Fibred spaces and non-linear connections

Summary We give the fibre structure to the two complementary distributions, one being holomonic and the other being in general non-holomonic, by assigning the structure preserving transformations of the coordinates and of the frames. By the conversion from such fibred spaces we derive the spaces of non-linear connections as their image, in which we point out that the usual conditions imposed on C_kji and the covariant differentiation of g_ji in the metric spaces of non-linear connections can be interpreted respectively as the parallel and isometric conditions imposed on the fibre of the corresponding fibred Riemannian spaces. To Enrico Bompiani on his scientific Jubilee.     

Differential geometry on almost tangent manifolds

Summary We start from a tensor field Q of type (1, 1) defined in a2n-dimensional manifold M which satisfies Q ²⁼⁰ and has rank n. The tensor field Q defines an almost tangent structure in M. We then introduce another tensor field P of the same type and having properties similar to those of Q. We then define and study the tensors H=PQ, V=QP, J=P−Q, K=P+Q, L=PQ−QP, (J, K, L) defining an almost quaternion structure of the second kind on M. We study the differential geometry on almost tangent manifolds in terms of these tensors. To ProfessorBeniamino Segre on his seventieth birthday Entrata in Redazione il 7 giugno 1973.     

Dynamic mechanical and dielectric relaxations of polystyrene below the glass temperature

Dynamic mechanical and dielectric properties of various kinds of polystyrene, including bulk-polymerized, monodisperse, isotactic, and thermally degraded samples, have been measured below the glass temperature to 4°K. Five relaxation processes are found, designated β, γ, γ′, δ, and ε in order of descending temperature. The β peak (350°K at 10 kHz) is attributed to the local oscillation mode of backbone chains and the γ′ peak (180°K at 10 kHz) to rotation of phenyl groups. The δ peak (100°K at 10 kHz) is observed only in dielectric properties of the bulk-polymerized sample and is assigned to weak polar bonds, such as oxygen bonds in the chain. The δ peak (55°K at 10 kHz) which is prominent in dynamic mechanical properties is interpreted in terms of lattice defects due to a syndiotactic diad inserted between isotactic sequences in a chain or vice versa. The ε peak (ca. 25°K at 10 kHz) is first reported in the present work, but the mechanism involved is not yet clear.     

Alternating copolymerization of polar vinyl monomers in the presence of zinc chloride. II. Properties of acrylonitrile–styrene copolymer

The properties of the acrylonitrile–styrene copolymer prepared in the presence of zinc chloride were investigated in comparison with those of a copolymer having the same overall composition and prepared by the ordinary radical procedure. The characteristics of the polymer prepared with ZnCl₂ were as follows: (1) less coloration by alkali treatment, (2) less coloration by thermal treatment and (3) higher glass transition temperature. These features may be attributed principally to the structure of the copolymer, which has more unlike bonds and less long sequences as described in the first article of this series. The effects of residual salt in the copolymer on the properties were also investigated.     

Oxygen permeability of surfactant/polymer composite films with multibilayer and inverted hexagonal structure

The permeability of oxygen through horizontally oriented multibilayer films of polyion complexes prepared from quaternary ammonium-type surfactants [CH₃(CH₂)_n-1]₂N⁺(CH₃)₂Br^?(n = 14, 16, 18), and poly(p-styrenesulfonate) or poly[2-(acrylamido)-2-methyl-1-propanesulfonate], was measured in water using an oxygen electrode. The permeability depended mainly on the phase of the multibilayers. Thus, it increased abruptly (about 10-fold) near each phase transition temperature because of the fluidity enhancement of the multibilayer. Inverted hexagonal type nonbilayer films prepared from the polyion complexes and cholesterol had greater permeability (2–20-fold) than the multibilayer films in both phases. The large permeability of the nonbilayer films was attributed to the lack of a barrier such as the bilayer and lower crystallinity of the films. It was associated neither with an increase in thermal movement of the lipid surfactant molecules nor with an increase in the water content of the films by the addition of cholesterol. © 1993 John Wiley & Sons, Inc.     

Nano‐imaging through tip‐enhanced Raman spectroscopy: Stepping beyond the classical limits

The spatial resolution in optical imaging is restricted by so‐called diffraction limit, which prevents it to be better than about half of the wavelength of the probing light. Tip‐enhanced Raman spectroscopy (TERS), which is based on the SPP‐induced plasmonic enhancement and confinement of light near a metallic nanostructure, can however, overcome this barrier and produce optical images far beyond the diffraction limit. Here in this article, the basic phenomenon involved in TERS is reviewed, and the high spatial resolution achieved in optical imaging through this technique is discussed. Further, it is shown that when TERS is combined with some other physical phenomena, the spatial resolution can be dramatically improved. Particularly, by including tip‐applied extremely localized pressure in TERS process, it has been demonstrated that a spatial resolution as high as 4 nm could be achieved.