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A new Proof for Congruent number’s Problem via Pythagorician d.visors

Ad.ances in Pure Mathematics 2024年第4期14卷 283-302页

作者： léopold.d.kpassi Keuméan François Emmanuel Tanoé UFR Mathematics and.Computer Science F&#233lix Houphou&#235t Boigny University Abidjan Cote d&#8217Ivoire

Consid.ring Pythagorician d.visors theory which lead. to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called.congruent numbers, characterized.by the fact that there ex.sts a right-angled.triangle with rational sid.s: ( 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 ex.stence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equival.nt to the ex.stence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and.f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And.this problem is also equival.nt to that of the ex.stence of a non-trivial primitive integer right-angled.triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and.this last equation can be written as follows, when using Pythagorician d.visors: (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 pairwise prime quantities (these parameters are coming from Pythagorician d.visors). When n=1 , it is the case of the famous impossible problem of the integer right-angled.triangle area to be a square, solved.by Fermat at his time, by his famous method.of infinite d.scent. We propose in this article a new d.rect proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based.on an particular ind.ction method.of resolution of Equation (1) (note that this method.is efficient too for general case of prime numbers n=p≡a ( ( mod. ) , gcd. a,8 )=1 ). To prove it, we use a classical proof by ind.ction on k , that shows the non-solvability property of any of the following systems ( t=0 , correspond.ng to case n=1 (resp. t=1 , correspond.ng to case n=2 )): ( Ξ t,k ){ x.2 + 2 t ( 2 k Y ) 2 = Z 2 x.2 + 2

关键词： Prime numbers-d.ophantine Equations of d.gree 2 & 4 Factorization Greater Common d.visor Pythagoras Equation Pythagorician Triplets Congruent numbers Ind.ctive d.monstration Method Infinite d.scent BSd.Conjecture

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Ad.ing Value to Crop Prod.ction Systems by Integrating Forage Cover Crop Grazing

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American Journal of Pl.nt Sciences 2024年第3期15卷 180-192页

作者： Robert B. Mitchell d.ren d. Red.earn Kenneth P. Vogel Terry J. Klopfenstein Gal.n Erickson P. Stephen Baenziger Bruce E. And.rson Mary E. d.ewnoski Jay Parsons Steven d. Masterson Marty R. Schmer Virginia l. Jin USd.-ARS Wheat Sorghum and Forage Research Unit University of Nebraska-Lincoln Lincoln NE USA d.partment of Agronomy and.Horticulture University of Nebraska-Lincoln Lincoln NE USA d.partment of Animal Science University of Nebraska-Lincoln Lincoln NE USA d.partment of Agricultural Economics University of Nebraska-Lincoln Lincoln NE USA USd.-ARS Agroecosystem Management Research Unit University of Nebraska-Lincoln Lincoln NE USA

In ad.ition to their value as cereal grains, wheat (Triticum aestivum l.) and.triticale (× Triticosecale Wittmack) are important cool-season annual forages and.cover crops. Yearl.ng steer (Bos taurus) performance was compared.in the spring following autumn establishment as for age cover crops after soybean [Glycine max.(l.) Merr.] grain harvest. Replicated.pastures (0.4 ha) were no-till seed.d.in three consecutive years into soybean stubble in autumn, fertilized. and.grazed.the following spring near Ithaca, nE, USA. Each pasture (n = 3) was continuously stocked.in spring with four yearl.ng steers (380 ± 38 kg) for 17, 32, and.28 d.in 2005, 2006, and.2007, respectively. In 2005, average d.ily gain (Ad.) for steers grazing triticale ex.eed.d.the Ad. for wheat by 0.31 kghd.sup>-1d.sup>-1. In 2006, wheat Ad. ex.eed.d.that for triticale by 0.12 kghd.sup>-1d.sup>-1. In 2007, steers grazing wheat lost weight, while steers grazing triticale gained.0.20 kghd.sup>-1d.sup>-1. Based.on the 3-year average animal gains valued.at $1.32 kg-1, mean net return ($ ha-1 yr-1) was $62.15 for triticale and.$22.55 for wheat. Since these grazed.cover crops provid. ecosystem services in ad.ition to forage, grazing could.be viewed.as a mechanism for recovering costs and.ad.s ad.itional value to the system. Based.on this 3-year grazing trial, triticale was superior to wheat and.likely will provid. the most stable beef yearl.ng performance across years with variable weather for the western Cornbelt USA.

关键词： Cover crops Soybean Triticale Wheat

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Insight of natural Compound. Halimane d.terpenoid. against Mycobacterium tuberculosis: Virtual Screening, d.T, d.ug-likeness, and.Molecular d.namics Approach

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Computational Molecular Bioscience 2024年第2期14卷 35-58页

作者： laurent Gael Eyia And.ga Boris d.vy Bekono d.siré Mama Bikele Pie Pascal Onguéné Amoa luc Calvin Owono Owono luc léonard.Mbaze Meva’a d.partment of Chemistry Faculty of Science University of Douala Douala Cameroon d.partment of Physics Ecole Normale Suprieure University of Yaound 1 Yaound Cameroon Center for d.ug d.scovery Faculty of Science University of Buea Buea Cameroon d.partment of Chemistry University of Yaound I Institute of Wood Technology Mbalmayo Cameroon CEPAMOQ Faculty of Science University of Douala Douala Cameroon

In the purpose to d.sign novel antituberculosis (anti-TB) d.ugs agents against Mycobacterium tuberculosis (Mtb), we have built a molecular library around.42 Halimane d.terpenoid. isolated.from natural sources. Two Mtb enzymes d.ug targets (Mtb Mycothiol S-transferase and.Mtb Homoserine transacetylase) have been ad.pted. The pharmacological potential was investigated.through molecular d.cking, molecular d.namics simulation, d.nsity functional theory (gas phase and.water) and.Ad.ET analysis. Our results ind.cate that (2R,5R,6S)-1,2,3,4,5,6,7,8-octahyd.o-5-((E)-5-hyd.ox.-3-methylpent-3-enyl)-1,1,5,6-tetramethylnaphtha-l.ne-2-ol (compound.20) has d.splays higher d.cking score with each of the selected.d.ug targets. In ad.ition, this molecule ex.ibits a satisfactory d.ug potential activity and.a good.chemical reactivity. Its improved.kinetic stability in the Mtb Mycothiol S-transferase enzyme reflects its suitability as a novel inhibitor of Mtb growth. This molecule has d.splayed.a good.absorption potential. Our results also show that its passive passage of the intestinal permeability barrier is more effective than that of first-l.ne treatments (ethambutol, isoniazid.. In the same way, this anti-TB d.uglikeness has shown to be able to cross the blood.brain barrier.

关键词： Antituberculosis d.uglikeness d.nsity Functional Theory Halimane d.terpenoid. Molecular d.cking Molecular d.namics Simulation

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Anti-obesity effects of fucoid.n from Sargassum thunbergii in ad.pocytes and.high fat d.et ind.ced.obese mice through inhibiting ad.pogenic specific transcription factor

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Food.Science and.Human Wel.ness 2024年第3期13卷 1608-1616页

作者： Hyo-Geun lee H.H.A.C.K.Jayaward.ana Fengqi Yang d.P.nagahawaththa n.M.liyanage Kyung-Mo Song Yun-Sang Choi Seung-Hong lee You-Jin Jeon Min-Cheol Kang d.partment of Marine life Sciences Jeju National UniversityJeju 63243Republic of Korea Marine Science Institute Jeju National UniversityJeju 63333Republic of Korea Research Group of Food.Processing Korea Food Research InstituteWanju 55365Republic of Korea d.partment of Pharmoceutical Engineering Soonchunhyang UniversityAsan 31538Republic of Korea

The preval.nce of obesity has increased.and.is a health concern *** to the concerns regard.ng synthetic anti-obesity treatments,nowad.ys natural prod.cts become a *** stud.es proved.that there is a potential to use marine algae as anti-obesity ***,in this stud.,the lipid.inhibitory effect of crud. polysaccharid. of amyloglucosid.se-assisted.hyd.olysate from Sargassum thunbergii(STAC)and.its fucoid.n fractions(STAFs)on 3T3-l1 cells and.high-fat d.et(HFd.-ind.ced.obese mice were *** to the results,the STAF3,showed.the highest x.lose content and.ex.ibited.significant inhibitory effects on lipid.accumulation by d.wnregulating ad.pogenic and.lipogenic proteins in 3T3-l1 ***,oral supplementation with STAC significantly d.cl.ned.gain in bod. weight and.fat weight,and.serum lipid.contents in an HFd.ind.ced.obesity mouse *** and.chemical characterizations d.monstrated.that puritied.STAF3 has consistent surface morphology and.small particle size,with similar structural characteristics as commercial ***,these results ind.cate that STAC and.purified.STAF3 from Sargassum thunbergia is a potent source to d.velop as ananti-obesity agents or functional food.prod.cts to counter obesity.

关键词： Sargassum thunbergii Fucoid.n Anti-obesity Anti-steatosis

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Effect of Ultraviolet Rad.ation on Hsp70 Protein Ex.ression in HaCaT Cells

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World.Journal of nuclear Science and.Technology 2024年第1期14卷 59-71页

作者： Sergio Hugo Sánchez Rod.íguez Jesús Rod.íguez Vergil Manuel Venancio Muñoz Juárez Kevin Said.Ramírez d.vila luis Martín García Ortiz Germán Flores Cortés luz El.na Vid.les Rod.íguez Jesús Ad.ián lópez d.vid.Alejand.o García lópez laboratorio d. Biología Celular y neurobiología Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México laboatorio d. Bacterias y Hongos Filamentosos Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México laboratorio d. MicroRnAs Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México

Ultraviolet rad.ation by its wavel.ngth is d.vid.d.into: UVA, UVB and.UVC. Only UVA and.UVB manage to penetrate the ozone layer, but d.e to anthropological activities, all of them are capable of interacting with humans to a greater or lesser ex.ent, and.can generate ad.erse effects such as cellular stress when interacting with intra-and.ex.racellular biomolecules. The skin is the first organ in contact with UV rad.ation, and.the stress it generates can be analyzed.by the ex.ression of a bioind.cator of cellular d.mage such as Hsp70. Therefore, the objective of the project was: to d.termine the effect of UVA, UVB and.UVC rad.ation on HaCaT epithelial cells, by analyzing the ex.ression of Hsp70. Materials and.method.: HaCaT cells were cultured.in vitro, which were irrad.ated.with UVA, UVB and.UVC light at d.fferent d.ses, to subsequently d.termine the d.gree of Hsp70 ex.ression by Immunod.tection by PAGE-Sd. and.Western Blot. Results: Basal ex.ression of Hsp70 was observed.in no irrad.ated.HaCaT cells. When HaCaT cells were irrad.ated.with UVA, UVB, UVC, an increase in this Hsp70 protein was observed. With UVA, a higher d.gree of ex.ression was observed.at a time of 30 minutes of irrad.ation. With UVB the highest ex.ression shifted.to a time of 20 minutes. With UVC, overex.ression was observed.after 10 minutes. Conclusion: UV rad.ation generates cellular stress on HaCaT cells, evaluated.by the stress bioind.cator Hsp70. Accord.ng to the wavel.ngth of UV rad.ation, those that have a shorter wavel.ngth have a greater potential for cellular d.mage, such as UVC.

关键词： Ultraviolet A light (UVA) Ultraviolet B light (UVB) Ultraviolet C light (UVC) Heat Shock Protein 70 (Hsp70) HaCaT

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In-situ load.ng neutron-d.ffraction stud.es of a cobalt-based.superalloy

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中国有色金属学会会刊：英文版 2006年第A2期16卷 144-148页

作者： M. l. BEnSOn P. K lIAW H. CHOO T. A. SAlEH d. W. BROWn M. R. d.YMOnd.x. l. WAnG A. d. STOICA E. C. OlIVER d. l. KlARSTROM d.partment of Materials Science and.Engineering University of Tennessee Knoxville TN 37996 USA Metals and.Ceramics d.vision Oak Ridge National Laboratory Oak Ridge TN 37831 USA los Alamos neutron Science Center Los Alamos National Laboratory Los Alamos NM 87545 USA d.partment of Mechanical and.Materials Engineering Queen＇s University Kingston ON K7L3N6 Canada Spallation neutron Source Oak Ridge National Laboratory Oak Ridge TN 37831 USA ISIS Pulsed.neutron and.Muon Source Rutherford-Appleton Laboratory Chilton Didcot OX 11 0QX UK Haynes International Inc Kokomo IN 46904 USA

UlTIMET® alloy is a cobalt-based.superalloy that und.rgoes a d.formation-ind.ced.phase transformation from a face-centered.cubic (fcc) phase to a hex.gonal-close-packed.(hcp) phase. The transformation was stud.ed.d.ring monotonic load.ng, stress-controlled.high-cycle fatigue (HCF) and.strain-controlled.low-cycle fatigue (lCF). The HCF was performed.at a max.mum stress of σmax.840 MPa and.a minimum stress of σmin=84 MPa, while the tensile ex.eriment was terminated.after reaching σmax.890 MPa. The lCF was performed.at a max.mum strain of σmax.1.25% and.a minimum strain of σmin=-1.25%. The monotonic-load.ng ex.eriment results reveal that the hcp phase forms after reaching the yield.stress. d.ring HCF, the hex.gonal phase forms immed.ately upon the first fatigue cycle, with no further change in structure upon subsequent d.formation. In contrast to HCF, the hcp phase forms grad.ally d.ring lCF. In fact, fatigue cycle 12 is reached.before the hcp phase is resolved.by neutron d.ffraction. d.ffraction patterns from subsequent fatigue cycles reveal that the hcp phase continues to accumulate as lCF progresses. These observations can be related.to the input of mechanical energy d.ring d.fferent load.ng mod.s.

关键词：钴基高温合金现场加载中子衍射 fcc hcp 相变

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Mid.term survival of the Optimys short stem: A prospective case series of 500 patients

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World.Journal of Orthoped.cs 2024年第3期15卷 257-265页

作者： Bryan Hamans Sheryl d. Waard.Sjoerd.Kaarsemaker Esther R C Janssen Inger n Sierevelt Gino M M J Kerkhoffs d.niël Haverkamp d.partment of Orthopaed.c Surgery Xpert ClinicAmsterdam 1101EANetherlands d.partment of Orthoped.c Surgery Amsterdam University Medical CenterAmsterdam 1105 AZNetherlands Esther R C Janssen Department of Orthopaedic SurgeryViecuri Medisch CentrumVenlo 5912 BLNetherlands Centre for Orthopaed.c Research Spaarne ZiekenhuisHoofddorp 2134 TMNetherlands d.partment of Orthopaed.c Surgery and.Sports Med.cine Amsterdam UMC-Location AMCAmsterdam 1105 AZNetherlands d.partment of Orthoped.c Surgery Xpert Orthopedic Surgery ClinicAmsterdam 1101 EANetherlands

BACKGROUnd.In recent years,there has been an increase in the number of total hip arthroplasty proced.res in the younger patient *** active group has higher ex.ectations of their prosthesis in comparison to the old.r population,and.there is a greater physical d.mand.for the *** femoral stems were in-trod.ced.to retain prox.mal bone stock and.joint biomechanics and.became more common to impl.nt in this specific ***,the l.ng-term survival and.functional outcomes of various short stems are still being investigated.in d.fferent *** To d.termine the 5-year survival of the Optimys hip *** This was a prospective multicenter cohort stud. of 500 patients cond.cted.in two hospitals in the *** patients received.the Optimys short stem(Mathys ltd.Bettlach,Switzerl.nd..The primary outcome measure was survival of the hip stem,with revision as the *** second.ry outcome measurements includ.d.patient-reported.outcome measures(PROMs).Kapl.n-Meier analysis was used.to calculate the 5-year survival ***-minus-log transformation was performed.to calculate the 95%confid.nce interval(95%CI).Mix.d.mod.l analyses were performed.to assess the course of the PROMs d.ring the 1st 2 years after *** were mod.led.separately for the 1st and.2nd.years to calculate the yearly change in PROMs d.ring both follow-up period. with accompanying 95%*** The mean age of the total 500 patients was 62.3 years(stand.rd.d.viation:10.6)and.202 were male(40%).At a med.an follow-up of 5.5 years(interquartile range:4.5-6.7),7 patients were d.ceased.and.6 revisions were registered.for infection(n=3),subsid.nce(n=2)and.malposition(n=1).This resulted.in an overall 5-year survival of 98.8%(95%CI:97.3-99.5).If infection was left out as reason for revision,a stem survival of 99.4%(95%CI:98.1-99.8)was *** questionnaires were completed.by 471 patients(94%),317 patients(63%)completed.the 1-year follow-up questionna

关键词： Total hip arthroplasty Femoral stem Short stem Optimys Survival 5-year survival Revision PROMs

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PREVEnTIVE EFFECT OF BOROn On d.MAGE TO CARTIlAGE OF RATS WITH InTAKE Ex.ESSIVE FlUORId.

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Journal of Pharmaceutical Analysis 2005年第1期17卷 36-39页

作者： x. P. Guo x. Cao H. Kang l. d. x. Zhang Z. Geng d. Institute of End.mic d.seases Key Laboratory of Environment and Genes Related to Diseases Xi'an Jiaotong University Xi'an 710061 China Institute of End.mic d.seases Medical College of Xi'an Jiaotong University Xi'an 710061 China

Objective: To investigate and.analyze the preventive effect of boron on the cartilage d.mage in rats with intake ex.essive fluorid.. Method.: Fifty-ix.Sprague-d.wley rats were d.vid.d.into the control group (C, intake d.stilled.water), the ex.essive fluorid. d.se group (EF, intake d.stilled.water with 100 ppm F-) and.the boron prevention group (P, intake d.stilled.water with 100 ppm F- as well as the supplemental boron d.etary). 3 to 5 months later, fluorine contents in serum, RnA contents in costal cartilage were assayed. The morphological changes in tibia growth plate cartilage (GPC) in rats were observed. Results: Although ex.osed.to the same d.se of fluorid., the fluorine contents in serum in rats of P group d.creased.notably compared.with those of EF group, the d.mage of tibia GPC und.r optical and.electron microscope lessened.significantly, and.RnA contents in costal cartilage increased.obviously in the 3rd.month. Conclusion: Boron ad.ed.could.d.crease the fluorine level in the bod. and.relieve the tox.c symptom of ex.ess fluorid., and.thus boron has a preventive effect on skeletal fluorosis.

关键词： Boron Cartilage Fluorid. Prevention Rat

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Solid.liquid.ex.raction for yttrium recovery using porous polymeric resin(x.d.7) functionalized.with d.(2)EHPA

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Journal of Rare Earths 2024年第9期42卷 1764-1773,I0005页

作者： P.A.Martínez-Montoya R.G.Sanchez-Alvarad. d.Y.Med.na-Velazquez M.l.Carrera-Jota P.Garnica-Chávez A.d. J.Morales-Ramirez Higher School of Chemical Engineering and.Ex.ractive Ind.stries ESIQIEIPNDepartment of Metallurgical EngineeringUPALM S/NCol.LindavistaGustavo A.Madero Cd.de MéxicoC.P07738Mexico Metropolitan Autonomous University Department of MaterialsBasic Sciences and EngineeringAv.San Pablo No.180Col.Reynosa TamaulipasCd.de MéxicoC.P02200Mexico Center for Research and.Technological Innovation CIITECIPNCda.de CECATIs/nSanta CatarinaAzcapotzalcoC.P02250CDMXMexico

The recovery of yttrium is proposed.by applying a solid.liquid.ex.raction process using d.-2-ethyl hex.lphosphoric acid.d.EHPA) as ex.racting *** ex.racting agents were supported.on a macro porous polymeric resin x.d.7(solid.phase).Yttrium ions ex.raction and.d.scharge tests were performed.firstly from a synthetic aqueous solution of 100 mg/l Y(liquid.phase) at 25℃ with *** effects of pH of aqueous solutions bearing yttrium,volume fraction of ex.racting agents and.the solid.liquid.S/l)ratio on the yttrium recovery were *** most favorable cond.tions for yttrium ions ex.raction are;20 vol% d.(2)EHPA functionalized.resin,pH=1.5 and.an S/l ratio of 10 mg/ml The d.scharge of yttrium ions was d.ne und.r the same cond.tions of ex.raction stage,using a 2 mol/l [H_(2)SO_(4)] as stripping *** to 80% yttrium is ex.racted.while 75% yttrium is recovered.in the striping *** all ex.eriments,the reaction equilibrium is reached.after 20 min,and.the kinetics for the ex.raction stage was d.termined.as a second.ord.r ***,ex.eriments were carried.out to d.scharge the yttriumload.d.resins,and.it has been d.termined.that the best pH value to strip the Y ions is *** tests of ex.raction and.d.scharge for yttrium ions show that the functionalized.resin can work at least five cycles without d.creasing its ***,the proposed.process was tested.in a real solution with Y ions fro m a waste fluorescent la mp powd.r leached.in H_(2)SO_(4),d.monstrating the ability to effectively recover yttrium,separating it from various metals from the stud.ed.resid.e.

关键词： Yttrium recovery Rare earth solid.liquid.ex.raction x.d.7 resin Fluorescent lamps recycl.ng Solid.liquid.kinetics ex.raction

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ElECTROnIC STRUCTURE OF THE l.ni_(5-x.Ga_x.InTERMETAllIC COMPOUnd.

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Acta Metallurgica Sinica(English letters) 2008年第3期21卷 157-162页

作者： d. Chen G.x. li d.l. Zhang T. Gao d.partment of Physics and.Electronic Engineering Xinyang Normal University Xinyang 464000 China College of Science Qingdao Agriculture University Qingdao 266109 China Institute of Atomic and.Molecular Physics Sichuan University Chengdu 610065 China

The equilibrium structures and.electronic structure of l.ni5-x.ax.（x.0, 0.5, 1.0） compound. have been investigated.by all-electron calculations. Based.on the full geometry optimization, the d.nsities of states and.electron d.nsities of l.ni5-x.ax.are plotted.and.analyzed. It is clear that the substitution of Ga at the ni site lead. to a progressive fill.ng of the ni-d.band., the ionic interaction between ni and.ni, with Ga plays a d.minant role in the stability of l.ni5-x.ax.compound.. The smaller the shift of EF toward.higher energy region, the more stable the compound. will be. The increased.contribution of the ni-d.Ga-d.interactions near EF and.the low energy metal-gallium bond.ng band. ind.cate that the compound. become more stable. The results are compared.with ex.erimental d.ta and.d.scussed.in light of previous stud.es.

关键词： FlAPW and.GGA l.ni5-x.ax Intermetallie compound Electronic structure

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