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Gorenstein projective modules and Frobenius extensions

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Science China Mathematics 2018年第7期61卷 1175-1186页

作者： wei ren School of Mathematical Sciences Chongqing Normal University School of Mathematical Sciences Fudan University

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extension is either left-Gorenstein or separable(e.g., the integral group ring extension ZZG).Moreover, for the Frobenius extension RA = R[x]/(x^2), we show that: a graded A-module is Gorenstein projective in GrMod(A), if and only if its ungraded A-module is Gorenstein projective, if and only if its underlying R-module is Gorenstein projective. It immediately follows that an R-complex is Gorenstein projective if and only if all its items are Gorenstein projective R-modules.

关键词： Gorenstein projective module Frobenius extension graded module

Mid-infrared optical modulator enabled by photothermal effect

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Light(Science & Applications) 2023年第1期12卷 5-7页

作者： Zhen Wang wei ren Department of Mechanical and Automation Engineering The Chinese University of Hong KongNew TerritoriesHong Kong SARChina

Photothermal effect in a gas-filled hollow-core fiber may result in agile mid-infrared optical modulators for broadband phase modulation and high extinction ratio intensity modulation.

关键词： modulator optical fiber

Black Hole Complementary Principle and Noncommutative Membrane

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Communications in Theoretical Physics 2006年第4X期46卷 679-682页

作者： wei ren Institute of Theoretical Physics the Chinese Academy of Sciences Beijing 100080 China Graduate School of the Chinese Academy of Sciences Beijing 100080 China

In the spirit of black hole complementary principle, we have found the noncommutative membrane of Scharzchild black holes. In this paper we extend our results to Kerr black hole and see the same story. Also we make a ... 详细信息

关键词： noncommutative spacetime quantum gravity stretched horizon

Nanodots of multiferroic oxide material BiFeO_3 from the first principles

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Advances in Manufacturing 2013年第2期1卷 166-175页

作者： wei ren Department of Physics Shanghai University Physics Department and Institute for Nanoscience and Engineering University of ArkansasFayetteville

Multiferroic nanodots can be harnessed to aid the development of the next generation of nonvolatile data storage and multi-functional devices. In this paper, we review the computational aspects of multiferroic nanodot materials and designs that hold promise for the future memory technology. Conception, methodology, and sys- tematical studies are discussed, followed by some up-to-date experimental progress towards the ultimate limits. At the end of this paper, we outline some challenges remaining in multiferroic research, and how the first principles based approach can be employed as an important tool providing critical information to understand the emergent phenomena in multiferroics.

关键词： Multiferroic Nanodot Vortex - Memory

Partial Regularity for the 3D Magneto-hydrodynamics System with Hyper-dissipation

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Acta Mathematica Sinica,English Series 2015年第7期31卷 1097-1112页

作者： wei ren Gang WU Department of Mathematics and Systems Science BeiHang University School of Mathematical Science University of Chinese Academy of Science

We prove that for the 3D MHD equations with hyper-dissipations （-△）^α （ 1 〈 α 〈 5/4） the Hausdorff dimension of singular set at the first blowing up time is at most 5 - 4α, by means of physical and frequency... 详细信息

关键词： 3D MHD system fractal dissipation partial regularity physical and frequency localization Bony's paraproduct decomposition

Finite-size-induced non-Hermitian phase transitions in real space

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Science China(Physics,Mechanics & Astronomy) 2024年第11期67卷 105-111页

作者： Hongfei Wang Biye Xie wei ren Department of Physics International Center for Quantum and Molecular StructuresShanghai UniversityShanghai 200444China School of Science and Engineering The Chinese University of Hong KongShenzhen 518172China

While non-Hermiticity provokes intriguing phenomena without Hermitian counterparts, e.g., the skin effect and the breakdown of bulk-boundary correspondence, attracting extensive attention both in fundamental physics and device engineering, the role of finite sizes therein remains elusive. Here, we propose a class of finite-size-induced non-Hermitian phase transitions, relying upon higher-order topological invariants associated with real-space wave functions. The phase diagrams for general non-Hermitian chiral models are further acquired to demonstrate our topological definition. Such phase transitions are elucidated qualitatively by an effective intercell coupling alteration that depends on finite sizes in respective directions. Besides, we mimic these phenomena by analogizing the circuit Laplacian in finite-size electric circuits with nonreciprocal couplings. The resultant admittance spectra agree with our theoretical predictions. Our findings shed light on the finite-size mechanism of non-Hermitian topological phase transitions and pave the way for applications in switching and sensing.

关键词： non-Hermitian phase transitions finite-size effects higher-order topological invariants

Regularity for minimizing sequences of some variational integrals

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Science China Mathematics 2023年第4期66卷 777-798页

作者： Hongya Gao Yanan Shan wei ren Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei UniversityBaoding 071002China

This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity *** some structural conditions,we derive that the minimizing sequence and the deriv... 详细信息

关键词： regularity minimizing sequence variational integral energy Ekeland variational principle

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Multi-leader multi-follower coordination with cohesion, dispersion, and containment control via proximity graphs

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Science China(Information Sciences) 2017年第11期60卷 109-128页

作者： Fei CHEN wei ren Zongli LIN Department of Automation Xiamen University Department of Electrical and Computer Engineering University of CaliforniaRiverside CA 92521 USA Charles L.Brown Department of Electrical and Computer Engineering University of Virginia

This paper studies the problem of multi-leader multi-follower coordination with proximity-based network topologies. The particular interest is to drive all the followers towards the convex hull formed by the moving leaders while producing cohesion behavior and keeping group dispersion. First, in the case of stationary leaders, we design a gradient-based continuous control algorithm. We show that with this continuous algorithm the control objective can be achieved, and the tracking error bound can be controlled by tuning some control parameters. We apply the continuous control algorithm to the moving leaders case and show that the tracking error bound is related to the velocities of the leaders. However, in this case, the algorithm has one restriction that the velocities of the leaders should depend on neighboring followers’ velocities, which might not be desirable in some scenarios. Therefore, we propose a nonsmooth algorithm for moving leaders which works under the mild assumption of boundedness of leaders’ velocities. Finally, we present numerical examples to show the validity of the proposed algorithms.

关键词： cooperative control multi-agent system containment control cohesion dispersion collision-free movement

RISE: A RelIable and SEcure Scheme for Wireless Machine to Machine Communications

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Tsinghua Science and Technology 2013年第1期18卷 100-107页

作者： wei ren Linchen Yu Liangli Ma Yi ren the Department of Information Security School of Computer Science China University of Geosciences the Department of Computer Science Naval University of Engineering Department of Computer Science "National" Chiao Tung University

Wireless Machine to Machine （M2M） communications enable ubiquitous sensing, controlling, and acting via sensors, actuators, and actors. Reliability and security are of foremost importance in wireless M2M systems. A simple, target distinguishing attack can result in M2M＇s failure. This paper presents a Reliable and SEcure scheme, RISE, which is a package of policies that guarantee the reliability of data （including sensor reports and actuator instructions） and devices （including sensors, actuators, and actors）. The data reliability is improved by four algorithms, ChooseMedian, ChooseMost, ChooseNearest, and Trust-based Enhancement. Report attainability is improved via m repeat-sending and n multiple-reporting algorithms. Device reliability is guaranteed by device-indistinguishability, which comprises data-indistinguishability and behavior-indistinguishability. The security requirements are formally defined, and the security analysis proves the soundness and completeness of the scheme,

关键词： Machine to Machine (M2M) reliability security target distinguishing attack