Mean Value of the Class Number in Function Fields Revisited

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this recordIn this paper an asymptotic formula for the sum ∑ (1, χ) is established for the family of quadratic Dirichlet L-functions over the rational function field over a finite field Fq with q fixed. Using the recent techniques developed by Florea we obtain an extra lower order terms that was never been predicted in number fields and function fields. As a corollary, we obtain a formula for the average of the class number over function fields which also contains strenuous lower order terms and so improving on previous results of Hoffstein and Rosen.The first author is grateful to the Leverhulme Trust (RPG-2017-320) for the support through the research grant “Moments of L-functions in Function Fields and Random Matrix Theory”. The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2017R1D1A1B03031464)

A Scaling Behavior of Spectral Weight Changes in Perovskite Manganites La_{0.7-y}Pr_{y}Ca_{0.3}MnO_3

Optical conductivity spectra of La_{0.7-y}Pr_{y}Ca_{0.3}MnO_3 were systematically investigated. For metallic samples, the spectral weight below 0.5 eV, whose magnitude can be represented by the effective carrier number N_{eff}(0.5 eV), increases as temperature becomes lower. Regardless of the Pr doping, all the measured values of N_{eff}(0.5 eV)/T_C fall into one scaling curve. This scaling behavior could be explained by the theoretical model by Roeder et al. [Phys. Rev. Lett. 76, 1356 (1996)], which includes spin double exchange and Jahn-Teller lattice coupling to holes. With the Pr doping, far-infrared conductivities were found to be suppressed, probably due to the Anderson localization.Comment: Latex 2e, 8 pages including 4 postscript figures, submitted at Apr 2

Study of Thick CZT Detectors for X-ray and Gamma-Ray Astronomy

CdZnTe (CZT) is a wide bandgap II-VI semiconductor developed for the spectroscopic detection of X-rays and {\gamma}-rays at room temperature. The Swift Burst Alert Telescope is using an 5240 cm2 array of 2 mm thick CZT detectors for the detection of 15-150 keV X-rays from Gamma-Ray Bursts. We report on the systematic tests of thicker (\geq 0.5 cm) CZT detectors with volumes between 2 cm3 and 4 cm3 which are potential detector choices for a number of future X-ray telescopes that operate in the 10 keV to a few MeV energy range. The detectors contacted in our laboratory achieve Full Width Half Maximum energy resolutions of 2.7 keV (4.5%) at 59 keV, 3 keV (2.5%) at 122 keV and 4 keV (0.6%) at 662 keV. The 59 keV and 122 keV energy resolutions are among the world-best results for \geq 0.5 cm thick CZT detectors. We use the data set to study trends of how the energy resolution depends on the detector thickness and on the pixel pitch. Unfortunately, we do not find clear trends, indicating that even for the extremely good energy resolutions reported here, the achievable energy resolutions are largely determined by the properties of individual crystals. Somewhat surprisingly, we achieve the reported results without applying a correction of the anode signals for the depth of the interaction. Measuring the interaction depths thus does not seem to be a pre-requisite for achieving sub-1% energy resolutions at 662 keV.Comment: 15 pages, 11 figure

Rescue Model for the Bystanders' Intervention in Emergencies

To investigate an effect of social interaction on the bystanders' intervention in emergency situations we introduce a rescue model which includes the effects of the victim's acquaintance with bystanders and those among bystanders. This model reproduces the surprising experimental result that the helping rate tends to decrease although the number of bystanders $k$ increases. The model also shows that given the coupling effect among bystanders, for a certain range of small $k$ the helping rate increases according to $k$ and that coupling effect plays both positive and negative roles in emergencies. Finally we find a broad range of coupling strength to maximize the helping rate.Comment: 10 pages, 4 figure

A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction

The acquisition of Magnetic Resonance Imaging (MRI) is inherently slow. Inspired by recent advances in deep learning, we propose a framework for reconstructing MR images from undersampled data using a deep cascade of convolutional neural networks to accelerate the data acquisition process. We show that for Cartesian undersampling of 2D cardiac MR images, the proposed method outperforms the state-of-the-art compressed sensing approaches, such as dictionary learning-based MRI (DLMRI) reconstruction, in terms of reconstruction error, perceptual quality and reconstruction speed for both 3-fold and 6-fold undersampling. Compared to DLMRI, the error produced by the method proposed is approximately twice as small, allowing to preserve anatomical structures more faithfully. Using our method, each image can be reconstructed in 23 ms, which is fast enough to enable real-time applications

Microstructure and pinning properties of hexagonal-disc shaped single crystalline MgB2

We synthesized hexagonal-disc-shaped MgB2 single crystals under high-pressure conditions and analyzed the microstructure and pinning properties. The lattice constants and the Laue pattern of the crystals from X-ray micro-diffraction showed the crystal symmetry of MgB2. A thorough crystallographic mapping within a single crystal showed that the edge and c-axis of hexagonal-disc shape exactly matched the (10-10) and the (0001) directions of the MgB2 phase. Thus, these well-shaped single crystals may be the best candidates for studying the direction dependences of the physical properties. The magnetization curve and the magnetic hysteresis for these single crystals showed the existence of a wide reversible region and weak pinning properties, which supported our single crystals being very clean.Comment: 5 pages, 3 figures. submitted to Phys. Rev.

Polaron Absorption in a Perovskite Manganite La0.7Ca0.3MnO3

Temperature dependent optical conductivity spectra of a La0.7Ca0.3MnO3 (LCMO) sample were measured. In the metallic regime at very low temperatures, they clearly showed two types of absorption features, i.e., a sharp Drude peak and a broad mid-infrared absorption band, which could be explained as coherent and incoherent bands of a large lattice polaron. This elementary excitation in LCMO was found to be in a strong coupling regime and to have interactions with the spin degree of freedom.Comment: 4 pages and separate 4 figure

Self-trapped Exciton and Franck-Condon Spectra Predicted in LaMnO3_3

Because the ground state has cooperative Jahn-Teller order, electronic excitations in LaMnO$_3$ are predicted to self-trap by local rearrangement of the lattice. The optical spectrum should show a Franck-Condon series, that is, a Gaussian envelope of vibrational sidebands. Existing data are reinterpreted in this way. The Raman spectrum is predicted to have strong multiphonon features.Comment: 5 pages with two embedded postscript figure

Transient differential reflectivity of ferromagnetic and paramagnetic phases in the bilayered manganite La1.24Sr1.76Mn2O7

Photoinduced effects in a single crystal of bilayered manganites, La2-2xSr1+2xMn2O7 (x=0.38), were investigated in a wide range of temperatures by pump-probe measurement at a photon energy of 1.6eV. In a ferromagnetic metallic state, significant enhancement of positive rise in differential reflectivity with a slow relaxing time of hundred picoseconds was observed just below Tc=127K, indicating that the reflectivity change with the slow relaxation time constant is induced by laser heating. We have also observed an unconventional fast relaxing component that has a time constant of the order of ten picoseconds. This fast relaxing component, whose absolute value has an asymmetric peak at Tc, is presumably due to short-range correlation of Jahn-Teller distortion.Comment: 13 pages, 4 figures, accepted to Solid State Communication

Photoinduced IR absorption in (La(1-x)Sr(x)Mn)(1-\delta)O3: changes of the anti-Jahn-Teller polaron binding energy with doping

Photoinduced IR absorption was measured in (La(1-x)Sr(x)Mn)(1-\delta)O3. A midinfrared peak centered at ~ 5000 cm$^{-1}$ was observed in the x=0 antiferromagnetic sample. The peak diminishes and softens as hole doping is increased. The origin of the photoinduced absorption peak is atributted to the photon assisted hopping of anti-Jahn-Teller polarons formed by photoexcited charge carriers, whose binding energy decreases with increasing hole doping. The shape of the peak indicates that the polarons are small.Comment: 5 pages, 3 figures, submitted to PR