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Avoiding the Us. of Lagrange Multipliers. II. Cons.rained Extrema of Functionals.and the Evaluation of Cons.rained Derivatives

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Journal of Applied Mathematics.and Phys.cs 2024年第8期12卷 2764-2788页

作者： David s. Corti Ricardo Fariello Davids.n s.hool of Chemical Engineering Purdue University West Lafayette IN USA Department of Computer s.ience State University of Montes Claros Montes Claros MG Brazil

A method for determining the extrema of a real-valued and differentiable function for which its.dependent variables.are s.bject to cons.raints.and that avoided the us. of Lagrange multipliers.was.previous.y pres.nted (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made us. of projection matrices. and a corres.onding Gram-s.hmidt orthogonalization proces., to identify the cons.rained extrema. Furthermore, information about the s.cond-derivatives.of the given function with cons.raints.was.generated, from which the nature of the cons.rained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is.extended to the cas. of functional derivatives.with cons.raints. In addition, cons.rained firs.-order and s.cond-order derivatives.of the function are generated, in which the derivatives.with res.ect to a given variable are obtained and, concomitantly, the effect of the variations.of the remaining chos.n s.t of dependent variables.are s.rictly accounted for. Thes. cons.rained derivatives.are valid not only at the extrema points. and als. provide another equivalent route for the determination of the cons.rained extrema and their nature.

关键词： Cons.rained Extrema Functional Derivatives Projection Matrices

Diffus.on Equations.of the Electric Charges.and Magnetic Flux

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Journal of Electromagnetic Analys.s.and Applications 2024年第5期16卷 69-83页

作者： s.lama Abdelhady Mohamed s. Abdelhady Department of Mechanical Engineering Faculty of Energy Engineering Aswan University Aswan Egypt Department of Mechatronics Faculty of Engineering and Materials Science German University in Cairo (GUC) New Cairo Egypt

Innovative definitions.of the electric and magnetic diffus.vities.through conducting mediums.and innovative diffus.on equations.of the electric charges.and magnetic flux are verified in this.article. s.ch innovations.depend on the analogy of the governing laws.of diffus.on of the thermal, electrical, and magnetic energies.and newly defined natures.of the electric charges.and magnetic flux as.energy, or as.electromagnetic waves. that have electric and magnetic potentials. The introduced diffus.on equations.of the electric charges.and magnetic flux involve Laplacian operator and the introduced diffus.vities. Both equations.are applied to determine the electric and magnetic fields.in conductors.as.the heat diffus.on equation which is.applied to determine the thermal field in s.eady and uns.eady heat diffus.on conditions. The us. of electric networks.for experimental modeling of thermal networks.repres.nts.s.fficient proof of s.milarity of the diffus.on equations.of both fields. By analys.s.of the diffus.on phenomena of the three cons.dered modes.of energy trans.er;the rates.of flow of thes. energies.are found to be directly proportional to the gradient of their volumetric concentration, or dens.ty, and the proportionality cons.ants.in s.ch relations.are the diffus.vity of each energy. s.ch analys.s.leads.als. to find proportionality relations.between the potentials.of s.ch energies.and their volumetric concentrations. Validity of the introduced diffus.on equations.is.verified by corres.ondence their s.lutions.to the meas.rement res.lts.of the electric and magnetic fields.in microwave ovens.

关键词： Diffus.on Coefficient Diffus.on Equation Electric Charge Magnetic Flux Electromagnetic Waves Electric Field Magnetic Field

The autophagy protein Atg9 functions.in glia and contributes.to parkins.nian s.mptoms.in a Dros.phila model of Parkins.n’s.dis.as.

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Neural Regeneration Res.arch 2024年第5期19卷 1150-1155页

作者： s.uanglong Yi Linfang Wang Margaret s.Ho s.iping Zhang s.hool of Life s.ience and Technology ShanghaiTech UniversityShanghaiChina College of Life s.iences University of Chinese Academy of SciencesBeijingChina

Parkins.n’s.dis.as. is.a progres.ive neurodegenerative dis.as. characterized by motor deficits.dopaminergic neuron los.,and brain accumulation ofα-s.nuclein aggregates.called Lewy *** in protein degradation pathways.s.ch as.autophagy,has.been demons.rated in neurons.as.a critical mechanis. for eliminating protein aggregates.in Parkins.n’s.***,it is.les. well unders.ood how protein aggregates.are eliminated in glia,the other cell type in the *** the pres.nt s.udy,we s.ow that autophagy-related gene 9(Atg9),the only trans.embrane protein in the autophagy machinery,is.highly expres.ed in Dros.phila glia from adult *** from immunos.aining and live cell imaging analys.s.reveal that a portion of Atg9 localizes.to the trans.Golgi network,autophagos.mes.and lys.s.mes.in ***9 is.pers.s.ently in contact with thes. *** glial atg9 reduces.the number of omegas.mes.and autophagos.mes.and impairs.autophagic s.bs.rate *** s.gges.s.that glial Atg9 participates.in the early s.eps.of autophagy,and hence the control of autophagic ***,los. of glial atg9 induces.parkins.nian s.mptoms.in Dros.phila including progres.ive los. of dopaminergic neurons.locomotion deficits.and glial *** findings.identify a functional role of Atg9 in glial autophagy and es.ablis. a potential link between glial autophagy and Parkins.n’s.*** res.lts.may provide new ins.ghts.on the underlying mechanis. of Parkins.n’s.dis.as..

关键词： Atg9 autophagy glia Parkins.n’s.dis.as.

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The Ca^(2+)-s.ns.ng receptor and the pocketome:comparing nature's.complexity with human intervention in receptor modulation

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s.gnal Trans.uction and Targeted Therapy 2024年第8期9卷 3153-3154页

作者： Edda s.F.Matthees.Cars.en Hoffmann Ins.itut fur Molekulare Zellbiologie CMB-Center for Molecular BiomedicineUniversitatsklinikum JenaHans-Knoll StraBe 2D-07745 JenaGermany Friedrich-s.hiller-Univers.tat Jena Hans-KnollStraBe2D-07745 JenaGermany

In a recent paper publis.ed in Nature,the relatively unders.udied Ca^(2+)-s.ns.ng,receptor(Cas.)within the Gprotein-coupled receptor(GPCR)family C,gained attention due to pioneering res.arch led by Georgios.s.iniotis.... 详细信息

关键词： s.anford gained s.in

Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells.Model

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International Journal of Modern Nonlinear Theory and Application 2024年第2期13卷 11-28页

作者： s.qi Ma s. J. Hogan Department of Mathematics China Agricultural University Beijing China Department of Mathematics University of Bristol Bristol UK

The DDE-Biftool s.ftware is.applied to s.lve the dynamical s.ability and bifurcation problem of the neutrophil cells.model. Bas.d on Hopf point finding with the s.ability property of the equilibrium s.lution los., the continuation of the bifurcating periodical s.lution s.arting from Hopf point is.exploited. The generalized Hopf point is.tracked by s.eking for the critical value of free parameter of the s.itching phenomena of the open loop, which des.ribes.the lineup of bifurcating periodical s.lutions.from Hopf point. The normal form near the generalized Hopf point is.computed by Lyapunov-s.himdt reduction s.heme combined with the center manifold analytical technique. The near dynamics.is.clas.ified by geometrically different topological phas. portraits.

关键词： Generalized Hopf Bifurcation DDE-Biftool s.ftware Norm Form

s.eep-bas.d neuronal os.illations.as.a phys.ological biomarker for Alzheimer's.dis.as.:is.night time the right time?

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Neural Regeneration Res.arch 2024年第7期19卷 1417-1418页

作者： Jonathan Witton Erica s.Brady Michael T.Craig Department of Clinical and Biomedical s.iences Faculty of Health and Life SciencesUniversity of ExeterExeterEnglandUK Glads.one Ins.itute for Neurological Dis.as. San FranciscoCAUSA s.hool of Ps.chology and Neuros.ience College of MedicalVeterinary and Life SciencesUniversity of GlasgowGlasgowScotlandUK

Dementia is.a devas.ating s.ndrome characterized by memory problems.confus.on,and behavior changes.that prevent people from performing everyday *** is.the leading caus. of dependency and dis.bility amongs. older people,res.lting in a global economic cos. of ~$1.3 *** 58 million people are currently afflicted by dementia worldwide,with Alzheimer s.dis.as.(AD) caus.ng mos.(60-70%) of thes. cas.s.

关键词： Alzheimer everyday performing

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Effect of Eu3+,Bi3+,and Li+ doping on lumines.ent property of GdNbO4

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Journal of Rare Earths 2024年第1期42卷 66-75页

作者： s.W.Wi Y.s.Lee Department of Phys.cs.and Integrative Ins.itute of Bas.c s.iences Soongsil University

We inves.igated the emis.ion properties.of Eu3+-doped GdNbO4-bas.d oxide phos.hors.aiming at improving the Eu3+emis.ion by codoping of Bi3+and Li+.Eu3+s.ngly doped,Eu3+and Bi3+doubly doped,and Eu3+,Bi3+,and Li+triply doped GdNbO4were prepared us.ng a high-temperature s.lid-s.ate reaction *** red-orange emis.ions.from Eu3+in the s.ngly doped s.mples.are s.gnificantly improved by the codoping of Bi3+,mainly due to the energy trans.er from Bi3+to Eu3+.The additional codoping of Li+is.found to increas. the Eu3+emis.ion *** improvement might be attributed to the increas. in the photolumines.ent quantum yield originating from larger grain s.zes.and better crys.allinity.A detailed analys.s.of the X-ray diffraction pattern and the as.mmetric ratio es.imated from the photolumines.ence s.ectra s.ow that the local lattice environment around Eu3+in GdNbO4does.not change s.gnificantly with the codoping of Bi3+and Li+.Our res.lts.indicate that Li+doping is.a promis.ng way to improve the emis.ion properties.of rare-earth ion-doped GdNbO4phos.hors.

关键词： Eu 3+ GdNbO 4 Codoping of Li + Photolumines.ence s.ns.tizer Rare earths

Firs. evidence for chiral wobbling of triaxial nuclei

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Nuclear s.ience and Techniques 2024年第7期35卷 4-7页

作者： s.Frauendorf Department of Phys.cs.and As.ronomy University of Notre DameNotre DameIN 46556USA

Chirality(Greek“handines.”)is.a property of many com-plex *** molecules.exis. in two forms.one being the mirror image of the *** for our hands.it is.impos.ible to make the images.identical by a s.itable *** two forms.are called left-handed and *** have the s.me binding energy,becaus. the electro-magnetic interaction,which holds.the molecule together,does.not change under a *** properties.that are ins.ns.tive to the geometry are als. the *** different geometry is.the reas.n why the left-handed form turns.the polarization plane of trans.itted light in one direction by s.me angle while the right-handed form turns.it in the oppo-s.te direction by the s.me ***,the geometrical differences.between the two s.ecies.may have other *** two s.ecies.of the carvon molecule s.own in Fig.1 tas.e quite differently.

关键词： turns Chiral mirror

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Tribological behavior of lubricant-impregnated porous.polyimide

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Friction 2024年第4期12卷 711-725页

作者： Jinbang LI Ningning ZHOU Janet s.s.WONG s.hool of Mechanical Engineering and Mechanics Ningbo UniversityNingbo 315211China Beijing Key Laboratory of Long-life Technology of Precis. Rotation and Trans.is.ion Mechanis.s Beijing Institute of Control EngineeringBeijing 100029China Department of Mechanical Engineering Imperial College LondonLondon SW72AZUK

Porous.materials.impregnated with lubricants.can be us.d in conditions.where limited lubricant is.*** this.work,three porous.polyimides.PPI)with different dens.ties.were ***(PAO)impregnated PPI(iPPI)dis.s.were rubbed agains. s.eel and s.pphire *** operando obs.rvations.of the iPPI-s.pphire contacts.s.ow that oil is.releas.d under an applied load,forming a menis.us.around *** at the outlet is.created at high s.iding *** amount of releas.d oil increas.s.with increas.ng PPI *** moduli,E*,es.imated bas.d on the actual contact s.ze s.ow that trapped oil in iPPIs.contributes.to load *** higher s.eeds.tribological rehydration of the contact occurs.in low dens.ty iPPI,with that E*ris.s.with *** high dens.ty PPIs.high s.eeds.give a cons.antly high E*which is.limited by the vis.oelas.ic properties.of the PPI network and pos.ibly the rate of oil *** of iPPI-s.eel contacts.is.governed by the mechanical properties.of the PPI,the flow of the lubricant,and the roughnes. of the PPI *** low-and medium-dens.ty(highly porous.high roughnes.)PPIs.large amount of oil is.releas.d,and lubrication is.mainly via lubricant res.ricted in the contact in the pores.and pos.ibly tribological *** high dens.ty(low poros.ty)PPI,with lower roughnes.,hydrodynamic lubrication is.achieved which gives.the lowes. *** res.lts.s.ow that polymeric porous.materials.for effective lubrication require the optimization of its.s.rface roughnes.,s.iffnes.,oil flow,and oil retentions.

关键词： polyimide porous.material friction mechanis. polymer limited lubrication