On cliques and Lagrangians of hypergraphs

Qingsong Tang,Xiangde Zhang,Cheng Zhao 대한수학회 2019 대한수학회보 Vol.56 No.3

Given a graph $G$, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph $G$ over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

ON CLIQUES AND LAGRANGIANS OF HYPERGRAPHS

Tang, Qingsong,Zhang, Xiangde,Zhao, Cheng Korean Mathematical Society 2019 대한수학회보 Vol.56 No.3

Given a graph G, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph G over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

Homogeneous multilinear functions on hypergraph cliques

Xiaojun Lu,Qingsong Tang,Xiangde Zhang,Cheng Zhao 대한수학회 2017 대한수학회보 Vol.54 No.3

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of $3$-uniform graphs, which supports the conjecture posed in this paper.

HOMOGENEOUS MULTILINEAR FUNCTIONS ON HYPERGRAPH CLIQUES

Lu, Xiaojun,Tang, Qingsong,Zhang, Xiangde,Zhao, Cheng Korean Mathematical Society 2017 대한수학회보 Vol.54 No.3

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

Preparation of Monodisperse Colloidal ZnO Nanoparticles and Their Optical Properties

Chong Yang,Limei Tang,Qingsong Li,Ailing Bai,Yanqiu Wang,Yingmin Yu 성균관대학교(자연과학캠퍼스) 성균나노과학기술원 2015 NANO Vol.10 No.5

Monodisperse colloidal zinc oxide (ZnO) nanospheres with a narrow size distribution were synthesized via a developed two-stage solution method. We controlled the size of the as-synthesized ZnO nanoparticles by varying the amount of ZnO/ethanol suspension added. Dynamic light scattering (DLS) and transmission electron microscopy (TEM) revealed that the diameter of the as-synthesized ZnO nanoparticles was in the range of 60 – 140 nm with a polydispersity index less than 5%. On high-resolution TEM images, we clearly observed that the ZnO nanospheres were actually composed of tiny ZnO subunits, several nanometers in size. Powder X-ray diffraction and TEM-selected area electron diffraction analysis showed that the spheres consisted of polycrystalline nanoparticles. The size of the subunits, which was confirmed by ultraviolet (UV)-visible spectroscopy, increased as the amount of ZnO/ethanol suspension added was decreased. A UV emission at about 374 nm was observed, and this emission of ZnO nanoparticles is found to depend on particle size due to the confinement effect. A red emission at about 651 nm, which has been reported for undoped ZnO, appeared due to the excess oxygen on the particles from O – H or C=O groups. The intensity of the red emission increased as the relative oxygen content increased. The formation mechanism of such ZnO nanospheres was also considered.

Low Chattering Trajectory Tracking Control of Non-singular Fast Terminal Sliding Mode Based on Disturbance Observer

Jiqing Chen,Chaoyang Zhao,Qingsong Tang,Xu Liu,Zhikui Wang,Chengzhi Tan,Jiahua Wu,Teng Long 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.2

The improvement of the performance of the multi-joint manipulator control system is of great significance to improve the level of industrial automation. The existing sliding mode control methods are difficult to ensure the high-precision and fast-tracking of joints of a manipulator to the desired trajectory under low chattering control input. Therefore, a non-singular fast terminal sliding mode control method based on a nonlinear disturbance observer is proposed. In addition, a new non-singular fast terminal sliding mode surface is designed. The performance comparison method of the sliding mode surface proves its better control quality. Aiming at the problem of serious chattering, the nonlinear disturbance observer technology, and saturation function method are introduced to effectively weaken the chattering. Finally, taking the 3-DOF manipulator as the research object, a comparative simulation experiment is carried out in the MATLAB / Simulink environment. The results show that under the uncertainty of modeling error, external disturbance, and joint friction, the designed control method not only solves the problems of singular control input and serious chattering but also realizes the high-precision and fast-tracking of each joint to the desired trajectory. Thus, the effectiveness and feasibility of the design method are verified. The improvement of the performance of the multi-joint manipulator control system is of great significance to improve the level of industrial automation. The existing sliding mode control methods are difficult to ensure the high-precision and fast-tracking of joints of a manipulator to the desired trajectory under low chattering control input. Therefore, a non-singular fast terminal sliding mode control method based on a nonlinear disturbance observer is proposed. In addition, a new non-singular fast terminal sliding mode surface is designed. The performance comparison method of the sliding mode surface proves its better control quality. Aiming at the problem of serious chattering, the nonlinear disturbance observer technology, and saturation function method are introduced to effectively weaken the chattering. Finally, taking the 3-DOF manipulator as the research object, a comparative simulation experiment is carried out in the MATLAB / Simulink environment. The results show that under the uncertainty of modeling error, external disturbance, and joint friction, the designed control method not only solves the problems of singular control input and serious chattering but also realizes the high-precision and fast-tracking of each joint to the desired trajectory. Thus, the effectiveness and feasibility of the design method are verified.

Environment-dependent Broadband Perfect Absorption of Metal-insulator-metal Metamaterial Systems

Feng Li,Yulong Tang,Qingsong Peng,Guosheng Hu 한국광학회 2023 Current Optics and Photonics Vol.7 No.2

Based on calculations using the macroscopic Maxwell’s equations with mesoscopic boundary conditions, light absorption by a layered metal-insulator-metal (MIM) metamaterial system embedded in three different environments is investigated. Increasing the top metal thickness shifts the broad absorption band to lower dielectric-constant regions and longer wavelengths, for either TM or TE waves. Boosting the dielectric-layer thickness redshifts the broadband absorption to regions of larger dielectric constant. In air, for the dielectric-constant range of 0.86–3.40, the absorption of the system exceeds 98% across680–1,033 nm. In seawater with optimized dielectric constant, ≥94% light absorption over 400–1,200nm can be achieved; particularly in the wavelength range of 480–960 nm and dielectric-constant range of 0.82–3.50, the absorption is greater than 98%. In an environment with even higher refractive index(1.74), ≥98% light absorption over 400–1,200 nm can be achieved, giving better performance. Theinfluence of angle of incidence on light absorption of the MIM system is also analyzed, and the angle tolerance for ≥90% broadband absorption of a TM wave is up to 40° in an environment with large re-fractive index. While the incident-angle dependence of the absorption of a TE wave is nearly the same for different circumstances, the situation is different for a TM wave.

An Improved Energy Recovery Clamp Circuit for PWM Converters with a Wide Range of Input Voltage

Honnyong Cha,Lihua Chen,Fang Z. Peng,Qingsong Tang 전력전자학회 2007 ICPE(ISPE)논문집 Vol.- No.-

A full-bridge dc-dc converter employing diode rectifier in the output experiences severe voltage overshoot and oscillation problem across the diode rectifier caused by the interaction between the junction capacitance of the rectifier diode and the leakage inductance of transformer. The pronounced reverse-recovery current of high power diodes enforces these issues significantly by increasing power loss and voltage overshoot. Conventional energy recovery clamping circuits suffer from high voltage overshoot if the input voltage of converter is wide. In this work, a novel energy recovery clamp circuit is proposed to overcome this problem. Performance of the proposed circuit is verified both theoretically and experimentally with a 70 ㎾ dc-dc converter.

Tourism Planning Platform Based on Big Data

李林(Li Lin),汪资,蕾,(Wang Zilei),黄,政霖(Huang Zhenglin),高雅(GaoYa),唐榕(Tang Rong),李青,嵩(Li Qingsong) 아시아사회과학학회 2021 International Science Research Vol.1 No.1

Due to the rapid development of economy, tourism has become a hot activity at present, and tourism planning has become an important planning. However, ordinary travel plans can no longer meet people s needs, and the travel plan platform based on big data can recommend travel routes and travel plans that users are interested in according to users browsing and their own relevant information, so as to reduce users travel troubles.

3.2-kW 9.7-GHz Polarization-maintaining Narrow-linewidth All-fiber Amplifier

Hang Liu,Yujun Feng,Xiaobo Yang,Yao Wang,Hongming Yu,Jue Wang,Wanjing Peng,Yanshan Wang,Yinhong Sun,Yi Ma,Qingsong Gao,Chun Tang 한국광학회 2024 Current Optics and Photonics Vol.8 No.1

We present a Yb-doped narrow-linewidth polarization-maintaining (PM) all-fiber amplifier that achieves a high mode-instability (MI) threshold, high output power, and 9.7-GHz spectral linewidth. Six wavelength-multiplexed laser diodes are used to pump this amplifier. First, we construct a high-power fiber amplifier based on a master oscillator-power amplifier (MOPA) configuration for experiments. Subsequently, we examine the MI threshold by individually pumping the amplifier with wavelengths of 976, 974, 981, 974, and 981 nm respectively. The experimental results demonstrate that the amplifier exhibits a high MI threshold (>3.5 kW) when pumped with a combination of wavelengths at 974 and 981 nm. Afterward, we inject an optimized phase-modulated seed with a nearly flat-top spectrum into this amplifier. Ultimately, laser output of 3.2 kW and 9.7 GHz are obtained.