The Theory of H-space

The theory of $\text{H}$-space, the four-dimensional manifold of those complex null hypersurfaces of an asymptotically flat space-time which are asymptotically shear-free, is reviewed.In addition to a discussion of the origins of the theory, we present two independent formalisms for the derivation of the basic properties of $\text{H}$-space: that it is endowed with a natural holomorphic complex Riemannian metric which satisfies the vacuum Einstein equations and whose Weyl tensor is self-dual.We show the connection of our work on $\text{H}$-space to that of Plebanski and to the theory of deformed twistor spaces, due to Penrose.Finally, there is a discussion of equations of motion in $\text{H}$-space.     

Heterogeneous nucleation of crystallization of high polymers from the melt. III. Nucleation kinetics and interfacial energies

In the melt crystallization of isotactic polypropylene, poly(ethylene oxide) and poly(butene-1) in contact with substrates, the existence of a fixed number of nucleating sites on the substrate surfaces has been established. When these sites become active successively (the transient in the number of nuclei is long) during crystallization, pseudohomogeneous nucleation on the substrate occurs. Nucleation rates for poly(butene-1) and poly(ethylene oxide) on substrates and in bulk have been measured. These data can be used for comparing the nucleating ability of substrates. Estimates of the variation of bulk nucleation rates from one volume element to another as well as for repeated crystallization within a given volume element have been included. Finally, the temperature coefficients of heterogeneous nucleation rates have been combined with the temperature coefficient of spherulitic growth rate of poly(butene-1), to yield values of the interfacial energy parameters appearing in the theory of heterogeneous nucleation. The quantitative characterization of the nucleating ability of substrates by this method is an improvement over the mere use of nucleation densities or nucleation rates.     

Muon spin relaxation studies of extremely concentrated paramagnetic electrolyte solutions

The diamagnetic signal in aqueous solutions of non-reacting salts arises from muons substituted for protons in water molecules. For concentrated solutions of paramagnetic salts, muon spin relaxation results from the strong dipolar and scalar interactions between the paramagnetic ion and the muon. Information on dynamic and structural aspects of such solutions is derived from measurements of the transverse relaxation rate as a function of applied field over a wide range. Data are presented for concentrated solutions of Mn(NO₃)₂ and solutions of composition Mn _x Ca_(1–x (NO₃)₂·6H₂O.     

A complex minkowski space approach to twistors

This paper is basically a review of known results in twistor theory. Its value is intended to lie in the connections presented between twistor concepts and structures in complex Minkowski space. The relationship of twistor theory to complex null infinity and a new proof of the Kerr theorem are presented; these results are to some extent original.     

γ–α transformation in isotactic polypropylene

A γ-phase to α-phase transformation in a specimen of isotactic polypropylene crystallized under conditions of high pressure was induced by drawing at 100°C. X-ray studies showed that the unoriented component remained in the γ-phase, and that the oriented component was found only in the α-phase. This evidence supports a previous suggestion that the phase transformation is martensitic in character. The consequences of such an assumption are discussed. The role of dislocations in polymeric systems is generally believed to be not too significant, but since martensitic reactions involve cooperative movements of atoms, an exception in this case is suggested. A possible mechanism for the phase transformation is suggested.     

Approximation of monomials by lower degree polynomials

Our topic is the uniform approximation ofx ^k by polynomials of degreen (n on the interval [–1, 1]. Our major result indicates that good approximation is possible whenk is much smaller thann ² and not possible otherwise. Indeed, we show that the approximation error is of the exact order of magnitude of a quantity,p _k,n , which can be identified with a certain probability. The numberp _k,n is in fact the probability that when a (fair) coin is tossedk times the magnitude of the difference between the number of heads and the number of tails exceedsn.     

Low threshold current proton-isolated (GaAl)As double heterostructure lasers

Very low threshold current laser sources are desirable for a number of potential applications including optical fibre telecommunications systems. Conventional proton-isolated stripe geometry (GaAl)As lasers can be designed to give threshold currents in the range 10–50 mA by proper optimization of device geometry. Experimentally, it is shown that such devices can be easily fabricated and bonded and that their characteristics are not adversely affected by the optimization procedure.