2,606 research outputs found
Smooth planar -splines of degree
In \cite{as}, Alfeld and Schumaker give a formula for the dimension of the
space of piecewise polynomial functions (splines) of degree and smoothness
on a generic triangulation of a planar simplicial complex (for ) and any triangulation (for ). In \cite{ss}, it was
conjectured that the Alfeld-Schumaker formula actually holds for all . In this note, we show that this is the best result possible; in
particular, there exists a simplicial complex such that for any ,
the dimension of the spline space in degree is not given by the formula
of \cite{as}. The proof relies on the explicit computation of the nonvanishing
of the first local cohomology module described in \cite{ss2}.Comment: 6 pages, 1 figur
Penetration depth, multiband superconductivity, and absence of muon-induced perturbation in superconducting PrOsSb
Transverse-field muon spin rotation (SR) experiments in the
heavy-fermion superconductor PrOsSb ( K) suggest that
the superconducting penetration depth is temperature-independent
at low temperatures, consistent with a gapped quasiparticle excitation
spectrum. In contrast, radiofrequency (rf) inductive measurements yield a
stronger temperature dependence of , indicative of point nodes in
the gap. This discrepancy appears to be related to the multiband structure of
PrOsSb. Muon Knight shift measurements in PrOsSb
suggest that the perturbing effect of the muon charge on the neighboring
Pr crystalline electric field is negligibly small, and therefore is
unlikely to cause the difference between the SR and rf results.Comment: 10 pages, 7 figure
A Super-Solar Metallicity for the Progenitor of Kepler's Supernova
We have performed deep X-ray observations of the remnant of Kepler's
supernova (SN 1604) as a Key Project of the Suzaku Observatory. Our main goal
is to detect secondary Fe-peak elements in the SN ejecta to gain insights into
the Type Ia supernova explosion mechanism and the nature of the progenitor.
Here we report our initial results. We made a conclusive detection of X-ray
emission lines from highly ionized Mn, Cr, and Ni as well as Fe. The observed
Mn-to-Cr line flux ratio is ~0.60, ~30% larger than that measured in Tycho's
remnant. We estimate a Mn-to-Cr mass ratio of ~0.77, which is strongly
suggestive of a large neutron excess in the progenitor star before the onset of
the thermonuclear runaway. The observed Ni-to-Fe line flux ratio (~0.03)
corresponds to a mass ratio of ~0.06, which is generally consistent with the
products of explosive Si-burning regime in Type Ia explosion models, and rules
out contamination from the products of neutron-rich nuclear statistical
equilibrium in the shocked ejecta. Together with the previously suggested
luminous nature of the explosion, these mass ratios provide strong evidence for
a super-solar metallicity in the SN progenitor (~3 Z_sun). Kepler's supernova
was likely the thermonuclear explosion of a white dwarf formed in the recent
past that must have exploded through a relatively prompt channel.Comment: Total 12 pages including 2 tables and 2 color figures. Accepted by
ApJ
Spin dynamics and spin freezing in the triangular lattice antiferromagnets FeGa2S4 and NiGa2S4
Magnetic susceptibility and muon spin relaxation (muSR) experiments have been
carried out on the quasi-2D triangular-lattice spin S = 2 antiferromagnet
FeGa2S4. The muSR data indicate a sharp onset of a frozen or nearly-frozen spin
state at T* = 31(2) K, twice the spin-glass-like freezing temperature T_f =
16(1) K. The susceptibility becomes field dependent below T*, but no sharp
anomaly is observed in any bulk property. A similar transition is observed in
muSR data from the spin-1 isomorph NiGa2S4. In both compounds the dynamic muon
spin relaxation rate lambda_d(T) above T* agrees well with a calculation of
spin-lattice relaxation by Chubukov, Sachdev, and Senthil in the renormalized
classical regime of a 2D frustrated quantum antiferromagnet. There is no firm
evidence for other mechanisms. At low temperatures lambda_d(T) becomes
temperature independent in both compounds, indicating persistence of spin
dynamics. Scaling of lambda_d(T) between the two compounds is observed from
~T_f to ~1.5T*. Although the muSR data by themselves cannot exclude a truly
static spin component below T*, together with the susceptibility data they are
consistent with a slowly-fluctuating "spin gel" regime between T_f and T*. Such
a regime and the absence of a divergence in lambda_d(T) at T* are features of
two unconventional mechanisms: (1) binding/unbinding of Z_2 vortex excitations,
and (2) impurity spins in a nonmagnetic spin-nematic ground state. The absence
of a sharp anomaly or history dependence at T* in the susceptibility of
FeGa2S4, and the weakness of such phenomena in NiGa2S4, strongly suggest
transitions to low-temperature phases with unconventional dynamics.Comment: 13 pages, 6 figures, accepted for publication in Physical Review
Detection of Neutron Scattering from Phase IV of Ce0.7La0.3B6: A Confirmation of the Octupole Order
We have performed a single crystal neutron scattering experiment on
Ce0.7La0.3B6 to investigate the order parameter of phase IV microscopically.
Below the phase transition temperature 1.5 K of phase IV, weak but distinct
superlattice reflections at the scattering vector (h/2,h/2,l/2) (h, l = odd
number) have been observed by neutron scattering for the first time. The
intensity of the superlattice reflections is stronger for high scattering
vectors, which is quite different from the usual magnetic form factor of
magnetic dipoles. This result directly evidences that the order parameter of
phase IV has a complex magnetization density, consistent with the recent
experimental and theoretical prediction in which the order parameter is the
magnetic octupoles Tbeta with Gamma5 symmetry of point group Oh. Neutron
scattering experiments using short wavelength neutrons, as done in this study,
could become a general method to study the high-rank multipoles in f electron
systems.Comment: 4 pages, 4 figure
Disorder, inhomogeneity and spin dynamics in f-electron non-Fermi liquid systems
Muon spin rotation and relaxation (SR) experiments have yielded evidence
that structural disorder is an important factor in many f-electron-based
non-Fermi-liquid (NFL) systems. Disorder-driven mechanisms for NFL behaviour
are suggested by the observed broad and strongly temperature-dependent SR
(and NMR) linewidths in several NFL compounds and alloys. Local disorder-driven
theories (Kondo disorder, Griffiths-McCoy singularity) are, however, not
capable of describing the time-field scaling seen in muon spin relaxation
experiments, which suggest cooperative and critical spin fluctuations rather
than a distribution of local fluctuation rates. A strong empirical correlation
is established between electronic disorder and slow spin fluctuations in NFL
materialsComment: 24 pages, 15 figures, submitted to J. Phys.: Condens. Matte
Bowel Preparation for Colonoscopy with Sodium Phosphate Solution versus Polyethylene Glycol-Based Lavage: A Multicenter Trial
Background: Adequate bowel preparation is essential for
accurate colonoscopy. Both oral sodium phosphate (NaP) and
polyethylene glycol-based lavage (PEG-ELS) are used predominantly
as bowel cleansing modalities. NaP has gained popularity due to
low drinking volume and lower costs. The purpose of this
randomized multicenter observer blinded study was to compare
three groups of cleansing (NaP, NaP + sennosides, PEG-ELS +
sennosides) in reference to tolerability, acceptance, and
cleanliness. Patient and Methods: 355 outpatients between 18 and
75 years were randomized into three groups (A, B, C) receiving NaP =
A, NaP, and sennosides = B or PEG-ELS and sennosides = C.
Gastroenterologists performing colonoscopies were blinded to the
type of preparation. All patients documented tolerance and adverse
events. Vital signs, premedication, completeness, discomfort, and
complications were recorded. A quality score (0–4) of cleanliness
was generated. Results: The three groups were similar
with regard to age, sex, BMI, indication for colonoscopy, and
comorbidity. Drinking volumes (L) (A = 4.33 + 1.2, B = 4.56 + 1.18, C = 4.93 + 1.71) were in favor of NaP
(P = .005). Discomfort from
ingested fluid was recorded in A = 39.8% (versus C: P = .015),
B = 46.6% (versus C: P = .147), and C = 54.6%. Differences in tolerability and acceptance between the three groups were
statistically not significant. No differences in adverse events
and the cleanliness effects occurred in the three groups (P = .113).
The cleanliness quality scores 0–2 were calculated in A:
77.7%, B: 86.7%, and C: 85.2%. Conclusions:
These data fail to demonstrate significant differences in
tolerability, acceptance, and preparation quality between the
three types of bowel preparation for colonoscopy. Cleansing with
NaP was not superior to PEG-ELS
Lattice Distortion and Octupole Ordering Model in CexLa1-xB6
Possible order parameters of the phase IV in CexLa1-xB6 are discussed with
special attention to the lattice distortion recently observed. A
\Gamma_{5u}-type octupole order with finite wave number is proposed as the
origin of the distortion along the [111] direction. The \Gamma_8 crystalline
electric field (CEF) level splits into three levels by a mean field with the
\Gamma_{5u} symmetry. The ground and highest singlets have the same quadrupole
moment, while the intermediate doublet has an opposite sign. It is shown that
any collinear order of \Gamma_{5u}-type octupole moment accompanies the
\Gamma_{5g}-type ferro-quadrupole order, and the coupling of the quadrupole
moment with the lattice induces the distortion. The cusp in the magnetization
at the phase transition is reproduced, but the internal magnetic field due to
the octupole moment is smaller than the observed one by an order of magnitude.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp
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