The central simple modules of Artinian Gorenstein algebras

Let A be a standard graded Artinian algebra over a field of characteristic zero and let z be a linear form in A. We define the central simple modules for each such pair (A, z). Assume that A is Gorenstein. Then we prove that A has the strong Lefschetz property if and only if there exists a linear form z in A such that all central simple modules of the pair (A,z) have the strong Lefschetz property. In the course of proof we need to extend the definition of the strong Lefschetz property to finite graded modules over graded Artinian algebra, which previously was defined only for standard graded Artinian algebras.Comment: 20 pages, To be published in Journal of Pure and Applied Algebr

Theory of Metal-Insulator Transition in PrRu4P12 and PrFe4P12

All symmetry allowed couplings between the 4f^2-electron ground state doublet of trivalent praseodymium in PrRu4P12 and PrFe4P12 and displacements of the phosphorus, iron or ruthenium ions are considered. Two types of displacements can change the crystal lattice from body-centred cubic to simple orthorhombic or to simple cubic. The first type lowers the point group symmetry from tetrahedral to orthorhombic, while the second type leaves it unchanged, with corresponding space group reductions Im3 --> Pmmm and Im3 --> Pm3 respectively. In former case, the lower point-group symmetry splits the degeneracy of the 4f^2 doublet into states with opposite quadrupole moment, which then leads to anti-quadrupolar ordering, as in PrFe4P12. Either kind of displacement may conspire with nesting of the Fermi surface to cause the metal-insulator or partial metal-insulator transition observed in PrFe4P12 and PrRu4P12. We investigate this scenario using band-structure calculations, and it is found that displacements of the phosphorus ions in PrRu4P12 (with space group reduction Im3 --> Pm3) open a gap everywhere on the Fermi surface.Comment: 6 page

The Weak and Strong Lefschetz Properties for Artinian K-Algebras

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal rank, for every i, and A has the Strong Lefschetz property if times ell^d : A_i --> A_{i+d} has maximal rank for every i and d. The main results obtained in this paper are the following. 1) EVERY height three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank two vector bundles on P^2 and the Grauert-Mulich theorem.) 2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one). 3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties. Some Hilbert functions in fact FORCE the algebra to have the maximal Betti numbers. 4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property. This is false in higher codimension.Comment: To appear in J. Algebr

Specific heat evidence for two-gap superconductivity in ternary-iron silicide Lu2_{2}Fe3_{3}Si5_{5}

We report low-temperature specific heat studies on single-crystalline ternary-iron silicide superconductor Lu$_{2}$Fe$_{3}$Si$_{5}$ with$T_c$ = 6.1 K down to $\sim T_c/20$. We confirm a reduced normalized jump in specific heat at $T_c$, and find that the specific heat divided by temperature $C/T$ shows sudden drop at $\sim T_c/5$ and goes to zero with further decreasing temperature. These results indicate the presence of two distinct superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$, similar to a typical two-gap superconductor MgB$_{2}$. We also report Hall coefficients, band structure calculation, and the anisotropy of upper critical fields for Lu$_{2}$Fe$_{3}$Si$_{5}$, which support the anisotropic multiband nature and reinforce the existence of two superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$.Comment: 5 pages, 5 figure

Design, characterization, and fabrication of solar-retroreflective cool-wall materials

Raising urban albedo increases the fraction of incident sunlight returned to outer space, cooling cities and their buildings. We evaluated the angular distribution of solar radiation incident on exterior walls in 17 U S. climates to develop performance parameters for solar-retroreflective walls, then applied first-principle physics and ray-tracing simulations to explore designs. Our analysis indicates that retroreflective walls must function at large incidence angles to reflect a substantial portion of summer sunlight, and that this will be difficult to attain with materials that rely on total internal reflection. Gonio-spectrophotometer measurements of the solar spectral bi-directional reflectivity of a bicycle reflector showed little to no retroreflection at large incidence angles. Visual comparisons of retroreflection to specular first-surface reflection for four different retroreflective safety films using violet and green lasers suggest their retroreflection to be no greater than 0.09 at incidence angles up to 45°, and no greater than 0.30 at incidence angles of up to 70°. Attempts to produce a two-surface retroreflector with orthogonal mirror grooves by cutting and polishing an aluminum block indicate that residual surface roughness impedes retroreflection. Ongoing efforts focus on forming orthogonal surfaces with aluminized Mylar film, a material with very high specular reflectance across the solar spectrum. We investigated (1) folding or stamping a free film; (2) adhering the film to a pre-shaped substrate; or (3) attaching the film to a flat ductile substrate, then shaping. The latter two methods were more successful but yielded imperfect right angles

Charge-Density-Wave Ordering in the Metal-Insulator Transition Compound PrRu4P12

X-ray and electron diffraction measurements on the metal-insulator (M-I) transition compound PrRu$_4$P$_{12}$ have revealed the emergence of a periodic ordering of charge density around the Pr atoms. It is found that the ordering is associated with the onset of a low temperature insulator phase. These conclusions are supported by the facts that the space group of the crystal structure transforms from Im$\bar{3}$ to Pm$\bar{3}$ below the M-I transition temperature and also that the temperature dependence of the superlattice peaks in the insulator phase follows the squared BCS function. The M-I transition could be originated from the perfect nesting of the Fermi surface and/or the instability of the $f$ electrons.Comment: 4 pages, 5 figures, Phys. Rev. B (2004) (in press

Fermi surface of the filled-skutterudite superconductor LaRu4P12: A clue to the origin of the metal-insulator transition in PrRu4P12

We report the de Haas-van Alphen (dHvA) effect and magnetoresistance in the filled-skutterudite superconductor LaRu4P12, which is a reference material of PrRu4P12 that exhibits a metal-insulator (M-I) transition at T_MI~60 K. The observed dHvA branches for the main Fermi surface (FS) are well explained by the band-structure calculation, using the full potential linearized augmented-plane-wave method with the local-density approximation, suggesting a nesting instability with q =(1,0,0) in the main multiply connected FS as expected also in PrRu4P12. Observed cyclotron effective masses of (2.6-11.8)m_0, which are roughly twice the calculated masses, indicate the large mass enhancement even in the La-skutterudites. Comparing the FS between LaRu4P12 and PrRu4P12, an essential role of c-f hybridization cooperating with the FS nesting in driving the the M-I transition in PrRu4P12 has been clarified.Comment: Appeared in Physical Review

Competition between unconventional superconductivity and incommensurate antiferromagnetic order in CeRh1-xCoxIn5

Elastic neutron diffraction measurements were performed on the quasi-two dimensional heavy fermion system CeRh1-xCoxIn5, ranging from an incommensurate antiferromagnet for low x to an unconventional superconductor on the Co-rich end of the phase diagram. We found that the superconductivity competes with the incommensurate antiferromagnetic (AFM) order characterized by qI=(1/2, 1/2, delta) with delta=0.298, while it coexists with the commensurate AFM order with qc=(1/2, 1/2, 1/2). This is in sharp contrast to the CeRh1-xIrxIn5 system, where both the commensurate and incommensurate magnetic orders coexist with the superconductivity. These results reveal that particular areas on the Fermi surface nested by qI play an active role in forming the superconducting state in CeCoIn5.Comment: RevTeX4, 4 pages, 4 eps figures; corrected a typo and a referenc

Definitive experimental evidence for two-band superconductivity in MgB2

The superconducting gap of MgB2 has been studied by high-resolution angle-resolved photoemission spectroscopy (ARPES). The momentum(k)-resolving capability of ARPES enables us to identify the s- and p-orbital derived bands predicted from band structure calculations and to successfully measure the superconducting gap on each band. The results show that superconducting gaps with values of 5.5 meV and 2.2 meV open on the s-band and the p-band, respectively, but both the gaps close at the bulk transition temperature, providing a definitive experimental evidence for the two-band superconductivity in MgB2. The experiments validate the role of k-dependent electron-phonon coupling as the origin of multiple-gap superconductivity in MgB2.Comment: PDF file onl