Physical parameters reconstruction of a fixed–fixed mass-spring system from its characteristic data

AbstractIn this paper, an inverse problem of constructing a linear n degree of freedom mass-spring system from part of its physical parameters and part of modality of its maximal or minimal natural frequencies is considered. The solvability and the expression of the solution is derived. The numerical algorithms and some numerical examples are given

The least-squares solutions of inconsistent matrix equation over symmetric and antipersymmetric matrices

AbstractIn this paper, we are concerned with the following two problems. In Problem I, we describe the set S of real n × n symmetric and antipersymmetric matrices such that minimize the Frobenius norm of LG − E for G, E in Rn × n. In Problem II, we find the unique Ľ in the setsfS, satisfying ∥L∗ − L∥ = minLϵS ∥L∗ − L∥, where L∗ ϵ Rn × n is a given matrix and ∥ · ∥ is the Frobenius norm. We derive a general expression of the set S. For Problem II, we prove the existence and the uniqueness of the solution and provide the expression of this unique solution. We also report some numerical results to support the theory established in the paper

BertNet: Harvesting Knowledge Graphs with Arbitrary Relations from Pretrained Language Models

It is crucial to automatically construct knowledge graphs (KGs) of diverse new relations to support knowledge discovery and broad applications. Previous KG construction methods, based on either crowdsourcing or text mining, are often limited to a small predefined set of relations due to manual cost or restrictions in text corpus. Recent research proposed to use pretrained language models (LMs) as implicit knowledge bases that accept knowledge queries with prompts. Yet, the implicit knowledge lacks many desirable properties of a full-scale symbolic KG, such as easy access, navigation, editing, and quality assurance. In this paper, we propose a new approach of harvesting massive KGs of arbitrary relations from pretrained LMs. With minimal input of a relation definition (a prompt and a few shot of example entity pairs), the approach efficiently searches in the vast entity pair space to extract diverse accurate knowledge of the desired relation. We develop an effective search-and-rescore mechanism for improved efficiency and accuracy. We deploy the approach to harvest KGs of over 400 new relations from different LMs. Extensive human and automatic evaluations show our approach manages to extract diverse accurate knowledge, including tuples of complex relations (e.g., "A is capable of but not good at B"). The resulting KGs as a symbolic interpretation of the source LMs also reveal new insights into the LMs' knowledge capacities.Comment: ACL 2023 (Findings); Code available at https://github.com/tanyuqian/knowledge-harvest-from-lm

Photometric Metallicity Calibration with SDSS and SCUSS and its Application to distant stars in the South Galactic Cap

Based on SDSS g, r and SCUSS (South Galactic Cap of u-band Sky Survey) $u$ photometry, we develop a photometric calibration for estimating the stellar metallicity from $u-g$ and $g-r$ colors by using the SDSS spectra of 32,542 F- and G-type main sequence stars, which cover almost $3700$ deg$^{2}$ in the south Galactic cap. The rms scatter of the photometric metallicity residuals relative to spectrum-based metallicity is $0.14$ dex when $g-r<0.4$, and $0.16$ dex when $g-r>0.4$. Due to the deeper and more accurate magnitude of SCUSS $u$ band, the estimate can be used up to the faint magnitude of $g=21$. This application range of photometric metallicity calibration is wide enough so that it can be used to study metallicity distribution of distant stars. In this study, we select the Sagittarius (Sgr) stream and its neighboring field halo stars in south Galactic cap to study their metallicity distribution. We find that the Sgr stream at the cylindrical Galactocentric coordinate of $R\sim 19$ kpc, $\left| z\right| \sim 14$ kpc exhibits a relative rich metallicity distribution, and the neighboring field halo stars in our studied fields can be modeled by two-Gaussian model, with peaks respectively at [Fe/H]$=-1.9$ and [Fe/H]$=-1.5$.Comment: 8 pages, 7 figures, Accepted for publication in MNRA

Project Overview of the Beijing-Arizona Sky Survey

The Beijing-Arizona Sky Survey (BASS) is a wide-field two-band photometric survey of the Northern Galactic Cap using the 90Prime imager on the 2.3 m Bok telescope at Kitt Peak. It is a four-year collaboration between the National Astronomical Observatory of China and Steward Observatory, the University of Arizona, serving as one of the three imaging surveys to provide photometric input catalogs for target selection of the Dark Energy Spectroscopic Instrument (DESI) project. BASS will take up to 240 dark/grey nights to cover an area of about 5400 deg$^2$ in the $g$ and $r$ bands. The 5$\sigma$ limiting AB magnitudes for point sources in the two bands, corrected for the Galactic extinction, are 24.0 and 23.4 mag, respectively. BASS, together with other DESI imaging surveys, will provide unique science opportunities that cover a wide range of topics in both Galactic and extragalactic astronomy.Comment: 10 pages, submitted to PAS

The Galactic extinction and reddening from the South Galactic Cap U-band Sky Survey: u band galaxy number counts and u−ru-r color distribution

We study the integral Galactic extinction and reddening based on the galaxy catalog of the South Galactic Cap U-band Sky Survey (SCUSS), where $u$ band galaxy number counts and $u-r$ color distribution are used to derive the Galactic extinction and reddening respectively. We compare these independent statistical measurements with the reddening map of \citet{Schlegel1998}(SFD) and find that both the extinction and reddening from the number counts and color distribution are in good agreement with the SFD results at low extinction regions ($E(B-V)^{SFD}<0.12$ mag). However, for high extinction regions ($E(B-V)^{SFD}>0.12$ mag), the SFD map overestimates the Galactic reddening systematically, which can be approximated by a linear relation $\Delta E(B-V)= 0.43[E(B-V)^{SFD}-0.12$]. By combing the results of galaxy number counts and color distribution together, we find that the shape of the Galactic extinction curve is in good agreement with the standard $R_V=3.1$ extinction law of \cite{ODonnell1994}

The First Data Release of the Beijing-Arizona Sky Survey

The Beijing-Arizona Sky Survey (BASS) is a new wide-field legacy imaging survey in the northern Galactic cap using the 2.3m Bok telescope. The survey will cover about 5400 deg$^2$ in the $g$ and $r$ bands, and the expected 5$\sigma$ depths (corrected for the Galactic extinction) in the two bands are 24.0 and 23.4 mag, respectively. BASS started observations in January 2015, and has completed about 41% of the whole area as of July 2016. The first data release contains both calibrated images and photometric catalogs obtained in 2015 and 2016. The depths of single-epoch images in the two bands are 23.4 and 22.9 mag, and the full depths of three epochs are about 24.1 and 23.5 mag, respectively.Comment: 16 pages, published by A