolved using a hexane-chloroform-2-propanol mixture.185 The first direct HPLC resolution of the smallest chiral... 

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