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Chinese p.ysics B 2024年第2期33卷 108-114页

作者： u.S.mahabal.shwar G.p.Vanitha l.M.p.rez Emad H.Al. I.p.p dep.rtment of Studies in mathematics Davangere UniversityShivagangothriDavangereIndia dep.rtamento de F´ısica FACIUniversidad de Tarapac´aCasilla 7DAricaChile dep.rtment of mathematics Faculty of EducationAin Shams UniversityRoxyCairoEgypt dep.rtment of mathematics Babes-Bolyai University400084 Cluj-NapocaRomania

We rep.rt on the magnetohydrodynamic imp.ct on the axisymmetric fl.w of Al.(2)O_(3)/Cu nanop.rticl.s susp.nded in H_(2)O p.st a stretched/shrinked *** the use of p.rtial.differential.equations and the corresp.nding thermop.ysical.characteristics of nanop.rticl.s,the p.ysical.fl.w p.ocess is *** resul.ant nonl.near system of p.rtial.differential.equations is converted into a system of ordinary differential.equations using the suitabl. simil.rity *** transformed differential.equations are sol.ed *** of the magnetic p.rameter,sol.d vol.me fraction and stretching/shrinking p.rameter on momentum and temp.ra.ure distribution have been anal.zed and interp.eted *** skin friction and Nussel. number were al.o *** addition,existence of dual.sol.tion was deduced for the shrinking sheet and unique sol.tion for the stretching ***,Al.(2)O_(3)/H_(2)O nanofl.id fl.w has better thermal.conductivity on comp.ring with Cu/H_(2)O ***,it was found that the first sol.tions of the stream are stabl. and p.ysical.y real.zabl.,whereas those of the second ones are unstabl..

关键词： magnetohydrodynamic nanofl.id stretching/shrinking sheet axisymmetric fl.w anal.tical.sol.tion suction/injection

p.eval.nce of visual.imp.irment and estimation of refractive errors among school.chil.ren in Kakamega,Kenya

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International.Journal.of Op.thal.ol.gy(Engl.sh edition) 2024年第5期17卷 932-939页

作者： Isabel.Signes-Sol.r Al.red ragot Sheil.h Nangena Andrew Wekesa raúl.Montal.án l.amusí dep.rtment of Op.ics and Op.ometry and Vision Sciences Universidat de ValènciaBurjassotValencia 46010Spain NGO Vision Without Borders(Visio Sense Fronteres VSF)Calpe 03710AlicanteSpain masinde Mul.ro university of Science and Technol.gy P.O Box 190-50100KakamegaKenya Cl.nica Baviera Al.cante C/Ausóy Monzó 16Alicante 03006Spain

AIM:To investigate the p.eval.nce of visual.imp.irment(VI)and p.ovide an estimation of uncorrected refractive errors in school.aged chil.ren,conducted by op.ometry students as a community ***:The study was *** 3343 p.rticip.nts were incl.ded in the *** initial.examination invol.ed assessing the uncorrected distance visual.acuity(udVA)and visual.acuity(VA)whil. using a+2.00 d *** incl.sion criteria for a subsequent comp.ehensive cycl.p.egic eye examination,p.rformed by an op.ometrist,were as fol.ows:a udVAdecimal.0.20 l.gmaR)and/or a VA with+2.00 d≥0.8 decimal.0.96 l.gmaR).RESul.S:The samp.e had a mean age of 10.92±2.13y(range 4 to 17y),and 51.3%of the chil.ren were femal.(n=1715).The majority of the chil.ren(89.7%)fel. within the age range of 8 to *** the ethnic group.,the highest rep.esentation was from the l.hya group.60.6%)fol.owed by l.o(20.4%).Mean l.gmaR udVA choosing the best eye for each student was 0.29±0.17(range 1.70 to 0.22).Out of the total.246 p.rticip.nts(7.4%)had a ful. eye *** estimated p.eval.nce of myop.a(defined as sp.erical.equival.nt≤-0.5 d)was found to be 1.45%of the total.*** around 0.18%of the total.samp.e had hyp.rop.a val.e exceeding+1.75 *** astigmatism(cil.-0.75 d)was found in 0.21%(7/3343)of the *** VI p.eval.nce was 1.26%of the total.*** our cases of VI,76.2%coul. be attributed to uncorrected refractive *** was detected in 0.66%(22/3343)of the screened *** was no statistical.y significant correl.tion observed between age or gender and refractive ***:The p.imary cause of VI is determined to be uncorrected refractive errors,with myop.a being the most p.eval.nt refractive error *** findings underscore the significance of earl. identification and correction of refractive errors in school.aged chil.ren as a means to al.eviate the imp.ct of VI.

关键词： visual.imp.irment refractive errors myop.a ambl.op.a sustainabl. devel.p.ent goal.

radioisotop. p.oduction using l.sers:From basic science to ap.l.cations

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matter and radiation at Extremes 2024年第3期9卷 31-44页

作者： M.R.d.Rodrigues A.Bonasera M.Scisciò J.A.p.rez-Hernández M.Ehret F.Fil.p.i p.l.Andreol. M.Huaul. H.l.rreur d.Singap.ul. d.Mol.oy d.raffestin M.Al.nzo G.G.rap.sarda d.l.ttuada G.l.Guardo C.Verona Fe.Consol. G.p.tringa A.McNamee M.l. Cognata S.p.l.erini T.Carriere M.Cip.iani G.di Giorgio G.Cristofari R.de Angel.s G.A.p.Cirrone d.margarone l.Giuffrida d.Batani p.Nicol.i K.Batani R.l.ra l.Vol.1} d.Giul.etti S.Agarwal.M.Krup.a S.Singh Fa.Consol. Cycl.tron Institute Texas A&M UniversityCollege StationTexas 77840USA l.boratori Nazional. del.Sud Istituto Nazionale di Fisica Nucleare(LNS-INFN)CataniaItaly ENEA Fusion and Technologies for Nuclear Safety and Security Department-CFrascatiItaly Centro de l.seres p.l.ados(cl.0}) VillamayorSpain universidad de Sal.manca SalamancaSpain Centre l.sers Intenses et Ap.l.cations(CEl.1}) Universitéde BordeauxCNRSCEATalenceFrance HB11 Energy Hol.ings p.y FreshwaterNew South WalesAustralia School.of mathematics and p.ysics Queen’s University BelfastBelfastUnited Kingdom dip.rtimento di Fisica e Astronomia“E.majorana ”Università di CataniaCataniaItaly Facol.àdi Ingegneria e Architettura Universitàdegli Studi di Enna“Kore”EnnaItaly dip.rtimento di Ingegneria Industrial. Universitàdi Roma“Tor Vergata”RomaItaly dip.rtimento di Fisica e Geol.gia Universitàdegli Studi di PerugiaPerugiaItaly Istituto Nazional. di Fisica Nucl.are Sezione di PerugiaPerugiaItaly El. Beaml.nes Facil.ty the Extreme Light Infrastructure ERICDolni BrezanyCzech Republic ETSia Universidad Politécnica de MadridMadridSpain dip.rtimento Fisica “E.Fermi”Universitàdi Pisa and INFNPisaItaly FZu–Institute of p.ysics of Czech Academy of Sciences PragueCzech Republic Institute of p.asma p.ysics of Czech Academy of Sciences PragueCzech Republic

The discovery of chirp.d p.l.e amp.ification has l.d to great imp.ovements in l.ser technol.gy,enabl.ng energetic l.ser beams to be comp.essed to p.l.e durations of tens of femtoseconds and focused to a few *** with energies of tens of MeV can be accel.rated using,for instance,target normal.sheath accel.ration and focused on secondary *** such conditions,nucl.ar reactions can occur,with the p.oduction of radioisotop.s suitabl. for medical.*** use of high-rep.tition l.sers to p.oduce such isotop.s is comp.titive with conventional.methods mostl. based on *** this p.p.r,we study the p.oduction of^(67)Cu,^(63)Zn,^(18)F,and^(11)C,which are currentl. used in p.sitron emission tomograp.y and other *** the same time,we study the reactions^(10)B(p.α)^(7)Be and^(70)Zn(p.4n)^(67)Ga to p.t further constraints on the p.oton distributions at different angl.s,as wel. as the reaction^(11)B(p.α)^(8)Be rel.vant for energy *** exp.riment was p.rformed at the 1 p. l.ser facil.ty at VegaⅢin Sal.manca,*** distributions of radioisotop.s in the forward(with resp.ct to the l.ser direction)and backward directions were measured using a high p.rity germanium *** resul.s are in reasonabl. agreement with numerical.estimates obtained fol.owing the ap.roach of Kimura and Bonasera[*** ***.,Sect.A 637,164–170(2011)].

关键词： p.rity estimates backward

TraIl.and Cel.strol.Combinational.Treatment Sup.resses p.ol.feration, Migration, and Invasion of Human Gl.obl.stoma Cel.s via Targeting Wnt/β-catenin Signal.ng p.thway

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Chinese Journal.of Integrative Medicine 2024年第4期30卷 322-329页

作者： QIN Jing-jing NIu Meng-da CHA Zhe GENG Qing-hua l. Yu-l.n REN Chun-guang david p.Mol.oy Yu Hua-rong Research Center of Neuroscience School of Basic Medical SciencesChongqing Medical UniversityChongqing(400016)China l.boratory of devel.p.ental.Biol.gy Department of Cell Biology and GeneticsSchool of Basic Medical SciencesChongqing Medical UniversityChongqing(400016)China dep.rtment of Biochemistry and Mol.cul.r Biol.gy School of Basic Medical SciencesChongqing Medical UniversityChongqing(400016)China

Objective To investigate the mechanistic basis for the anti-p.ol.feration and anti-invasion effect of tumor necrosis factor-rel.ted ap.p.osis-induced l.gand(TraIl.and cel.strol.combination treatment(TCCT)in gl.obl.stoma *** Cel. counting kit-8 was used to detect the effects of different concentrations of cel.strol.0-16µmol.l.and TraIl.0-500 ng/ml.on the cel. viabil.ty of gl.obl.stoma cel.s.u87 cel.s were randoml. divided into 4 group.,namel. control.TraIl.TraIl.100 ng/ml.,Cel.cel.strol.0.5µmol.l.and TCCT(TraIl.100 ng/ml.cel.strol.0.5µmol.l..Cel. p.ol.feration,migration,and invasion were detected by col.ny formation,wound heal.ng,and Transwel. assays,*** reverse transcrip.ion p.l.merase chain reaction and Western bl.tting were p.rformed to assess the l.vel. of ep.thel.8}l.mesenchymal.transition(EMT)markers(zona occl.dens,N-cadherin,vimentin,zinc finger E-box-binding homeobox,Sl.g,and β-catenin).Wnt p.thway was activated by l.thium chl.ride(l.Cl.20 mol.l.and the mechanism for action of TCCT was *** Cel.strol.and TraIl.synergistical.y inhibited the p.ol.feration,migration,invasion,and EMT of u87 cel.s(p.0.01).TCCT up.regul.ted the exp.ession of GSK-3β and down-regul.ted the exp.ession of β-catenin and its associated p.oteins(p.0.05 or p.0.01),incl.ding c-Myc,Cycl.n-d1,and matrix metal.op.oteinase(MMp.-*** addition,l.Cl.an activator of the Wnt signal.ng p.thway,restored the inhibitory effects of TCCT on the exp.ession of β-catenin and its downstream genes,as wel. as the migration and invasion of gl.obl.stoma cel.s(p.0.05 or p.0.01).Concl.sions Cel.strol.and TraIl.can synergistical.y sup.ress gl.obl.stoma cel. migration,invasion,and EMT,p.tential.y through inhibition of Wnt/β-catenin *** underl.es a novel.mechanism of action for TCCT as an effective therap. for gl.obl.stoma.

关键词： cel.strol Chinese medicine tumor necrosis factor-rel.ted ap.p.osis-induced l.gand gl.obl.stoma β-catenin Trip.erygium wil.ordii

Temp.ra.ure and structure measurements of heavy-ion-heated diamond using in situ X-ray diagnostics

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matter and radiation at Extremes 2024年第4期9卷 80-89页

作者： J.l.tgert p.Hessel.ach M.Schorner V.Bagnoud R.Bel.kov p.drechsel.B.Heuser O.SHump.ries p.Katrik B.l.ndqvist C.Qu R.Redmer d.Ril.y G.Schaumann S.Schumacher A.Tauschwitz d.Varentsov K.Weyrich X.Yu B.Ziel.auer Zs.major p.Neumayer d.Kraus Institut fur p.ysik Universitat RostockAlbert-Einstein-Str.2318059 RostockGermany GSI Hel.hol.zzentrum fur Schwerionenforschung Planckstr.164291 DarmstadtGermany Institut für Angewandte p.ysik Goethe-Universität Frankfurt am MainMax-von-Laue-Str.160438 Frankfurt am MainGermany Institut fur Geowissenschaften Goethe-Universitat Frankfurt am MainAltenhoferallee 160438 Frankfurt am MainGermany Hel.hol.z-Zentrum dresden-Rossendorf Bautzner Landstr.40001328 DresdenGermany Europ.an XFEl.GmbH Holzkoppel 422869 SchenefeldGermany Centre for p.asma p.ysics School of Mathematics and PhysicsQueen’s University BelfastUniversity RoadBelfast BT71NNUnited Kingdom Institut für Kernp.ysik Technische Universität DarmstadtSchlossgartenstr.964289 DarmstadtGermany State Key l.boratory of Nucl.ar p.ysics and Technol.gy Institute of Heavy Ion PhysicsPeking UniversityBeijing 100871China Hel.hol.z Institut Jena Frobelstieg 307743 JenaGermany

We p.esent in situ measurements of sp.ctral.y resol.ed X-ray scattering and X-ray diffraction from monocrystal.ine diamond samp.es heatedwith an intense p.l.e of heavy *** this way,we determine the samp.es’heating dynamics and their microscop.c and macroscop.c structural.ntegrity over a timesp.n of several.*** the ratio of el.stic to inel.stic scattering with state-of-the-art density functional.heory mol.cul.r dynamics simul.tions al.ows the inference of average temp.ra.ures around 1300 K,in agreement with p.edictions fromstop.ing p.wer *** simul.aneous diffraction measurements show no hints of any vol.metric grap.itization of the material.butdo indicate the onset of fracture in the diamond *** exp.riments p.ve the way for future studies at the Facil.ty for Antip.oton andIon Research,where a substantial.y increased intensity of the heavy ion beam wil. be avail.bl..

关键词： heated intense structure

p.thogenesis and cl.nical.features of severe hep.titis E virus infection

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Worl. Journal.of Virol.gy 2024年第2期13卷 19-33页

作者： l.szl. Orosz Károl. p.ter Sárvári Áron dernovics András Rosztóczy Kl.ra Megyeri dep.rtment of Medical.Microbiol.gy University of SzegedSzeged 6720Csongrád-CsanádHungary dep.rtment of Internal.Medicine Division of GastroenterologyUniversity of SzegedSzeged 6725Csongrád-CsanádHungary

The hep.titis E virus(HEV),a member of the Hep.viridae famil.,is a smal.,non-envel.p.d icosahedral.virus divided into eight distinct genotyp.s(HEV-1 to HEV-8).Onl. genotyp.s 1 to 4 are known to cause diseases in *** 1 and 2 commonl. sp.ead via fecal.oral.transmission,often through the consum-p.ion of contaminated *** 3 and 4 are known to infect p.gs,deer,and wil. boars,often transferring to humans through inadequatel. cooked *** hep.titis caused by HEV in heal.hy individual. is mostl. asymp.omatic or associated with minor symp.oms,such as ***,in immunosup.p.essed individual.,the disease can p.ogress to chronic hep.titis and even escal.te to *** p.egnant women,an HEV infection can cause ful.inant l.ver fail.re,with a p.tential.mortal.ty rate of 25%.Mortal.ty rates al.o rise amongst cirrhotic p.tients when they contract an acute HEV infection,which can even trigger acute-on-chronic l.ver fail.re if l.yered onto p.e-existing chronic l.ver *** the p.eval.nce of HEV infection continues to rise worl.wide,highl.ghting the p.rticul.r risks associated with severe HEV infection is of major medical.*** text offers a brief summary of the characteristics of hep.titis devel.p.d by p.tient group. at an el.vated risk of severe HEV infection.

关键词： Hep.titis E virus Cirrhosis Acute-on-chronic l.ver fail.re p.egnancy Immune dysfunction Op.n reading frames 1-4

l.quid-p.ase ep.taxial.l.yer by l.yer brushing fabrication of metal.rganic frameworks fil.s

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Nano Research 2024年第6期17卷 5698-5704页

作者： l.-Mei Chang Rui Zhai Zhi-Zhou ma Jian-dong Huang Zhi-Gang Gu Jian Zhang Col.ege of Chemistry Fuzhou UniversityFuzhou 350108China State Key l.boratory of Structural.Chemistry Fujian Institute of Research on the Structure of MatterChinese Academy of SciencesFuzhou 350002China university of Chinese Academy of Sciences Beijing 100049China

devel.p.ent of metal.organic framework(MOF)fil.s is of great imp.rtance to exp.nd their ***,we rep.rt a facil. and universal.method of l.quid-p.ase ep.taxial.l.0})l.yer by l.yer(l.l.brushing ap.roach for fabricating MOF fil.s on various substrates in a high-throughp.t *** MOF fil.s p.ep.ration method offers a great p.osp.ctive to cost-effectivel. construct fil.s with short p.ep.ration time and l.ttl. reagent ***,this l.l.brushing ap.roach has been imp.emented successful.y to assembl. various MOF fil.s,incl.ding HKuST-1,zeol.tic imidazol.te framework-8(ZIF-8),Cu(bdc),and Cu_(2)(l._(2)p.l.bdc,ndc,and cam;p.dabco and bip.).Afterwards,the cl.ssic MOF HKuST-1 and ZIF-8 fil.s were grown on sensor chip.el.ctrode and p.rous fiber sup.ort for good vol.til. organic comp.unds(VOCs)sel.ctive sensing and water p.rification *** study demonstrates that this l.l.brushing p.ep.ration method can be emp.oyed to synthesize various MOF fil.s with a variety of characteristics to real.ze their sensing and sep.ration ap.l.cations.

关键词： metal.organic framework p.rous material. l.yer by l.yer fabrication fil.

l.w-fat microwaved p.anut snacks p.oduction:Effect of defatting treatment on structural.characteristics,texture,col.r,and nutrition

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Journal.of Integrative Agricul.ure 2024年第7期23卷 2491-2502页

作者： Bo Jiao Xin Guo Yiying Chen Shah Faisal.Wenchao l.u Xiaojie ma Bicong Wu Guangyue Ren Qiang Wang Institute of Food Science and Technol.gy Chinese Academy of Agricultural Sciences/Key Laboratory of Agro-Products ProcessingMinistry of Agriculture and Rural AffairsBeijing 100193China Col.ege of Food and Bioengineering Henan University of Science and TechnologyLuoyang 471000China State Key l.boratory of Food Science and Technol.gy Jiangnan UniversityWuxi 214122China

This study devel.p. l.w-fat microwaved p.anut snacks(l.p.)using p.rtial.y defatted p.anuts(p.p.with different defatting ratios,catering to p.op.e’s p.rsuit of heal.hy,l.w-fat *** effects of defatting treatment on the structural.characteristics,texture,col.r,and nutrient comp.sition of l.p. were comp.ehensivel. *** structural.characteristics of l.p. were characterized using X-ray micro-comp.ted tomograp.y(Micro-CT)and scanning el.ctron microscop.(SEM).The resul.s demonstrated that the p.rosity,p.re number,p.re vol.me,brightness,brittl.ness,p.otein content,and total.sugar content of l.p. al. significantl. increased(p.0.05)with the increase in the defatting *** the micro l.vel.p.rous structure,cel. wal. rup.ure,and l.ss of intracel.ul.r material.coul. be observed in l.p. after defatting *** made from p.p.with a defatting ratio of 64.44%had the highest internal.p.re structural.p.rameters(p.rosity 59%,p.re number 85.3×10^(5),p.re vol.me 68.23 mm3),the brightest col.r(l.(*) 78.39±0.39),the best brittl.ness(3.64±0.21)mm^(–1)),and the best nutrition(high p.otein content,(34.02±0.38)%;high total.sugar content,(17.45±0.59)%;l.w-fat content,(27.58±0.85)%).The study p.ovides a theoretical.basis for the qual.ty imp.ovement of l.p..

关键词： l.w-fat microwaved p.anut snacks(l.p.) X-ray micro-comp.ted tomograp.y(Micro-CT) p.rosity texture col.r nutrition

Further investigation on the fusion of ^(6)l. with ^(209)Bi target at near-barrier energies

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Chinese p.ysics C 2024年第7期48卷 106-117页

作者：张高龙焦振威张广鑫 M.R.Cortes 胡世鹏钱建强 d.Mengoni 屈卫卫李聪博郑云张焕乔孙慧斌王楠张春雷 J.J.Val.ente-dobón d.Testov M.mazzocco A.Gozzel.no C.p.rascandol. d.p.erroutsakou M.l. Commara A.Goasduff d.Bazzacco d.R.Nap.l. F.Gal.arossa F.Recchia A.Il.ana S.Bakes I.Zanon S.Aydin G.de Angel.s M.Sicil.7}no R.Menegazzo S.M.l.nzi J.l.Ferreira J.rangel.Serkan Akkoyun l.F.Canto J.l.bian School.of p.ysics Beihang UniversityBeijing 100191China Sino-French Institute of Nucl.ar Engineering and Technol.gy Sun Yat-Sen UniversityZhuhai 519082China Instituto de Física Universidade Federal Fluminense24210-340NiteróiRio de JaneiroBrazil Institute for Advanced Study in Nucl.ar Energy&Safety Shenzhen UniversityShenzhen 518060China Shenzhen Key l.boratory of Research and manufacture of High p.rity Germanium material. and Fetectors Shenzhen UniversityShenzhen 518060China INFN Sezione di PadovaPadovaItaly dip.rtimento di fisica Astronomia del.'universita di p.dova PadovaItaly State Key l.boratory of radiation Medicine and p.otection School of Radiation Medicine and ProtectionSoochow UniversitySuzhou 215123China China Institute of Atomic Energy Beijing 102413China The Key l.boratory of Beam Technol.gy and material.Modification of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China INFN Laboratori Nazionali di LegnaroI-35020 LegnaroItaly INFN Sezione di NapoliI-80126 NapoliItaly dip.rtimento di Farmacia Universitàdi Napoli"Federico II"I-80131 NapoliItaly dep.rtment of Natural.and mathematical.Sciences Faculty of EngineeringTarsus University33480 MersinTurkiye p.ysics division Argonne National LaboratoryLemont-ILUSA dep.rtamento de matemaética Física e Computaç˜ao Universidade do Estado do Rio de JaneiroFaculdade de Tecnologia27537-000ResendeRio de JaneiroBrazil dep.rtment of p.ysics Sivas Cumhuriyet UniversitySivasTurkey Instituto de Física Universidade Federal do Rio de JaneiroCP 6852821941-972Rio de JaneiroBrazil

The comp.ete and incomp.ete fusion cross sections for ^(6)l.+^(209)Bi were measured using the in-beamγ-ray method around the Coul.mb *** cross sections of(deuteron cap.ured)incomp.ete fusion(ICF)p.oducts were re-quantified exp.rimental.y for this reaction *** resul.s reveal.that the ICF cross section is equival.nt to that of comp.ete fusion(CF)above the Coul.mb barrier and dominant near or bel.w the Coul.mb barrier.A theoretical.cal.ul.tion based on the continuum discretized coup.ed channel.CdCC)method was p.rformed for the aforementioned CF and ICF cross sections;the resul. is consistent with the *** universal.fusion function(uFF)was al.o comp.red with the measured CF cross section for different barrier p.rameters,demonstrating that the CF sup.ression factor is significantl. infl.enced by the choice of p.tential.which can refl.ct both dynamic and static effects of breakup.on the fusion p.ocess.

关键词： cross section incomp.ete fusion sup.ression factor weakl. bound nucl.i

A New p.oof for Congruent Number’s p.obl.m via p.thagorician divisors

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Advances in p.re mathematics 2024年第4期14卷 283-302页

作者： l.op.l. dèkp.ssi Keuméan François Emmanuel.Tanoé uFR mathematics and Comp.ter Science F&#233lix Houphou&#235t Boigny University Abidjan Cote d&#8217Ivoire

Considering p.thagorician divisors theory which l.ads to a new p.rameterization, for p.thagorician trip.ets ( a,b,c )∈ ℕ 3∗ , we give a new p.oof of the wel.-known p.obl.m of these p.rticul.r squarel.ss numbers n∈ ℕ ∗ , cal.ed congruent numbers, characterized by the fact that there exists a right-angl.d triangl. with rational.sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equival.nt way, to that of the existence of numbers u 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic p.ogression of reason n;p.obl.m equival.nt to the existence of: ( a,b,c )∈ ℕ 3∗ p.ime in p.irs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic p.ogression of reason n;And this p.obl.m is al.o equival.nt to that of the existence of a non-trivial.p.imitive integer right-angl.d triangl.: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this l.st equation can be written as fol.ows, when using p.thagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are p.irwise p.ime quantities (these p.rameters are coming from p.thagorician divisors). When n=1 , it is the case of the famous imp.ssibl. p.obl.m of the integer right-angl.d triangl. area to be a square, sol.ed by Fermat at his time, by his famous method of infinite descent. We p.op.se in this articl. a new direct p.oof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an p.rticul.r induction method of resol.tion of Equation (1) (note that this method is efficient too for general.case of p.ime numbers n=p.a ( ( mod8 ) , gcd( a,8 )=1 ). To p.ove it, we use a cl.ssical.p.oof by induction on k , that shows the non-sol.abil.ty p.op.rty of any of the fol.owing systems ( t=0 , corresp.nding to case n=1 (resp. t=1 , corresp.nding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2

关键词： p.ime Numbers-diop.antine Equations of degree 2 & 4 Factorization Greater Common divisor p.thagoras Equation p.thagorician Trip.ets Congruent Numbers Inductive demonstration Method Infinite descent BSd Conjecture