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Uniqueness on Difference Operators of Meromorphic Functions of Infinite Order

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Acta Mathematica Sinica,English Series 2024年第2期40卷 511-527页

作者： Hui LI Ming Liang fang Xiao YAO School of Science China University of Mining and TechnologyBeijing 100083P.R.China Institute of Mathematics Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100190P.R.China School of Sciences Hangzhou Dianzi UniversityHangzhou 310012P.R.China School of Mathematical sciences and LPMC Nankai UniversityTianjin 300071P.R.China

We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new *** is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of *** method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding *** makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the ***,the idea in this paper can also be applied to the case for several variables.

关键词： Uniqueness meromorphic functions difference operators infinite order

Lorentz violation induces isospectrality breaking in Einstein-bumblebee gravity theory

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Science China(Physics,Mechanics & Astronomy) 2024年第8期67卷 87-96页

作者： Wentao Liu Xiongjun fang Jiliang Jing Jieci Wang Department of Physics Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of EducationSynergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangsha 410081China

In this study,we investigate the quasinormal modes(QNMs)of a Lorentz-violating spacetime,factoring in a cosmological constant,within the framework of Einstein-bumblebee *** findings reveal that the interaction of spacetime with an anisotropic bumblebee field imparts distinct contributions to the axial and polar sectors of the vector *** subsequently breaks the isospectrality typically observed in vector *** evidence strongly indicates isospectral breaking in the vector modes of Einstein-bumblebee black holes:a pronounced breakage in the real part of the frequencies,while the imaginary component seems less *** isospectral breaking indicates the existence of two different waveforms in the Ringdown phase of the black hole,which provides a potential signal of quantum gravity observable in current experiments.

关键词： Lorentz-violating isospectral breaking quasinormal modes

Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 159-173页

作者： PAN Jie JIA Yu-ming LI fang School of Mathematical Sciences Zhejiang UniversityHangzhou 310058China Henan Experimental High School Zhengzhou 450003China

Fermat’s Last Theorem is a famous theorem in number theory which is diﬃcult to ***,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very *** aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.

关键词： Fermat's last theorem polynomial ring skew polynomial ring

Finite Groups with Some Bounded Codegrees

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1778-1784页

作者： Dong fang YANG Yu ZENG Heng LV School of Mathematics and Statistics Southwest UniversityChongqing400715P.R.China Department of Mathematics Changshu Institute of TechnologyChangshu215500P.R.China

For a characterχof a finite group G,the number cod(χ) := ∣G:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group G depending on the minimum of the ratioχ(1)^(... 详细信息

关键词： Finite group codegree degree simple group

Skill enhancement learning with knowledge distillation

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Science China(Information Sciences) 2024年第8期67卷 206-220页

作者： Naijun LIU Fuchun SUN Bin fang Huaping LIU Department of Computer Science and Technology Tsinghua University

Skill learning through reinforcement learning has significantly progressed in recent years. However, it often struggles to efficiently find optimal or near-optimal policies due to the inherent trial-and-error exploration in reinforcement learning. Although algorithms have been proposed to enhance skill learning efficacy, there is still much room for improvement in terms of skill learning performance and training stability. In this paper, we propose an algorithm called skill enhancement learning with knowledge distillation(SELKD), which integrates multiple actors and multiple critics for skill learning. SELKD employs knowledge distillation to establish a mutual learning mechanism among actors. To mitigate critic overestimation bias,we introduce a novel target value calculation method. We also perform theoretical analysis to ensure the convergence of SELKD. Finally, experiments are conducted on several continuous control tasks, illustrating the effectiveness of the proposed algorithm.

关键词： skill learning enhancement learning reinforcement learning knowledge distillation

Data-driven discovery of linear dynamical systems from noisy data

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Science China(Technological Sciences) 2024年第1期67卷 121-129页

作者： WANG YaSen YUAN Ye fang HuaZhen DING Han School of Mechanical Science and Engineering Huazhong University of Science and TechnologyWuhan 430074China State Key Lab of Digital Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074China School of Artificial Intelligence and Automation Huazhong University of Science and TechnologyWuhan 430074China Department of Mechanical Engineering University of KansasLawrence 66045USA

In modern science and engineering disciplines,data-driven discovery methods play a fundamental role in system modeling,as data serve as the external representations of the intrinsic mechanisms within ***,empirical data contaminated by process and measurement noise remain a significant obstacle for this type of *** this study,we have developed a data-driven method capable of directly uncovering linear dynamical systems from noisy *** method combines the Kalman smoothing and sparse Bayesian learning to decouple process and measurement noise under the expectation-maximization framework,presenting an analytical method for alternate state estimation and system ***,the discovered model explicitly characterizes the probability distribution of process and measurement noise,as they are essential for filtering,smoothing,and stochastic *** have successfully applied the proposed algorithm to several simulation *** results demonstrate its potential to enable linear dynamical system discovery in practical applications where noise-free data are intractable to capture.

关键词： system identification sparse Bayesian learning Kalman smoothing process and measurement noise

Surface engineering with ionic polymers on membranes for boron removal

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Frontiers of Chemical Science and Engineering 2024年第5期18卷 61-69页

作者： Xiting Zhang Chenyi fang J Paul Chen Sui Zhang Department of Chemical and Biomolecular Engineering National University of SingaporeSingapore 117576Singapore Department of Civil and Environmental Engineering National University of SingaporeSingapore 119260Singapore College of Chemistry and Environmental Engineering Shenzhen UniversityShenzhen 518060China

Removal of boric acid from seawater and wastewater using reverse osmosis membrane technologies is imperative and yet remains inadequately addressed by current commercial *** research efforts performed post-modification of reverse osmosis membranes to enhance boron rejection,which is usually accompanied by substantial sacrifice in water *** study delves into the surface engineering of low-pressure reverse osmosis membranes,aiming to elevate boron removal efficiency while maintaining optimal salt rejection and water *** were modified by the self-polymerization and co-deposition of dopamine and polystyrene sulfonate at varying ratios and *** surfaces became smoother and more hydrophilic after *** optimum membrane exhibited a water permeability of 9.2±0.1 L·m^(-2)·h^(-1)·bar^(-1),NaCl rejection of 95.8%±0.3%,and boron rejection of 49.7%±0.1% and 99.6%±0.3% at neutral and alkaline pH,*** water permeability is reduced by less than 15%,while the boron rejection is 3.7 times higher compared to the blank *** research provides a promising avenue for enhancing boron removal in reverse osmosis membranes and addressing water quality concerns in the desalination process.

关键词： membrane low-pressure reverse osmosis boron surface engineering

Grain size effect on the assembly quality of micro-scaled barrel formed by microforming

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Advances in Manufacturing 2024年第1期12卷 19-32页

作者： Dien Hu Jieyichen fang Feng Zeng Ming-Wang Fu Department of Mechanical Engineering Research Institute of Advanced ManufacturingThe Hong Kong Polytechnic UniversityHung HomKowloonHong KongPeople’s Republic of China Xiamen Yulong Machinery Co.Ltd. Xiamen361023FujianPeople’s Republic of China

In this research,a method employing micro-extrusion was designed to produce the micro-scaled barrel-shaped parts with complex geometrical features to study the feasibility of the proposed microforming method and its grain size effect on the formability of the complicated internal features in terms of deformation behavior,material evolution,accuracy of dimensions and final components *** results reveal that the deformation behavior is highly affected by grain size and becomes unpredictable with increased grain *** addition,assembly parameters including feature dimension,tolerance and coaxiality also vary with grain size,and the variation of grain size needs to be accommodated by different assembly types,viz.,clearance fit or transition *** the microstructural evolution aspect,it was identified there were two dead zones and four shear bands,and the formation of these deformation zones was barely affected by the variation in grain *** bulges,cracks,and fracture induced voids were observed on the surface of the final components,tailoring the microstructure of the working material with finer grains could significantly avoid these *** study advances the understanding of forming microparts by extrusion processes and provides guidance for microforming of similar microparts.

关键词： Microformed part Size effect Extrusion Microstructural evolution Dimensions Assembly accuracy

Carbon felt electrode coated with WS2 enables a high-performance polysulfide/ferricyanide flow battery

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Rare Metals 2024年第10期43卷 5039-5047页

作者： Liang-Yu Li Su Yan Ying-Jia Huang fang-fang Zhong Jin-Chao Cao Mei Ding Chuan-Kun Jia College of Materials Science and Engineering Changsha University of Science and Technology Institute of Energy Storage Technology College of Energy and Power EngineeringChangsha University of Science and Technology Binzhou Institute of Technology Weiqiao-UCAS Science and Technology Park

Polysulfide/ferricyanide flow batteries （S/Fe RFBs）,with the advantages of abundant earth reservation low cost,high safety,and environmental friendliness,have attracted significant interest and demonstrated noteworthy potential for practical ***,the battery performance,including the energy efficiency （EE）,voltage efficiency （VE）,and power density of the S/Fe RFBs remains low owing to the slow redox kinetics of polysulfide *** address these concerns,WS2was selected as the booster and deposited on a commercial carbon felt electrode （WS2–CF） to stimulate the redox reactions of polysulfide *** better hydrophilicity and smaller charge-transfer resistance,WS2–CF exhibits enhanced electrochemical activity toward polysulfide redox ***,the battery performance of S/Fe RFB with WS2–CF as the anode has been improved,with EE of 84%,VE of 84%,and a peak power density of 175.7 mW·cm-2,which are all higher than the cell only with the bare carbon felt （CF） as electrodes (76%,77% and 155.8 mW·cm-2,respectively).Furthermore,the cycling life of the S/Fe RFB with WS2–CF has been prolonged to 2200 cycles with a capacity retention of 96% a 40 mA·cm-2because of the good stability of WS2–CF as the ***,under the same conditions,the S/Fe RFB without WS2–CF terminated after 1500 cycles with a fast capacity *** successful utilization of WS2as a booster on an electrode provides an efficient strategy for obtaining advanced S/Fe RFBs for practical applications.

关键词： Carbon felt Energy storage Polysulfide/ferricyanide flow battery Tungsten disulfide