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A New Proof for Congruent Number’s Problem via Pythagorician divisors

Advances in Pure Mathematics 2024年第4期14卷 283-302页

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

Considering Pythagorician divisors theory which leads 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 exists a right-angled triangle 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 equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence 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 equivalent to that of the existence 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 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 pairwise prime quantities (these parameters are coming from Pythagorician divisors). 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 descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding 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-diophantine Equations of degree 2 & 4 Factorization Greater Common divisor Pythagoras Equation Pythagorician Triplets Congruent Numbers Inductive demonstration Method Infinite descent Bsd Conjecture

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Enabling Technologies for Autonomous Robotic systems in Manufacturing

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Transactions of Nanjing University of Aeronautics and Astronautics 2024年第4期41卷 403-431页

作者： ERdŐs Gábor ABAI Kristóf BEREGI Richárd CsEMPEsZ János CsERTEG Tamás GOdÓGábor HAJÓs Mátyás HÁY Borbála HORVÁTH dániel HORVÁTH Gergely JUNIKIÁdám KEMÉNY Zsolt KOVÁCs András NACsA János PANITI Imre PEdONE Gianfranco TAKÁCs Emma TIPARY Bence ZAHORÁN lászló VÁNCZA József Institute for Computer science and Control Hungarian Research Network(HUN-REN SZTAKI)BudapestHungary department of Manufacturing science and Technology Budapest University of Technology and Economics(BME)BudapestHungary EPIC Innolabs Nonprofit ltd. BudapestHungary Eötvös loránd University(ElTE) BudapestHungary

Research of autonomous manufacturing systems is motivated both by the new technical possibilities of cyber-physical systems and by the practical needs of the *** operation in semi-structured industrial environments can now be supported by advanced sensor technologies,digital twins,artificial intelligence and novel communication *** enable real-time monitoring of production processes,situation recognition and prediction,automated and adaptive(re)planning,teamwork and performance improvement by *** paper summarizes the main requirements towards autonomous industrial robotics and suggests a generic workflow for realizing such *** case studies will be presented from recent practice at HUN-REN sZTAKI in a broad range of domains such as assembly,welding,grinding,picking and placing,and *** various solutions have in common that they use a generic digital twin concept as their *** making general recommendations for realizing autonomous robotic solutions in the industry,open issues for future research will be discussed.

关键词： industrial robotics autonomy digital twin enabling technology

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Therapeutic advances in neural regeneration for Huntington’s disease

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Neural Regeneration Research 2024年第9期19卷 1991-1997页

作者： Francesco d’Egidio Vanessa Castelli Giorgia lombardozzi Fabrizio Ammannito Annamaria Cimini Michele d’Angelo department of life Health and Environmental SciencesUniversity of L’AquilaL’AquilaItaly

Huntington’s disease is a neurodegenerative disease caused by the expansion mutation of a cytosine-adenine-guanine triplet in the exon 1 of the HTT gene which is responsible for the production of the huntingtin (Htt) protein. In physiological conditions, Htt is involved in many cellular processes such as cell signaling, transcriptional regulation, energy metabolism regulation, dNA maintenance, axonal trafficking, and antiapoptotic activity. When the genetic alteration is present, the production of a mutant version of Htt (mHtt) occurs, which is characterized by a plethora of pathogenic activities that, finally, lead to cell death. Among all the cells in which mHtt exerts its dangerous activity, the GABAergic Medium spiny Neurons seem to be the most affected by the mHtt-induced excitotoxicity both in the cortex and in the striatum. However, as the neurodegeneration proceeds ahead the neuronal loss grows also in other brain areas such as the cerebellum, hypothalamus, thalamus, subthalamic nucleus, globus pallidus, and substantia nigra, determining the variety of symptoms that characterize Huntington’s disease. From a clinical point of view, Huntington’s disease is characterized by a wide spectrum of symptoms spanning from motor impairment to cognitive disorders and dementia. Huntington’s disease shows a prevalence of around 3.92 cases every 100,000 worldwide and an incidence of 0.48 new cases every 100,000/year. To date, there is no available cure for Huntington’s disease. several treatments have been developed so far, aiming to reduce the severity of one or more symptoms to slow down the inexorable decline caused by the disease. In this context, the search for reliable strategies to target the different aspects of Huntington’s disease become of the utmost interest. In recent years, a variety of studies demonstrated the detrimental role of neuronal loss in Huntington’s disease condition highlighting how the replacement of lost cells would be a reasonable strategy to o

关键词： cell therapy exosomes extracellular vesicles Huntingtin Huntington’s disease medium spiny neurons neurodegenerative disease neurogenesis neuronal loss stem cells

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Effect of biochar on the metabolome of soybean seedlings

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Oil Crop science 2024年第1期9卷 60-68页

作者： Nathalia E.silva Mariana G.Aguilar Osania E.Ferreira Gleicia M.Paulino Jaqueline C.l.Carvalho lúcia P.s.Pimenta Alan R.T.Machado Programa de Pos-graduaçao em Ciencias Ambientais Universidade do Estado de Minas GeraisFrutalMinas Gerais38202-436Brazil departamento de Química Universidade Federal de Minas GeraisMinas GeraisBelo Horizonte31270-901Brazil departamento de Engenharia Aplicada e Tecnologias Ambientais Universidade do Estado de Minas GeraisJoao MonlevadeMinas Gerais35930-314Brazil departamento de Ciencias Exatas Universidade do Estado de Minas GeraisJoao MonlevadeMinas Gerais35930-314Brazil

The use of biochar can have several effects on plant germination,depending on raw material,preparation method and application ***,the molecular mechanisms that lead to those results have yet to be *** aim of this research was to improve the understanding of these mechanisms by characterizing the metabolic effects of sugarcane bagasse biochar on soybean *** types of biochars were prepared by pyrolysis at 300℃(sCB300),400℃(sCB400)and 600℃(sCB600).Then,each one was mixed into sand at 1%,3%,5%(w/w)dose,*** experiment was performed in 8 days of incubation,when the number of germinated seeds and the average radicle length were *** evaluate the metabolome,the dry biomass(dB)was subjected to extraction with a mixture of methanol-d4 and d2O(1:1 v/v).The extracts were submitted to metabolomics analysis by Proton Nuclear Magnetic *** Relative Germination,Relative Average Radicle Growth and Germination Index increased in all treatments compared to *** the other hand,the dB increased in all treatments,except for sCB300,at doses of 1%and 3%w/*** metabolites(alanine,asparagine,acetic acid,citric acid,glycerol,fatty acids and sucrose)were identified and quantified in dB extracts as the most influential finding for the separation of *** together,these results strongly suggested that biochars accelerated the catabolism of triacylglycerols to sucrose and induced a slight osmotic stress.

关键词： Germination Metabolomics 1H NMR Pyrolysis sugarcane bagasse

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Highly enhanced UV absorption and light emission of monolayer Ws_(2)through hybridization with Ti_(2)N MXene quantum dots and g-C_(3)N_(4)quantum dots

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Opto-Electronic Advances 2024年第6期7卷 31-39页

作者： Anir s.sharbirin Rebekah E.Kong Wendy B.Mato Trang Thu Tran Eunji lee Jolene W.P.Khor Afrizal l.Fadli Jeongyong Kim department of Energy science Sungkyunkwan UniversitySuwon 16419Republic of Korea

Two-dimensional(2d)transition metal dichalcogenides(TMd)are atomically thin semiconductors with promising optoelectronic applications across the visible ***,their intrinsically weak light absorption and the low photoluminescence quantum yield(PlQY)restrict their performance and potential use,especially in ultraviolet(UV)wavelength light *** dots(Qd)derived from 2d materials(2d/Qd)provide efficient light absorption and emission of which energy can be tuned for desirable light *** this study,we greatly enhanced the photon absorption and PlQY of monolayer(1l)tungsten disulfide(Ws_(2))in the UV range via hybridization with 2d/Qd,particularly titanium nitride MXene Qd(Ti_(2)N MQd)and graphitic carbon nitride Qd(GCNQd).With the hybridization of MQd or GCNQd,1lWs_(2)showed a maximum Pl enhancement by 15 times with 300 nm wavelength excitation,while no noticeable enhancement was observed when the excitation photon energy was less than the bandgap of the Qd,indicating that UV absorption by the Qd played a crucial role in enhancing the light emission of 1l-Ws_(2)in our 0d/2d hybrid *** findings present a convenient method for enhancing the photo-response of 1l-Ws_(2)to UV light and offer exciting possibilities for harvesting UV energy using 1l-TMd.

关键词： monolayer TMd Ws_(2) 2d-derived quantum dots UV absorption energy transfer

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Electron kinetic effects in back-stimulated Raman scattering bursts driven by broadband laser pulses

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Matter and Radiation at Extremes 2024年第4期9卷 54-67页

作者： Q.K.liu l.deng Q.Wang X.Zhang F.Q.Meng Y.P.Wang Y.Q.Gao H.B.Cai s.P.Zhu Graduate school China Academy of Engineering PhysicsBeijing 100088China Institute of Applied Physics and Computational Mathematics Beijing 100094China school of Nuclear science and Technology University of Science and Technology of ChinaHefei 230026China shanghai Institute of laser Plasma Shanghai 201800China HEdPs Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China school of Physics Zhejiang UniversityHangzhou 310027China

We examine electron kinetic effects in broadband-laser-driven back-stimulated Raman scattering(BsRs)bursts using particle-in-cell *** bursts occur during the nonlinear stage,causing reflectivity spikes and generating large numbers of hot ***-duration simulations are performed to observe burst events,and a simplified model is developed to eliminate the interference of the broadband laser’s random intensity *** the simplified model,we isolate and characterize the spectrum of electron plasma *** spectrum changes from a sideband structure to a turbulence-like structure during the burst.A significant asymmetry in the spectrum is *** asymmetry is amplified and transferred to electron phase space by high-intensity broadband laser pulses,leading to violent vortex-merging and generation of hot *** proportion of hot electrons increases from 6.76%to 14.7%during a single violent burst *** demonstrate that kinetic effects profoundly influence the BsRs evolution driven by broadband lasers.

关键词： scattering kinetic simplified

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Generation of polarized electron beams through self-injection in the interaction of a laser with a pre-polarized plasma

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High Power laser science and Engineering 2024年第3期12卷 62-68页

作者： l.R.Yin X.F.li Y.J.Gu N.Cao Q.Kong M.Büscher s.M.Weng M.Chen Z.M.sheng Key laboratory of Nuclear Physics and Ion-beam Application(MoE) Institute of Modern PhysicsDepartment of Nuclear Science and TechnologyFudan UniversityShanghaiChina state Key laboratory of High Field laser Physics Shanghai Institute of Optics and Fine MechanicsChinese Academy of SciencesShanghaiChina sANKEN(Institute of scientific and Industrial Research) Osaka UniversityOsakaJapan sichuan Research Institute Shanghai Jiao Tong UniversityChengduChina Peter Grünberg Institut(PGI-6) Forschungszentrum JülichJülichGermany Institut für laser-und Plasmaphysik Heinrich-Heine-Universität DüsseldorfDüsseldorfGermany Key laboratory for laser Plasmas(MoE) School of Physics and AstronomyShanghai Jiao Tong UniversityShanghaiChina Collaborative Innovation Center of IFsA Shanghai Jiao Tong UniversityShanghaiChina Tsung-dao lee Institute Shanghai Jiao Tong UniversityShanghaiChina

Polarized electron beam production via laser wakefield acceleration in pre-polarized plasma is investigated by particlein-cell *** evolution of the electron beam polarization is studied based on the Thomas±Bargmann±Michel±Telegdi equation for the transverse and longitudinal self-injection,and the depolarization process is found to be influenced by the injection *** the case of transverse self-injection,as found typically in the bubble regime,the spin precession of the accelerated electrons is mainly influenced by the ***,in the case of longitudinal injection in the quasi-1d regime(for example,*** et al.,***.110,135002(2013)),the direction of electron spin oscillates in the laser *** the electrons move around the laser axis,the net influence of the laser field is nearly zero and the contribution of the wakefield can be ***,an ultra-short electron beam with polarization of 99%can be obtained using longitudinal self-injection.

关键词： laser wakefield acceleration longitudinal self-injection particle-in-cell simulation polarized electron beam

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Effect of Ultraviolet Radiation on Hsp70 Protein Expression 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 Rodríguez Jesús Rodríguez Vergil Manuel Venancio Muñoz Juárez Kevin said Ramírez dávila luis Martín García Ortiz Germán Flores Cortés luz Elena Vidales Rodríguez Jesús Adrián lópez david Alejandro García lópez laboratorio de Biología Celular y Neurobiología Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México laboatorio de Bacterias y Hongos Filamentosos Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México laboratorio de MicroRNAs Unidad Académica de Ciencias Biológicas Universidad Autónoma de Zacatecas Zacatecas México

Ultraviolet radiation by its wavelength is divided into: UVA, UVB and UVC. Only UVA and UVB manage to penetrate the ozone layer, but due to anthropological activities, all of them are capable of interacting with humans to a greater or lesser extent, and can generate adverse effects such as cellular stress when interacting with intra-and extracellular biomolecules. The skin is the first organ in contact with UV radiation, and the stress it generates can be analyzed by the expression of a bioindicator of cellular damage such as Hsp70. Therefore, the objective of the project was: to determine the effect of UVA, UVB and UVC radiation on HaCaT epithelial cells, by analyzing the expression of Hsp70. Materials and methods: HaCaT cells were cultured in vitro, which were irradiated with UVA, UVB and UVC light at different doses, to subsequently determine the degree of Hsp70 expression by Immunodetection by PAGE-sds and Western Blot. Results: Basal expression of Hsp70 was observed in no irradiated HaCaT cells. When HaCaT cells were irradiated with UVA, UVB, UVC, an increase in this Hsp70 protein was observed. With UVA, a higher degree of expression was observed at a time of 30 minutes of irradiation. With UVB the highest expression shifted to a time of 20 minutes. With UVC, overexpression was observed after 10 minutes. Conclusion: UV radiation generates cellular stress on HaCaT cells, evaluated by the stress bioindicator Hsp70. According to the wavelength of UV radiation, those that have a shorter wavelength have a greater potential for cellular damage, 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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dose-response effect of pre-exercise carbohydrates under muscle glycogen unavailability:Insights from McArdle disease

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Journal of sport and Health science 2024年第3期13卷 398-408页

作者： Pedro l.Valenzuela Alfredo santalla lidia B.Alejo Andrea Merlo Asuncion Bustos laura Castellote-Belles Roser Ferrer-Costa Nicola A.Maffiuletti david Barranco-Gil Tomas Pinos Alejandro lucia Physical Activity and Health Research Group(“PaHerg”) Research Institute of Hospital“12 de Octubre”(“imas12”)Madrid 28041Spain department of systems Biology University of AlcalaMadrid 28871Spain department of sport and Computer science Section of Physical Education and SportsFaculty of SportUniversidad Pablo de OlavideSevilla 41013Spain EVOPREd Research Group Universidad Europea de CanariasTenerife 38300Spain Faculty of sport sciences Universidad Europea de MadridMadrid 28670Spain Gait&Motion Analysis laboratory Sol et Salus HospitalTorre Pedrera di Rimini(RN)47922Italy department of Clinical Biochemistry Laboratoris ClınicsHospital Universitari Vall d’HebronBarcelona 08035Spain Human Performance lab Schulthess ClinicZurich 8008Switzerland Biomedical Research Networking Center on Rare disorders(CIBERER) Barcelona 08035Spain Mitochondrial and Neuromuscular disorders Unit Vall d’Hebron Institut de RecercaUniversitat Autonoma de BarcelonaBarcelona 08035Spain

Background:This study aimed to determine the effect of different carbohydrate(CHO)doses on exercise capacity in patients with McArdle disease—the paradigm of“exercise intolerance”,characterized by complete muscle glycogen unavailability—and to determine whether higher exogenous glucose levels affect metabolic responses at the McArdle muscle cell(in vitro)***:Patients with McArdle disease(n=8)and healthy controls(n=9)underwent a 12-min submaximal cycling constant-load bout followed by a maximal ramp test 15 min after ingesting a non-caloric *** a randomized,double-blinded,cross-over design,patients repeated the tests after consuming either 75 g or 150 g of CHO(glucose:fructose=2:1).Cardiorespiratory,biochemical,perceptual,and electromyographic(EMG)variables were ***,glucose uptake and lactate appearance were studied in vitro in wild-type and McArdle mouse myotubes cultured with increasing glucose concentrations(0.35,1.00,4.50,and 10.00 g/l).Results:Compared with controls,patients showed the“classical”second-wind phenomenon(after prior disproportionate tachycardia,myalgia,and excess electromyographic activity during submaximal exercise,all pd an impaired endurance exercise capacity(-51%ventilatory threshold and55%peak power output,both pdless of the CHO dose(pdoses compared with the placebo),CHO intake increased blood glucose and lactate levels,decreased fat oxidation rates,and attenuated the second wind in the ***,only the higher dose increased ventilatory threshold(+27%,p=0.010)and peak power output(+18%,p=0.007).In vitro analyses revealed no differences in lactate levels across glucose concentrations in wild-type myotubes,whereas a doseresponse effect was observed in McArdle ***:CHO intake exerts beneficial effects on exercise capacity in McArdle disease,a condition associated with total muscle glycogen *** of these benefits are dose dependent.

关键词： Endurance Glycogen storage disease Glycogenosis Nutrition supplement

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Water quality, habitat, and fish assemblage relationships in middle-order agriculture and forest streams of the Mississippi Alluvial Plain

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Ecological Processes 2024年第1期13卷 217-236页

作者： Matthew l.skoog Michael A.Eggleton Yushun Chen department of Aquaculture and Fisheries University of Arkansas at Pine Bluff Minnesota department of Natural Resources state Key laboratory of Freshwater Ecology and Biotechnology Institute of Hydrobiology Chinese Academy of Sciences University of Chinese Academy of sciences

Background Agriculture has greatly influenced water quality, habitats, and fish assemblages in streams of the Mississippi Alluvial Plain(MAP) ecoregion. However, MAP streams have historically been understudied compared to streams in other agricultural regions of the UsA. In this study, water quality, habitat, and fish assemblage composition were assessed seasonally(spring, summer, and fall) in eight representative MAP streams located across three U.s. states. The study design included four streams containing highly agricultural watersheds(herein termed “agriculture” streams) and four streams containing mostly forested watersheds(herein termed “forest” streams), which were intended to represent reference conditions for MAP *** In general, forest streams contained significantly better instream and riparian habitats than agriculture streams(P = 0.010–0.040) whereas agriculture streams contained significantly greater levels of primary nutrients(P differences between agriculture and forest streams with respect to other physical and chemical variables were intermittent and season dependent. Fish assemblages in agriculture and forest streams were structured primarily along an environmental gradient reflecting instream habitat conditions, water nutrient concentrations, and benthic chlorophyll-a production. structurally, fish assemblages in both stream types contained many regionally common species, though some species appeared to exhibit affinities for a particular stream type. Functionally, fish assemblages in agriculture streams contained more tolerant species, more omnivores, and fewer insectivores compared to forest stream assemblages, which were nearly all insectivores. Overall, one-third of the fish specimens collected in forest streams classified as intolerant *** Our results suggested that stream water quality, habitat, and fish assemblages differed between agriculture and forest streams in the MAP, with fish assemblages e

关键词： Agriculture stream land use Water quality Habitat Fish Multivariate statistics Mississippi Alluvial Plain

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