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On the Mean Value of the Complete Trigonometric Sums with Dirichlet Characters

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1341-1344页

作者： zhe feng xu Department of Mathematics Northwest University

The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power... 详细信息

关键词： complete trigonometric sums Dirichlet character mean value

High-dimensional *** Problem over Short Intervals

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Acta Mathematica Sinica,English Series 2014年第2期30卷 213-228页

作者： zhe feng xu Tian Ping ZHANG Department of Mathematics Northwest University College of Mathematics and Information Science Shaanxi Normal University

Letk be a positive integer and n a nonnegative integer,0 〈 λ1,...,λk＋1 ≤ 1 be real numbers and w =（λ1,λ2,...,λk＋1）.Let q ≥ max{[1/λi ]：1 ≤ i ≤ k ＋ 1} be a positive integer,and a an integer coprime to *** by N（a,k,w,q,n） the 2n-th moment of（b1··· bk c） with b1··· bk c ≡ a（mod q）,1 ≤ bi≤λiq（i = 1,...,k）,1 ≤ c ≤λk＋1 q and 2（b1＋ ··· ＋ bk ＋ c）.We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N（a,k,w,q,n）,which generalized the result of *** we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N（a,k,w,q,n） in the case ofw =（1/2,1/2,...,1/2） and n = *** order to show our result is close to the best possible,the mean-square value of N（a,k,q） φk（q）/2k＋2and the mean value weighted by the high-dimensional Cochrane sum are studied too.

关键词： D. H. Lehmer problem short intervals trigonometric sum character sum Cochrane sum

Recent Advances in Fibrous Materials for Hydroelectricity Generation

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Nano-Micro Letters 2025年第2期17卷 109-133页

作者： Can Ge Duo xu Xiao feng Xing Yang zheheng Song Yuhang Song Jingyu Chen Yingcun Liu Chong Gao Yong Du zhe Sun Weilin xu Jian Fang College of Textile and Clothing Engineering Soochow UniversitySuzhou 215123People’s Republic of China National Engineering Laboratory for Modern Silk Soochow UniversitySuzhou 215123People’s Republic of China State Key Laboratory of New Textile Materials and Advanced Processing Technologies Wuhan Textile UniversityWuhan 430200People’s Republic of China Institute of Functional Nano&Soft Materials(FUNSOM) Soochow UniversitySuzhou 215123People’s Republic of China Department of Electrical and Computer Engineering University of MassachusettsAmherstMA 01003USA Department of Materials Imperial College LondonSouth Kensington CampusLondon SW72AZUK College of Textile Science and Engineering Zhejiang Sci-Tech UniversityHangzhou 310018People’s Republic of China School of Materials Science and Engineering Shanghai Institute of Technology100 Haiquan RoadShanghai 201418People’s Republic of China

Depleting fossil energy sources and conventional polluting power generation pose a threat to sustainable *** generation from ubiquitous and spontaneous phase transitions between liquid and gaseous water has been considered a promising strategy for mitigating the energy *** materials with unique flexibility,processability,multifunctionality,and practicability have been widely applied for fibrous materials-based hydroelectricity generation(FHG).In this review,the power generation mechanisms,design principles,and electricity enhancement factors of FHG are first ***,the fabrication strategies and characteristics of varied constructions including 1D fiber,1D yarn,2D fabric,2D membrane,3D fibrous framework,and 3D fibrous gel are ***,the advanced functions of FHG during water harvesting,proton dissociation,ion separation,and charge accumulation processes are analyzed in ***,the potential applications including power supply,energy storage,electrical sensor,and information expression are also ***,some existing challenges are considered and prospects for future development are sincerely proposed.

关键词： Hydroelectricity Fibrous material Streaming potential Ion diffusion

Rapid and scalable preparation of highly quaternized polymer networks to achieve efficient simultaneous adsorption of iodide and pertechnetate

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Science China Chemistry 2025年第1期68卷 337-349页

作者： Meiyun xu Song Gu Fulong Chen zhe Zhao Peng Liu Daoben Hua State Key Laboratory of Radiation Medicine and Protection School of Radiological and Interdisciplinary Sciences (RAD-X) Collaborative Innovation Center of Radiological Medicine of Jiangsu Higher Education Institutions Soochow University

The efficient separation of fission products,such as TcO4-and I-,holds strategic significance for the management of radioactive wastes and environmental *** this study,we propose an ultrafast strategy for scalable preparation of a highly quaternized organic network to facilitate efficient and synchronous separation of iodide and *** network can be prepared within a few minutes at room temperature,using polyethylenimine and 1,2,4,5-tetrakis（bromomethyl）benzene as building *** chlorine replacement,the network,abundantly decorated with quaternary ammonium groups （Cl@QPN）,exhibits an ultrahigh positive charge density of 7.6 mmol/*** enables the rapid and efficient enrichment of target anions through strong electrostatic Coulomb *** a result,Cl@QPN exhibits significantly higher adsorption rate constants of 0.830 g/（mg min） for ReO4-（a nonradioactive surrogate of TcO4-） and 0.677 g/（mg min） for I-compared to other ***,it possesses high adsorption capacities,reaching 1,681 mg/g for ReO4-and 917.4 mg/g for I-.Cl@QPN also demonstrates good selectivity towards target ions and shows efficient adsorption for99TcO4-.Additionally,Cl@QPN exhibits high dynamic processing capacities,handling up to 3,100 and 7,400 kg of simulated streams per kilogram of material for I-and ReO4-,respectively.

关键词： quaternized polymer networks adsorption pertechnetate iodide liquid radioactive streams

Rock fracture mechanism of buffer blasting with cushion layer at the borehole bottom

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 325-334页

作者： Xinguang Zhu Chenxi Ding zhe Sui Hong Su xu Guo School of Civil and Resources Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory for Mechanics in Fluid Solid Coupling Systems Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of Mechanics and Civil Engineering China University of Mining and Technology(Beijing)Beijing 100083China School of Chemical and Blasting Engineering Anhui University of Science and TechnologyHuainan 232001China

This study primarily investigates the rock fracture mechanism of bottom cushion layer blasting and explores the effects of the bottom cushion layer on rock *** involves analyses of the evolution patterns of blasting stress,characteristics of crack distribution,and rock fracture features in the ***,blasting model experiments were carried out using the dynamic caustics principle to investigate the influence of bottom cushion layers and initiation methods on the integrity of the bottom rock *** experimental results indicate that the combined use of bottom cushion layers and inverse initiation effectively protects the integrity of the bottom rock ***,the process of stress wave propagation and dynamic crack propagation in rocks was simulated using the continuum-discontinuum element method(CDEM)and the Landau explosion source model,with varying thicknesses of bottom cushion *** numerical simulation results indicate that with increasing cushion thickness,the absorption of energy generated by the explosion becomes more pronounced,resulting in fewer cracks in the bottom rock *** illustrates the positive role of the cushion layer in protecting the integrity of the bottom rock mass.

关键词： bottom cushion layer blasting crack propagation continuum-discontinuum element method dynamic stress intensity factor

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Smarandache函数的值分布性质

数学学报（中文版） 2006年第5期49卷 1009-1012页

作者：徐哲峰西北大学数学系西安710069

对于给定的自然数n,著名的Smarandache函数S(n)定义为S(n)=min{m: m∈N,n|m!|.本文主要目的是利用初等方法研究S(n)的值分布性质,并给出了一些有趣的渐近公式．

关键词： Smarandache函数 Smarandache可乘函数渐近公式

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Smarandache幂函数的均值

数学学报（中文版） 2006年第1期49卷 77-80页

作者：徐哲峰西北大学数学系西安710069

对于给定的自然数n,Smarandache幂函数SP(n)定义为SP(n)=min{m: n|mm,m∈N}．本文研究了这个函数的均值分布性质,并利用解析方法得到了Smarandache幂函数的一个较强的均值公式．

关键词： Smarandache幂函数均值渐近公式

Mainchain conformation ordering self-assembly tailored room temperature phosphorescence emission

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Science China Chemistry 2025年第1期68卷 329-336页

作者： Yuzhu Li Yumeng Gao feng Tian Yu Wang Yuan Yao Shaoliang Lin Xiang Ma Binbin xu Shanghai Key Laboratory of Advanced Polymeric Materials Key Laboratory for Ultrafine Materials of Ministry of Education School of Materials Science and Engineering East China University of Science and Technology Shanghai Synchrotron Radiation Facility Shanghai Advanced Research Institute Chinese Academy of Sciences Key Laboratory for Advance Materials and Feringa Noble Prize Scientist Joint Research Centre Frontiers Science for Materiobiology and Dynamic Chemistry School of Chemistry and Molecular Engineering East China University of Science & Technology

Developing organic room-temperature phosphorescence （RTP） materials with a wide range of tunable-emission is significant in expanding the applications of RTP ***,we rationally designed amphiphilic alternating copolymers poly(1,2-bis（4-alkoxyphenyl）ethane-1,2-dione-alt-（ethylene glycol）x)(P（Bz-alt-EGx）) that combined the advantage of alternating benzil and EGxskeleton,and tunable mainchain *** a mainchain conformation ordering assembly （COA） process,P（Bz-alt-EGx） self-assembled into well-defined platelets,and such assemblies emitted blue RTP at ca.425 nm due to the ordered folded-chain conformation and confined *** contrast,traditional self-assembly （TA） of P（Bz-alt-EGx） obtained less ordered aggregates,such as asymmetric worms,vesicles,and rod-like *** resultant less ordered aggregates exhibited yellow-green RTP at ca.550 *** wide-tuning RTP emission in solution （between blue and yellow-green,over125 nm） is realized using the P（Bz-alt-EGx） alternating copolymers under the treatment of different self-assembly *** study uncovers a new strategy to tailor the RTP emission through different self-assembly pathways and holds great promise for the fabrication of advanced optical materials.

关键词： self-assembly conformation ordering alternating copolymer phosphorescence emission

Microstructural evolution and hot tensile behavior of Mg−3Zn−0.5Zr alloy subjected to multi-pass friction stir processing

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Transactions of Nonferrous Metals Society of China 2024年第11期34卷 3615-3628页

作者： Ji WANG Rui-dong FU Tian-xiang HU Yi-jun LI Yue LIU Zhi-hua ZHU Shi-de LI zhe-feng xu State Key Laboratory of Metastable Materials Science and Technology Yanshan UniversityQinhuangdao 066004China CITIC Dicastal Co. Ltd.Qinhuangdao 066004China College of Materials Science and Engineering Yanshan UniversityQinhuangdao 066004China Capital Aerospace Machinery Co. Ltd.Beijing 100076China

The microstructures and hot tensile behaviors of ZK30 alloys subjected to single-and multi-pass friction stir processing(FSP)were systematically *** single-pass FSP(S-FSP),coarse grains underwent refinement to 1−2μm,with a distinct basal texture emerging in the stir zone(SZ).Additionally,second-phase particles were fragmented,dispersed,and partially ***-pass FSP(M-FSP)further enhanced the homogeneity of the microstructure,reduced texture intensity differences,and decreased the fraction of second-phase particles by 50%.Both S-FSP and M-FSP SZs demonstrated superplasticity at strain rates below 1×10^(−3)s^(−1)and at temperatures of 250−350℃.The S-FSP SZ exhibited an elongation of 390%at 250℃and 1×10^(−4)s^(−1),while the M-FSP SZ achieved an elongation of 406%at 350℃and 1×10^(−3)s^(−1).The superplastic deformation of SZ was co-dominated by grain boundary sliding(GBS)and the solute-drag mechanism in S-FSP and mainly by GBS in M-FSP.

关键词： ZK30 alloys multi-pass friction stir processing superplasticity microstructure hot tensile behavior