We study the well-posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions. We give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3D under null condition, with small
scaling invariant $dot{W}^{2,1}(mathbb{R}^3)$ data. We obtain a bilinear estimate that is effective to the hyperbolic systems which do not have any time decay. It allows us to achieve the boundedness of the weighted BV norm of the radial solution.
Matrix-parametrized models, including multiclass logistic regression and sparse coding, are used in machine learning (ML) applications ranging from computer vision to computational biology. When these models are applied to large-scale ML problems sta
rting at millions of samples and tens of thousands of classes, their parameter matrix can grow at an unexpected rate, resulting in high parameter synchronization costs that greatly slow down distributed learning. To address this issue, we propose a Sufficient Factor Broadcasting (SFB) computation model for efficient distributed learning of a large family of matrix-parameterized models, which share the following property: the parameter update computed on each data sample is a rank-1 matrix, i.e., the outer product of two sufficient factors (SFs). By broadcasting the SFs among worker machines and reconstructing the update matrices locally at each worker, SFB improves communication efficiency --- communication costs are linear in the parameter matrixs dimensions, rather than quadratic --- without affecting computational correctness. We present a theoretical convergence analysis of SFB, and empirically corroborate its efficiency on four different matrix-parametrized ML models.
A GEM detector with an effective area of 30*30 cm2 has been constructed using an improved self-stretch technique, which enables an easy and fast GEM assembling. The design and assembling of the detector is described. Results from tests of the detecto
r with 8 keV X-rays on effective gain and energy resolution are presented.
Layered antiferromagnetic spin density wave (LAF) state is one of the plausible ground states of charge neutral Bernal stacked bilayer graphene. In this paper, we use determinant quantum Monte Carlo method to study the effect of the electric field on
the magnetic order in bilayer Hubbard model on a honeycomb lattice. Our results qualitatively support the LAF ground state found in the mean field theory. The obtained magnetic moments, however, are much smaller than what are estimated in the mean field theory. As electric field increases, the magnetic order parameter rapidly decreases.
The regular spatial filters comprised of lens and pinhole are essential component in high power laser systems, such as lasers for inertial confinement fusion, nonlinear optical technology and directed-energy weapon. On the other hand the pinhole is t
reated as a bottleneck of high power laser due to harmful plasma created by the focusing beam. In this paper we present a spatial filter based on angular selectivity of Bragg diffraction grating to avoid the harmful focusing effect in the traditional pinhole filter. A spatial filter consisted of volume phase gratings in two-pass amplifier cavity were reported. Two-dimensional filter was proposed by using single Pi-phase-shifted Bragg grating, numerical simulation results shown that its angular spectrum bandwidth can be less than 160urad. The angular selectivity of photo-thermo-refractive glass and RUGATE film filters, construction stability, thermal stability and the effects of misalignments of gratings on the diffraction efficiencies under high-pulse-energy laser operating condition are discussed. Keywords: spatial filter, pinhole spatial filter, RUGATE filter, angular selectivity of volume phase grating, Pi-phase-shifted Bragg grating, high-energy pulsed laser, multi-pass laser amplifier
Superconductivity in iron pnictides is studied by using a two-orbital Hubbard model in the large U limit. The Coulomb repulsion induces an orbital-dependent pairing between charge carriers. The pairing is found mainly from the scattering within the s
ame Fermi pocket. The inter-pocket pair scatterings determine the symmetry of the superconductivity, which is extended s-wave at small Hunds coupling, and d-wave at large Hunds coupling and large U. The former is consistent with recent experiments of ARPES and Andreev reflection spectroscope.
In the present paper, we propose the parity even,orbital singlet and spin triplet pairing state as the ground state of the newly discovered super-conductor $LaO_{1-x}F_xFeAs$.The pairing mechanism involves both the special shape of the electron fermi
surface and the strong ferromagnetic fluctuation induced by Hunds rule coupling.The special behavior of the Bogoliubov quasi-particle spectrum may leads to Fermi arc like anisotropy super-conducting gap, which can be detected by angle resolved photo emission(ARPES).The impurity effects are also discussed.
