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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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Adaptive Control of a Flexible Manipulator With Unknown Hysteresis and Intermittent Actuator Faults

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IEEE/CAA Journal of Automatica Sinica 2025年第1期12卷 148-158页

作者： Shouyan Chen Weitian He Zhijia Zhao Yun Feng Zhijie liu keum-Shik Hong School of Mechanical and Electrical Engineering Guangzhou University the School of Control Science and Engineering Shandong University IEEE the College of Electrical and Information Engineering Hunan University the National Engineering Research Center for Robot Visual Perception and Control Technology Hunan University the School of Intelligence Science and Technology University of Science and Technology Beijing (USTB) the Institute for Future the School of AutomationQingdao University the School of Mechanical Engineering Pusan National University

In this study, we consider a single-link flexible manipulator in the presence of an unknown Bouc-Wen type of hysteresis and intermittent actuator faults. First, an inverse hysteresis dynamics model is introduced, and then the control input is divided into an expected input and an error compensator. Second,a novel adaptive neural network-based control scheme is proposed to cancel the unknown input hysteresis. Subsequently,by modifying the adaptive laws and local control laws, a fault-tolerant control strategy is applied to address uncertain intermittent actuator faults in a flexible manipulator system. Through the direct lyapunov theory, the proposed scheme allows the state errors to asymptotically converge to a specified interval. Finally,the effectiveness of the proposed scheme is verified through numerical simulations and experiments.

关键词： Adaptive control flexible manipulator intermittent actuator faults inverse hysteresis dynamics vibration control

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Anti-amyloid antibodies in Alzheimer’s disease: what did clinical trials teach us?

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Neural Regeneration Research 2025年第4期20卷 1092-1093页

作者： danko Jeremic lydia Jiménez-díaz Juan d.Navarro-lópez NeuroPhysiology&Behavior lab University of Castilla-La ManchaBiomedical Research Center(CRIB)School of Medicine of Ciudad RealCiudad RealSpain

Although many causes of Alzheimer’s disease(Ad)may exist,both the original amyloid cascade and tau hypotheses posit that abnormal misfolding and accumulation of amyloid-β(Aβ)and tau protein is the central event causing the ***,that conclusion could be only partly true,and there is conflicting evidence about the role of both proteins in Ad,being able to precede and influence one *** researchers argue that these proteins are mere executors rather than primary causes of ***,there have been continuing refinements of both hypotheses,with alternative explanations proposed.Aβand tau proteins may be independently involved in specific neurotoxic pathways;yet there may be other crucial processes going on in early ***,accumulating evidence suggests that Aβand tau act synergistically,rather than additively in disease onset(Jeremic et al.,2021,2023a).

关键词： amyloid Alzheimer additive

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Knotting ligands to control metal coordination geometry

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Science China Chemistry 2025年第2期68卷 403-404页

作者： Fabien B.l.Cougnon department of Chemistry and Nanoscience Centre University of JyväskyläJyväskyläFinland

Zinc is a metal of particular importance for life[1].It is the most abundant transition metal in biological systems after iron and contributes both structural and catalytic roles to many cellular *** properties of Zn^(Ⅱ),unlike those of any other first-row transition metal ions,explain its biological *** to its filled d-shell orbitals,Zn^(Ⅱ) is redox-stable,has a ligand-field energy stabilization of zero and,consequently,no typical coordination number and *** metalloproteins exploit these features to carry a broad range of chemical reactions in mild *** metalloenzymes,unsaturated ZnII centres often act as redox-stable lewis *** protein backbone provides a highly preorganized environment around the metal centre and accompanies the changes in coordination geometry occurring as substrate transformation proceeds,thereby modulating the metal reactivity.

关键词： coordination geometry centre

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Tailored design of novel Co0-Coδ+dual phase nanoparticles for selective CO2 hydrogenation to ethanol

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Journal of Environmental Sciences 2025年第3期149卷 598-615页

作者： Subhasis das Ganapati d.Yadav department of Chemical Engineering Institute of Chemical TechnologyNathalal Parekh MargMatunga 400019MumbaiIndia

Catalytic hydrogenation of CO_(2)to ethanol is a promising solution to address the greenhouse gas(GHG)emissions,but many current catalysts face efficiency and cost *** based catalysts are frequently examined due to their abundance,cost-efficiency,and effectiveness in the reaction,where managing the Co^(0)to Co^(δ+)ratio is *** this study,we adjusted support nature(Al_(2)O_(3),MgO-MgAl_(2)O_(4),and MgO)and reduction conditions to optimize this balance of Co^(0)to Co^(δ+)sites on the catalyst surface,enhancing ethanol *** selectivity of ethanol reached 17.9%in a continuous flow fixed bed micro-reactor over 20 mol%Co@MgO-MgAl_(2)O_(4)(CoMgAl)catalyst at 270°C and 3.0 MPa,when reduced at 400°C for 8 *** results coupled with activity analysis confirmed that mild reduction condition(400°C,10%H_(2)balance N_(2),8 h)with intermediate metal support interaction favoured the generation of partially reduced Co sites(Co^(δ+)and Co^(0)sites in single atom)over MgO-MgAl_(2)O_(4)surface,which promoted ethanol synthesis by coupling of dissociative(CHx^(∗))/non-dissociative(CHxO^(∗))intermediates,as confirmed by density functional theory ***,the CoMgAl,affordably prepared through the coprecipitation method,offers a potential alternative for CO_(2)hydrogenation to yield valuable chemicals.

关键词： CO_(2)hydrogenation Ethanol Co-based catalysts Metal support ineraction dFT analysis

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Morphology and phylogeny of two species of Bathypathes from the tropical western Pacific,with description of a new species

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Journal of Oceanology and limnology 2025年第1期43卷 248-260页

作者： Ting lÜ Zifeng ZHAN Kuidong XU laboratory of Marine Organism Taxonomy and Phylogeny Qingdao Key Laboratory of Marine Biodiversity and ConservationInstitute of OceanologyChinese Academy of SciencesQingdao 266071China laboratory for Marine Biology and Biotechnology Laoshan LaboratoryQingdao 266237China University of Chinese Academy of Sciences Beijing 100049China

The black coral genus Bathypathes Brook,1889 represents a relatively diverse and ecologically important assemblage comprising the deep-sea hard substrate *** phylogenetic investigations have revealed the polyphyletic nature of Bathypathes,urging further morphological analysis to understand its *** combing morphological and molecular data,we describe Bathypathes multifurcata *** report *** Molodtsova,Opresko&Wagner,2022based on the specimens collected from the tropical western *** phylogenetic topology reconstructed using nuclear ITS1-5.8S-ITS2 and three mitochondrial fragments suggests the separation of Bathypathes into four *** analysis of morphological characters,particularly the colony branch and pinnule patterns also roughly classify Bathypathes into four morphological groups A–*** A is characterized by the unbranched colony and the subopposite arrangement of *** contrast to Group A,Groups B–d have the alternately arranged *** these,Group C exhibits a distinctly long unpinnulated stem compared to Groups B and *** B has unbranched colony,relatively short unpinnulated stem,and spines on pinnules have blunt *** Group d,large colonies(higher than 40 cm)have one or a few branches,small colonies(less than 40 cm)are unbranched,and spines on pinnules have acute *** data particularly those species without sequences are necessary to verify the classification of these groups.

关键词： Antipatharia black coral taxonomy phylogeny seamount western Pacific

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Are urbanization, biotic and social factors associated with the song frequency and song entropy attributes of three urban syntopic passerines?

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Avian Research 2025年第01期 96-109页

作者： Xhareni díaz-lezama Alejandro Ariel Ríos-Chelén Jorge Castellanos-Albores Paula l.Enríquez Programa de Posgrado en Ciencias en Recursos Naturales y desarrollo Rural El Colegio de la Frontera Sur.Carr.Panamericana y Periférico Sur s/n Barrio Ma.Auxiliadora Centro Tlaxcala de Biología de la Conducta Universidad Autónoma de Tlaxcala departamento Conservación de la Biodiversidad El Colegio de la Frontera Sur Carr.Panamericana y Periférico Sur s/n Barrio Ma.Auxiliadora

Urban environments have challenging characteristics for bird acoustic communication. High levels of anthropogenic noise, as well as vegetation structure(e.g., in urban parks), can potentially affect the song frequency characteristics of several bird species. An additional factor such as the abundance of conspecific and heterospecific vocalizing birds may play an important role in determining the structure of bird songs. In this study, we analyzed whether noise levels, vegetation percentage, and abundance of conspecifics and heterospecifics influence the song characteristics of three syntopic songbird species: House Finch(Haemorhous mexicanus), Rufouscollared Sparrow(Zonotrichia capensis), and House Sparrow(Passer domesticus) living in urban sites. We recorded songs of these species and measured the peak frequency and entropy of their songs at 14 sites in the city of San Cristobal de las Casas, Chiapas, Mexico. We found that the song peak frequency of House Finch and House Sparrow's songs was negatively related to the vegetation. The peak frequency of neither of the three species correlated with the average noise level. However, the abundances of conspecific and heterospecific were related to the peak frequency of the three species' songs. The entropy of the House Finch and House Sparrow songs was positively and negatively related, respectively, to noise levels. House Sparrow song entropy was negatively related to the percentage of vegetation. Song entropy of House Finches was negatively associated to conspecific and House Sparrow abundance. Song entropy of Rufous-collared Sparrows was positively related to conspecific abundance. In conclusion, the song peak frequency and song entropy of the three songbird species were differentially related to urban noise, vegetation, and conspecific and heterospecific abundance, suggesting these factors influence bird song characteristics.

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Polyethylene glycol has immunoprotective effects on sciatic allografts, but behavioral recovery and graft tolerance require neurorrhaphy and axonal fusion

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Neural Regeneration Research 2025年第4期20卷 1192-1206页

作者： Tyler A.Smith liwen Zhou Cameron l.Ghergherehchi Michelle Mikesh Cathy Z.Yang Haley O.Tucker JuliAnne Allgood Jared S.Bushman George d.Bittner department of Molecular Biosciences University of Texas at AustinAustinTXUSA department of Neuroscience University of Texas at AustinAustinTXUSA division of Pharmaceutical Sciences University of WyomingLaramieWYUSA

Behavioral recovery using(viable)peripheral nerve allografts to repair ablation-type(segmental-loss)peripheral nerve injuries is delayed or poor due to slow and inaccurate axonal ***,such peripheral nerve allografts undergo immunological rejection by the host immune *** contrast,peripheral nerve injuries repaired by polyethylene glycol fusion of peripheral nerve allografts exhibit excellent behavioral recovery within weeks,reduced immune responses,and many axons do not undergo Wallerian *** relative contribution of neurorrhaphy and polyethylene glycol-fusion of axons versus the effects of polyethylene glycol per se was unknown prior to this *** hypothesized that polyethylene glycol might have some immune-protective effects,but polyethylene glycol-fusion was necessary to prevent Wallerian degeneration and functional/behavioral *** examined how polyethylene glycol solutions per se affect functional and behavioral recovery and peripheral nerve allograft morphological and immunological responses in the absence of polyethylene glycol-induced axonal ***-type sciatic nerve injuries in outbred Sprague–dawley rats were repaired according to a modified protocol using the same solutions as polyethylene glycol-fused peripheral nerve allografts,but peripheral nerve allografts were loose-sutured(loose-sutured polyethylene glycol)with an intentional gap of 1–2 mm to prevent fusion by polyethylene glycol of peripheral nerve allograft axons with host *** to negative control peripheral nerve allografts not treated by polyethylene glycol and in contrast to polyethylene glycol-fused peripheral nerve allografts,animals with loose-sutured polyethylene glycol peripheral nerve allografts exhibited Wallerian degeneration for all axons and myelin degeneration by 7 days postoperatively and did not recover sciatic-mediated behavioral functions by 42 days *** morphological signs of rejection,such as col

关键词： allograft rejection axotomy macrophage myelin nerve repair polyethylene glycol(PEG) sciatic nerve T cell transplantation Wallerian degeneration

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Biochemical dissection of STAT3 signaling in amyotrophic lateral sclerosis

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Neural Regeneration Research 2025年第11期20卷 3229-3230页

作者： Savina Apolloni Nadia d’Ambrosi department of Biology University of Rome Tor VergataRomeItaly

Amyotrophic lateral sclerosis(AlS)is a progressive neurodegenerative disease characterized by the loss of upper and lower motor neurons,clinically marked by muscle atrophy and *** the clinical course is highly variable,the average time from the onset of symptoms to the need for respiratory support or death is 3-5 *** is the most prevalent motor neuron disease in adults,occurring at a rate of 2 per 100,000 individuals and affecting 5.4 per 100,000 individuals overall.

关键词： STAT3 dissection sclerosis

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From Imperfection to Perfection: Advanced 3d Facial Reconstruction Using MICA Models and Self-Supervision learning

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Computer Modeling in Engineering & Sciences 2025年第2期142卷 1459-1479页

作者： Thinh d.le duong Q.Nguyen Phuong d.Nguyen H.Nguyen-Xuan CIRTECH Institute HUTECH UniversityHo Chi Minh City72308Viet Nam

Research on reconstructing imperfect faces is a challenging *** this study,we explore a data-driven approach using a pre-trained MICA(MetrIC fAce)model combined with 3d printing to address this *** propose a training strategy that utilizes the pre-trained MICA model and self-supervised learning techniques to improve accuracy and reduce the time needed for 3d facial structure *** results demonstrate high accuracy,evaluated by the geometric loss function and various statistical *** showcase the effectiveness of the approach,we used 3d printing to create a model that covers facial *** findings indicate that our method produces a model that fits well and achieves comprehensive 3d facial *** technique has the potential to aid doctors in treating patients with facial injuries.

关键词： 3d face reconstruction self-supervised learning face defect 3d printed prototypes

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