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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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Role of pituitary adenylate cyclase-activating polypeptide in peripheral nerve regeneration:a cellular and molecular perspective

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Neural Regeneration Research 2024年第7期19卷 1429-1430页

作者： Grazia Maugeri Velia d’Agata Section of Anatomy Histology and Movement SciencesDepartment of Biomedical and Biotechnological SciencesUniversity of CataniaCataniaItaly

Neuro regeneration is a very complex phenomenon characterized by the generation of new neurons and synapses,involving connections between adjacent cells and axonal *** supplies additional longterm resources to replace... 详细信息

关键词： replace functional regeneration

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Approximate contact solutions for non-axisymmetric homogeneous and power-law graded elastic bodies:A practical tool for design engineers and tribologists

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Friction 2024年第2期12卷 340-355页

作者： Valentin l.POPOV Qiang lI Emanuel WIllERT Institute of Mechanics Technische Universität BerlinBerlin 10623Germany

In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution *** solutions were derived for profiles,which only slightly deviate from the axisymmetric *** the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

关键词： normal contact non-axisymmetric indenter extremal principle generalized method of dimensionality reduction(MdR) functional elastic grading

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Guaranteed Cost Attitude Tracking Control for Uncertain Quadrotor Unmanned Aerial Vehicle Under Safety Constraints

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1447-1457页

作者： Qian Ma Peng Jin Frank l.lewis School of Automation Nanjing University of Science and TechnologyNanjing 210094China UTA Research Institute University of Texas at ArlingtonFort WorthTexas 76118 USA IEEE

In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is ***,an augmented system is constructed by the tracking error system and reference *** transformation aims to convert the tracking control prob-lem into a stabilization control ***,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty *** on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is ***,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal *** proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety *** performance of the algorithm is evaluated by the numerical simulation.

关键词： Attitude tracking control quadrotor unmanned aerial vehicle(QUAV) reinforcement learning safety constraints uncertain disturbances.

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The influence of various grease compositions and silver nanoparticle additives on electrically induced rolling-element bearing damage

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Friction 2024年第4期12卷 796-811页

作者： Samuel BONd Robert l.JACKSON German MIllS department of Chemistry and Biochemistry Auburn UniversityAuburn 36849-5412USA department of Mechanical Engineering Auburn UniversityAuburn 36849-5412USA

leakage currents accelerate surface degradation of metal contacts via small scale arcing across lubricating films,but recent observations suggest that metallic nanoparticle additives in lubricants may be useful to improve contact *** findings prompted a study that examined electrically induced surface pitting of steel contacts in the presence of several lubricating greases including some containing nanometer-sized colloidal silver(Ag)*** rolling sphere-on-disk experiments were conducted under electro-tribological loads employing polyurea greases derived from mineral and synthetic base oils with and without *** forces and electrical resistance were monitored continuously during the tests;surface changes were characterized by means of optical spectroscopy,stylus profilometry,and scanning electron microscopy(SEM)including compositional analysis using energy dispersive spectroscopy(EdS).The observations demonstrate that surface pitting induced by arcing occurs mainly at the points were the rolling motion changes direction and that eroded metal is deposited along the wear ***-sized pits are formed which contain carbon and oxygen indicating that arcing causes decomposition of the hydrocarbon *** findings indicate a significant inhibition of pitting is induced by the Ag nanoparticles;some greases containing other additives exhibit a similar,although less pronounced,effect.

关键词： electric motor bearings wheel bearings electric vehicles arcing electrically induced bearing damage pitting leakage current stray current

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Process engineering of demineralisation of moderate to high ash Indian coals through NaOH‑HCl leaching and HF leaching

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International Journal of Coal Science & Technology 2024年第2期11卷 111-122页

作者： Heena dhawan d.K.Sharma ANRF Ministry of ScienceNew DelhiIndia department of Energy Science and Engineering Indian Institute of Technology DelhiNew Delhi 110016India

Chemical leaching of coals would be required to produce cleaner coals for some special applications where physical benefi-ciation may not be effective *** would also help in recovering li and rare earth metals besides in the sequestration of CO_(2).About 20 Indian coals having complexly distributed moderate to high ash contents were sequentially treated with various alkali–acid such as NaOH-HCl,HF,HCl,HCl-HF,and NaOH-HCl-HF *** aimed to establish and design the best stepwise sequential process for the highest degree of demineralisation through a chemical leaching *** and process intensification studies were carried *** than 80%demineralisation of Madhaipur and Neemcha coals was observed using the best sequential treatment designed *** repeated stepwise treatment of the alkali and the acid was also studied,which was found to significantly enhance the degree of demineralisation of *** integrated process of alkali–acid leaching followed by solvent extraction(Organo-refining)and vice versa of the treated coal was also studied for producing cleaner coals.

关键词： Alkali–acid leaching demineralisation Integrated process Rare earth elements

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Improved leap-frog Method for Time-domain Fault location

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Journal of Modern Power Systems and Clean Energy 2024年第2期12卷 670-674页

作者： Izudin džafić Rabih A.Jabr Faculty of Electrical Engineering University of SarajevoSarajevo 71000Bosnia and Herzegovina department of Electrical and Computer Engineering American University of BeirutBeirut 11072020Lebanon IEEE

The partial differential equation(PdE)solution of the telegrapher is a promising fault location method among time-domain and model-based *** research works have shown that the leap-frog process is superior to other explicit methods for the PdE ***,its implementation is challenged by determining the initial conditions in time and the boundary conditions in *** letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal *** results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme,particularly in the presence of harmonics.

关键词： Fault location leap-frog partial differential equation time-domain analysis transmission line

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

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Chinese Physics 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.Valiente-dobón d.Testov M.Mazzocco A.Gozzelino C.Parascandolo d.Pierroutsakou M.la Commara A.Goasduff d.Bazzacco d.R.Napoli F.Galtarossa F.Recchia A.Illana S.Bakes I.Zanon S.Aydin G.de Angelis M.Siciliano R.Menegazzo S.M.lenzi J.l.Ferreira J.Rangel Serkan Akkoyun l.F.Canto J.lubian School of Physics Beihang UniversityBeijing 100191China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-Sen UniversityZhuhai 519082China Instituto de Física Universidade Federal Fluminense24210-340NiteróiRio de JaneiroBrazil Institute for Advanced Study in Nuclear Energy&Safety Shenzhen UniversityShenzhen 518060China Shenzhen Key laboratory of Research and Manufacture of High Purity Germanium Materials and Fetectors Shenzhen UniversityShenzhen 518060China INFN Sezione di PadovaPadovaItaly dipartimento di fisica Astronomia dell'Universita di padova PadovaItaly State Key laboratory of Radiation Medicine and Protection School of Radiation Medicine and ProtectionSoochow UniversitySuzhou 215123China China Institute of Atomic Energy Beijing 102413China The Key laboratory of Beam Technology 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 dipartimento di Farmacia Universitàdi Napoli"Federico II"I-80131 NapoliItaly department of Natural and Mathematical Sciences Faculty of EngineeringTarsus University33480 MersinTurkiye Physics division Argonne National LaboratoryLemont-ILUSA departamento de Matemaética Física e Computaç˜ao Universidade do Estado do Rio de JaneiroFaculdade de Tecnologia27537-000ResendeRio de JaneiroBrazil department of Physics Sivas Cumhuriyet UniversitySivasTurkey Instituto de Física Universidade Federal do Rio de JaneiroCP 6852821941-972Rio de JaneiroBrazil

The complete and incomplete fusion cross sections for ^(6)li+^(209)Bi were measured using the in-beamγ-ray method around the Coulomb *** cross sections of(deuteron captured)incomplete fusion(ICF)products were re-quantified experimentally for this reaction *** results reveal that the ICF cross section is equivalent to that of complete fusion(CF)above the Coulomb barrier and dominant near or below the Coulomb barrier.A theoretical calculation based on the continuum discretized coupled channel(CdCC)method was performed for the aforementioned CF and ICF cross sections;the result is consistent with the *** universal fusion function(UFF)was also compared with the measured CF cross section for different barrier parameters,demonstrating that the CF suppression factor is significantly influenced by the choice of potential,which can reflect both dynamic and static effects of breakup on the fusion process.

关键词： cross section incomplete fusion suppression factor weakly bound nuclei

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Corrosion testing of X52 and X80 steels immersed in stimulated emulsions using a real petroleum sample

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Petroleum Research 2024年第2期9卷 304-316页

作者： l.M.Quej-Ake J.l.Alamilla A.Contreras Instituto Mexicano del Petróleo Eje Central Lázaro CárdenasNorte 152San Bartolo AtepehuacanGustavo A.MaderoCiudad de MéxicoC.P.07730México

The aim of this study is to evaluate the internal corrosion process on X52 and X80 steels/real petroleum interfaces containing condensed hydrocarbon plus oilfield-produced water,which were subjected to stimulated emulsions using 50/50 vol ratio mixtures at 45℃,different hydrodynamic conditions,1 h,and 24 h.A washing process by using deionized water was proposed to simulate and identify the corrosiveness of the hydrocarbon phase after 24 h of exposure *** characterization by electrochemical impedance spectroscopy and the monitoring of the polarization curves indicated that X80 steel/oilfield-produced water interfaces were more susceptible to corrosion than X52 steel exposed to oilfield-produced *** combined speed rotation of 600 rpm using a magnetic stirrer+600 rpm using a rotating disk electrode decreased the corrosion rate on X52 *** stimulated emulsions made of hydrocarbon+oilfield-produced water and hydrocarbon+deionized water at 24 h increased the corrosion rate on X80 steel(0.34 mm/year and 0.43 mm/year,respectively),promoting the formation of erosion and pitting *** types of corrosion depended mainly on the physicochemical properties of the hydrocarbon,oilfield-produced water,exposure times,and hydrodynamic systems in which the hydrocarbon was studied.

关键词： Corrosion Emulsions X52 steel X80 steel

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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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