Topologies spherical

Valuable applications of this principle have been described by Paquette for the synthesis of topologically spheric molecules. Coates used this reductive fragmentation for the synthesis of bicy-clo[6.3.0]undecenecarboxylates, compounds which bear a structural resemblance to the a-b rings of the fusicoccin and ophiobolane natural products. Reduction of the unsaturated keto ester (164) affords an isomeric mixture of esters, the equilibration of which effects conversion to the single ester (165 Scheme 56). 

Though a powerful classification result for topologically spherical S, this theorem does not seem to extend (simply) to x(-S ) 5 0. Still for thexf-S) = 0 case this theorem reduces the characterization of these equivalence classes to a standard graph-theoretic problem. 

A simple remedy to stabilize these modes is to introduce a conducting shell around the plasma. We consider here topologically spherical walls that do not link the plasma. The spherical wall radius is normalized so that = 1 corresponds to the wall on the outer surface of the plasma. The analysis carried out in Ref [12] for the Taylor current profile i) gave a rather stringent condition for the location of the wall ... 

Figure 10. Formal process of insertion of a spherical separatrix (associated with two isolated singularities) into a (locally) homogeneous field. A local deformation of the lines of flow creates the space where the topologically spherical separatrix is located. This is shown in the lower part with the toroidal circulation that may exist inside.

Pardon [4] used local surgery theory to extend the work of Madsen, Thomas and Wall on the classification of free acti of finite groups on spheres ("the topological spherical space form problem") to the classification of free actions of finit groups on manifolds which are 3p-homology spheres. 

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. 

In all of these investigations, the topology of the simulated object was kept fixed (spherical). Current work is devoted to the study of systems with... 

Recently considerable attention has been directed at anion binding ligands. Macrobicyclic 27 29) and macrotricyclic amines 30,31) were topologically designed to host anions such as spherical Cl-, linear Nf 32). These anion substrates are incorporated into macrocyclic cavities lined with appropriate anion-binding sites capable of forming hydrogen bonds like those of protonated amines (see /, below). 

Some of the more remarkable examples of this form of topologically controlled radical polymerization were reported by Percec et cii.231 234 Dendron maeromonomers were observed to self-assemble at a concentration above 0.20 mol/L in benzene to form spherical micellar aggregates where the polymerizable double bonds are concentrated inside. The polymerization of the aggregates initiated by AIBN showed some living characteristics. Diversities were narrow and molecular weights were dictated by the size of the aggregate. The shape of the resultant macroniolecules, as observed by atomic force microscopy (ATM), was found to depend on Xn. With A, <20, the polymer remained spherical. On the other hand, with X>20, the polymer became cylindrical.231,232... 

Porphyrin is a multi-detectable molecule, that is, a number of its properties are detectable by many physical methods. Not only the most popular nuclear magnetic resonance and light absorption and emission spectroscopic methods, but also the electron spin resonance method for paramagnetic metallopor-phyrins and Mossbauer spectroscopy for iron and tin porphyrins are frequently used to estimate the electronic structure of porphyrins. By using these multi-detectable properties of the porphyrins of CPOs, a novel physical phenomenon is expected to be found. In particular, the topology of the cyclic shape is an ideal one-dimensional state of the materials used in quantum physics [ 16]. The concept of aromaticity found in fuUerenes, spherical aromaticity, will be revised using TT-conjugated CPOs [17]. 

If the observed reflections are not on spherical arcs, the computation of an orientation parameter becomes an arbitrary operation that is not exclusively related to misorientation of structure. Most probably the topology of the structural entities is coupled to their orientation6, and Chap. 10 applies. 

MCM-50 consists of stacks of silica and surfactant layers. Obviously, no pores are formed upon removal of the surfactant layers. The silica layers contact each other resulting in a nonporous silica. It is noteworthy to mention that materials of M41S type were probably already synthesized by Sylvania Electric Products in 1971 [32], However, at that time the high ordering of the materials was not realized [33], M41S-type materials are synthesized under basic reaction conditions. Scientists from the University of Santa Barbara developed an alternative synthesis procedure under acidic conditions. They also used alkyltrimethyl ammonium as the surfactant. The porous silica materials obtained (e.g., hexagonal SBA-3 Santa BArbara [SBA]) had thicker pore walls but smaller pore diameters. Furthermore, they developed materials with novel pore topologies, e g., the cubic SBA-1 with spherical pores. 

The discovery that members of the resorcin[4]arene family self-assemble to form 1, owing to its classification as an Archimedean solid, prompted us to examine the topologies of related spherical hosts with a view to understanding their structures on the basis of symmetry. In addition to providing grounds for classification, we anticipated that such an approach would allow us to identify similarities at the structural level, which, at the chemical level, may not seem obvious and may be used to design large, spherical host assemblies similar to 1. 

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