Smooth planar rr-splines of degree 2r2r

In \cite{as}, Alfeld and Schumaker give a formula for the dimension of the space of piecewise polynomial functions (splines) of degree $d$ and smoothness $r$ on a generic triangulation of a planar simplicial complex $\Delta$ (for $d \ge 3r+1$) and any triangulation (for $d\geq 3r+2$). In \cite{ss}, it was conjectured that the Alfeld-Schumaker formula actually holds for all $d \ge 2r+1$. In this note, we show that this is the best result possible; in particular, there exists a simplicial complex $\Delta$ such that for any $r$, the dimension of the spline space in degree $d=2r$ 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 PrOs4_{4}Sb12_{12}

Transverse-field muon spin rotation ($\mu$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $\lambda(T)$ 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 $\lambda(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the perturbing effect of the muon charge on the neighboring Pr$^{3+}$ crystalline electric field is negligibly small, and therefore is unlikely to cause the difference between the $\mu$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 ($\mu$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 $\mu$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