Closed topology

Marko (1993) has considered microphase separation in cyclic block copolymers, and found that the spinodal is shifted to higher for a given copolymer composition compared to a diblock. This is due to the suppression of composition fluctuations because of the closed topology of the ring polymer. 

CNTs were discovered in the early 1990s [312]. CNTs have a tubular structure of closed topology and consist of hexagonal honeycomb lattices made up of sp carbon units. A schematic of the structure of CNTs is shown in Figure 1.15. The diameters of CNTs are typically several nanometers. The length of CNTs can be up to several micrometers. Two basic forms are distinguished, single-walled... 

This new type of vector is derived from plasmids and contains a minimalistic expression cassette. It shows a linear covalently closed topology, with single-stranded loops at both ends (Fig. 7.1). The covalently closed loops protect the vectors from degradation... 

The inference from all this is that the vacuum is a universal wave field of long wavelength. In an open universe the wavelength becomes infinitely long, resulting in a quiet flat space-time. In a universe of closed topology there is endless wave motion, which we identify here with the quantum potential and which Milo Wolff (1990)describes as the solution of a universal scalar wave equation. Our interpretation of cosmic physics differs from Wolff s model only in his proposal (p. 171)... 

The reasonable, but not essential assumption, that the general curvature of space-time be constant, predicts a closed topology in the form of either a hypersphere or a four-dimensional projective plane. Additional evidence is needed to decide between these possibilities. 

The mathematics of infinity is crucial and in order to avoid this unphysical situation projective geometry and a topologically closed cosmos are adopted at the outset. Projective topology is shown to satisfy the demands of both special and general relaticity. The periodic properties of both quantum and chemical systems arise naturally from closed topology and the gauge principle within projective relativity. 

FIGURE 7.4 (a) The patterned gate layout (b) Top view of the closed topology interdigitated source and drain contacts (note that the source in enclosed within the drain). 

In both metal lattices and closo polyhedral metal clusters there are cavities present, whose dimensions are a function of the number of vertices, the shape of the polyhedral moiety, and the interatomic separation. Partial occupation of these sites within the metal lattice by main group elements results in the formation of interstitial alloys such as, for example, metal hydrides, carbides, and nitrides. Occupation of the cavity within a molecular metal cluster gives rise to interstitial clusters. Although close topological relationships are sometimes found between interstitial alloys and interstitial clusters, the greater degree of freedom of a molecular assembly of metals, in comparison to a three dimensional infinite array of metals, increases the possible number of interstitially lodged elements... 

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