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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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Sustainable graywater reuse for residential landscape irrigation-a critical review

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Chinese Journal of Population,Resources and Environment 2015年第3期13卷 250-264页

作者： u.Pinto B.l.Maheshwari School of Science & Health University of Western Sydney

The demand for potable water is rising rapidly due to an ever-increasing population,economic activities,and dwindling water *** provide adequate water supplies in the future,understanding the issues and challenges in the reuse of water and developing appropriate strategies for reuse will be *** way to augment water supplies for residential.use is to reuse graywater- the wastewater from kitchens,bathrooms,and *** this article,we critically review the evolution of water reuse,the definition of graywater,graywater reuse practices,volumes and flow in different situations,and graywater *** then examine the issues associated with different graywater treatment methods and how using graywater for irrigation around homes affects soil quality and plant *** study concludes that graywater treatment costs,human health risks,and its effect on soil quality are some of the challenges that need to be addressed in the future for widespread and sustainable reuse of graywater for irrigation around homes.

关键词： water reuse graywater irrigation sustainability urban water water treatment

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Integrated Approaches of Mechanical Barrier, Insecticide and Botanicals against Mango Mealybug (Drosicha mangiferae)

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Advances in Entomology 2024年第3期12卷 195-202页

作者： N. Akhter M. Z. Alam M. A. Rahaman M. R. u. Miah I. H. Mian M. A. latif Department of Entomology Faculty of Agriculture Sher-e-Bangla Agricultural University Dhaka Bangladesh Department of Entomology Faculty of Agriculture Bangabandhu Sheikh Mujibur Rahman Agricultural University Gazipur Bangladesh Department of Plant Pathology Faculty of Agriculture Sher-e-Bangla Agricultural University Dhaka Bangladesh Department of Plant Pathology Bangabandhu Sheikh Mujibur Rahman Agricultural University Gazipur Bangladesh

An experiment was conducted to test the efficacy of a mechanical barrier around the tree trunk with one spray of Cypermethrin @ 1 ml/l and turmeric powder extract @ 15 g/500ml of water applied in integrated approaches against mango mealybug on mango tree. There were 7 treatments including a control. The treatments were Mechanical barrier, Cypermethrin spray @ 1 ml/l, Turmeric powder spray @ 15 g/500ml of water, Cypermethrin spray + Turmeric spray, Cypermethrin spray + Mechanical barrier, Turmeric + Mechanical barrier and untreated control. Three-year-old mango plants grafted from a 5-year-old mango tree (Variety Amropali) and planted in pots were used in the experiment. The treatment, Cypermethrin spray + Mechanical barrier gave the highest reduction of mango mealybug population 87.06% to 93.90% followed by Turmeric spray + Mechanical barrier and showed 81.13% to 86.04% and Mechanical barrier alone showed 81.13% to 84.59% population reduction. Turmeric powder extract showed only (8.42% to 23.77%) population reduction of mango mealybug which was lowest compared to other treatments.

关键词： Mango Mealybug Integrated Management

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luminescence investigation of Dy2O2S and Dy2O2SO4 obtained by thermal decomposition of sulfate hydrate

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Journal of Rare Earths 2016年第8期34卷 814-819页

作者： R.V.Rodngues l.Marciniak l.u.Khan J.R.Matos H.F.Brito W.Strek Institute of Chemistry University of Sao Paulo Butanta 748 26077 Sao Paulo Brasil Institute of low Temperature and Structure Research University of Wroctaw Oko1na 250-422 Wroclaw Poland

The yellow emitting dysprosium oxysulfide （Dy2O2S） and dysprosium oxysulfate （Dy202SO4） compounds were prepared from the thermal decomposition of hydrated dysprosium sulphate. The materials were characterized by using thermogravimetry （TG/DTG）, X-ray powder diffraction （XRD）, Fourier transform infrared （FTIR） and Raman spectroscopies. The thermal stability temperatures at around 1151 and 1313 K were determined for the Dy202S and Dy202SO4 materials, respectively. The photolumines- cence properties of the dysprosium oxysulfide were investigated, showing narrow emission bands assigned to the 4F9/2----＊6HJ intracon- figurational transitions of the Dy3＋ ion. The yellow emission color of this phosphor suggests that the Dy202S is a promising material for applications in lEDs.

关键词： Dy202S/Dy202SO4 sulfate thermal decomposition luminescence rare earths

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Cerebral small vessel disease modifies outcomes after minimally invasive surgery for intracerebral haemorrhage

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Stroke & Vascular Neurology 2024年第4期9卷 446-456,I0147页

作者： Yunke li Sung-Min Cho Radhika Avadhani Hassan Ali Yi Hao Santosh B Murthy Joshua N Goldstein Fan Xia Xin Hu Natalie l.ullman Issam Awad Daniel Hanley Wendy C Ziai The George Institute for Global Health BeijingChina Department of Neurology Division of Neurocritical CareJohns Hopkins Medical InstitutionsBaltimoreMarylandUSA Department of Neurology Division of Brain Injury OutcomesJohns Hopkins Medical Institutions CampusBaltimoreMarylandUSA Department of Neurology Weill Cornell Medical CollegeNew YorkNew YorkUSA Department of Emergency Medicine Massachusetts General HospitalBostonMassachusettsUSA Department of Neurosurgery West China Hospital of MedicineChengduSichuanChina Department of Neurosurgery University of Chicago Pritzker School of MedicineChicagoIllinoisUSA

Background Minimally invasive surgery(MIS)for spontaneous supratentorial intracerebral haemorrhage(ICH)is controversial but may be beneficial if end-of-treatment(EOT)haematoma volume is reduced to≤15 *** explored whether MRI findings of cerebral small vessel disease(CSVD)modify the effect of MIS on long-term *** Prespecified blinded subgroup analysis of 288 subjects with qualified imaging sequences from the phase 3 Minimally Invasive Surgery Plus Alteplase for Intracerebral Haemorrhage Evacuation(MISTIE)*** tested for heterogeneity in the effects of MIS and MIS+EOT volume≤15 ml on the trial’s primary outcome of good versus poor function at 1 year by the presence of single CSVD features and CSVD scores using multivariable *** Of 499 patients enrolled in MISTIE III,288 patients had MRI,149(51.7%)randomised to MIS and 139(48.3%)to standard medical care(SMC).Median(IQR)ICH volume was 42(30–53)*** the full MRI cohort,there was no statistically significant heterogeneity in the effects of MIS versus SMC on 1-year outcomes by any specific CSVD feature or by CSVD scores(all P_(interaction)>0.05).In 94 MIS patients with EOT ICH volume≤15 ml,significant reduction in odds of poor outcome was found with cerebral amyloid angiopathy scorelacunes(OR,0.37(0.18–0.80);P_(interaction)=0.02)and absence of severe white matter hyperintensities(WMHs)(OR,0.22(0.08–0.58);P_(interaction)=0.03).Conclusions Following successful haematoma reduction by MIS,we found significantly lower odds of poor functional outcome with lower total burden of CSVD in addition to absence of lacunes and severe *** features may have utility for prognostication and patient selection in clinical trials of MIS.

关键词： Surgery surgery absence

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Pressure Distinguishes the Dual Emissions in Pseudohalide 2D Ruddlesden-Popper Perovskite Cs_(2)Pb(SCN)_(2)Br_(2)

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CCS Chemistry 2024年第7期6卷 1748-1756页

作者： Songhao Guo Yuhong Mao Congcong Chen Yao Zhang Guoxiang Zhao Kejun Bu Qingyang Hu Haiming Zhu Guifu Zou Wenge Yang lingling Mao Xujie lü Center for High Pressure Science and Technology Advanced Research(HPSTAR) Shanghai Department of Chemistry Southern University of Science and TechnologyShenzhen Department of Chemistry Zhejiang UniversityHangzhou College of Energy Key Laboratory of Advanced Carbon Materials and Wearable Energy Technologies of Jiangsu ProvinceSoochow UniversitySuzhou

Two-dimensional(2D)Ruddlesden-Popper(RP)halide perovskites with diverse structures and properties have drawn increasing attention due to their promising optoelectronic ***,a new all-inorganic Cs_(2)Pb(SCN)_(2)Br_(2) has been reported that opens up new potential for the development of 2D RP ***,recent reports of unusual dual emissions and two-edge absorption in Cs_(2)Pb(SCN)_(2)Br_(2) have generated intense debate about its origin and remains ***,by combining continuous pressure tuning with in situ diagnostics,we have unambiguously revealed the underlying mechanisms that the 2D Cs_(2)Pb(SCN)_(2)Br_(2) exhibits an intrinsic blue emission at 2.66 eV and an absorption edge close to the emission *** the gradually formed CsPbBr_(3) is responsible for the green emission at 2.33 eV with the absorption shoulder at 2.41 ***,by fitting the temperature-dependent intensity of the intrinsic blue emission,we have determined the corrected value of exciton binding energy for 2D Cs_(2)Pb(SCN)_(2)Br_(2) to be 90 ***,an emission enhancement of 2.5 times is achieved in Cs_(2)Pb(SCN)_(2)Br_(2) under a mild pressure within 0.8 GPa,caused by the pressuresuppressed exciton-phonon *** work not only elucidates the origin of the dual emissions and two-edge absorption in Cs_(2)Pb(SCN)_(2)Br_(2),but it also provides a potential means to regulate and optimize the optoelectronic properties of 2D perovskites.

关键词： two-dimensional perovskite dual emissions two-edge absorption high pressure in situ characterization enhanced photoluminescence

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Neuroprotective effects of G9a inhibition through modulation of peroxisome-proliferator activator receptor gamma-dependent pathways by miR-128

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Neural Regeneration Research 2024年第11期19卷 2532-2542页

作者： Aina Bellver-Sanchis Pedro AAvila-lópez Iva Tic David Valle-García Marta Ribalta-Vilella luis labrador Deb Ranjan Banerjee Ana Guerrero Gemma Casadesus Coralie Poulard Mercè Pallàs Christian Grinán-Ferré Department of Pharmacology and Therapeutic Chemistry Institut de Neurociències-Universitat de BarcelonaBarcelonaSpain Department of Biochemistry and Molecular Genetics Feinberg School of MedicineNorthwestern UniversityChicagoILUSA Institute of Biotechnology National Autonomous University of MexicoCuernavacaMexico Department of Pharmacology and Therapeutics Health Science Center-University of FloridaGainesvilleFLUSA Department of Chemistry National Institute of Technology DurgapurM G AvenueDurgapurWest BengalIndia Cancer Research Cancer lyon Universitéde LyonLyonFrance Inserm u1052 Centre de Recherche en Cancérologie de LyonLyonFrance CNRS uMR5286 Centre de Recherche en Cancérlogie de LyonLyonFrance Centro de Investigación en Red Enfermedades Neurodegenerativas(CIBERNED)Instituto de Salud Carlos IIIMadridSpain Neuroimmunology Department National Institute of Neurology and Neurosurgery“Manuel Velasco Suárez”Mexico CityMexico

Dysregulation of G9a,a histone-lysine N-methyltransferase,has been observed in Alzheimer’s disease and has been correlated with increased levels of chronic inflammation and oxidative ***,microRNAs are involved in many biological processes and diseases playing a key role in pathogenesis,especially in multifactorial diseases such as Alzheimer’s ***,our aim has been to provide partial insights into the interconnection between G9a,microRNAs,oxidative stress,and *** better understand the biology of G9a,we compared the global microRNA expression between senescence-accelerated mouse-prone 8(SAMP8)control mice and SAMP8 treated with G9a inhibitor *** found a downregulation of miR-128 after a G9a inhibition treatment,which interestingly binds to the 3′untranslated region(3′-uTR)of peroxisome-proliferator activator receptor γ(PPARG)***,Pparg gene expression levels were higher in the SAMP8 group treated with G9a inhibitor than in the SAMP8 control *** also observed modulation of oxidative stress responses might be mainly driven Pparg after G9a *** confirm these antioxidant effects,we treated primary neuron cell cul.ures with hydrogen peroxide as an oxidative *** this setting,treatment with G9a inhibitor increases both cell survival and antioxidant ***,up-regulation of PPARγby G9a inhibitor could also increase the expression of genes involved in DNA damage responses and *** addition,we also described that the PPARγ/AMPK axis partially explains the regulation of autophagy markers ***,PPARγ/GADD45αpotentially contributes to enhancing synaptic plasticity and neurogenesis after G9a ***,we propose that pharmacological inhibition of G9a leads to a neuroprotective effect that could be due,at least in part,by the modulation of PPARγ-dependent pathways by miR-128.

关键词： aging cognitive decline epigenetics G9a inhibition microRNAs miR-128 peroxisome-proliferator activator receptorγ(PPARγ) PPARG SAMP8

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A comparison of animal color measurements using a commercially available digital color sensor and photograph analysis

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Current Zoology 2020年第6期66卷 601-606页

作者： Alex D.Potash Daniel.u.Greene Gabrielle A.Foursa Verity l.Mathis l.Mike Conner Robert A.McCleery Department of Wildlife Ecology and Conservation University of Florida Institute of Food and Agricultural ScienceGainesvilleFL 32611USA Weyerhaeuser Company Environmental Research SouthColumbusMS 39701USA Department of Biology University of FloridaGainesvilleFL 32611USA Florida Museum of Natural History University of FloridaGainesvilleFL 32611USA The Jones Center at Ichauway NewtonGA 39870USA

An animal's pelage,feather,or skin color can serve a variety of functions,so it is important to have multiple standardized methods for measuring *** of the most common and reliable methods for measuring animal coloration is the use of standardized digital photographs of *** tech no logy in the form of a commercially available handheld digital color sensor could provide an alter native to photography-based animal color *** determine whether a digital color sensor could be used to measure animal coloration,we tested the ability of a digital color sensor to measure coloration of mammalian,avian,and lepidopteran museums *** compared results from the sensor to measurements taken using traditional photography *** study yielded significant differences between photography-based and digital color sensor measurements of brightness(light to dark)and colors along the green to red *** was no difference between photographs and the digital color sensor measurements for colors along the blue to yellow *** average difference in recorded color(AE)by the 2 methods was above the threshold at which humans can perceive a *** were sign讦icant correlations between the sensor and photographs for all measurements indicating that the sensor is an effective animal coloration measuring ***,the sensor's small aperture and narrow light spectrum range designed for human-vision limit its value for ecological *** discuss the conditions in which a digital color sensor can be an effective tool for measuring animal coloration in both laboratory settings and in the field.

关键词： animal coloration color measurement comparative method digital photography museum specimens Nix color sensor

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Physics-based,data-driven approach for predicting natural ventilation of residential high-rise buildings

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Building Simulation 2022年第1期15卷 129-148页

作者： Vincent J.l.Gan Boyu Wang C.M.Chan A.u.Weerasuriya Jack C.P.Cheng Department of Building School of Design and EnvironmentNational University of SingaporeSingapore117566 Department of Civil and Environmental Engineering The Hong Kong University of Science and TechnologyHong Kong999077China

Natural ventilation is particularly important for residential high-rise buildings as it maintains indoor human comfort without incurring the energy demands that air-conditioning *** improve a building’s natural ventilation,it is essential to develop models to understand the relationship between wind flow characteristics and the building's *** more effort is still needed for developing such reliable,accurate,and computationally economical models instead of currently the most popular physics-based models such as computational fluid dynamics(CFD)*** paper,therefore,presents a novel model developed based on physics-based modelling and a data-driven approach to evaluate natural ventilation in residential high-rise *** model first uses CFD to simulate wind pressures on the exterior surfaces of a high-rise *** the surface pressures have been obtained,multizone modelling is used to predict the air change per hour(ACH)for different flats in various ***-driven prediction models are then developed using data from the simulation and deep neural networks that are based on mean absolute error,mean absolute percentage error,and a fusion algorithm *** data-driven models are used to predict the ACH of 25 *** results from multizone modelling and data-driven modelling are *** results imply a high accuracy of the data-driven prediction in comparison with physics-based *** fusion algorithm-based neural network performs best,achieving 96%accuracy,which is the highest of all models *** study contributes a more efficient and robust method for predicting wind-induced natural *** findings describe the relationship between building design(e.g.,plan layout),distribution of surface pressure,and the resulting ACH,which serve to improve the practical design of sustainable buildings.

关键词： computational fluid dynamics data-driven prediction machine learning multizone model natural ventilation residential building

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The AlMaQuEST Survey ⅩⅤ:The dependence of the molecular-to-atomic gas ratios on resolved optical diagnostics

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Science China(Physics,Mechanics & Astronomy) 2024年第9期67卷 174-196页

作者： Niankun Yu Zheng Zheng Chao-Wei Tsai Pei Zuo Sara l.Ellison David V.Stark Di li Jingwen Wu Karen l.Masters Ting Xiao Yinghui Zheng Zongnan li Kai Zhang Hongying Chen Shu l.u Sihan Jiao Fanyi Meng National Astronomical Observatories Chinese Academy of SciencesBeijing 100101China Key laboratory of Radio Astronomy and Technology Chinese Academy of SciencesBeijing 100101China Institute for Frontiers in Astronomy and Astrophysics Beijing Normal UniversityBeijing 102206China School of Astronomy and Space Science University of Chinese Academy of SciencesBeijing 100049China Department of Physics&Astronomy University of VictoriaVictoriaV8P 1A1Canada Departments of Physics and Astronomy Haverford CollegeHaverford19041USA Space Telescope Science Institute San Martin Dr.Baltimore 21218USA Zhejiang laboratory Hangzhou 311121China New Cornerstone Science laboratory Shenzhen 518054China School of Physics Zhejiang UniversityHangzhou 310058China

The atomic-to-molecular gas conversion is a critical step in the baryon cycle of galaxies,which sets the initial conditions for subsequent star formation and influences the multi-phase interstellar *** compiled a sample of 94 nearby galaxies with observations of multi-phase gas contents by utilizing public H_(Ⅰ),CO,and optical IFu data from the Ma NGA survey together with new FAST H_(Ⅰ)*** agreement with previous results,our sample shows that the global molecular-to-atomic gas ratio(R_(mol)≡log M_(H2)/M_(H_(Ⅰ)))is correlated with the global stellar mass surface densityμ_*with a Kendall'sτcoefficient of 0.25 and pless tightly but still correlated with stellar mass and NuV-r color,and not related to the specific star formation rate(sSFR).The cold gas distribution and kinematics inferred from the H_(Ⅰ)and CO global profile asymmetry and shape do not significantly rely on R_(mol).Thanks to the availability of kpc-scale observations of MaNGA,we decompose galaxies into H_(Ⅱ),composite,and AGN-dominated regions by using the BPT *** increasing R_(mol),the fraction of H_(Ⅱ)regions within 1.5 effective radius decreases slightly;the density distribution in the spatially resolved BPT diagram also changes significantly,suggesting changes in metallicity and ionization *** with high R_(mol)tend to have high oxygen abundance,both at one effective radius with a Kendall'sτcoefficient of 0.37(pl *** all parameters investigated here,the oxygen abundance at one effective radius has the strongest relation with global R_(mol).The dependence of gas conversion on gas distribution and galaxy ionization states is *** contrast,the observed positive relation between oxygen abundance(μ_(*))and R_(mol)indicates that the gas conversion is efficient in regions of high metallicity(density).

关键词： Galaxies baryon cycle radio lines H_(Ⅰ)21 cm atomic-to-molecular gas conversion

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