arXiv subjects
Publications and source records attributed to Qi Han.
In this note, we will prove that $\mathboldζ$ and $\mathboldΓ$ can not satisfy any differential equation generated through a family of functions continuous in $\mathboldζ$ with polynomials in $\mathboldΓ$.
In recent years, bike-sharing systems have been deployed in many cities, which provide an economical lifestyle. With the prevalence of bike-sharing systems, a lot of companies join the market, leading to increasingly fierce competition. To be competitive, bike-sharing companies and app developers need to make strategic decisions for mobile apps development. Therefore, it is significant to predict and compare the popularity of different bike-sharing apps. However, existing works mostly focus on predicting the popularity of a single app, the popularity contest among different apps has not been explored yet. In this paper, we aim to forecast the popularity contest between Mobike and Ofo, two most popular bike-sharing apps in China. We develop CompetitiveBike, a system to predict the popularity contest among bike-sharing apps. Moreover, we conduct experiments on real-world datasets collected from 11 app stores and Sina Weibo, and the experiments demonstrate the effectiveness of our approach.
Intensity interferometry (II) exploits the second-order correlation to acquire the spatial frequency information of an object, which has been used to observe distant stars since 1950s. However, due to unreliability of employed imaging reconstruction algorithms, II can only image simple and sparse objects such as double stars. We here develop a method that overcomes this unreliability problem and enables imaging complex objects by combing II and a ptychography iterative algorithm. Different from previous ptychography iterative-type algorithms that work only for diffractive objects using coherence light sources, our method obtains the objects spatial spectrum from the second-order correlation of intensity fluctuation by using an incoherent source, which therefore largely simplifies the imaging process. Furthermore, by introducing loose supports in the ptychography algorithm, a high-quality image can be recovered without knowing the precise size and position of the scanning illumination, which is a strong requirement for traditional ptychography iterative algorithm.
We discuss equivalence conditions on the non-existence of non-trivial meromorphic solution to the Fermat Diophantine equations $f^m(z)+g^n(z)=1$ with integers $m,n\geq2$, from which other approaches to prove little Picard theorem are provided.
We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{αz+β}$ and $f^n(z)+f^n(z+c)=e^{αz+β}$ ($c\neq0$) over the complex plane $\mathbf{C}$ for integers $n\geq1$.
In this paper, a non-integrated defect relation for meromorphic maps from complete Kähler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on $k$, $\dim_{\,\mathbb{C}}(V)$ and the degrees of the hypersurfaces considered. In addition, this defect relation recovers Hirotaka Fujimoto [Theorem 1.1; MR0884636 (88m:32049); Japan. J. Math. (N.S.) 11 (1985), no. 2, 233-264.] when subjected to the same conditions.
Worker selection is a key issue in Mobile Crowd Sensing (MCS). While previous worker selection approaches mainly focus on selecting a proper subset of workers for a single MCS task, multi-task-oriented worker selection is essential and useful for the efficiency of large-scale MCS platforms. This paper proposes ActiveCrowd, a worker selection framework for multi-task MCS environments.
We study the intervalley scattering in defected graphene by low-temperature transport measurements. The scattering rate is strongly suppressed when defects are charged. This finding highlights "screening" of the short-range part of a potential by the long-range part. Experiments on calcium-adsorbed graphene confirm the role of a long-range Coulomb potential. This effect is applicable to other multivalley systems, provided that the charge state of a defect can be electrically tuned. Our result provides a means to electrically control valley relaxation and has important implications in valley dynamics in valleytronic materials.
Enhancement of the spin-orbit coupling in graphene may lead to various topological phenomena and also find applications in spintronics. Adatom absorption has been proposed as an effective way to achieve the goal. In particular, great hope has been held for indium in strengthening the spin-orbit coupling and realizing the quantum spin Hall effect. To search for evidence of the spin-orbit coupling in graphene absorbed with indium adatoms, we carry out extensive transport measurements, i.e., weak localization magnetoresistance, quantum Hall effect and non-local spin Hall effect. No signature of the spin-orbit coupling is found. Possible explanations are discussed.
Previous studies of electron-phonon interaction in impure graphene have found that static disorder can give rise to an enhancement of electronic cooling. We investigate the effect of dynamic disorder and observe over an order of magnitude suppression of electronic cooling compared with clean graphene. The effect is stronger in graphene with more vacancies, confirming its vacancy-induced nature. The dependence of the coupling constant on the phonon temperature implies its link to the dynamics of disorder. Our study highlights the effect of disorder on electron-phonon interaction in graphene. In addition, the suppression of electronic cooling holds great promise for improving the performance of graphene-based bolometer and photo-detector devices.
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a transcendental entire function f that shares a non-zero polynomial a with f', together with its linear differential polynomials of the form with rational function coefficients.
We introduce a variant of the capacitated vehicle routing problem that is encountered in sensor networks for scientific data collection. Consider an undirected graph $G=(V \cup \{\mathbf{sink}\},E)$. Each vertex $v \in V$ holds a constant-sized reading normalized to 1 byte that needs to be communicated to the $\mathbf{sink}$. The communication protocol is defined such that readings travel in packets. The packets have a capacity of $k$ bytes. We define a {\em packet hop} to be the communication of a packet from a vertex to its neighbor. Each packet hop drains one unit of energy and therefore, we need to communicate the readings to the $\mathbf{sink}$ with the fewest number of hops. We show this problem to be NP-hard and counter it with a simple distributed $(2-\frac{3}{2k})$-approximation algorithm called {\tt SPT} that uses the shortest path tree rooted at the $\mathbf{sink}$. We also show that {\tt SPT} is absolutely optimal when $G$ is a tree and asymptotically optimal when $G$ is a grid. Furthermore, {\tt SPT} has two nice properties. Firstly, the readings always travel along a shortest path toward the $\mathbf{sink}$, which makes it an appealing solution to the convergecast problem as it fits the natural intuition. Secondly, each node employs a very elementary packing strategy. Given all the readings that enter into the node, it sends out as many fully packed packets as possible followed by at most 1 partial packet. We show that any solution that has either one of the two properties cannot be a $(2-ε)$-approximation, for any fixed $ε> 0$. This makes \spt optimal for the class of algorithms that obey either one of those properties.