arXiv subjects
Publications and source records attributed to Yuan Chang.
In this paper, we obtain the upper bound of the number of zeros of Abelian integral for a class of cubic Hamiltonian systems with nesting period annuli under perturbations of polynomials of degree n. Furthermore, we consider the Hopf and homoclinic bifurcation when a=-1,b=-2,c=1 and n=3, and obtain 18 distributions in which system has at least 3 limit cycles for each case.
The small atomic mass of boron indicates strong electron-phonon coupling, so it may have a brilliant performance in superconductivity. Recently, a new 2D boride sheet with ordered metal vacancies and surface terminals (Mo4/3B2-x) was realized in experiments (Science 2021, 373, 801). Here, the 2D monolayer freestanding Mo4/3B2is evidenced to be thermodynamically stable. Through electronic structure, phonon spectrum and electron-phonon coupling, monolayer Mo4/3B2 is found to be an intrinsic phonon-mediated superconductor. The superconducting transition temperature (Tc) is determined to be 4.06 K by the McMillian-Allen-Dynes formula. Remarkably, the Tc of monolayer Mo4/3B2 can be increased to 6.78 K with an appropriate biaxial tensile strain (+5%). Moreover, we predict that other transition metal replacing Mo atoms is also stable and retaining the superconductivity. Such as monolayer W4/3B2 is also a superconductor with the Tc of 2.37 K. Our research results enrich the database of 2D monolayer superconductors and boron-related formed materials science.
Facing with grave climate change and enormous energy demand, catalyzer gets more and more important due to its significant effect on reducing fossil fuels consumption. Hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) by water splitting are feasible ways to produce clean sustainable energy. Here we systematically explored atomic structures and related STM images of Se defects in PtSe2. The equilibrium fractions of vacancies under variable conditions were detailly predicted. Besides, we found the vacancies are highly kinetic stable, without recovering or aggregation. The Se vacancies in PtSe2 can dramatically enhance the HER performance, comparing with, even better than Pt(111). Beyond, we firstly revealed that PtSe2 monolayer with Se vacancies is also a good OER catalyst. The excellent bipolar catalysis of Se vacancies were further confirmed by experimental measurements. We produced defective PtSe2 by direct selenization of Pt foil at 773 K using a CVD process. Then we observed the HER and OER performance of defective PtSe2 is much highly efficient than Pt foils by a series of measurements. Our work with compelling theoretical and experimental studies indicates PtSe2 with Se defects is an ideal bipolar candidate for HER and OER.
Bilayer borophene, very recently synthesized on Ag and Cu, possesses extremely flat large surface and excellent conductivity. Besides, the van der Waals gap of bilayer borophene can be intercalated by metal atoms, thereby tailoring the properties of bilayer borophene. Herein, we propose that sandwiched B/TM/B (TM=Co, Ni, Cu, Pd) could be a new 2D formation by transiton metal atoms intercalated into bilayer borophene network, it is quiet robust with both energetic, structural and thermal stability, and exhibits heat resistance of at least 1300 K. Besides, it is novel platform for electrocatalytic hydrogen evolution reaction (HER). The interecalation metal atom serves as single-atomic catalyst, which acting the nonmetal boron layers. Beyond that, the transtion metal is protected by outside boron layers from being corroded by acidic/alkaline solution. B/Cux/B, B/Pdx/B and B/Alx/B with different metal coverage exhibit defect-independent extremely low HER free energy in the range of -0.162 ~ 0.179 eV, -0.134 ~ 0.183 eV and -0.082 ~ 0.086 eV which are comparable to noble metal Pt. Combining excellent conduction, high structural and thermal stability, low resistance to intercalated behaviour, effortless water splitting process, excellent defect-independent catalytic performance, cheapness and abundance of raw materials, free of corrodation, 2D sandwiched B/TM/B (TM=Co, Ni, Cu, Pd) is believed to promising for electrocatalytic HER applications.
Given a linear equation $\mathcal{E}$, the $k$-color Rado number $R_k(\mathcal{E})$ is the smallest integer $n$ such that every $k$-coloring of $\{1,2,3,\dots,n\}$ contains a monochromatic solution to $\mathcal E$. The degree of regularity of $\mathcal E$, denoted $dor(\mathcal E)$, is the largest value $k$ such that $R_k(\mathcal E)$ is finite. In this article we present new theoretical and computational results about the Rado numbers $R_3(\mathcal{E})$ and the degree of regularity of three-variable equations $\mathcal{E}$. % We use SAT solvers to compute many new values of the three-color Rado numbers $R_3(ax+by+cz = 0)$ for fixed integers $a,b,$ and $c$. We also give a SAT-based method to compute infinite families of these numbers. In particular, we show that the value of $R_3(x-y = (m-2) z)$ is equal to $m^3-m^2-m-1$ for $m\ge 3$. This resolves a conjecture of Myers and implies the conjecture that the generalized Schur numbers $S(m,3) = R_3(x_1+x_2 + \dots x_{m-1} = x_m)$ equal $m^3-m^2-m-1$ for $m\ge 3$. Our SAT solver computations, combined with our new combinatorial results, give improved bounds on $dor(ax+by = cz)$ and exact values for $1\le a,b,c\le 5 $. We also give counterexamples to a conjecture of Golowich.
The 3D pose estimation from a single image is a challenging problem due to depth ambiguity. One type of the previous methods lifts 2D joints, obtained by resorting to external 2D pose detectors, to the 3D space. However, this type of approaches discards the contextual information of images which are strong cues for 3D pose estimation. Meanwhile, some other methods predict the joints directly from monocular images but adopt a 2.5D output representation $P^{2.5D} = (u,v,z^{r}) $ where both $u$ and $v$ are in the image space but $z^{r}$ in root-relative 3D space. Thus, the ground-truth information (e.g., the depth of root joint from the camera) is normally utilized to transform the 2.5D output to the 3D space, which limits the applicability in practice. In this work, we propose a novel end-to-end framework that not only exploits the contextual information but also produces the output directly in the 3D space via cascaded dimension-lifting. Specifically, we decompose the task of lifting pose from 2D image space to 3D spatial space into several sequential sub-tasks, 1) kinematic skeletons \& individual joints estimation in 2D space, 2) root-relative depth estimation, and 3) lifting to the 3D space, each of which employs direct supervisions and contextual image features to guide the learning process. Extensive experiments show that the proposed framework achieves state-of-the-art performance on two widely used 3D human pose datasets (Human3.6M, MuPoTS-3D).
Illumination estimation from a single image is critical in 3D rendering and it has been investigated extensively in the computer vision and computer graphic research community. On the other hand, existing works estimate illumination by either regressing light parameters or generating illumination maps that are often hard to optimize or tend to produce inaccurate predictions. We propose Earth Mover Light (EMLight), an illumination estimation framework that leverages a regression network and a neural projector for accurate illumination estimation. We decompose the illumination map into spherical light distribution, light intensity and the ambient term, and define the illumination estimation as a parameter regression task for the three illumination components. Motivated by the Earth Mover distance, we design a novel spherical mover's loss that guides to regress light distribution parameters accurately by taking advantage of the subtleties of spherical distribution. Under the guidance of the predicted spherical distribution, light intensity and ambient term, the neural projector synthesizes panoramic illumination maps with realistic light frequency. Extensive experiments show that EMLight achieves accurate illumination estimation and the generated relighting in 3D object embedding exhibits superior plausibility and fidelity as compared with state-of-the-art methods.
This paper presents a time-efficient scheme for Mars exploration by the cooperation of multiple drones and a rover. To maximize effective coverage of the Mars surface in the long run, a comprehensive framework has been developed with joint consideration for limited energy, sensor model, communication range and safety radius, which we call TIME-SC2 (TIme-efficient Mars Exploration of Simultaneous Coverage and Charging). First, we propose a multi-drone coverage control algorithm by leveraging emerging deep reinforcement learning and design a novel information map to represent dynamic system states. Second, we propose a near-optimal charging scheduling algorithm to navigate each drone to an individual charging slot, and we have proven that there always exists feasible solutions. The attractiveness of this framework not only resides on its ability to maximize exploration efficiency, but also on its high autonomy that has greatly reduced the non-exploring time. Extensive simulations have been conducted to demonstrate the remarkable performance of TIME-SC2 in terms of time-efficiency, adaptivity and flexibility.
This paper concentrates on the collaborative target tracking control of a pair of tracking vehicles with formation constraints. The proposed controller requires only distance measurements between tracking vehicles and the target. Its novelty lies in two aspects: 1) the elliptic coordinates are used to represent an arbitrary tracking formation without singularity, which can be deduced from inter-agent distances, and 2) the regulation of the tracking vehicle system obeys a binocular coordination principle, which simplifies the design of the control law by leveraging rich physical meanings of elliptic coordinates. The tracking system with the proposed controller is proven to be exponentially convergent when the target is stationary. When the target drifts with a small velocity, the desired tracking formation is achieved within a small margin proportional to the magnitude of the target's drift velocity. Simulation examples are provided to demonstrate the tracking performance of the proposed controller.
Let $K$ denote the contact Lie superalgebra $K(m,n;\underline{t})$ over a field of characteristic $p>3$, which has a finite $\mathbb{Z}$-graded structure. Let $T_K$ be the canonical torus of $K$, which is an abelian subalgebra of $K_{0}$ and operates on $K_{-1}$ by semisimple endomorphisms. Utilizing the weight space decomposition of $K$ with respect to $T_K$, %we show the action of the skew-symmetric super-biderivation on the elements of $T$ and the contact of $K$. %Moreover, we prove that each skew-symmetric super-biderivation of $K$ is inner.
Let $W_{\overline{1}}$ and $H_{\overline{0}}$ denote the odd parts of the general Witt modular Lie superalgebra $W$ and the even parts of the Hamiltonian Lie superalgebra $H$ over a field of characteristic $p>3$, respectively. We give a torus of $H_{\overline{0}}$ and the weight space decomposition of the special subalgebra of $W_{\overline{1}}$ with respect to the torus. By means of the derivations of the weight 0 and three series of outer derivations from $H_{\overline{0}}$ into $W_{\overline{1}}$, the derivations from the even parts of Hamiltonian superalgebra to the odd parts of Witt superalgebra are determined.