Incommensurate-Commensurate Magnetic Phase Transition in SmRu2_{2}Al10_{10}

Magnetic properties of single crystalline SmRu$_{2}$Al$_{10}$ have been investigated by electrical resistivity, magnetic susceptibility, and specific heat. We have confirmed the successive magnetic phase transitions at $T_{\text{N}}=12.3$ K and $T_{\text{M}}=5.6$ K. Resonant x-ray diffraction has also been performed to study the magnetic structures. Below $T_{\text{N}}$, the Sm$^{3+}$ moments order in an incommensurate structure with $q_1=(0, 0.759, 0)$. The magnetic moments are oriented along the orthorhombic $b$ axis, which coincides with the magnetization easy axis in the paramagnetic phase. A very weak third harmonic peak is also observed at $q_3=(0, 0.278, 0)$. The transition at $T_{\text{M}}$ is a lock-in transition to the commensurate structure described by $q_1=(0, 0.75, 0)$. A well developed third harmonic peak is observed at $q_3=(0, 0.25, 0)$. From the discussion of the magnetic structure, we propose that the long-range RKKY interaction plays an important role, in addition to the strong nearest neighbor antiferromagnetic interaction.Comment: 11 pages, 12 figures, accepted in PR

Effects of applied pressure on hot-pressing of Beta-SiC

The effects of applied pressure on the densification during hot pressing of beta-SiC compacts were investigated. Beta-SiC powder is Starck made and has the average particle size of about 0.7 micrometer. Hot pressing experiments were carried out in graphite dies at temperatures of 1700 deg to 2300 deg C and at the pressures up to 1000 kg/sq cm. The compacts containing 1 weight percent B4C were examined. Sintered compacts were examined for microstructure and the Rockwell A-scale hardness was measured. The B4C addition was very effective to mitigate the hot pressing conditions. It is found that densification goes with the strengthening of the bonding and does not occur in particle deformation due to concentrated stress

Stable Existence of Phase IV inside Phase II under Pressure in Ce0.8_{0.8}La0.2_{0.2}B6_{6}

We investigate the pressure effect of the electrical resistivity and magnetization of Ce$_{0.8}$La$_{0.2}$B$_{6}$. The situation in which phase IV stably exists inside phase II at H=0 T could be realized by applying a pressure above $P\sim 1.1$ GPa. This originates from the fact that the stability of phase II under pressure is larger than those of phases IV and III. The results seem to be difficult to reproduce by taking the four interactions of $\Gamma_{\mathrm{5u}}$-type AFO, $O_{xy}$-type AFQ, $T_{xyz}$-type AFO, and AF exchange into account within a mean-field calculation framework.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn. 79 (2010) No.

On Hasse--Schmidt derivations: the action of substitution maps

We study the action of substitution maps between power series rings as an additional algebraic structure on the groups of Hasse--Schmidt derivations. This structure appears as a counterpart of the module structure on classical derivations.Comment: 42 pages; Dedicated to Antonio Campillo on the occasion of his 65th birthday; minor corrections; final versio

An Avoidance Principle with an Application to the Asymptotic Behaviour of Graded Local Cohomology

We present an Avoidance Principle for certain graded rings. As an application we fill a gap in the proof of a result by Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert-Samuel multiplicity of the graded components of the local cohomology modules of a finitely generated module over a Noetherian homogeneous ring with two-dimensional local base ring.Comment: 6 pages; to appear in Journal of Pure and Applied Algebra; corrected typo

A Millimeter-Wave Achromatic Half Wave Plate

We have constructed an achromatic half wave plate (AHWP) suitable for the millimeter wavelength band. The AHWP was made from a stack of three sapphire a-cut birefringent plates with the optical axes of the middle plate rotated by 50.5 degrees with respect to the aligned axes of the other plates. The measured modulation efficiency of the AHWP at 110 GHz was $96 \pm 1.5$%. In contrast, the modulation efficiency of a single sapphire plate of the same thickness was $43 \pm 4$%. Both results are in close agreement with theoretical predictions. The modulation efficiency of the AHWP was constant as a function of incidence angles between 0 and 15 degrees. We discuss design parameters of an AHWP in the context of astrophysical broad band polarimetry at the millimeter wavelength band.Comment: In print - Applied Optics, 14 pages, 7 figure

On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians