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Multi-dimensional Central Limit Theorems and Laws of Large Numbers under Sublinear Expectations

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Acta Mathematica Sinica,English Series 2015年第2期31卷 305-318页

作者： ze chun hu Ling ZHOU Department of Mathematics Nanjing University

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.

关键词： Central limit theorem law of large numbers sublinear expectation

Some Inequalities and Limit Theorems Under Sublinear Expectations

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 451-462页

作者： ze-chun hu Yan-Zhi YANG College of Mathematics Sichuan University Department of Mathematics Nanjigng University

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob＇s inequality for submartingale and Kolmogrov＇s inequality. By Kolmogrov＇s inequality, we obtain a special version of Kolmogrov＇s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.

关键词： sublinear expectation inequality the law of large numbers submartingale

hunt’s Hypothesis(H)for the Sum of Two Independent Levy Processes

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Communications in Mathematics and Statistics 2018年第2期6卷 227-247页

作者： ze-chun hu Wei Sun College of Mathematics Sichuan UniversityChengdu 610064China Department of Mathematics and Statistics Concordia UniversityMontreal H3G 1M8Canada

Which Levy processes satisfy hunt’s hypothesis(H)is a long-standing open problem in probabilistic potential *** study of this problem for one-dimensional Levy processes suggests us to consider(H)from the point of view of the sum of Levy *** this paper,we present theorems and examples on the validity of(H)for the sum of two independent Levy *** also give a novel condition on the Levy measure which implies(H)for a large class of one-dimensional Levy processes.

关键词： hunt’s hypothesis(H) Getoor’s conjecture Levy process

Some Explorations on Two Conjectures About Rademacher Sequences

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Acta Mathematicae Applicatae Sinica 2021年第1期37卷 1-16页

作者： ze-chun hu Guo-lie LAN Wei SUN College of Mathematics Sichuan UniversityChengdu 610065China School of Economics and Statistics Guangzhou UniversityGuangzhou 510006China Department of Mathematics and Statistics Concordia UniversityMontreal H3G 1M8Canada

In this paper,we explore two conjectures about Rademacher ***(εi)be a Rademacher sequence,i.e.,a sequence of independent{-1,1}-valued symmetric random *** Sn=aiε1+…+anεn for a=(a1,…,an)∈*** first *** says that P(|Sn|≤‖a‖)>1/2 for all a∈Rn and n∈*** second conjecture says that P(|Sn|>‖a‖)≥7/32 for all a∈Rn and n∈*** the first conjecture,we present several new equivalent *** include a topological view,a combinatorial version and a strengthened version of the *** the second conjecture,we prove that it holds true when n<7.

关键词： Rademacher sequence Tomaszewaki’s constant Hitczenko and Kwapien’s constant

Effect of Nb-V microalloying on the hot deformation behavior of medium Mn steels

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 360-368页

作者： Yumeng Wang Qinyi Guo Bin hu Haiwen Luo School of Metallurgical and Ecological Engineering University of Science and Technology BeijingBeijing 100083China

The influence of Nb-V microalloying on the hot deformation behavior and microstructures of medium Mn steel(MMS)was investigated by uniaxial hot compression *** establishing the constitutive equations for simulating the measured flow curves,we successfully constructed deformation activation energy(Q)maps and processing maps for identifying the region of flow *** concluded the following consequences of Nb-V alloying for MMS.(i)The critical strain increases and the increment diminishes with the increasing deformation temperature,suggesting that NbC precipitates more efficiently retard dynamic recrystallization(DRX)in MMS compared with solute Nb.(ii)The deformation activation energy of MMS is significantly increased and even higher than that of some reported high Mn steels,suggesting that its ability to retard DRX is greater than that of the high Mn content.(iii)The hot workability of MMS is improved by narrowing the hot processing window for the unstable flow stress,in which fine recrystallized and coarse unrecrystallized grains are present.

关键词： medium manganese steel niobium-vanadium microalloying flow behavior dynamic recrystallization hot workability

Co/Co_(7)Fe_(3)heterostructures with controllable alloying degree on carbon spheres as bifunctional electrocatalyst forrechargeable zinc-air batteries

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 476-487页

作者： Junkang Chen Yongyue Zhuang Yanxin Qiao Yu Zhang Aihua Yuan hu Zhou School of Materials Science and Engineering Jiangsu University of Science and TechnologyZhenjiang 212003China School of Environmental and Chemical Engineering Jiangsu University of Science and TechnologyZhenjiang 212003China

Exploring efficient and nonprecious metal electrocatalysts of oxygen reduction reaction(ORR)and oxygen evolution reaction(OER)is crucial for developing rechargeable zinc-air batteries(ZABs).Herein,an alloying-degree control strategy was employed to fabricate nitrogen-doped carbon sphere(NCS)decorated with dual-phase Co/Co_(7)Fe_(3)heterojunctions(CoFe@NCS).The phase composition of materials has been adjusted by controlling the alloying *** optimal CoFe_(0.08)@NCS electrocatalyst displays a half-wave potential of 0.80 V for ORR and an overpotential of 283 mV at 10 mA·cm^(-2)for OER in an alkaline *** intriguing bifunctional electrocatalytic activity and durability is attributed to the hierarchically porous structure and interfacial electron coupling of highly-active Co_(7)Fe_(3)alloy and metallic Co *** the CoFe_(0.08)@NCS material is used as air-cathode catalyst of rechargeable liquid-state zinc-air battery(ZAB),the device shows a high peak power-density(157 mW·cm^(-2))and maintains a stable voltage gap over 150 h,outperforming those of the benchmark(Pt/C+RuO_(2))-based *** particular,the as-fabricated solid-state flexible ZAB delivers a reliable compatibility under different bending *** work provides a promising strategy to develop metal/alloy-based electrocatalysts for the application in renewable energy conversion technologies.

关键词： bifunctional electrocatalysts oxygen reduction reaction oxygen evolution reaction zinc-air battery metal/alloy carbon sphere

Photo‑Energized MoS_(2)/CNT Cathode for High‑Performance Li–CO_(2)Batteries in a Wide‑Temperature Range

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Nano-Micro Letters 2025年第1期17卷 160-175页

作者： Tingsong hu Wenyi Lian Kang hu Qiuju Li Xueliang Cui Tengyu Yao Laifa Shen Jiangsu Key Laboratory of Materials and Technologies for Energy Storage College of Materials Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjing 210016People’s Republic of China

Li–CO_(2) batteries are considered promising energy storage systems in extreme environments such as Mars;however,severe performance degradation will occur at a subzero temperature owning to the sluggish reaction ***,a photo-energized strategy adopting sustainable solar energy in wide working temperature range Li–CO_(2) battery was achieved with a binder-free MoS_(2)/carbon nanotube(CNT)photo-electrode as *** unique layered structure and excellent photoelectric properties of MoS_(2) facilitate the abundant generation and rapid transfer of photo-excited carriers,which accelerate the CO_(2) reduction and Li_(2)CO_(3) decomposition upon *** illuminated battery at room temperature exhibited high discharge voltage of 2.95 V and mitigated charge voltage of 3.27 V,attaining superior energy efficiency of 90.2%and excellent cycling stability of over 120 *** at an extremely low temperature of−30℃,the battery with same electrolyte can still deliver a small polarization of 0.45 V by the photoelectric and photothermal synergistic mechanism of MoS_(2)/CNT *** work demonstrates the promising potential of the photo-energized wide working temperature range Li–CO_(2) battery in addressing the obstacle of charge overpotential and energy efficiency.

关键词： Li-CO_(2)batteries Photo-energized Wide operation-temperature Kinetics MoS_(2)

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新型N-芳基哌嗪取代苯并呋喃衍生物的合成

合成化学 2017年第1期25卷 60-63页

作者：毛泽伟虎春艳陈文君余珏林玉萍云南中医学院中药学院云南昆明650500

以5-二甲氨基水杨醛和2-溴-4'-氟苯乙酮为原料,经缩合和取代反应制得中间体6-二乙氨基-2-[4'-(N-哌嗪基)苯甲酰基]苯并呋喃(2);2与卤代烃反应合成了6个新型的N-芳基哌嗪取代苯并呋喃衍生物(4a^4f),收率76%~93%,其结构经1H NMR,13C NMR和... 详细信息

以5-二甲氨基水杨醛和2-溴-4'-氟苯乙酮为原料,经缩合和取代反应制得中间体6-二乙氨基-2-[4'-(N-哌嗪基)苯甲酰基]苯并呋喃(2);2与卤代烃反应合成了6个新型的N-芳基哌嗪取代苯并呋喃衍生物(4a^4f),收率76%~93%,其结构经1H NMR,13C NMR和HR-MS(ESI-TOF)表征。

关键词： 5-二甲氨基水杨醛 2-溴-4'-氟苯乙酮 N-芳基哌嗪苯并呋喃衍生物合成

Electrochemical conversion of methane to bridge the gap in the artificial carbon cycle

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Journal of Energy Chemistry 2025年第1期100卷 286-308页

作者： Yuhao Peng Yuefeng Song Ihar Razanau Juanxiu Xiao Wei Xiao Di hu Guoxiong Wang College of Chemistry and Molecular Sciences Hubei Key Laboratory of Electrochemical Power Sources Wuhan University State Key Laboratory of Catalysis Dalian National Laboratory for Clean Energy iChEM (Collaborative Innovation Center of Chemistry for Energy Materials) Dalian Institute of Chemical Physics Chinese Academy of Sciences Laboratory of Physical-Chemical Technologies SSPA Scientific and Practical Materials Research Centre of NAS of Belarus State Key Laboratory of Marine Resources Utilization in South China Sea Collaborative Innovation Center of Marine Science and Technology School of Marine Science and Engineering Hainan University Department of Chemical and Environmental Engineering University of Nottingham Ningbo China

Methane, an abundant one-carbon（C1） resource, is extensively used in the industrial production of vital fuels and value-added chemicals. However, current industrial methane conversion technologies are energy-and carbon-intensive, mainly due to the high activation energy required to break the inert C–H bond, low selectivity, and problematic side reactions, including CO2emissions and coke deposition. Electrochemical conversion of methane（ECM） using intermittent renewable energy offers an attractive solution, due to its modular reactor design and operational flexibility across a broad spectrum of temperatures and pressures. This review emphasizes conversion pathways of methane in various reaction systems, highlighting the significance and advantages of ECM in facilitating a sustainable artificial carbon cycle. This work provides a comprehensive overview of conventional methane activation mechanisms and delineates the complete pathways of methane conversion in electrolysis contexts. Based on surface/interface chemistry, this work systematically analyzes proposed reaction pathways and corresponding strategies to enhance ECM efficiency towards various target products, including syngas, hydrocarbons, oxygenates, and advanced carbon materials. The discussion also encompasses opportunities and challenges for the ECM process, including insights into ECM pathways, rational electrocatalyst design, establishment of benchmarking protocols, electrolyte engineering, enhancement of CH4conversion rates, and minimization of CO2emission.

关键词： Methane Electrochemical conversion Reaction mechanism Catalyst design Electrode Electrocatalysis