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Initial successive coefficients for certain classes of univalent functions involving the exponential function

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arXiv 2020年

作者： SHI, LEI WANG, ZHI-GANG SU, REN-LI ARIF, MUHAMMAD School of Mathematics and Statistics Anyang Normal University Anyang Henan455002 China School of Mathematics and Computing Science Hunan First Normal University Changsha Hunan410205 China School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha Hunan410114 China Department of Mathematics Abdul Wali Khan University Mardan23200 Pakistan

关键词： Exponential functions

Exploring Lorentz Invariance Violation from Ultrahigh-Energy γ Rays Observed by LHAASO

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Physical Review Letters 2022年第5期128卷 051102-051102页

作者： Zhen Cao F. Aharonian Q. An Axikegu L. X. Bai Y. X. Bai Y. W. Bao D. Bastieri X. J. Bi Y. J. Bi H. Cai J. T. Cai Zhe Cao J. Chang J. F. Chang B. M. Chen E. S. Chen J. Chen Liang Chen Long Chen M. J. Chen M. L. Chen Q. H. Chen S. H. Chen S. Z. Chen T. L. Chen X. L. Chen Y. Chen N. Cheng Y. D. Cheng S. W. Cui X. H. Cui Y. D. Cui B. D’Ettorre Piazzoli B. Z. Dai H. L. Dai Z. G. Dai Danzengluobu D. della Volpe X. J. Dong K. K. Duan J. H. Fan Y. Z. Fan Z. X. Fan J. Fang K. Fang C. F. Feng L. Feng S. H. Feng Y. L. Feng B. Gao C. D. Gao L. Q. Gao Q. Gao W. Gao M. M. Ge L. S. Geng G. H. Gong Q. B. Gou M. H. Gu F. L. Guo J. G. Guo X. L. Guo Y. Q. Guo Y. Y. Guo Y. A. Han H. H. He H. N. He J. C. He S. L. He X. B. He Y. He M. Heller Y. K. Hor C. Hou X. Hou H. B. Hu S. Hu S. C. Hu X. J. Hu D. H. Huang Q. L. Huang W. H. Huang X. T. Huang X. Y. Huang Z. C. Huang F. Ji X. L. Ji H. Y. Jia K. Jiang Z. J. Jiang C. Jin T. Ke D. Kuleshov K. Levochkin B. B. Li Cheng Li Cong Li F. Li H. B. Li H. C. Li H. Y. Li Jian Li Jie Li K. Li W. L. Li X. R. Li Xin Li Y. Li Y. Z. Li Zhe Li Zhuo Li E. W. Liang Y. F. Liang S. J. Lin B. Liu C. Liu D. Liu H. Liu H. D. Liu J. Liu J. L. Liu J. S. Liu J. Y. Liu M. Y. Liu R. Y. Liu S. M. Liu W. Liu Y. Liu Y. N. Liu Z. X. Liu W. J. Long R. Lu H. K. Lv B. Q. Ma L. L. Ma X. H. Ma J. R. Mao A. Masood Z. Min W. Mitthumsiri T. Montaruli Y. C. Nan B. Y. Pang P. Pattarakijwanich Z. Y. Pei M. Y. Qi Y. Q. Qi B. Q. Qiao J. J. Qin D. Ruffolo V. Rulev A. Sáiz L. Shao O. Shchegolev X. D. Sheng J. R. Shi H. C. Song Yu. V. Stenkin V. Stepanov Y. Su Q. N. Sun X. N. Sun Z. B. Sun P. H. T. Tam Z. B. Tang W. W. Tian B. D. Wang C. Wang H. Wang H. G. Wang J. C. Wang J. S. Wang L. P. Wang L. Y. Wang R. N. Wang W. Wang X. G. Wang X. J. Wang X. Y. Wang Y. Wang Y. D. Wang Y. J. Wang Y. P. Wang Z. H. Wang Z. X. Wang Zhen Wang Zheng Wang D. M. Wei J. J. Wei Y. J. Wei T. Wen C. Y. Wu H. R. Wu S. Wu W. X. Wu X. F. Wu S. Q. Xi J. Xia J. J. Xia G. M. Xiang D. X. Xiao G. Xiao H. B. Xiao G. G. Xin Y. L. Xin Y. Xing D. L. Xu R. X. Xu L. Xue Key Laboratory of Particle Astrophysics and Experimental Physics Division and Computing Center Institute of High Energy Physics Chinese Academy of Sciences 100049 Beijing China University of Chinese Academy of Sciences 100049 Beijing China TIANFU Cosmic Ray Research Center Chengdu 610000 Sichuan China Dublin Institute for Advanced Studies 31 Fitzwilliam Place 2 Dublin Ireland Max-Planck-Institut for Nuclear Physics P.O. Box 103980 69029 Heidelberg Germany State Key Laboratory of Particle Detection and Electronics 100049 Beijing China University of Science and Technology of China 230026 Hefei Anhui China School of Physical Science and Technology and School of Information Science and Technology Southwest Jiaotong University 610031 Chengdu Sichuan China College of Physics Sichuan University 610065 Chengdu Sichuan China School of Astronomy and Space Science Nanjing University 210023 Nanjing Jiangsu China Center for Astrophysics Guangzhou University 510006 Guangzhou Guangdong China School of Physics and Technology Wuhan University 430072 Wuhan Hubei China Key Laboratory of Dark Matter and Space Astronomy Purple Mountain Observatory Chinese Academy of Sciences 210023 Nanjing Jiangsu China Hebei Normal University 050024 Shijiazhuang Hebei China Key Laboratory for Research in Galaxies and Cosmology Shanghai Astronomical Observatory Chinese Academy of Sciences 200030 Shanghai China Key Laboratory of Cosmic Rays (Tibet University) Ministry of Education 850000 Lhasa Tibet China National Astronomical Observatories Chinese Academy of Sciences 100101 Beijing China School of Physics and Astronomy and School of Physics (Guangzhou) Sun Yat-sen University 519000 Zhuhai Guangdong China Dipartimento di Fisica dell’Università di Napoli “Federico II ” Complesso Universitario di Monte Sant’Angelo via Cinthia 80126 Napoli Italy School of Physics and Astronomy Yunnan University 650091 Kunming Yunnan China Département de Physique Nucléaire et Corpusculaire Faculté de S

Recently, the LHAASO Collaboration published the detection of 12 ultrahigh-energy γ-ray sources above 100 TeV, with the highest energy photon reaching 1.4 PeV. The first detection of PeV γ rays from astrophysical sources may provide a very sensitive probe of the effect of the Lorentz invariance violation (LIV), which results in decay of high-energy γ rays in the superluminal scenario and hence a sharp cutoff of the energy spectrum. Two highest energy sources are studied in this work. No signature of the existence of the LIV is found in their energy spectra, and the lower limits on the LIV energy scale are derived. Our results show that the first-order LIV energy scale should be higher than about 105 times the Planck scale MPl and that the second-order LIV scale is >10−3MPl. Both limits improve by at least one order of magnitude the previous results.

关键词： Cosmic rays & astroparticles Gamma ray astronomy Lorentz symmetry

Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems

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Communications in Computational Physics 2018年第6期24卷 86-103页

作者： Dongfang Li Hong-Lin Liao Weiwei Sun Jilu Wang Jiwei Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics City University of Hong KongKowloonHong Kong Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing211106China Department of Scientific Computing Florida StateUniversityTallahasseeFL 32306USA Beijing Computational Science Research Center Beijing 100094China.

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element *** analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type *** this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional *** terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear *** theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.

关键词： Time-fractional nonlinear parabolic problems L1-Galerkin FEMs Error estimates discrete fractional Gronwall type inequality Linearized schemes

General propagation lattice Boltzmann model for nonlinear advection-diffusion equations

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Physical Review E 2018年第4期97卷 043310-043310页

作者： Xiuya Guo Baochang Shi Zhenhua Chai School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, a general propagation lattice Boltzmann model is proposed for nonlinear advection-diffusion equations (NADEs), and the Chapman-Enskog analysis shows that the NADEs with variable coefficients can be recovered correctly from the present model. We also perform some simulations of the linear advection-diffusion equation, nonlinear heat conduction equation, NADEs with anisotropic diffusion, and variable coefficients to test the present model, and find that the numerical results agree well with the corresponding analytical solutions. Moreover, it is also shown that by properly adjusting the two free parameters introduced into the propagation step, the present model could be more stable and more accurate than the standard lattice Bhatnagar-Gross-Krook model.

关键词： Lattice-Boltzmann methods

Phase retrieval for sub-Gaussian measurements

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arXiv 2019年

作者： Gao, Bing Liu, Haixia Wang, Yang School of Mathematical Sciences Nankai University Tianjin300071 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function. Computationally the phase retrieval problem is very challenging. Many algorithms for phase retrieval are based on i.i.d. Gaussian random measurements. However, Gaussian random measurements remain one of the very few classes of measurements. In this paper, we develop an efficient phase retrieval algorithm for sub-gaussian random frames. We provide a general condition for measurements and develop a modified spectral initialization. In the algorithm, we first obtain a good approximation of the solution through the initialization, and from there we use Wirtinger Flow to solve for the solution. We prove that the algorithm converges to the global minimizer linearly. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

Shielding collaborative learning: Mitigating poisoning attacks through client-side detection

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arXiv 2019年

作者： Zhao, Lingchen Hu, Shengshan Wang, Qian Jiang, Jianlin Shen, Chao Luo, Xiangyang School of Cyber Science and Engineering Wuhan University Wuhan Hubei430072 China School of Computer Science Wuhan University Wuhan Hubei430072 China School of Cyberspace Security Xian Jiaotong University Xi’an Shaanxi710049 China State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou Henan450002 China

Collaborative learning allows multiple clients to train a joint model without sharing their data with each other. Each client performs training locally and then submits the model updates to a central server for aggregation. Since the server has no visibility into the process of generating the updates, collaborative learning is vulnerable to poisoning attacks where a malicious client can generate a poisoned update to introduce backdoor functionality to the joint model. The existing solutions for detecting poisoned updates, however, fail to defend against the recently proposed attacks, especially in the non-IID setting. In this paper, we present a novel defense scheme to detect anomalous updates in both IID and non-IID settings. Our key idea is to realize client-side cross-validation, where each update is evaluated over other clients’ local data. The server will adjust the weights of the updates based on the evaluation results when performing aggregation. To adapt to the unbalanced distribution of data in the non-IID setting, a dynamic client allocation mechanism is designed to assign detection tasks to the most suitable clients. During the detection process, we also protect the client-level privacy to prevent malicious clients from stealing the training data of other clients, by integrating differential privacy with our design without degrading the detection performance. Our experimental evaluations on two real-world datasets show that our scheme is significantly robust to two representative poisoning attacks. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep learning

A NEW PHYSICS-PRESERVING IMPES SCHEME FOR INCOMPRESSIBLE AND IMMISCIBLE TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA

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arXiv 2019年

作者： Chen, Huangxin Shuyu, S.U.N. School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling High Performance Scientific Computing Xiamen University Fujian361005 China Computational Transport Phenomena Laboratory Division of Physical Science Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this work we consider a new efficient IMplicit Pressure Explicit Saturation (IMPES) scheme for the simulation of incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure. Compared with the conventional IMPES schemes, the new IMPES scheme is inherently physics-preserving, namely, the new algorithm is locally mass conservative for both phases and it also enjoys another appealing feature that the total velocity is continuous in the normal direction. Moreover, the new scheme is unbiased with regard to the two phases and the saturations of both phases are bounds-preserving if the time step size is smaller than a certain value. The key ideas in the new scheme include that the Darcy flows for both phases are rewritten in the formulation based on the total velocity and an auxiliary velocity referring to as the capillary potential gradient, and the total discretized conservation equation is obtained by the summation of the discretized conservation equation for each phase. The upwind strategy is applied to update the saturations explicitly, and the upwind mixed finite element methods are used to solve the pressure-velocity systems which can be decoupled. We also present some interesting examples to demonstrate the efficiency and robustness of the new algorithm. Copyright © 2019, The Authors. All rights reserved.

关键词： Capillarity

Ergodic optimization theory for a class of typical maps

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arXiv 2019年

作者： Huang, Wen Lian, Zeng Ma, Xiao Xu, Leiye Zhang, Yiwei Wu Wen-Tsun Key Laboratory of Mathematics USTC Chinese Academy of Sciences Department of Mathematics University of Science and Technology of China Hefei Anhui China College of Mathematical Sciences Sichuan University Chengdu Sichuan610016 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems T: X → X where X is a compact metric space and T is Lipschitz continuous. We show that once T: X → X satisfies both the Anosov shadowing property (ASP) and the Mañé-Conze-Guivarc'h-Bousch property (MCGBP), the minimizing measures of generic Hölder observables are unique and supported on a periodic orbit. Moreover, if T: X → X is a subsystem of a dynamical system f: M → M (i.e. X ⊂ M and f|X= T ) where M is a compact smooth manifold, the above conclusion holds for C1observables. Note that a broad class of classical dynamical systems satisfies both ASP and MCGBP, which includes Axiom A attractors, Anosov diffeomorphisms and uniformly expanding maps. Therefore, the open problem proposed by Yuan and Hunt in [YH] for C1-observables is solved consequentially. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamical systems

Designing and Training of A Dual CNN for Image Denoising

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arXiv 2020年

作者： Zuo, Wangmeng Zhang, David Lin, Chia-Wen Xu, Yong Tian, Chunwei Du, Bo Bio-Computing Research Center Harbin Institute of Technology Shenzhen China Shenzhen Key Laboratory of Visual Object Detection and Recognition ShenzhenGuangdong518055 China Peng Cheng Laboratory Shenzhen518055 China School of Computer Science and Technology Harbin Institute of Technology 150001 HarbinHeilongjiang China Peng Cheng Laboratory Shenzhen518055 China School of Computer Science Wuhan University 430072 WuhanHubei China Department of Electrical Engineering Institute of Communications Engineering National Tsing Hua University Hsinchu Taiwan 518172 ShenzhenGuangdong China Shenzhen Institute of Artificial Intelligence and Robotics for Society Shenzhen China

Deep convolutional neural networks (CNNs) for image denoising have recently attracted increasing research interest. However, plain networks cannot recover fine details for a complex task, such as real noisy images. In this paper, we propose a Dual denoising Network (DudeNet) to recover a clean image. Specifically, DudeNet consists of four modules: a feature extraction block, an enhancement block, a compression block, and a reconstruction block. The feature extraction block with a sparse mechanism extracts global and local features via two sub-networks. The enhancement block gathers and fuses the global and local features to provide complementary information for the latter network. The compression block refines the extracted information and compresses the network. Finally, the reconstruction block is utilized to reconstruct a denoised image. The DudeNet has the following advantages: (1) The dual networks with a parse mechanism can extract complementary features to enhance the generalized ability of denoiser. (2) Fusing global and local features can extract salient features to recover fine details for complex noisy images. (3) A Small-size filter is used to reduce the complexity of denoiser. Extensive experiments demonstrate the superiority of DudeNet over existing current state-of-the-art denoising methods. Copyright © 2020, The Authors. All rights reserved.

关键词： Recovery