509 research outputs found
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 LuFeSi
We report low-temperature specific heat studies on single-crystalline
ternary-iron silicide superconductor LuFeSi with = 6.1 K
down to . We confirm a reduced normalized jump in specific heat at
, and find that the specific heat divided by temperature shows
sudden drop at and goes to zero with further decreasing
temperature. These results indicate the presence of two distinct
superconducting gaps in LuFeSi, similar to a typical two-gap
superconductor MgB. We also report Hall coefficients, band structure
calculation, and the anisotropy of upper critical fields for
LuFeSi, which support the anisotropic multiband nature and
reinforce the existence of two superconducting gaps in
LuFeSi.Comment: 5 pages, 5 figure
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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
Metamagnetic Transition in UCoAl Probed by Thermoelectricity Measurements
We report field and temperature dependent measurements of the thermoelectric
power (TEP) and the Nernst effect in the itinerant metamagnet UCoAl. The
magnetic field is applied along the easy magnetization c-axis in the hexagonal
crystal structure. The metamagnetic transition from the paramagnetic phase at
zero field to the field induced ferromagnetic (FM) state is of first order at
low temperatures and becomes a broad crossover above the critical temperature
K. The field-dependence of the TEP reveals that the
effective mass of the hole carriers changes significantly at the metamagnetic
transition. The TEP experiment reflects the existence of different carrier
types in good agreement with band structure calculations and previous Hall
effect experiments. According to the temperature dependence of the TEP, no
Fermi liquid behavior appears in the paramagnetic state down to 150 mK, but is
achieved only in the field induced ferromagnetic state.Comment: 5 pages, 4 figure
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 PrRuP 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 to Pm 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 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
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