Let $(A,\mathfrak m)$ be an excellent two-dimensional normal local domain. In this paper, we study the elliptic and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and Yau. In analogy with the rational singularities, in the main result, we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed $\mathfrak m$-primary ideals of A. Unlike $p_g$-ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary, and sufficient conditions for being normal are given. In the last section, we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.

We suggest a new method for fabricating diamond nanoclusters by employing a coaxial arc plasma gun. Diamond powder comprised of diamond nanoclusters and amorphous carbon was fabricated in vacuum and a hydrogen atmosphere, and the diamond crystallite sizes were estimated to be 1.8, 2.3, and 2.3 nm for the powders prepared at hydrogen pressures of 0, 53.3, and 159.6 Pa respectively, from the X-ray diffraction peaks. The hydrogen ambient gas is not necessarily required for the diamond nanoclusters formation. We consider that this method enables us to form diamond nanoclusters in nucleation owing to a supersaturated condition at a facing plate located in front of an arc plasma gun.

Block copolymer lithography is a promising method for fabricating periodical nano patterns less than 20nm by self-assembly and can be applicable for fabricating patterned magnetic media with recording density over 1Tbit/inch2. We found a simple technique to control the orientation of cylindrical microdomains in thin films. Only by mixing polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers with the constituent homopolymer (PS or PMMA), we could align the cylindrical microdomains perpendicular to the film surface. The added homopolymer induces conformational entropic relaxation of the block chains in microdomain space and stabilizes perpendicular orientation of hexagonally packed cylindrical microdomains. Thus formed perpendicular cylinders can be readily aligned in a regular array with a grating substrate.