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On the Terai-Jésmanowicz Conjecture

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2061-2064页

作者： Jian Ye XIA Ping zhi yuan Department of Basic Science Guangdong University of Finance Guangzhou 510521 P. R. China School of Mathematics South China Normal University Guangzhou 510631 P. R. China

In this paper, we prove that if a, b and c are pairwise coprime positive integers such that a^2＋b^2=c^r,a〉b,a≡3 （mod4）,b≡2 （mod4） and c-1 is not a square, thena a^x＋b^y=c^z has only the positive integer solution （x, y, z） = （2, 2, r）. Let m and r be positive integers with 2｜m and 2 r, define the integers Ur, Vr by （m ＋√-1）^r=Vr＋Ur√-1. If a = ｜Ur｜,b=｜Vr｜,c = m^2＋1 with m ≡ 2 （mod 4）,a ≡ 3 （mod 4）, and if r 〈 m/√1.5log3（m^2＋1）-1, then a^x ＋ b^y = c^z has only the positive integer solution （x,y, z） = （2, 2, r）. The argument here is elementary.

关键词： exponential diophantine equations Terai-Jesmanowicz conjecture Lucas sequences

Proton Orbital[541]1/2 and Backbending in ^(178)W

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Communications in Theoretical Physics 2008年第9期50卷 715-718页

作者： WEI zhi-yuan LIU Shu-Xin School of Physics Peking University Beijing 100871 China Center of Theoretical Nuclear Physics National Laboratory of Heavy Ion Collisions Lanzhou 730000 China

The microscopic mechanism of nine experimentally observed bands in ^178W is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of nine bands in ^178W, are reproduced well by the particle-number conserving calculations, in which no free parameter is involved. Calculations demonstrate that occurrence of sharp backbending comes mainly from the contribution of high-j intruder orbitals vi13/2 or πh11/2 and their interference effect with orbitals near the Fermi surface. Theω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.

关键词： backbending cranked shell model moment of inertia pairing interaction

The inequality of educational resources and its countermeasures for rural revitalization in southwest China

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Journal of Mountain Science 2020年第2期17卷 304-315页

作者： GUO yuan-zhi ZHOU Yang LIU Yan-sui Key Laboratory of Regional Sustainable Development Modeling Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China College of Resources and Environment University of Chinese Academy of SciencesBeijing 100049China

Equal access to education has long been a global concern and is important for rural revitalization strategy in the new era. However, little is known about the regional differences of educational resources in China, especially southwest China, where the spatial heterogeneity of human and physical geography is extremely significant. Using a dataset of primary and secondary schools of southwest China at county level in 2015, this study builds an index system to comprehensively measure the supply of educational resources, investigates the spatial pattern of educational resources via exploratory spatial data analysis(ESDA), and explores its influence factors through spatial econometrics. Results indicated that the supply level of educational resources in southwest China was relatively low;the high-high clusters of the supply of educational resources were mainly located in Sichuan Basin and the east of Western Sichuan Plateau, while the concentrated poverty-stricken areas of Guizhou and the border areas of Yunnan-SichuanGuizhou, especially Wumeng mountain area, were characterized by the low-low clusters. Furthermore, this study suggested that altitude, population density, local government revenue and rural residents' income were positively correlated with the supply of educational resources, while the negative influenceswere exerted by proportion of ethnic minority population and urbanization rate. And there were differences in the specific objects of actions of each factor. Ultimately, we proposed that village relocation and combination, as well as sustainable urbanization and regional development were practical paths to optimize the supply of educational resources in rural areas, thus promoting the modernization of agriculture and countryside.

关键词： Educational resources Rural revitalization Spatial heterogeneity Spatial error model Southwest China

Intense Near- and Mid-infrared Absorbing Films of Electrochemically Crosslinked Multinuclear Metallodithiolene Complex Polymers

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Chemical Research in Chinese Universities 2016年第2期32卷 296-301页

作者： LIU Bo QIAO Wenqiang WANG zhi yuan State Key Laboratory of Polymer Physics and Chemistry Changchun Institute of Applied Chemistry Chinese Academy of Sciences Changchun 130022 P R. China University of Chinese Academy of Sciences Beijing 100049 P. R. China Department of Chemistry Carleton University Ontario K1S 5B6 Canada

Novel multinuclear metallodithiolene complexes [（Cbz）2-BTT-Pd（dppf）]2Ni[6b, Cbz=carbazole, BTT= benzene-1,2,4,5-tetrathiotate, dppf=1,1＇-bis（diphenylphosphino） ferrocene] and polymer [（Cbz）2-BTT-Ni]n· [（Et）3（PhCH2）N]x（7b） with the carbazole pendent groups were synthesized and characterized. The thin films of crosslinked polymers P6b and P7b were prepared by electrochemical polymerization of compounds 6b and 7b, respectively. These films show intense and broad absorption in the near- and mid-infrared spectral regions（P6b： 1000-1600 nm, λmax=1297 nm, P7b： 800 nm--8 μm, λmax=3.9 μm） and are potentially useful as infrared optical materials.

关键词： Metallodithiolene Carbazole Electrochemical polymerization Infrared absorption

Critical Shear Offset of Fracture in a Zr-based Metallic Glass

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Journal of Iron and Steel Research International 2016年第1期23卷 53-56页

作者： zhi-yuan LIU Yong YANG Chain-tsuan LIU Shenzhen Key Laboratory of Advanced Manufacturing Technology for Mold & Die Department of Mechanical and Electronic EngineeringShenzhen University Centre for Advanced Structural Materials Department of Mechanical and Biomedical EngineeringCollege of CSECity University of Hong Kong

The nanoscale shear band operation process of Zr_（55）Pd_（10）Cu_（20）Ni_5Al_（10） metallic glass（MG）was reined in by constant force during well-designed loading-holding-unloading cyclic microcompression *** the test,it is revealed that the whole shear banding process involves three stages：shear band initiation,shear sliding and shear band *** on the energy balance principle,the size-affected speed of shear sliding is *** energy originated from the shear sliding leads to heat-up of the shear plane;therefore,the temperature in shear band increases with the size of shear offset caused by the energy accumulation during shear *** the glass transition temperature as the critical temperature of fracture for the Zr-based MG,the critical shear offset is predicted to be approximately 190μm,fully in line with the experimental *** directly proved that the fracture of the MG is caused by the temperature rise during shear sliding.

关键词： metallic glass shear band fracture temperature rise

Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer-aided therapy

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Applied Mathematics(A Journal of Chinese Universities) 2016年第1期31卷 37-52页

作者： NI Bo HE Fa-zhi PAN Yi-teng yuan zhi-yong School of Computer Science Wuhan University School of Computer Science Hubei Polytechnic University

Segmenting the lesion regions from the ultrasound （US） images is an important step in the intra-operative planning of some computer-aided therapies. High-Intensity Focused Ultrasound （HIFU）, as a popular computer-aided therapy, has been widely used in the treatment of uterine fibroids. However, such segmentation in HIFU remains challenge for two reasons：（1） the blurry or missing boundaries of lesion regions in the HIFU images and （2） the deformation of uterine fibroids caused by the patient＇s breathing or an external force during the US imaging process, which can lead to complex shapes of lesion regions. These factors have prevented classical active contour-based segmentation methods from yielding desired results for uterine fibroids in US images. In this paper, a novel active contour-based segmentation method is proposed, which utilizes the correlation information of target shapes among a sequence of images as prior knowledge to aid the existing active contour method. This prior knowledge can be interpreted as a unsupervised clustering of shapes prior modeling. Meanwhile, it is also proved that the shapes correlation has the low-rank property in a linear space, and the theory of matrix recovery is used as an effective tool to impose the proposed prior on an existing active contour model. Finally, an accurate method is developed to solve the proposed model by using the Augmented Lagrange Multiplier （ALM）. Experimental results from both synthetic and clinical uterine fibroids US image sequences demonstrate that the proposed method can consistently improve the performance of active contour models and increase the robustness against missing or misleading boundaries, and can greatly improve the efficiency of HIFU therapy.

关键词： Active contour shapes correlation ultrasound image segmentation matrix recovery computer-aided therapy.

Grain boundary segregation of minor arsenic and nitrogen at elevated temperatures in a microalloyed steel

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International Journal of Minerals,Metallurgy and Materials 2012年第5期19卷 399-403页

作者： yuan-zhi Zhu Zhe Zhu Jian-ping Xu The Key Laboratory of the Ministry of Education of China for Ferrous Metallurgy and Resources Utilization Wulaan University of Science and Technology Wuhan430081 China School of Materials and Metallurgy Wuhan University of Science and Technology Wuhan 430081 China

Auger electron spectroscopy （AES） was used to investigate the grain boundary segregation of arsenic and nitrogen in a kind of microalloyed steel produced by a compact strip production （CSP） technology at 950 to 1100℃, which are similar to the hot working temperature of the steel on a CSP production line. It was discovered that arsenic segregated on grain boundaries when the steel was annealed at 950℃ for 2 h. When the annealing temperature increased to 1100℃, arsenic was also found to have segregated on grain boundaries in the early annealing stage, for instance, within the first 5 min annealing time. However, if the holding time of the steel at this temperature increased to 2 h, arsenic diffused away from grain boundaries into the matrix again. Nitrogen was not found to have segregated on grain boundaries when the steel was annealed at a relatively low temperature, such as 950℃. But when the annealing temperature increased to 1100℃, nitrogen was detected to have segregated at grain boundaries in the steel.

关键词： alloy steel arsenic nitrogen segregation grain boundaries

Effects of creep characteristics of natural gas hydrate-bearing sediments on wellbore stability

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Petroleum Science 2022年第1期19卷 220-233页

作者： Yang Li yuan-Fang Cheng Chuan-Liang Yan zhi-yuan Wang Li-Fang Song School of Petroleum Engineering China University of Petroleum(East China)66 West Changjiang RoadHuangdao DistrictQingdao 266000China

Natural gas hydrate(NGH)reservoirs consist of the types of sediments with weak cementation,low strength,high plasticity,and high *** on the kinetics and thermodynamic characteristics of NGH decomposition,herein a heat-fluid-solid coupling model was established for studying the wellbore stability in an NGH-bearing formation to analyze the effects of the creep characteristics of NGH-bearing sediments during long-term *** results demonstrated that the creep characteristics of sediments resulted in larger plastic yield range,thus aggravating the plastic strain accumulation around the ***,the creep characteristics of NGH-bearing sediments could enhance the effects induced by the difference in horizontal in situ stress,as a result,the plastic strain in the formation around the wellbore increased nonlinearly with increasing difference in in situ *** lower the pore pressure,the greater the stress concentration effects and the higher the plastic strain at the ***,the lower the initial NGH saturation,the greater the initial plastic strain and yield range and the higher the equivalent creep *** plastic strain at the wellbore increased nonlinearly with decreasing initial saturation.

关键词： Natural gas hydrates Wellbore stability Creep Plastic yield

Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

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Communications in Theoretical Physics 2007年第6期47卷 1135-1142页

作者： CHEN zhi-yuan ZHANG Duan-Ming ZHONG zhi-Cheng LI Rui Department of Physics Huazhong University of Science and Technology Wuhan 430074 China Department of Physics Xianning College Xianning 437005 China Department of Physics Xiangfan University Xiangfan 441053 China

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state. The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effacts on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.

关键词： inelasticity restitution coefficient e inhomogeneity fractal dimension D polydisperse granulax gases