The Beurling-type theorem in the Bergman space Aα2(D)A^2_\alpha(D) for any −1<α<+∞-1<\alpha<+\infty

In this paper, we show that the Beurling-type theorem holds in the Bergman space A^2_\alpha(\DD) for any $-1<\alpha < +\infty$. That is, every invariant subspace $H$ for the shift operator $S$ on A^2_\alpha(\DD) $(-1<\alpha < +\infty)$ has property $H=[H\ominus zH]_{S}$

A review of NIST projects in surface and topography metrology for firearm evidence identification in forensic science

This is a review of the National Institute of Standards and Technology’s (NIST) efforts in surface metrology and topography measurements for firearm evidence identifications in forensic science. Based on the research projects in surface metrology and standardization, NIST researchers have developed Standard Reference Material (SRM) Bullets and Cartridge Cases (Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose) and established a 2D/3D Ballistics Topography Measurement System. They formulated a Traceability and Quality System to support nationwide ballistics identifications within the National Integrated Ballistics Information Network (NIBIN) in the United States. They have recently proposed a Congruent Matching Cells (CMC) method for accurate ballistic identification and error rate estimation, which provides a statistical foundation and a practical method to promote firearm evidence identifications from qualitative image comparisons to quantitative topography measurements

Large Magnetoresistance in Compensated Semimetals TaAs2_2 and NbAs2_2

We report large magnetoresistance (MR) at low temperatures in single-crystalline nonmagnetic compounds TaAs$_2$ and NbAs$_2$. Both compounds exhibit parabolic-field-dependent MR larger than $5\times10^3$ in a magnetic field of 9 Tesla at 2 K. The MR starts to deviate from parabolic dependence above 10 T and intends to be saturated in 45 T for TaAs$_2$ at 4.2 K. The Hall resistance measurements and band structural calculations reveal their compensated semimetal characteristics. The large MR at low temperatures is ascribed to a resonance effect of the balanced electrons and holes with large mobilities. We also discuss the relation of the MR and samples' quality for TaAs$_2$ and other semimetals. We found that the magnitudes of MR are strongly dependent on the samples' quality for different compounds.Comment: 26 pages, 11 figures, 2 table