arXiv subjects

Zhang Xiang

Publications and source records attributed to Zhang Xiang.

6 recordsLinked to original sources

arXiv2021

High-precision Time-Frequency Signal Simultaneous Transfer System via a WDM-based Fiber Link

In this paper, we demonstrate a wavelength division multiplexing (WDM) based system for simultaneously delivering ultrastable optical frequency reference, 10 GHz microwave frequency reference, and one pulse per second (1 PPS) time signal via a 50 km fiber network. For each signal, a unique noise cancellation technique is used to maintain the precision of them. After being compensated, the transfer frequency instability in terms of overlapping Allan deviation (OADEV) for the optical frequency achieves 2E-17/s and scales down to 2E-20/10000 s, which for the 10 GHz microwave reference approaches 4E-15/s and decreases to 1.4E-17/10000 s, and the time uncertainty of the 1 PPS time signal along the system is 2.08 ps. In this scheme, specific channels of WDM are respectively occupied for different signals to avoid the possible crosstalk interference effect between the transmitted reference signals. To estimate the performance of the above scheme, independent of these signals is also demonstrated in this 50 km link, the results are similar to that in the case of simultaneous delivery. This work shows that the WDM-based system is a promising method for building a nationwide time and frequency fiber transfer system with a communication optical network.

physics.ins-det↗

arXiv2020

A Low Frequency Blind Survey of the Low Earth Orbit Environment using Non-Coherent Passive Radar with the Murchison Widefield Array

We have extended our previous work to use the Murchison Widefield Array (MWA) as a non-coherent passive radar system in the FM frequency band, using terrestrial FM transmitters to illuminate objects in Low Earth Orbit LEO) and the MWA as the sensitive receiving element for the radar return. We have implemented a blind detection algorithm that searches for these reflected signals in difference images constructed using standard interferometric imaging techniques. From 20 hours of archived MWA observations, we conduct a survey of LEO, detecting 74 unique objects over multiple passes and demonstrating the MWA to be a valuable addition to the global Space Domain Awareness network. We detected objects with ranges up to 977 km and as small as 0.03 m^2 radar cross section. We found that 30 objects were either non-operational satellites or upper-stage rocket body debris. Additionally, we also detected FM reflections from Geminid meteors and aircraft flying over the MWA. Most of the detections of objects in LEO were found to lie within the parameter space predicted by previous feasibility studies, verifying the performance of the MWA for this application.

astro-ph.IM↗

arXiv2018

A Survey of Privacy Infrastructures and Their Vulnerabilities

Over the last two decades, the scale and complexity of Anonymous networks and its associated technologies grows exponentially as privacy has become a major concern of individuals. Also, some cyber attackers make use of privacy infrastructures including botnets and Tor to do illegal activities like drug, contraband or DDoS attack. However, anonymous networks are not perfect, there are some methods could exploit the vulnerabilities and track user information. In this paper, we analyze few of privacy infrastructures and their vulnerabilities.

cs.CR↗

arXiv2014

The embedding flows of $C^\infty$ hyperbolic diffeomorphisms

In [{\it American J. Mathematics}, 124(2002), 107--127] we proved that for a germ of $C^\infty$ hyperbolic diffeomorphisms $F(x)=Ax+f(x)$ in $(\mathbb R^n,0)$, if $A$ has a real logarithm with its eigenvalues weakly nonresonant, then $F(x)$ can be embedded in a $C^\infty$ autonomous differential system. Its proof was very complicated, which involved the existence of embedding periodic vector field of $F(x)$ and the extension of the Floquet's theory to nonlinear $C^\infty$ periodic differential systems. In this paper we shall provide a simple and direct proof to this last result. Next we shall show that the weakly nonresonant condition in the last result on the real logarithm of $A$ is necessary for some $C^\infty$ diffeomorphisms $F(x)=Ax+f(x)$ to have $C^\infty$ embedding flows. Finally we shall prove that a germ of $C^\infty$ hyperbolic diffeomorphisms $F(x)=Ax+f(x)$ with $f(x)=O(|x|^2)$ in $(\mathbb R^2,0)$ has a $C^\infty$ embedding flow if and only if either $A$ has no negative eigenvalues or $A$ has two equal negative eigenvalues and it can be diagonalizable.

math.CA↗

arXiv2014

The $16$th Hilbert problem on algebraic limit cycles

For real planar polynomial differential systems there appeared a simple version of the $16$th Hilbert problem on algebraic limit cycles: {\it Is there an upper bound on the number of algebraic limit cycles of all polynomial vector fields of degree $m$?} In [J. Differential Equations, 248(2010), 1401--1409] Llibre, Ramírez and Sadovskia solved the problem, providing an exact upper bound, in the case of invariant algebraic curves generic for the vector fields, and they posed the following conjecture: {\it Is $1+(m-1)(m-2)/2$ the maximal number of algebraic limit cycles that a polynomial vector field of degree $m$ can have?} In this paper we will prove this conjecture for planar polynomial vector fields having only nodal invariant algebraic curves. This result includes the Llibre {\it et al}\,'s as a special one. For the polynomial vector fields having only non--dicritical invariant algebraic curves we answer the simple version of the 16th Hilbert problem.

math.CA↗

arXiv2014

Analytic integrable systems: Analytic normalization and embedding flows

In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we will prove that any complete analytic integrable diffeomorphism $F(x)=Bx+f(x)$ in $(\mathbb C^n,0)$ with $B$ having eigenvalues not modulus $1$ and $f(x)=O(|x|^2)$ is locally analytically conjugate to its normal form. Meanwhile, we also prove that any complete analytic integrable differential system $\dot x=Ax+f(x)$ in $(\mathbb C^n,0)$ with $A$ having nonzero eigenvalues and $f(x)=O(|x|^2)$ is locally analytically conjugate to its normal form. Furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow. We note that parts of our results are the improvement of Moser's one in {\it Comm. Pure Appl. Math.} 9$($1956$)$, 673--692 and of Poincaré's one in {\it Rendiconti del circolo matematico di Palermo} 5$($1897$)$, 193--239. These results also improve the ones in {\it J. Diff. Eqns.} 244$($2008$)$, 1080--1092 in the sense that the linear part of the systems can be nonhyperbolic, and the one in {\it Math. Res. Lett.} 9$($2002$)$, 217--228 in the way that our paper presents the concrete expression of the normal form in a restricted case.

math.CA↗