arXiv subjects

Shihai Yang

Publications and source records attributed to Shihai Yang.

8 recordsLinked to original sources

arXiv2026

Power quasinormal operators and the root problem

In this paper, we construct an $n$-power quasinormal operator $T$ such that $T^n$ is not quasinormal for some positive integer $n$, thereby providing a counterexample to \cite[Lemma 3.1]{ko-filomat-2023}. We then investigate the relationships among the $n$-power quasinormality of $T$, the normality of $T^n$, and the quasinormality of $T^n$, and show that these three conditions are equivalent in finite-dimensional spaces. We also provide a new proof that $n$-power quasinormal operators have the single-valued extension property \cite[Theorem 3.2]{ko-filomat-2023}; unlike the original proof, our argument does not rely on \cite[Lemma 3.1]{ko-filomat-2023} and thus closes the gap in the original argument. In addition, for a fixed operator $T$, we characterize all positive integers $n$ for which $T$ is $n$-power quasinormal. As consequences, several results of Sid Ahmed \cite{ahmed-bmaa-2011} are extended. Finally, we prove that every paranormal $n$-power quasinormal operator is quasinormal. Closely related to this, we also give an affirmative answer to the root problem of Stankovi\'c and Kubrusly \cite[Question 2.11]{stankovic-afa-2025}.

math.FA↗

arXiv2026

Power mean transforms of operators

In this paper, we introduce the power mean transform $P_{\lambda}(T)$ of an operator $T$ on a Hilbert space, which is a convex combination of some classical operator transforms such as the mean transform $M(T)$, the Aluthge transform $\Delta(T)$, and the Duggal transform $T^D$. In particular, when $T$ is invertible, this transform coincides with the induced Aluthge transform $\Delta_{\mathsf{m}_{f}}(T)$ recently defined by Yamazaki \cite{yamazaki-laa-2021} with $f(x)=(\lambda+(1-\lambda)\sqrt{x})^2$ for $x\in(0,\infty)$ and $\lambda\in(0,1)$. We study basic properties of $P_{\lambda}(T)$ including its spectrum, norm and numerical radius. Moreover, we use the power mean transform to give new characterizations of normal, quasinormal and binormal operators. The questions of Golla et al. \cite{yamazaki-laa-2023} and some new results on the Duggal transform are also mentioned. We obtain a result close to the recent one of Osaka and Yamazaki \cite[Theorem 3.3]{yamazaki-tams-2025} on the iteration of the induced Aluthge transform for centered operators. Finally, we describe the form of bijective maps commuting with the power mean transform of the product of matrices.

math.FA↗

arXiv2025

Mean transforms of unbounded weighted composition operator pairs

In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs $\textbf{C}_{\phi,\omega}$ in an $L^2$-space. Based on this characterization, we introduce the $\lambda$-spherical mean transform $\mathcal{M}_\lambda(\textbf{C}_{\phi,\omega})$ for $\lambda\in[0,1]$. We then investigate the dense definiteness of $\mathcal{M}_\lambda(\textbf{C}_{\phi,\omega})$. As an application, we provide an example of a $p$-hyponormal operator whose Aluthge transform is densely defined, while its $\lambda$-mean transform has a trivial domain. Furthermore, we establish the relationship between the dense definiteness of $\textbf{C}_{\phi,\omega}$ and $\mathcal{M}_{\lambda}(\textbf{C}_{\phi,\omega})$, based on the notion of powers for operator pairs in the sense of M{\"u}ller and Soltysiak. We also give a characterization of spherically quasinormal weighted composition operator pairs via the $\lambda$-spherical mean transform, revealing some properties that differ from the single operator case. Finally, we characterize a class of spherically $p$-hyponormal weighted composition operators on discrete measure spaces. As a corollary, we present corresponding results on the spherical $p$-hyponormality of unbounded $2$-variable weighted shifts and theirs $\lambda$-spherical mean transforms.

math.FA↗

arXiv2022

Antarctic Survey Telescope 3-3: Overview, System Performance and Preliminary Observations at Yaoan, Yunnan

The third Antarctic Survey Telescope array instrument at Dome A in Antarctica, the AST3-3 telescope, has been in commissioning from March 2021. We deployed AST3-3 at the Yaoan astronomical station in Yunnan Province for an automatic time-domain survey and follow-up observations with an optimised observation and protection system. The telescope system of AST3-3 is similar to that of AST3-1 and AST3-2, except that it is equipped with a 14K~$ \times$~10K QHY411 CMOS camera. AST3-3 has a field of view of $1.65^\circ \times 1.23^\circ$ and is currently using the $g$ band filter. During commissioning at Yaoan, AST3-3 aims to conduct an extragalactic transient survey, coupled with prompt follow-ups of opportunity targets. In this paper, we present the architecture of the AST3-3 automatic observation system. We demonstrate the data processing of observations by representatives SN 2022eyw and GRB 210420B.

astro-ph.IM↗

arXiv2018

Meteorological data from KLAWS-2G for an astronomical site survey of Dome A, Antarctica

We present an analysis of meteorological data from the second generation of the Kunlun Automated Weather Station (KLAWS-2G) at Dome A, Antarctica during 2015 and 2016. We find that a strong temperature inversion exists for all the elevations up to 14 m that KLAWS-2G can reach, and lasts for more than 10 hours for 50% or more of the time when temperature inversion occurs. The average wind speeds at 4 m elevation are 4.2 m/s and 3.8 m/s during 2015 and 2016, respectively. The strong temperature inversion and moderate wind speed lead to a shallow turbulent boundary layer height at Dome A. By analyzing the temperature and wind shear profiles, we note telescopes should be elevated by at least 8 m above the ice. We also find that the duration of temperature inversions, and the wind speed, vary considerably from year to year. Therefore, long-term and continuous data are still needed for the site survey at Dome A.

astro-ph.IM↗

arXiv2018

The First Release of the AST3-1 Point Source Catalogue from Dome A, Antarctica

The three Antarctic Survey Telescopes (AST3) aim to carry out time domain imaging survey at Dome A, Antarctica. The first of the three telescopes (AST3-1) was successfully deployed on January 2012. AST3-1 is a 500\,mm aperture modified Schmidt telescope with a 680\,mm diameter primary mirror. AST3-1 is equipped with a SDSS $i$ filter and a 10k $\times$ 10k frame transfer CCD camera, reduced to 5k $\times$ 10k by electronic shuttering, resulting in a 4.3 deg$^2$ field-of-view. To verify the capability of AST3-1 for a variety of science goals, extensive commissioning was carried out between March and May 2012. The commissioning included a survey covering 2000 deg$^2$ as well as the entire Large and Small Magellanic Clouds. Frequent repeated images were made of the center of the Large Magellanic Cloud, a selected exoplanet transit field, and fields including some Wolf-Rayet stars. Here we present the data reduction and photometric measurements of the point sources observed by AST3-1. We have achieved a survey depth of 19.3\,mag in 60 s exposures with 5\,mmag precision in the light curves of bright stars. The facility achieves sub-mmag photometric precision under stable survey conditions, approaching its photon noise limit. These results demonstrate that AST3-1 at Dome A is extraordinarily competitive in time-domain astronomy, including both quick searches for faint transients and the detection of tiny transit signals.

astro-ph.IM↗

arXiv2017

Optical Observations of LIGO Source GW 170817 by the Antarctic Survey Telescopes at Dome A, Antarctica

The LIGO detection of gravitational waves (GW) from merging black holes in 2015 marked the beginning of a new era in observational astronomy. The detection of an electromagnetic signal from a GW source is the critical next step to explore in detail the physics involved. The Antarctic Survey Telescopes (AST3), located at Dome A, Antarctica, is uniquely situated for rapid response time-domain astronomy with its continuous night-time coverage during the austral winter. We report optical observations of the GW source (GW~170817) in the nearby galaxy NGC 4993 using AST3. The data show a rapidly fading transient at around 1 day after the GW trigger, with the $i$-band magnitude declining from $17.23\pm0.13$ magnitude to $17.72\pm0.09$ magnitude in $\sim 1.8$ hour. The brightness and time evolution of the optical transient associated with GW~170817 are broadly consistent with the predictions of models involving merging binary neutron stars. We infer from our data that the merging process ejected about $\sim 10^{-2}$ solar mass of radioactive material at a speed of up to $30\%$ the speed of light.

astro-ph.HE↗

arXiv2005

Film Growth and Surface Roughness with Fluctuating Covalent Bonds in Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A Computer Simulation Model

A computer simulation model is proposed to study film growth and surface roughness in aqueous ($A$) solution of hydrophobic ($H$) and hydrophilic ($P$) groups on a simple three dimensional lattice of size $L_x \times L_y \times L_z$ with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of $H$ and $P$ is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness ($h$) and its interface width ($W$) are examined for hard-core and interacting particles for a range of temperature ($T$). Simulation data show a rapid increase in $h$ and $W$ is followed by its non-monotonic growth and decay before reaching steady-state equilibrium ($h_s, W_s$) in asymptotic time step limit. The growth can be described by power-laws, e.g., $h \propto t^γ, W \propto t^β$ with a typical value of $γ\approx 2, β\approx 1$ in initial time regime followed by $γ\approx 1.5, β\approx 0.8$ at $T = 0.5$. For hard-core system, the equilibrium film thickness ($h_s$) and surface roughness ($w_s$) seem to scale linearly with the temperature, i.e., $h_s = 6.206 + 0.302 T, W_s = 1,255 + 0.425 T$ at low $T$ and $h_s = 6.54 + 0.198 T, W_s = 1.808 + 0.202 T$ at higher $T$. For interacting functional groups in contrast, $h_s$ and $W_s$ decay rapidly followed by a slow increase on raising the temperature.

cond-mat.soft↗