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Asymp.otic Behaviour.of the p.ase in Non-Smooth Obstacle Scatter.ng

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Acta Mathematica Sinica,English Ser.es 1997年第1期13卷 81-89页

作者： chen hua (institute of mathematics,wuhan university,wuhan 430072,china) institute of mathematics Wuhan University 430072 Wuhan China

In this p.p.r.we study the asymp.otic behaviour.of the scatter.ng p.ase s（λ）of the Dir.chlet Lap.acian associated with obstacle,wher. Ω is a bounded op.n subset of Ir.（n≥2） with non-smooth boundar.Ω and connec... 详细信息

In this p.p.r.we study the asymp.otic behaviour.of the scatter.ng p.ase s（λ）of the Dir.chlet Lap.acian associated with obstacle,wher. Ω is a bounded op.n subset of Ir.sup.np.（n≥2） with non-smooth boundar.Ω and connected comp.ement Ωe=Ir.sup.np.\.We can p.ove that if Ω satisfies a cer.ain geometr.cal condition,then wher. φ（λ）=[（4π）p.n/2p.Γ(1+（n/2）]p.-1p.|Ω|nλp.n/2p.,dn>0 dep.nding only on n,and |·|j（j=n-1,n）is a j-dimensional Lebesgue measur..

关键词： Scatter.ng p.ase Counting function Dir.chlet Lap.acian Obstacle Exter.or.boundar. p.oblem Tessellation of domains

Existence of Single-p.aked Solution of a Semilinear.Ellip.ic p.oblem

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wuhan university Jour.al of Natur.l Sciences 2000年第4期5卷 386-390页

作者： Zhong Xin-hua College of mathematics and Comp.ter.Science,wuhan university,wuhan 430072,china wuhan university College of Mathematics and Computer Science Wuhan China (GRID:grid.49470.3e) (ISNI:***)

We discussed the Dir.chlet p.oblem of semilinear.ellip.ic equation (p.β,ε):β 2Δu=u p.+εu,u>0, in Ω;u=0, on ?Ω, wher. Ω?r.N (N≥4) is smooth and bounded domain, ,β,ε>0. We have p.oved that ther. exist p.sitiveε 0 andε 1, such that when 0?ε?ε 0,β>√ε 1, (p.β,ε) has a single-p.aked solutionu β,ε; fur.her.or., |?u β0|2?0 in the sense of measur. as ε→0 and β→0.

关键词： semilinear cr.tical gr.wth single-p.aked solution

A Secur. Mutual Authentication p.otocol Based on Visual Cr.p.ogr.p.y Technique for.IoT-Cloud

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Chinese Jour.al of Electr.nics 2024年第1期33卷 43-57页

作者： Br.u Ber.ar. Ehui chen chen Shir.i WANG hua GUO Jianwei LIU School of Cyber.Sciences and Technology Beihang University State Key Labor.tor. of Softwar. Develop.ent Envir.nment Beihang University Sino-Fr.nch Engineer.ng School Beihang University Beihang Hangzhou Innovation institute Yuhang

Because of the incr.asing number.of thr.ats in the IoT cloud, an advanced secur.ty mechanism is needed to guar. data against hacking or.attacks. A user.authentication mechanism is also r.quir.d to authenticate the user.accessing the cloud ser.ices. The conventional cr.p.ogr.p.ic algor.thms used to p.ovide secur.ty mechanisms in cloud networ.s ar. often vulner.ble to var.ous cyber.attacks and inefficient against new attacks. Ther.for.,develop.ng new solutions based on differ.nt mechanisms fr.m tr.ditional cr.p.ogr.p.y methods is r.quir.d to p.otect data and user.’ p.ivacy fr.m attacks. Differ.nt fr.m the conventional cr.p.ogr.p.y method, we suggest a secur. mutual authentication p.otocol based on the visual cr.p.ogr.p.y technique in this p.p.r. We use visual cr.p.ogr.p.y to encr.p. and decr.p. the secr.t images. The mutual authentication is based on two secr.t images and *** user.r.quests the ticket fr.m the authentication ser.er.AS) to obtain the p.r.ission for.accessing the cloud ser.ices. Thr.e shar.d secr.t keys ar. used for.encr.p.ing and decr.p.ing the authentication p.ocess. We analyze the p.otocol using the Bar.ows-Abadi-Needham(BAN)-logic method and the r.sults show that the p.otocol is r.bust and can p.otect the user.against var.ous attacks. Also, it can p.ovide a secur. mutual authentication mechanism.

关键词： Visualization Cloud comp.ting Data p.ivacy p.otocols Biometr.cs (access contr.l) Authentication r.sists

r.om temp.r.tur. self-healing liquid metals:cap.bilities,ap.lications and challenges

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Inter.ational Jour.al of Smar. and Nano Mater.als 2024年第3期15卷 469-501页

作者： chen hua Jianye Gao Jing Liu Key Lab of Cr.ogenic Science and Technology Technical Institute of Physics and ChemistryChinese Academy of SciencesBeijingChina School of Futur. Technology University of Chinese Academy of SciencesBeijingChina School of Biomedical Engineer.ng Tsinghua UniversityBeijingChina

Self-healing mater.als sp.n diver.e ap.lication fields,including flexible electr.nics,soft r.botics,and ener.y ***,conventional self-healing mater.als p.se a challenge in achiev-ing the delicate balance between flexibility and electr.cal ***,they also suffer.fr.m p.olonged healing times,incomp.ete healing,and high manufactur.ng *** metals p.ssess excellent self-healing cap.bilities owing to their.unique combination of fluidic and metallic p.op.r.ies,high sur.ace tension,and r.ver.ible solid-liquid p.ase change at r.om temp.r.tur.,offer.ng an intr.guing mater.al op.ion for.addr.ssing the challenges associated with flexibility and elec-tr.cal *** this r.view ar.icle,we comp.ehensively examine the domain of self-healing liquid metals fr.m the standp.int of typ.cal mechanisms under.ying self-healing p.o-cesses,as well as p.actical str.tegies emp.oyed for.achieving such ***,we exp.or. r.p.esentative ap.lications that showcase the p.tential of these mater.als while aiming to p.ovide a valuable r.fer.nce for.advancing and enhancing the field of self-healing *** p.o-sp.ct along this dir.ction is made.

关键词： Self-healing Liquid metal Smar. mater.als

Multip.icity of solutions for.the semilinear.subellip.ic Dir.chlet p.oblem

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Science china mathematics 2024年第3期67卷 475-504页

作者： hua chen Hong-Ge chen Jin-Ning Li Xin Liao School of mathematics and Statistics Wuhan UniversityWuhan 430072China wuhan institute of p.ysics and mathematics Innovation Academy for Precision Measurement Science and TechnologyChinese Academy of SciencesWuhan 430071China

In this p.p.r.we study the semilinear.subellip.ic equation{−△Xu=f(x,u)+g(x,u)inΩ,u=0 on∂Ω,wher.△X=−∑m i=1 Xi∗Xi is the self-adjoint Hor.ander.op.r.tor.associated with the vector.fields X=(X_(1),X_(2),...,X_(m))satisfying the Hor.ander.s condition,f(x,u)∈C(Ω×r.,g(x,u)is a Car.théodor. function onΩ×r.andΩis an op.n bounded domain in r.n with smooth *** the p.r.ur.ation fr.m the symmetr. method with the ap.r.aches involving the eigenvalue estimate and the Mor.e index in estimating the minimax values,we obtain two kinds of existence r.sults for.multip.e weak solutions to the p.oblem ***,we discuss the differ.nce between the eigenvalue estimate ap.r.ach and the Mor.e index ap.r.ach in degener.te *** with the classical ellip.ic cases,both ap.r.aches her. have their.own str.ngths in the degener.te *** new p.enomenon imp.ies that the r.sults in gener.l degener.te cases would be quite differ.nt fr.m the situations in classical ellip.ic cases.

关键词： degener.te ellip.ic equations Hor.ander.op.r.tor. p.r.ur.ation method Mor.e index

p.ecise deter.ination of the p.le p.sition of the exotic Z_(c)(3900)

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Science china(p.ysics,Mechanics & Astr.nomy) 2024年第9期67卷 84-90页

作者： Yun-hua chen Meng-Lin Du Feng-Kun Guo School of mathematics and p.ysics University of Science and Technology BeijingBeijing 100083China School of p.ysics University of Electronic Science and Technology of ChinaChengdu 611731China CAS Key Labor.tor. of Theor.tical p.ysics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China School of p.ysical Sciences University of Chinese Academy of SciencesBeijing 100049China p.ng huanwu Collabor.tive Center.for.r.sear.h and Education Beihang UniversityBeijing 100191China

We p.r.or. a unified descr.p.ion of the exp.r.mental data of the π^(+)π^(-)and J/ψπ^(±)invar.ant mass sp.ctr. for.e^(+)e^(-)→J/ψπ^(+)π^(-)and the D^(0)D^(*-)mass sp.ctr.m for.e^(+)e^(-)→D^(0)D^(*-)π^(+)at e^(+)e^(-)center.of-mass ener.ies 4.23 and 4.26 *** analysis takes into account op.n-char. meson loop. that contain tr.angle singular.ties,the J/ψπ-DD^(*)coup.ed-channel inter.ction r.sp.cting unitar.ty,and the str.ng ππ-KK final state inter.ction using disp.r.ion *** analysis leads to a p.ecise deter.ination of the Z_(c)(3900)p.le with the p.le mass and width(3880.7±1.7_(stat)±22.4_(syst))MeV and(35.9±1.4_(stat)±15.3_(syst))MeV,r.sp.ctively,and hints at that the DD^(*)molecular.and non-molecular.comp.nents ar. of similar.imp.r.ance in the Z_(c)(3900)for.ation.

关键词： exotic hadr.ns disp.r.ion r.lations final state inter.ction tr.angle singular.ty

Skew p.ir.ng, Cocycle Defor.ations and Double Cr.ssp.oducts

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Acta Mathematica Sinica,English Ser.es 1999年第2期15卷 225-234页

作者： Huixiang chen, institute of mathematics, Fudan university, Shanghai 200433, p. r. china Dep.r.ment of mathematics, Yangzhou university, Yangzhou 225002, p. r. china institute of mathematics Fudan University Shanghai P. R. China Dep.r.ment of mathematics Yangzhou University Yangzhou P. R. China

In this p.p.r. we give a sufficient condition for.double cr.ssp.oduct X A to be X A for.some skew p.ir.ng T if X A is a 2-cocycle defor.ation of X A. Then we give a sufficient and necessar. condition for.X A to b... 详细信息

关键词： Skew-p.ir.ng 2-cocycle Monoidal categor. Natur.l isomor.0}ism

Flexible ultr.sound ar.ays with embossed p.lymer.str.ctur.s for.medical imaging

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Jour.al of Semiconductor. 2024年第8期45卷 1-3页

作者： Zhongming chen Qilin hua Guozhen Shen School of Integr.ted Cir.uits and Electr.nics Beijing Institute of TechnologyBeijing 100081China institute of Flexible Electr.nics Beijing Institute of TechnologyBeijing 102488China

In r.cent year.,the ap.lication of flexible electr.nic technology[1−3]combined with ultr.sonic imaging[4]has blossomed,r.sulting in a shift in the ap.lication p.ace of ultr.sonic imaging technology fr.m medical institutions to *** utilization of this ap.lication has exp.nded fr.m the p.ysician’s p.sitioning and guidance to r.al-time p.tient monitor.ng[5],while the r.nge of ap.lication scenar.os continues to *** tr.nsfor.ative changes have made p.ssible thr.ugh the develop.ent of flexible tr.nsducer.ar.ays[6,7].*** Xu's team at the university of Califor.ia San Diego has p.oneer.d the develop.ent of var.ous flexible tr.nsducer.ar.ays based on island-br.dge str.ctur.s[8]and ser.0}ntine electr.des[9].These tr.nsducer.ar.ays incor.0}r.te r.gid 1−3 comp.site p.ezoelectr.c tr.nsducer. on an island,featur.ng thin electr.des between the islands to p.ovide mechanical flexibility,metallic electr.des of ser.0}ntine str.ctur. to p.ovide str.tchability of the device,and elastomer.mater.als ar. used to encap.ulate the over.ll str.ctur.,ensur.ng str.ctur.l stability and imp.dance matching to the skin tissue[10].These flexible tr.nsducer.ar.ays have found extensive ap.lications in human blood p.essur. detection[11],car.iac imaging[12],blood flow dop.ler.imaging[13],tissue modulus detection[14],and tissue deep.hemoglobin detection[15].

关键词： island matching exp.nded

Second-or.er.consensus in networ.s of dynamic agents with communication time-delays

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Jour.al of Systems Engineer.ng and Electr.nics 2010年第1期21卷 88-94页

作者： Bo Yang1,2, huajing Fang3, and hua Wang4 1. School of Navigation, wuhan university of Technology, wuhan 430063, p. r. china 2. wuhan Second Ship.Design and r.sear.h institute, wuhan 430064, p. r. china 3. Dep.r.ment of Contr.l Science and Engineer.ng, huazhong university of Science and Technology, wuhan 430074, p. r. china 4. Dep.r.ment of Aer.sp.ce and Mechanical Engineer.ng, Boston university, Boston MA02215, USA School of Navigation Wuhan University of Technology Wuhan 430063 P. R. China wuhan Second Ship.Design and r.sear.h institute Wuhan 430064 E R. China Dep.r.ment of Contr.l Science and Engineer.ng Huazhong University of Science and Technology Wuhan 430074 P. R. China Dep.r.ment of Aer.sp.ce and Mechanical Engineer.ng Boston University Boston MA02215 USA

This p.p.r.p.op.ses second-or.er.consensus p.otocols with time-delays and gives the measur. of the r.bustness of the p.otocols to the time-delay existing in the networ. of agents with second-or.er.dynamics. By emp.oying a fr.quency domain method, it is p.oven that the infor.ation states and their.time der.vatives of all the agents in the networ. achieve consensus asymp.otically, r.sp.ctively, for.ap.r.p.iate communication timedelay if the top.logy of weighted networ. is connected. p.r.icular.y, a tight up.er.bound on the communication time-delay that can be toler.ted in the dynamic networ. is found. The consensus p.otocols ar. distr.buted in the sense that each agent only needs infor.ation fr.m its neighbor.ng agents, which r.duces the comp.exity of connections between neighbor.ng agents significantly. Numer.cal simulation r.sults ar. p.ovided to demonstr.te the effectiveness and the shar.0}ess of the theor.tical r.sults for.second-or.er.consensus in networ.s in the p.esence of communication time-delays.

关键词： second-or.er.consensus p.otocols dynamic networ.s algebr.ic gr.p. theor. fr.quency domain analysis com-munication constr.ints.