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The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

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Acta Mathematica Sinica,English Series 2005年第5期21卷 1137-1148页

作者： shui Cao zheng huo Nan LIN Di He hu School of Mathematics Sciences Peking University Beijing 100871 P. R. China School of Sciences Jimei University Xiamen 361021 P. R. China Department of Mathematics Fujian Normal University Fuzhou 350007 P. R. China College of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.

关键词： Stable process Level sets Local time Hausdorit measure

High Strength and Stable Proton Exchange Membrane Based on Perfluorosulfonic Acid/Polybenzimidazole

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Chinese Journal of Polymer Science 2022年第7期40卷 764-771页

作者： Tang-Cheng Xu Chang-shui Wang Zhao-Yu hu Jiao-Jiao zheng Shao-hua Jiang shui-Jian He Hao-Qing Hou College of Chemistry and Chemical Engineering Jiangxi Normal UniversityNanchang330022China Co-Innovation Center of Efficient Processing and Utilization of Forest Resources College of Materials Science and EngineeringNanjing Forestry UniversityNanjing210037China

In this work,a series of high strength,thermal stable and antioxidant proton exchange membranes were designed with solution processible polybenzimidazole(PBI)as the matrix and perfluorosulfonic acid(PFSA)as the fortifier for proton *** processible PBI was successfully synthesized by introducing 4,4’-dicarboxydiphenyl ether into the molecular chains of ***/PBI composite membranes were obtained by solution blending and film *** and PFSA/PBI composite membranes exhibited greatly enhanced tensile strength and Young’s modulus compared to ***/PBI composite membranes are stable below 300℃ which are suitable for practical application in proton exchange membrane fuel *** PFSA/PBI composite membranes show good dimensional stability with low water uptake and swelling *** PFSA/PBI composite membranes also exhibit excellent antioxidation stability with less than 5%initial mass loss over 120 h in Fenton *** proton conductivity of PBI is greatly enhanced by blending with PFSA and the proton conductivities of the composite membranes are increased with the raise of PFSA content and *** work offers valuable insights into the exploration of PBI based high-performance proton exchange membranes.

关键词： Solution processible polybenzimidazole Perfluorosulfonic acid Proton exchange membrane Film casting High strength

Precision spectroscopy of atomic helium

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National Science Review 2020年第12期7卷 1818-1827页

作者： Yu R.Sun shui-Ming hu Hefei National Laboratory for Physical Sciences at Microscale iChem CenterUniversity of Science and Technology of China CAS Center for Excellence in Quantum Information and Quantum Physics University of Science and Technology of China

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational *** fine-structure splitting in the 2;P state of helium is considered to be the most suitable for determining the fine-structure constant α in *** more than 50 years of efforts by many theorists and experimentalists,we are now working toward a determination ofα with an accuracy of a few parts per billion,which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum ***,the precision spectroscopy of helium allows determination of the nuclear charge radius,and it is expected to help resolve the ’proton radius puzzle’.In this review,we introduce the latest developments in the precision spectroscopy of the helium atom,especially the discrepancies among theoretical and experimental results,and give an outlook on future progress.

关键词： precision spectroscopy helium, quantum electrodynamics fine-structure constant nuclear charge radius

Precise Asymptotics for Lévy Processes

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1265-1270页

作者： Zhi shui hu Chun SU Department of Statistics and Finance University of Science and Technology of China

Let {X（t）, t ≥ 0} be a Lévy process with EX（1） = 0 and EX^2（1）〈 ∞. In this paper, we shall give two precise asymptotic theorems for {X（t）, t 〉 0}. By the way, we prove the corresponding conclusions for s... 详细信息

关键词： precise asymptotic Lévy process stable process Fuk-Nagaev type inequality

Relationship between red blood cell distribution width levels and atrial fibrillation in hypertensive patients

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Journal of Geriatric Cardiology 2020年第8期17卷 486-494页

作者： Li-hui zheng Shang-Yu LIU Feng hu Zhi-Cheng hu Li-shui SHEN Ling-Min WU Yan YAO Arrhythmia Center Fuwai HospitalNational Center for Cardiovascular DiseasesChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingChina

Background Information on the relationship between red blood cell distribution width(RDW)and atrial fibrillation(AF)in patients with essential hypertension are *** study aimed to assess the relationship between AF and RDW in hypertensive *** We enrolled 432 hypertensive patients,including 350 AF patients and 82 patients as ***'demographic,clinical,laboratory and echocardiographic characteristics were *** AF patients were further divided into the persistent and paroxysmal AF *** were monitored to identify the cardiac rhythm during blood sampling,and based on the rhythm,the paroxysmal AF group was categorized into the presence(with AF rhythm during blood sampling)and absence(with sinus rhythm during blood sampling)*** The AF group had elevated RDW levels than the controls(12.7%±0.8%vs.12.4%±0.7%,P=0.002),and the persistent AF subgroup had higher RDW levels than the paroxysmal AF subgroup(12.9%±0.8%vs.12.6%±0.8%,P=0.007).Furthermore,in the paroxysmal AF group,the presence group had higher RDW levels than the absence group(13.0%±0.6%vs.12.5%±0.9%,P=0.001).There was no significant difference in RDW levels between the persistent AF subgroup and presence group of the paroxysmal AF subgroup(P=0.533)and between the absence group of the paroxysmal AF subgroup and control group(P=0.262).In multivariate regression analysis,in hypertensive patients,the presence of AF rhythm is an independent predictor for increased RDW concentration(P=0.001).Conclusions The RDW may be associated with the presence of AF rhythm,which implies the importance of maintaining the sinus rhythm in hypertensive patients.

关键词： Atrial fibrillation Hypertension Inflammation Red blood cell distribution width

Influence of rolling temperature on the interfaces and mechanical performance of graphene-reinforced aluminum-matrix composites

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International Journal of Minerals,Metallurgy and Materials 2019年第6期26卷 752-759页

作者： Chen-yang huang shui-ping hu Kai Chen Institute of Engineering Technology University of Science and Technology BeijingBeijing 100083China School of Materials Science and Engineering University of Science and Technology BeijingBeijing 100083China

To study the influence of rolling on the interfaces and mechanical performance of graphene-reinforced Al-matrix composites,a rolling method was used to process *** scanning electron microscopy(SEM),transmission electron microscopy(TEM),X-ray diffraction(XRD),Raman spectroscopy,and tensile testing,this study analyzed the micromorphology,interfaces,and mechanical performance of the composites before and after *** experimental results demonstrates that the composites after hot rolling has uniform structures with strong interfacial *** an increase in rolling temperature,the tensile strength and elastic modulus of the composites gradually ***,when the rolling temperature is higher than 500°C,granular and rod-like Al4C3 phases are observed at the interfaces and the mechanical performance of the composites is *** the rolling temperature is 480°C,the composites show the optimal comprehensive mechanical performance,with a tensile strength and elastic modulus of 403.3 MPa and 77.6 GPa,respectively,which represent increases of 31.6%and 36.9%,respectively,compared with the corresponding values prior to rolling.

关键词： rolling graphene composite interface mechanical performance

Strong invariance principle for a counterbalanced random walk

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 370-380页

作者： TAN hui-qun hu Zhi-shui DONG Liang International Institute of Finance School of ManagementUniversity of Science and Technology of ChinaHefei 230026China Center for Basic Teaching and Experiment Nanjing University of Science and TechnologyJiangyin 214443China

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as *** n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

关键词： random walk martingale invariance principle

Novel estradiol sensors based on carbon nanotube multilayer modified gold hair microelectrodes

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Chinese Chemical Letters 2009年第10期20卷 1248-1250页

作者： Jun hui Xu Cheng Guo hu Sheng shui hu Department of Chemistry Wuhan University Wuhan 430072 China State Key Laboratory of Transducer Technology Chinese Academy of Sciences Beijing 100080 China

Multi-walled carbon nanotube multilayers were modified onto a newly proposed gold hair microelectrode via a simple layer-bylayer assembling method. The resulting electrode showed a sensitive oxidation response to estradiol with detection limit as low as 1.0 × 10^-8 mol/L, foreseeing a promising approach to the fabrication of high-sensitive microsensors.

关键词： Layer-by-layer assembly Carbon nanotubes Hair microsensors Estradiol

Predominating stable adsorption and direct electrochemistry of glucose oxidase on carbon nanotubes by oxygen-containing groups

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Chinese Chemical Letters 2007年第3期18卷 313-315页

作者： Chun Hai Yang Cheng Guo hu Sheng shui hu Departraent of Chemistry Wuhan University Wuhan 430072 China Key Laboratory of Biological Resources Protection and Utilization of hubei Province Enshi 445000 China

Stable adsorption and direct electrochemistry of glucose oxidase （COx） occurred on nitric acid （HNO3）-treated multi-walled carbon nanotubcs （MWNTs） instead of as-received MWNTs, demonstrating the critical roles ... 详细信息

关键词： Glucose oxidase Adsorption Direct electrochemistry Carbon nanotubes Oxygen-containing groups