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Dynamic properties of a class of van der Pol-Duffing oscillators

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arXiv 2024年

作者： Kuang, Yelei Li, Xuemei Key Laboratory of High Performance Computing and Stochastic Information Processing Department of Mathematics Hunan Normal University Hunan Changsha410081 China

In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and find that it has two kinds of local bifurcations and a global bifurcation: pitchfork bifurcation, Hopf bifurcation, homoclinic bifurcation. It is worth noting that the disappearance of the homoclinic orbit is synchronized with the emergence of a large limit cycle. Then, by discussing the stability of equilibria at infinity and the orientation of the trajectory, the existence and stability of limit circles of the autonomous system are analyzed by combining the Poincaré-Bendixson theorem and the index theory. The global phase portrait and the numerical simulation of the autonomous system in different parameter values are given. Finally, the existence of periodic and quasi-periodic solutions to periodic forced system is proved by a KAM theorem. © 2024, CC BY.

关键词： Hopf bifurcation

Online Optimization in Power Systems With high Penetration of Renewable Generation:Advances and Prospects

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IEEE/CAA Journal of Automatica Sinica 2023年第4期10卷 839-858页

作者： Zhaojian Wang Wei Wei John Zhen Fu Pang Feng Liu Bo Yang Xinping Guan Shengwei Mei Key Laboratory of System Control and Information Processing Ministry of Education of ChinaDepartment of AutomationShanghai Jiao Tong UniversityShanghai 200240China State Key Laboratory of Power System and the Department of Electrical Engineering Tsinghua UniversityBeijing 100084China Institute of High Performance Computing(IHPC) Agency for Science Technology and Research(A*STAR)Singapore 138632Singapore

Traditionally,offline optimization of power systems is acceptable due to the largely predictable loads and reliable *** increasing penetration of fluctuating renewable generation and internet-of-things devices allowing for fine-grained controllability of loads have led to the diminishing applicability of offline optimization in the power systems domain,and have redirected attention to online optimization ***,online optimization is a broad topic that can be applied in and motivated by different settings,operated on different time scales,and built on different theoretical *** paper reviews the various types of online optimization techniques used in the power systems domain and aims to make clear the distinction between the most common techniques *** particular,we introduce and compare four distinct techniques used covering the breadth of online optimization techniques used in the power systems domain,i.e.,optimization-guided dynamic control,feedback optimization for single-period problems,Lyapunov-based optimization,and online convex optimization techniques for multi-period ***,we recommend some potential future directions for online optimization in the power systems domain.

关键词： optimization Lyapunov optimization online convex optimization online optimization optimization-guided control

RIESZ TYPE THEOREMS FOR κ-PLURIHARMONIC MAPPINGS, INVARIANT HARMONIC QUASIREGULAR MAPPINGS AND HARMONIC QUASIREGULAR MAPPINGS

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arXiv 2023年

作者： Chen, Shaolin Huang, Manzi College of Mathematics and Statistics Hengyang Normal University Hunan Hengyang421002 China Hunan Provincial Key Laboratory of Intelligent Information Processing and Application 421002 China Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics and Statistics Hunan Normal University Hunan Changsha410081 China

The main purpose of this paper is to develop some methods to improve and generalize the main results in a recent paper by Liu and Zhu (Adv. Math., 2023, i.e., [19]). The paper consists of two parts. In the first part, we discuss the Riesz type theorem in the setting of n-dimensional complex spaces for all n ≥ 1. In this part, we first introduce the family of κ-pluriharmonic mappings of the n-dimensional complex unit ball. Then we establish two Riesz type theorems for these mappings, which are the n-dimensional versions of Theorems 1.1 and 1.2 in [19], respectively. Furthermore, even when n = 1, our first result shows that the assumption of the real parts of the mappings not being negative (or being negative) in [19, Theorem 1.1] is redundant;and our second result illustrates that the assumption of "quasiconformality" on the mappings in [19, Theorem 1.2] can be replaced by the weaker one of "quasiregularity". In the second part, we investigate the Riesz type theorem in the setting of n-dimensional real spaces for all n ≥ 2. In this part, first, we prove a Riesz type theorem for invariant harmonic quasiregular mappings of the unit n-dimensional real ball. Our result indicates that (i) the range of the parameter p discussed in [19, Theorem 1.3] can be changed from (1, 2) to (1, ∞);(ii) the assumption of the first coordinate functions of the mappings being non-zero in [19, Theorem 1.3] is redundant. In this way, we complete the discussions carried out in [19, Theorems 1.3 and 1.4]. Second, we obtain a Riesz type theorem for harmonic K-quasiregular mappings of the unit n-dimensional real ball. Our result demonstrates that the range of the parameter p discussed in [15, Theorem 2.1] can be changed from (1, 2) to (1, ∞).MSC Codes 30H10, 30C62 Copyright © 2023, The Authors. All rights reserved.

关键词： Harmonic analysis

A New Method for Evaluating Core Developers In Open Source Software 13

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A New Method for Evaluating Core Developers In Open Source S...

13th IEEE International Conference on Software Engineering and Service Science, ICSESS 2022

作者： Song, Yulin Wang, Tao Shen, Yang Chang, Junsheng National University of Defense Technology National Laboratory for Parallel and Distributed Processing Hunan Province Changsha China National University of Defense Technology Institute for Quantum Information State Key Laboratory of High Performance Computing Hunan Province Changsha China

ISBN: (数字)9781665410328

ISBN: (纸本)9781665410311

The high-quality development of Open Source Software(OSS) benefits from the contributions of developers. An important research question is how to truly assess the extent of contribution of all developers in open source software and effectively identify the core developers to avoid their loss. In this paper, we use the undirected weighted network model to build a Developer Collaboration Network(DCN) based on developers and their contributions to the GitHub community's open source software Rails, analyse the characteristics of developer partnerships through the Developer Collaboration Network, and propose a Developer Personal Impact Factor(DPIF) to evaluate the importance of developer, select the top 10 core developers in Rails, focus on their participation in the open source software process, and predicting the changes of their contributions. The experimental results show that core developers with extensive partnerships are more likely to associate with developers with fewer partnerships. The average degree of developer contribution does not increase with more developers. Developer partnerships are characterized by close localization and loose overall relationships. The Developer Personal Impact Factor identifies the core developers in open source software well. The Developer Personal Impact Factor gives a ranking in which the core team members rank in the top 1.17% on average. © 2022 IEEE.

关键词： Open source software

Distributed Online Generalized Nash Equilibrium Tracking for Prosumer Energy Trading Games

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Distributed Online Generalized Nash Equilibrium Tracking for...

American Control Conference (ACC)

作者： Yongkai Xie Zhaojian Wang John Z.F. Pang Bo Yang Xinping Guan Department of Automation Key Laboratory of System Control and Information Processing Ministry of Education of China Shanghai Jiao Tong University Shanghai China Agency for Science Technology and Research (A*STAR) Institute of High Performance Computing (IHPC) Singapore Republic of Singapore

With the proliferation of distributed generations, traditional passive consumers in distribution networks are evolving into "prosumers", which can both produce and consume energy. Energy trading with the main grid or between prosumers is inevitable if the energy surplus and shortage exist. To this end, this paper investigates the peer-to-peer (P2P) energy trading market, which is formulated as a generalized Nash game. We first prove the existence and uniqueness of the generalized Nash equilibrium (GNE). Then, an distributed online algorithm is proposed to track the GNE in the time-varying environment. Its regret is proved to be bounded by a sublinear function of learning time, which indicates that the online algorithm has an acceptable accuracy in practice. Finally, numerical results with six microgrids validate the performance of the algorithm.

关键词：

dugMatting: Decomposed-Uncertainty-Guided Matting

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arXiv 2023年

作者： Wu, Jiawei Zhang, Changqing Li, Zuoyong Fu, Huazhu Peng, Xi Zhou, Joey Tianyi College of Mechanical and Electrical Engineering Fujian Agriculture and Forestry University Fuzhou China College of Intelligence and Computing Tianjin University Tianjin China Fujian Provincial Key Laboratory of Information Processing and Intelligent Control Minjiang University Fuzhou China Institute of High Performance Computing Agency for Science Technology and Research Singapore College of Computer Science Sichuan University Chengdu China Singapore

Cutting out an object and estimating its opacity mask, known as image matting, is a key task in image and video editing. Due to the highly ill-posed issue, additional inputs, typically user-defined trimaps or scribbles, are usually needed to reduce the uncertainty. Although effective, it is either time consuming or only suitable for experienced users who know where to place the strokes. In this work, we propose a decomposed-uncertainty-guided matting (dugMatting) algorithm, which explores the explicitly decomposed uncertainties to efficiently and effectively improve the results. Basing on the characteristic of these uncertainties, the epistemic uncertainty is reduced in the process of guiding interaction (which introduces prior knowledge), while the aleatoric uncertainty is reduced in modeling data distribution (which introduces statistics for both data and possible noise). The proposed matting framework relieves the requirement for users to determine the interaction areas by using simple and efficient labeling. Extensively quantitative and qualitative results validate that the proposed method significantly improves the original matting algorithms in terms of both efficiency and efficacy. Copyright © 2023, The Authors. All rights reserved.

关键词： Uncertainty analysis

The existence of full dimensional invariant tori for an almost-periodically forced nonlinear beam equation

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arXiv 2020年

作者： Liu, Shujuan Shi, Guanghua Key Laboratory of High Performance Computing and Stochastic Information Processing Department of Mathematics Hunan Normal University ChangshaHunan410083 China

In this paper, we prove the existence of full dimensional invariant tori for a non-autonomous, almost-periodically forced nonlinear beam equation with a periodic boundary condition via KAM theory. Copyright © 202... 详细信息

关键词： Continuum mechanics

A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation Jacobi collocation method convergence

Sketch2Relief: Generating Bas-relief from Sketches with Deep Generative Networks

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Sketch2Relief: Generating Bas-relief from Sketches with Deep...

International Conference on Tools for Artificial Intelligence (ICTAI)

作者： Shizhe Zhou Zeyu Liu Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of China College of Computer Science and Electronic Engineering Hunan University Changsha China

ISBN: (数字)9781728192284

ISBN: (纸本)9781728185361

We present a novel sketch-based system for generating digital bas-relief sculptures. All existing computational methods for generating digital bas-reliefs first require the input of a three-dimensional (3D) scene, thus preventing artists from freely creating or exploring designs when 3D data are not available. Motivated by this limitation, we propose a generative adversarial network (GAN)-based sketch modeling system for generating digital bas-reliefs from freehand user sketches (see Figure 1, 5). The basic tool underpinning the interface is a conditional GAN (cGAN) that digitally learns a functional map from a contour image to a 3D model for any given viewpoint of the corresponding bas-relief model. When using our system for designing bas-reliefs, the user only needs to draw 2D sketch lines without having to designate any additional hints on the lines. The interface returns bas-relief results in interactive time (500 ms per bas-relief on average). We tested the quality and robustness of our approach with extensive and comprehensive experiments. By carefully analyzing the results, we verified that our system can faithfully reconstruct bas-reliefs from a test dataset and can generate completely new reliefs from raw amateur sketches.

关键词： Solid modeling Three-dimensional displays Two dimensional displays Neural networks Tools Generative adversarial networks Robustness