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SOLVING SYSTEMS OF PHASELESS EQUATIONS VIA RIEMANNIAN OPTIMIZATION WITH OPTIMAL SAMPLING COMPLEXITY

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Journal of Computational Mathematics 2024年第3期42卷 755-783页

作者： Jianfeng Cai ke Wei Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong SARChina School of Data Science Fudan UniversityShanghaiChina

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=*** algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite *** recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of *** key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear *** evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.

关键词： Phaseless equations Riemannian gradient descent Manifold of rank-1 and positive semidefinite matrices Optimal sampling complexity

Theoretical optimization of micropillar arrays for structurally stable bioinspired dry adhesives

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 124-129页

作者： ke Ni Zhengzhi Wang Department of Engineering Mechanics School of Civil EngineeringWuhan UniversityWuhan 430072China Wuhan University Shenzhen Research Institute Shenzhen 518108China

Inspired by the excellent adhesion performances of setae structure from organisms,micro/nano-pillar array has become one of the paradigms for adhesive *** micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for *** stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays,yet the design for the stability of the micropillar array lacks systematical and quantitative *** this work,we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical *** predictions for the stress within the singularity field can be obtained based on the full expressions of the *** good agreement between the predictions and the FEM results demonstrates the high reliability of our *** adopting the strain energy density factor approach,the stability of the pillar-substrate corner is assessed by predicting the failure at the *** the elastic mismatch between the pillar and substrate given in this paper,the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the *** study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.

关键词： Micropillar array Stability Bi-material corner Dry adhesive

Mapping super-resolution image quality

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Light(Science & Applications) 2024年第2期13卷 178-180页

作者： Megan A.Steves ke Xu Department of Chemistry University of CaliforniaBerkeleyCA94720USA

The local quality of super-resolution microscopy images can be assessed and mapped by rolling Fourier ring correlation,even when image quality varies within a single image.

关键词： image resolution Mapping

A risk assessment method considering risk attributes and work safety informational needs and its application

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Chinese Journal of Chemical Engineering 2024年第4期68卷 253-262页

作者： Cong Luo Yunsheng Zhao ke Xu School of Political Science and Public Administration Shandong UniversityQingdao 266200China Faculty of Engineering China University of GeosciencesWuhan 430074China Department of Emergency Management of Hubei Province Wuhan 430064China

The technological revolution has spawned a new generation of industrial systems,but it has also put forward higher requirements for safety management accuracy,timeliness,and *** assessment needs to evolve to address the existing and future challenges by considering the new demands and advancements in safety *** study aims to propose a systematic and comprehensive risk assessment method to meet the needs of process system safety *** methodology first incorporates possibility,severity,and dynamicity(PSD)to structure the“51X”evaluation indicator system,including the inherent,management,and disturbance risk ***,the four-tier(risk point-unit-enterprise-region)risk assessment(RA)mathematical model has been established to consider supervision *** in conclusion,the application of the PSD-RA method in ammonia refrigeration workshop cases and safety risk monitoring systems is presented to illustrate the feasibility and effectiveness of the proposed PSD-RA method in safety *** findings show that the PSD-RA method can be well integrated with the needs of safety work informatization,which is also helpful for implementing the enterprise's safety work responsibility and the government's safety supervision responsibility.

关键词： Risk assessment Safey “51X”evaluation indicator system Four-tier risk assessment model Risk attributes Process system

Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

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Applied Mathematics and Mechanics(English Edition) 2024年第4期45卷 619-632页

作者： Xin FENG Liaoliang ke Yang GAO College of Science China Agricultural UniversityBeijing 100083China School of Mechanical Engineering Tianjin UniversityTianjin 300350China

The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are *** electro-elastic model is developed to investigate the anti-plane strain problem of Love wave *** introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated *** the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary *** examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.

关键词： piezoelectric quasicrystal(PQC)material multilayered plate dispersion characteristic surface effect

Review on Security Defense Technology Research in Edge Computing Environment

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Chinese Journal of Electronics 2024年第1期33卷 1-18页

作者： ke SHANG Weizhen HE Shuai ZHANG National Digital Switching System Engineering and Technological R&D Center

Edge computing, which achieves quick data processing by sinking data computing and storage to the network edge, has grown rapidly along with the Internet of things. The new network architecture of edge computing brings new security challenges. Based on this, this paper investigates the edge computing security literature published in recent years and summarizes and analyzes research work on edge computing security from different attack surfaces. We start with the definition and architecture of edge computing. From the attack surface between device and edge server, as well as on edge servers, the research describes the security threats and defense methods of edge computing. In addition, the cause of the attack and the pros and cons of defense methods is introduced. The challenges and future research directions of edge computing are given.

关键词： Cloud computing Systems architecture Computer architecture Network architecture Data processing Security Servers

Partial Collapsing Degeneration of Floer Trajectories and Adiabatic Gluing

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Acta Mathematica Sinica,English Series 2024年第1期40卷 161-249页

作者： Yong-Geun OH ke ZHU Center for Geometry and Physics Institute for Basic Science(IBS)79 Jigok-ro 127beon-gilNam-guPohang-siGyeongsangbuk-doKorea 37673&POSTECHGyeongsangbuk doKorea Department of Mathematics and Statistics Minnesota State UniversityMankatoMN 56001USA

In the present paper,we study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic ε-family and its reversal adiabatic gluing,as the prototype of the partial collapsing degeneration of 2-dimensional(perturbed)J-holomorphic maps to 1-dimensional gradient *** consider the case when the Floer equations are S^(1)-invariant on parts of their domains whose adiabatic limit has positive length as ε→0,which we call thimble-flow-thimble *** main gluing theorem we prove also applies to the case with Lagrangian boundaries such as in the problem of recovering holomorphic disks out of pearly *** particular,our gluing theorem gives rise to a new direct proof of the chain isomorphism property between the Morse-Bott version of Lagrangian intersection Floer complex of L by Fukaya-Oh-Ohta-Ono and the pearly complex of L Lalonde and *** also provides another proof of the present authors’earlier proof of the isomorphism property of the PSS map without involving the target rescaling and the scale-dependent gluing.

关键词： Floer trajectory equation partial collapsing degeneration thimble-flow-thimble moduli space adiabatic gluing exponential decay estimates three-interval method

Strong Edge Coloring of Outerplane Graphs with Independent Crossings

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 467-477页

作者： ke-Jie LI Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi’an 710071China

The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same *** outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end *** is proved that every outerplane graph with independent crossings and maximum degreeΔhas strong chromatic index at most 4Δ-6 if Δ≥4,and at most 8 ifΔ≤*** bounds are sharp.

关键词： outer-1-planar graph IC-planar graph strong edge coloring crossing

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Incidence Coloring of Outer-1-planar Graphs

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 840-848页

作者： Meng-ke QI Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi'an 710071China

A graph is outer-1-planar if it can be drawn in the plane so that all vertices lie on the outer-face and each edge crosses at most one another *** is known that every outer-1-planar graph is a planar *** this paper,we conjecture that every planar graph G has a proper incidence(Δ(G)+2)-coloring and confirm it for outer-1-planar graphs with maximum degree at least 8 or with girth at least ***,we prove that every outer-1-planar graph G has an incidence(Δ(G)+3,2)-coloring,and every outer-1-planar graph G with maximum degree at least 8 or with girth at least 4 has an incidence(Δ(G)+2,2)-coloring.

关键词： incidence coloring outer--planar graph planar graph