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Nuc.ear.ty and Finite-r.p.esentability in the System of c.mp.etely Integr.l Map.ing Sp.c.s

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第5期40卷 1197-1214页

作者： Zhe DONG Ji c.eng TAO Ya Fei ZHAO Dep.r.ment of Mathematic. Zhejiang UniversityHangzhou 310027P.R.China Dep.r.ment of Mathematic. China Jiliang UniversityHangzhou 310018P.R.China Dep.r.ment of Mathematic. Zhejiang International Studies UniversityHangzhou 310023P.R.China

In this p.p.r.we investigate loc.l p.op.r.ies in the system of c.mp.etely integr.l map.ing *** intr.duc. notions of injec.ivity,loc.l r.flexivity,exac.ness,nuc.ear.ty,finite-r.p.esent ability and WEp.in the system of c.mp.etely integr.l map.ing *** we obtain that any finite-dimensional op.r.tor.sp.c. is injec.ive in the system of c.mp.etely integr.l map.ing *** we p.ove that c.is the unique nuc.ear.op.r.tor.sp.c. and the unique exac. op.r.tor.sp.c. in this *** also show that c.is the unique op.r.tor.sp.c. whic. is finitely r.p.esentable in{T_(n)}n∈Nin this *** c.r.llar.es,Kir.hber.’s c.njec.ur. and QWEp.c.njec.ur. in the system of c.mp.etely integr.l map.ing sp.c.s ar. false.

关键词： c.mp.etely integr.l map.ing sp.c. injec.ivity exac.ness nuc.ear.ty finite-r.p.esentability WEp

Homologic.l Tr.nsfer.between Additive c.tegor.es and Higher.Differ.ntial Additive c.tegor.es

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第5期40卷 1325-1344页

作者： Xi TANG Zhao Yong HUANG Sc.ool of Sc.enc. Guilin University of Aerospace TechnologyGuilin 541004P.R.China Dep.r.ment of Mathematic. Nanjing UniversityNanjing 210093P.R.China

Given an additive c.tegor. c.and an integer.n≥*** higher.differ.ntial additive c.tegor. c.nsists of objec.s X in c.equip.ed with an endomor.0}ism ϵ_(X)satisfying ϵ_(X)^(n).Let r.be a,finite-dimensional basic.algebr. over.an algebr.ic.lly c.osed field and T the augmenting func.or.fr.m the c.tegor. of finitely gener.ted left r.modules to that of finitely gener.ted left r.(t^(n))-*** is p.oved that a finitely gener.ted left r.module M isτ-r.gid(r.sp.c.ively,(sup.or.)τ-tilting,almost c.mp.eteτ-tilting)if and only if so is T(M)as a left r.t]/(t^(n))-***,r.isτm-selfinjec.ive if and only if so is r.t]/(t^(n)).

关键词： Higher.differ.ntial objec.s Wakamatsu tilting subc.tegor.es G_(ω)-p.ojec.ive modules sup.p.r.τ-tilting modules τ_(m)-selfinjec.ive algebr.s p.ec.uster.tilting subc.tegor.es

Gener.c.Existenc. of Infinitely Many Non-c.ntr.c.ible c.osed Geodesic. on c.mp.c. Sp.c. For.s

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第7期40卷 1674-1684页

作者： Hui Liu Yu c.en Wang Sc.ool of Mathematic. and Statistic. Wuhan UniversityWuhan430072P.R.China Sc.ool of Mathematic. Tianjin Normal UniversityTianjin300384P.R.China

Let M=S^(n)/Γand h be a nontr.vial element of finite or.er.p.inπ_(1)(Μ),wher. the integer. n,p.2,Γis a finite abelian gr.up.whic. ac.s fr.ely and isometr.c.lly on the n-sp.er. and ther.for. M is diffeomor.0}ic.to a c.mp.c. sp.c. *** this p.p.r.we p.ove that ther. ar. infinitely many non-c.ntr.c.ible c.osed geodesic. of c.ass[h]on the c.mp.c. sp.c. for. with c.(r.-gener.c.Finsler.metr.c.,wher. 4≤r.∞.The c.nc.usion also holds for.c.0}gener.c.r.emannian metr.c. for.2≤r.∞.The p.oof is based on the r.sonanc. identity of non-c.ntr.c.ible c.osed geodesic. on c.mp.c. sp.c. for.s.

关键词： c.mp.c. sp.c. for.s non-c.ntr.c.ible c.osed geodesic. gener.c.Finsler.metr.c. r.sonanc. identity

Uniqueness on Differ.nc. Op.r.tor. of Mer.mor.0}ic.Func.ions of Infinite Or.er

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第2期40卷 511-527页

作者： Hui LI Ming Liang FANG Xiao YAO Sc.ool of Sc.enc. China University of Mining and TechnologyBeijing 100083P.R.China Institute of Mathematic. Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100190P.R.China Sc.ool of Sc.enc.s Hangzhou Dianzi UniversityHangzhou 310012P.R.China Sc.ool of Mathematic.l sc.enc.s and Lp.c Nankai UniversityTianjin 300071P.R.China

We investigate the uniqueness p.oblems of mer.mor.0}ic.func.ions and their.differ.nc. op.r.tor. by using a new *** is p.oved that if a non-c.nstant mer.mor.0}ic.func.ion f shar.s a non-zer. c.nstant and ∞ c.unting multip.ic.ties with its differ.nc. op.r.tor. Δc.(z) and Δ_(c.^(2)f(z), thenΔc.(z)≡Δ_(c.^(2)f(z).In p.r.ic.lar.we give a differ.nc. analogue of a r.sult of *** method has two distinc. featur.s:(ⅰ) It c.nver.s the r.lations between func.ions into the c.r.esp.nding *** makes it p.ssible to deal with the uniqueness p.oblem by linear.algebr. and c.mbinator.c..(ⅱ) It c.r.umvents the obstac.e of the differ.nc. logar.thmic.der.vative lemma for.mer.mor.0}ic.func.ions of infinite or.er.sinc. this method does not dep.nd on the gr.wth of the ***,the idea in this p.p.r.c.n also be ap.lied to the c.se for.sever.l var.ables.

关键词： Uniqueness mer.mor.0}ic.func.ions differ.nc. op.r.tor. infinite or.er

Homoc.inic.Solutions for.a c.ass of p.r.ur.ed Fr.c.ional Hamiltonian Systems with Subquadr.tic.c.nditions

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第5期40卷 1177-1196页

作者： Ying LUO Fei GUO Yan LIU Sc.ool of Mathematic. Tianjin UniversityTianjin 300354P.R.China Tianjin Key Labor.tor. of Br.in-Insp.r.d Intelligenc. Tec.nology Tianjin300354P.R.China

In this p.p.r.we c.nsider.the following p.r.ur.ed fr.c.ional Hamiltonian systems{tD_(∞)^(α)(_(-∞)D_(t)^(α)u(t))+L(t)u(t)=■_(u)W(t,u(t))+■(u)G(t,u(t)),t∈r.u∈H^(α)(r.r.(N)),wher.α∈(1/2,1],L∈c.r.r.(N×N))is symmetr.c.and not nec.ssar.ly r.quir.d to be p.sitive definite,W∈c.(r.r.(N,r.)is loc.lly subquadr.tic.and loc.lly even near.the or.gin,and p.r.ur.ed ter. G∈c.(r.r.(N,r.)maybe has no p.r.ty in *** the p.r.ur.ed method imp.oved by the author.,a sequenc. of nontr.vial homo c.inic.solutions is obtained,whic. gener.lizes p.evious r.sults.

关键词： p.r.ur.ed fr.c.ional Hamiltonian systems subquadr.tic.c.ndition p.r.ur.ed method homoc.inic.solutions multip.ic.ty

Gp.-ac.eler.ted Oc. imaging: r.al-time data p.oc.ssing and ar.ifac. sup.r.ssion for.enhanc.d monitor.ng of 3D biop.inted tissues and vasc.lar.like networ.s

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Jour.al of Innovative Op.ic.l Health Sc.enc.s 2024年第6期17卷 67-82页

作者： Shanshan Yang Jinhao Zhou Hao Guo Ling Wang Mingen Xu Hangzhou Dianzi Univer.ity Automation College HangzhouZhejiangP.R.China Zhejiang p.ovinc.al Key Labor.tor. of Medic.l Infor.ation and Biologic.l 3D p.inting Hangzhou ZhejiangP.R.China

Op.ic.l c.her.nc. tomogr.p.y(Oc.)imaging tec.nology has signific.nt advantages in in situ and noninvasive monitor.ng of biologic.l ***,it still fac.s the following c.allenges:inc.uding data p.oc.ssing sp.ed,image quality,and imp.ovements in thr.e-dimensional(3D)visualization *** tec.nology,esp.c.ally func.ional imaging tec.niques like op.ic.l c.her.nc. tomogr.p.y angiogr.p.y(Oc.A),r.quir.s a long ac.uisition time and a lar.e data *** the substantial inc.1}ase in the ac.uisition sp.ed of swep. sour.e op.ic.l c.her.nc. tomogr.p.y(SS-Oc.),it still p.ses signific.nt c.allenges for.data ***,dur.ng in situ ac.uisition,image ar.ifac.s r.sulting fr.m inter.ac. r.flec.ions or.str.ng r.flec.ions fr.m biologic.l tissues and c.ltur.ng c.ntainer. p.esent obstac.es to data visualization and fur.her.***,a c.stomized fr.quenc. domainfilter.with anti-banding sup.r.ssion p.r.meter. was designed to sup.r.ss ar.ifac. ***,this study p.op.sed a gr.p.ic. p.oc.ssing unit(Gp.)-based r.al-time data p.oc.ssing p.p.line for.SS-Oc.,ac.ieving a measur.d line-p.oc.ss r.te of 800 kHz for.3D fast and high-quality data ***,a Gp.-based r.altime data p.oc.ssing for.c.-Oc.A was integr.ted to ac.uir. dynamic.***,a vasc.lar.like networ. c.ip.was p.ep.r.d using extr.sion-based 3D p.inting and sac.1}fic.al mater.als,with sac.1}fic.al mater.al being p.inted at the desir.d vasc.lar.networ. loc.tions and then r.moved to for. the vasc.lar.like *** imaging tec.nology was used to monitor.the p.ogr.ssion of sac.1}fic.al mater.al r.moval and vasc.lar.like networ. ***,Gp.-based Oc. enables r.al-time p.oc.ssing and visualization with ar.ifac. sup.r.ssion,making it p.r.ic.lar.y suitable for.in situ noninvasive longitudinal monitor.ng of 3D biop.inting tissue and vasc.lar.like networ.s in mic.1}fluidic.c.ip..

关键词： SS-Oc. Gp. ac.eler.tion ar.ifac. noise 3D biop.inted mic.0}fluidic.c.ip.

Attr.c.or.for.the Extensible Beam Equation with Nonloc.l Weak Damp.ng on Time–Dep.ndent Sp.c.

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第4期40卷 1115-1126页

作者： c.un Xiang ZHAO Feng Juan MENG Institute of Ap.lied System Analysis Jiangsu UniversityZhenjiang 212013P.R.China Sc.ool of Mathematic. and p.ysic. Jiangsu University of TechnologyChangzhou 213001P.R.China

In this ar.ic.e,we c.nsider.the long-time behavior.of extensible beams with nonloc.l weak damp.ng:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p.(u_(t)))+f(u)=h,wher.ε(t)is a dec.0}asing func.ion vanishing at *** the theor. of p.oc.ss on time-dep.ndent sp.c.s,we investigate the existenc. of the time-dep.ndent attr.c.or.by using the c.ndition(c.(t))method and mor. detailed *** r.sults obtained essentially imp.ove and c.mp.ete some p.evious wor.s.

关键词： Time-dep.ndent attr.c.or extensible beams equation nonloc.l weak damp.ng

Quasi-shadowing for.Z^(d)-ac.ions

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Ac.a Mathematic. Sinic.,English Ser.es 2024年第6期40卷 1563-1580页

作者： Juan p.N Xian Kun r.N Yun Hua ZHOU Sc.ool of Mathematic. and Statistic. Chongqing Technology and Business UniversityChongqing 400067P.R.China c.llege of Mathematic. and Statistic. Chongqing UniversityChongqing 401331P.R.China

A diffeomor.0}ism is non-unifor.ly p.r.ially hyp.r.olic.if it p.eser.es an er.odic.measur. with at least one zer. Lyap.nov *** p.ove that a c.(1)-smooth Z^(d)-ac.ion has the quasishadowing p.op.r.y if one of the gener.... 详细信息

关键词： Quasi-shadowing Z^(d)-ac.ion non-unifor.ly p.r.ially hyp.r.olic er.odic.measur.

Label-fr.e in-vivo c.assi-c.tion and tr.c.ing of r.d blood c.lls and p.atelets using Dynamic.YOLOv4 networ.

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Jour.al of Innovative Op.ic.l Health Sc.enc.s 2024年第5期17卷 89-103页

作者： c.izhong Guan Bin He Hongting Zhang Shangp.n Yang Yang Xu Honglian Xiong Yaguang Zeng Mingyi Wang Xunbin Wei Guangdong-Hong Kong-Mac.o Joint Labor.tor. for.Intelligent Mic.0}-Nano Op.oelec.r.nic.Tec.nology Sc.ool of p.ysic. and Op.oelec.r.nic.Engineer.ng Foshan University Foshan 528225P.R.China Shenzhen Inter.ational Gr.duate Sc.ool Tsinghua University Shenzhen 518055P.R.China The Sec.nd Affliated Hosp.tal of Heilongjiang Univer.ity of c.inese Medic.ne Har.in 150001 P.R.China p.king Univer.ity c.nc.r.Hosp.tal&Institute Beijing 100142 P.R.China Biomedic.l Engineer.ng Dep.r.ment Peking University Beijing 100081P.R.China Institute of Medic.l Tec.nology Peking University Health Science Center Beijing 100191P.R.China Inter.ational c.nc.r.Institute Peking University Beijing 100191P.R.China

In-vivo flow c.tometr. is a noninvasive r.al-time diagnostic.tec.nique that fac.litates c.ntinuous monitor.ng of c.lls without p.r.ur.ing their.natur.l biologic.l envir.nment,whic. r.nder. it a valuable tool for.both sc.enti¯c.r.sear.h and c.inic.l ***,the c.nventional ap.r.ac. for.imp.oving c.assi¯c.tion ac.ur.c. often involves labeling c.lls with fluor.sc.nc.,whic. c.n lead to p.tential *** study p.op.ses a label-fr.e in-vivo flow c.tometr. tec.nique,c.lled dynamic.YOLOv4(D-YOLOv4),whic. imp.oves c.assi¯c.tion ac.ur.c. by integr.ting absor.0}ion intensity°uc.uation modulation(AIFM)into YOLOv4 to demodulate the temp.r.l featur.s of moving r.d blood c.lls(r.c.)and *** zebr.¯sh as an exp.r.mental model,the D-YOLOv4 method ac.ieved aver.ge p.ec.sions(Ap.)of 0.90 for.r.c. and 0.64 for.thr.mboc.tes(similar.to p.atelets in mammals),r.sulting in an over.ll Ap.of *** sc.r.s notably sur.0}ss those attained by alter.ative networ. models,ther.by demonstr.ting that the c.mbination of p.ysic.l models with neur.l networ.s p.ovides an innovative ap.r.ac. towar. develop.ng label-fr.e in-vivoflow c.tometr.,whic. holds p.omise for.diver.e in-vivo c.ll c.assi¯c.tion ap.lic.tions.

关键词： Label-fr.e in-vivoflow c.tometr. c.ll c.assi¯c.tion and tr.c.ing D-YOLOv4