arXiv subjects
Publications and source records attributed to Zhongjie Li.
We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an application, we provide several examples of P-recursive sequences of order greater than two.
In recent years, the log-concavity or log-convexity of combinatorial sequences and their root sequences, higher order Tur{á}n inequalities, and Laguerre inequalities of order two have been widely studied. However, the research of the Fourier coefficient $c(n)$ of the $j$-function is limited to its asymptotic form. In this paper, we give the appropriate upper and lower bounds of $c(n)$ to establish the inequalities associated with it.
In recent years, the asymptotic normality of some famous combinatorial sequences has been the subject of extensive study. However, the methods used to prove the asymptotic normality of various combinatorial sequences differ significantly. In this paper, we present a sufficient condition for establishing the asymptotic normality of the coefficients of a general P-recursive polynomial sequence. Additionally, we provide two examples that illustrate the application of this sufficient condition.
Due to their flexibility, aerial vehicles (AVs), such as unmanned aerial vehicles and airships, are widely employed as relays to assist communications between massive ground users (GUs) and satellites, forming an AV-relayed ground-air-satellite solution (GASS). In GASS, the deployment of AVs is crucial to ensure overall performance from GUs to satellites. This paper develops a stochastic geometry-based analytical model for GASS under Matern hard-core point process (MHCPP) distributed AVs. The 3D distributions of AVs and GUs are modeled by considering their locations on spherical surfaces in the presence of high-altitude satellites. Accordingly, we derive an overall connectivity analytical model for GASS, which includes the average performance of AV-relayed two-hop transmissions. Extensive numerical results validate the accuracy of the connectivity model and provide essential insights for configuring AV deployments.
The Tur{á}n inequalities and the Laguerre inequalities are closely related to the Laguerre-Pólya class and the Riemann hypothesis. These inequalities have been extensively studied in the literature. In this paper, we propose a method to determine a positive integer $N$ such that the sequences $\{\sqrt[n]{a_n}/n!\}_{n \ge N}$ and $\{\sqrt[n+1]{a_{n+1}}/(\sqrt[n]{a_n} n!)\}_{n \ge N}$ satisfy the higher order Tur{á}n inequalities and the Laguerre inequalities of order two for a P-recursive sequence $\{a_n\}_{n \ge 1}$.
In recent years, Sun has proposed numerous conjectures regarding the log-concavity of root sequences $\{\sqrt[n]{a_n}}_{n\geqslant 1}$. We establish criteria for the asymptotic log-concavity of $\{\sqrt[n]{a_n}}_{n\geqslant 1}$ and the asymptotic ratio log-convexity of $\{\sqrt[n]{a_n}}_{n\geqslant 1}$ for $P$-recursive sequences $\{\sqrt[n]{a_n}}_{n\geqslant{0}}$. Additionally, by the aid of symbolic computation, we present a systematic approach to determine the explicit integer $N$ such that the sequence $\{\sqrt[n]{a_n}}_{n\geqslant{N}}$ is log-concave and the sequence $\{\sqrt[n]{a_n}}_{n\geqslant N}$ is ratio log-convex.
By multiplexing information symbols in the delay-Doppler (DD) domain, orthogonal time frequency space (OTFS) is a promising candidate for future wireless communication in high-mobility scenarios. In addition to the superior communication performance, OTFS is also a natural choice for radar sensing since the primary parameters (range and velocity of targets) in radar signal processing can be inferred directly from the delay and Doppler shifts. Though there are several works on OTFS radar sensing, most of them consider the integer parameter estimation only, while the delay and Doppler shifts are usually fractional in the real world. In this paper, we propose a two-step method to estimate the fractional delay and Doppler shifts. We first perform the two-dimensional (2D) correlation between the received and transmitted DD domain symbols to obtain the integer parts of the parameters. Then a difference-based method is implemented to estimate the fractional parts of delay and Doppler indices. Meanwhile, we implement a target detection method based on a generalized likelihood ratio test since the number of potential targets in the sensing scenario is usually unknown. The simulation results show that the proposed method can obtain the delay and Doppler shifts accurately and get the number of sensing targets with a high detection probability.
Acute lower respiratory infections caused by respiratory viruses are common and persistent infectious diseases worldwide and in China, which have pronounced seasonal patterns. Meteorological factors have important roles in the seasonality of some major viruses. Our aim was to identify the dominant meteorological factors and to model their effects on common respiratory viruses in different regions of China. We analysed monthly virus data on patients from 81 sentinel hospitals in 22 provinces in mainland China from 2009 to 2013. The geographical detector method was used to quantify the explanatory power of each meteorological factor, individually and interacting in pairs. 28369 hospitalised patients with ALRI were tested, 10387 were positive for at least one virus, including RSV, influenza virus, PIV, ADV, hBoV, hCoV and hMPV. RSV and influenza virus had annual peaks in the north and biannual peaks in the south. PIV and hBoV had higher positive rates in the spring summer months. hMPV had an annual peak in winter spring, especially in the north. ADV and hCoV exhibited no clear annual seasonality. Temperature, atmospheric pressure, vapour pressure, and rainfall had most explanatory power on most respiratory viruses in each region. Relative humidity was only dominant in the north, but had no significant explanatory power for most viruses in the south. Hours of sunlight had significant explanatory power for RSV and influenza virus in the north, and for most viruses in the south. Wind speed was the only factor with significant explanatory power for human coronavirus in the south. For all viruses, interactions between any two of the paired factors resulted in enhanced explanatory power, either bivariately or non-linearly.