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A Blockchain-Based Proxy Re-Encryption Scheme with Conditional Privacy Protection and Auditability
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作者 Chen Guo PengWeijun +3 位作者 Wu Jing Fang Youxuan Ye Keke Xin Yanshuang 《China Communications》 SCIE CSCD 2024年第7期267-277,共11页
With the development of Internet of Things technology,intelligent door lock devices are widely used in the field of house leasing.In the traditional housing leasing scenario,problems of door lock information disclosur... With the development of Internet of Things technology,intelligent door lock devices are widely used in the field of house leasing.In the traditional housing leasing scenario,problems of door lock information disclosure,tenant privacy disclosure and rental contract disputes frequently occur,and the security,fairness and auditability of the housing leasing transaction cannot be guaranteed.To solve the above problems,a blockchain-based proxy re-encryption scheme with conditional privacy protection and auditability is proposed.The scheme implements fine-grained access control of door lock data based on attribute encryption technology with policy hiding,and uses proxy re-encryption technology to achieve auditable supervision of door lock information transactions.Homomorphic encryption technology and zero-knowledge proof technology are introduced to ensure the confidentiality of housing rent information and the fairness of rent payment.To construct a decentralized housing lease transaction architecture,the scheme realizes the efficient collaboration between the door lock data ciphertext stored under the chain and the key information ciphertext on the chain based on the blockchain and InterPlanetary File System.Finally,the security proof and computing performance analysis of the proposed scheme are carried out.The results show that the scheme can resist the chosen plaintext attack and has low computational cost. 展开更多
关键词 attribute encryption blockchain homomorphic encryption house leasing proxy re-encryption zero-knowledge proof
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Recurrent Neural Network Inspired Finite-Time Control Design
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作者 Jianan Liu Shihua Li Rongjie Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1527-1529,共3页
Dear Editor,This letter is concerned with the role of recurrent neural networks(RNNs)on the controller design for a class of nonlinear systems.Inspired by the architectures of RNNs,the system states are stacked accord... Dear Editor,This letter is concerned with the role of recurrent neural networks(RNNs)on the controller design for a class of nonlinear systems.Inspired by the architectures of RNNs,the system states are stacked according to the dynamic along with time while the controller is represented as the neural network output.To build the bridge between RNNs and finite-time controller,a novel activation function is imposed on RNNs to drive the convergence of states at finite-time and propel the overall control process smoother.Rigorous stability proof is briefly provided for the convergence of the proposed finite-time controller.At last,a numerical simulation example is presented to illustrate the efficiency of the proposed strategy.Neural networks can be classified as static(feedforward)and dynamic(recurrent)nets[1].The former nets do not perform well in dealing with training data and using any information of the local data structure[2].In contrast to the feedforward neural networks,RNNs are constituted by high dimensional hidden states with dynamics. 展开更多
关键词 DYNAMICS FINITE PROOF
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Thermally Conductive and UV-EMI Shielding Electronic Textiles for Unrestricted and Multifaceted Health Monitoring
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作者 Yidong Peng Jiancheng Dong +8 位作者 Jiayan Long Yuxi Zhang Xinwei Tang Xi Lin Haoran Liu Tuoqi Liu Wei Fan Tianxi Liu Yunpeng Huang 《Nano-Micro Letters》 SCIE EI CAS CSCD 2024年第10期149-162,共14页
Skin-attachable electronics have garnered considerable research attention in health monitoring and artificial intelligence domains,whereas susceptibility to elec-tromagnetic interference(EMI),heat accumulation issues,... Skin-attachable electronics have garnered considerable research attention in health monitoring and artificial intelligence domains,whereas susceptibility to elec-tromagnetic interference(EMI),heat accumulation issues,and ultraviolet(UV)-induced aging problems pose significant constraints on their potential applications.Here,an ultra-elas-tic,highly breathable,and thermal-comfortable epidermal sensor with exceptional UV-EMI shielding performance and remarkable thermal conductivity is developed for high-fidelity monitoring of multiple human electrophysiological signals.Via filling the elastomeric microfibers with thermally conductive boron nitride nanoparticles and bridging the insulating fiber interfaces by plating Ag nanoparticles(NPs),an interwoven thermal con-ducting fiber network(0.72 W m^(-1) K^(-1))is constructed benefiting from the seamless thermal interfaces,facilitating unimpeded heat dissipation for comfort skin wearing.More excitingly,the elastomeric fiber substrates simultaneously achieve outstanding UV protection(UPF=143.1)and EMI shielding(SET>65,X-band)capabilities owing to the high electrical conductivity and surface plasmon resonance of Ag NPs.Furthermore,an electronic textile prepared by printing liquid metal on the UV-EMI shielding and thermally conductive nonwoven textile is finally utilized as an advanced epidermal sensor,which succeeds in monitoring different electrophysiological signals under vigorous electromagnetic interference.This research paves the way for developing protective and environmentally adaptive epidermal electronics for next-generation health regulation. 展开更多
关键词 Skin electronics Thermal regulating textiles Electromagnetic interference shielding Ultraviolet proof Health monitoring
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Glia-to-neuron reprogramming to the rescue?
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作者 Jack W.Hickmott Cindi M.Morshead 《Neural Regeneration Research》 SCIE CAS 2025年第5期1395-1396,共2页
Over the last two decades,the dogma that cell fate is immutable has been increasingly challenged,with important implications for regenerative medicine.The brea kth rough discovery that induced pluripotent stem cells c... Over the last two decades,the dogma that cell fate is immutable has been increasingly challenged,with important implications for regenerative medicine.The brea kth rough discovery that induced pluripotent stem cells could be generated from adult mouse fibroblasts is powerful proof that cell fate can be changed.An exciting extension of the discovery of cell fate impermanence is the direct cellular reprogram ming hypothesis-that terminally differentiated cells can be reprogrammed into other adult cell fates without first passing through a stem cell state. 展开更多
关键词 programming PASSING proof
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Corrigendum: MicroRNA-502-3p regulates GABAergic synapse function in hippocampal neurons
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《Neural Regeneration Research》 SCIE CAS 2025年第4期945-945,共1页
There is an error in the name of the cell line in the abstract of the published paper“MicroRNA-502-3p regulates GABAergic synapse function in hippocampal neurons”published on pages 2698-2707,Issue 12,Volume 19 of Ne... There is an error in the name of the cell line in the abstract of the published paper“MicroRNA-502-3p regulates GABAergic synapse function in hippocampal neurons”published on pages 2698-2707,Issue 12,Volume 19 of Neural Regeneration Research(Sharma et al.,2024),because of oversight during final proof checking.The correct description should be“human-GABA receptor A-α1/β2/γ2L human embryonic kidney(HEK)recombinant cell line.”The authors apologize for any inconvenience this correction may cause for readers and editors of Neural Regeneration Research. 展开更多
关键词 FUNCTION PROOF correction
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A Fair and Trusted Trading Scheme for Medical Data Based on Smart Contracts
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作者 Xiaohui Yang Kun Zhang 《Computers, Materials & Continua》 SCIE EI 2024年第2期1843-1859,共17页
Data is regarded as a valuable asset,and sharing data is a prerequisite for fully exploiting the value of data.However,the current medical data sharing scheme lacks a fair incentive mechanism,and the authenticity of d... Data is regarded as a valuable asset,and sharing data is a prerequisite for fully exploiting the value of data.However,the current medical data sharing scheme lacks a fair incentive mechanism,and the authenticity of data cannot be guaranteed,resulting in low enthusiasm of participants.A fair and trusted medical data trading scheme based on smart contracts is proposed,which aims to encourage participants to be honest and improve their enthusiasm for participation.The scheme uses zero-knowledge range proof for trusted verification,verifies the authenticity of the patient’s data and the specific attributes of the data before the transaction,and realizes privacy protection.At the same time,the game pricing strategy selects the best revenue strategy for all parties involved and realizes the fairness and incentive of the transaction price.The smart contract is used to complete the verification and game bargaining process,and the blockchain is used as a distributed ledger to record the medical data transaction process to prevent data tampering and transaction denial.Finally,by deploying smart contracts on the Ethereum test network and conducting experiments and theoretical calculations,it is proved that the transaction scheme achieves trusted verification and fair bargaining while ensuring privacy protection in a decentralized environment.The experimental results show that the model improves the credibility and fairness of medical data transactions,maximizes social benefits,encourages more patients and medical institutions to participate in the circulation of medical data,and more fully taps the potential value of medical data. 展开更多
关键词 Blockchain data transactions zero-knowledge proof game pricing
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A Cloud-Fog Enabled and Privacy-Preserving IoT Data Market Platform Based on Blockchain
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作者 Yurong Luo Wei You +3 位作者 Chao Shang Xiongpeng Ren Jin Cao Hui Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期2237-2260,共24页
The dynamic landscape of the Internet of Things(IoT)is set to revolutionize the pace of interaction among entities,ushering in a proliferation of applications characterized by heightened quality and diversity.Among th... The dynamic landscape of the Internet of Things(IoT)is set to revolutionize the pace of interaction among entities,ushering in a proliferation of applications characterized by heightened quality and diversity.Among the pivotal applications within the realm of IoT,as a significant example,the Smart Grid(SG)evolves into intricate networks of energy deployment marked by data integration.This evolution concurrently entails data interchange with other IoT entities.However,there are also several challenges including data-sharing overheads and the intricate establishment of trusted centers in the IoT ecosystem.In this paper,we introduce a hierarchical secure data-sharing platform empowered by cloud-fog integration.Furthermore,we propose a novel non-interactive zero-knowledge proof-based group authentication and key agreement protocol that supports one-to-many sharing sets of IoT data,especially SG data.The security formal verification tool shows that the proposed scheme can achieve mutual authentication and secure data sharing while protecting the privacy of data providers.Compared with previous IoT data sharing schemes,the proposed scheme has advantages in both computational and transmission efficiency,and has more superiority with the increasing volume of shared data or increasing number of participants. 展开更多
关键词 IoT data sharing zero-knowledge proof authentication privacy preserving blockchain
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Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron
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作者 Declan Traill 《Journal of Applied Mathematics and Physics》 2024年第4期1134-1162,共29页
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an... The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles. 展开更多
关键词 ELECTRON POSITRON Wave Function Solution Electromagnetic Spin Mass Charge Proof Fundamental Particle Properties Quantum Mechanics Classical Physics Computer 3D Model Schrödinger Equation RMS KLEIN GORDON Electric Magnetic Lorentz Invariant Hertzian Vector Point Potential Field Density Phase Flow Attraction REPULSION Shell Theorem Ehrenfest VIRIAL Normalization Harmonic Oscillator
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Corigendum to“Efficient benzaldehyde photosynthesis coupling photocatalytic hydrogen evolution”[J.Energy Chem.66(2022)52-60]
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作者 Juanjuan Luo Min Wang +1 位作者 Lisong Chen Jianlin Shi 《Journal of Energy Chemistry》 SCIE EI CAS CSCD 2023年第2期122-122,共1页
It is regretful that the wrong image of Fig.4 was used in the paperin the final proof stage by editor.The correct one should be as follow.
关键词 BENZALDEHYDE PROOF COUPLING
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A bioinspired flexible optical sensor for force and orientation sensing
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作者 Lei Zhang Limin Tong 《Opto-Electronic Advances》 SCIE EI CAS CSCD 2023年第5期4-6,共3页
Flexible optical sensors have been an emerging paradigm for applications in robotics,healthcare,and human–machine interfaces due to their high sensitivity,fast response,and anti-electromagnetic interference.Recently,... Flexible optical sensors have been an emerging paradigm for applications in robotics,healthcare,and human–machine interfaces due to their high sensitivity,fast response,and anti-electromagnetic interference.Recently,Marques reports a bioinspired multifunctional flexible optical sensor(BioMFOS),achieving a forces sensitivity of 13.28μN,and a spatial resolution of 0.02 mm.The BioMFOS has a small dimension(around 2 cm)and a light weight(0.8 g),making it suitable for wearable application and clothing integration.As proof-of-concept demonstrations,monitoring of finger position,trunk movements,and respiration rate are realized,implying their prominent applications in remote healthcare,intelligent robots,assistance devices teleoperation,and human-machine interfaces. 展开更多
关键词 optical PROOF sensor
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An Effective Security Comparison Protocol in Cloud Computing
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作者 Yuling Chen Junhong Tao +2 位作者 Tao Li Jiangyuan Cai Xiaojun Ren 《Computers, Materials & Continua》 SCIE EI 2023年第6期5141-5158,共18页
With the development of cloud computing technology,more and more data owners upload their local data to the public cloud server for storage and calculation.While this can save customers’operating costs,it also poses ... With the development of cloud computing technology,more and more data owners upload their local data to the public cloud server for storage and calculation.While this can save customers’operating costs,it also poses privacy and security challenges.Such challenges can be solved using secure multi-party computation(SMPC),but this still exposes more security issues.In cloud computing using SMPC,clients need to process their data and submit the processed data to the cloud server,which then performs the calculation and returns the results to each client.Each client and server must be honest.If there is cooperation or dishonest behavior between clients,some clients may profit from it or even disclose the private data of other clients.This paper proposes the SMPC based on a Partially-Homomorphic Encryption(PHE)scheme in which an addition homomorphic encryption algorithm with a lower computational cost is used to ensure data comparability and Zero-Knowledge Proof(ZKP)is used to limit the client’s malicious behavior.In addition,the introduction of Oblivious Transfer(OT)technology also ensures that the semi-honest cloud server knows nothing about private data,so that the cloud server of this scheme can calculate the correct data in the case of malicious participant models and safely return the calculation results to each client.Finally,the security analysis shows that the scheme not only ensures the privacy of participants,but also ensures the fairness of the comparison protocol data. 展开更多
关键词 Secure comparison protocols zero-knowledge proof homomorphic encryption cloud computing
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A Leaking-Proof Theranostic Nanoplatform for Tumor-Targeted and Dual-Modality Imaging-Guided Photodynamic Therapy
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作者 Duo Jin Yang Zhu +8 位作者 Manman Liu Wenxin Yu Jiaji Yu Xinwei Zheng Lulu Wang Yun Wu Kaiju Wei Junjie Cheng Yangzhong Liu 《Biomedical Engineering Frontiers》 CAS 2023年第1期187-196,共10页
Objective:A protein-based leaking-proof theranostic nanoplatform for dual-modality imaging-guided tumor photodynamic therapy(PDT)has been designed.Impact Statement:A site-specific conjugation of chlorin e6(Ce6)to ferr... Objective:A protein-based leaking-proof theranostic nanoplatform for dual-modality imaging-guided tumor photodynamic therapy(PDT)has been designed.Impact Statement:A site-specific conjugation of chlorin e6(Ce6)to ferrimagnetic ferritin(MFtn-Ce6)has been constructed to address the challenge of unexpected leakage that often occurs during small-molecule drug delivery.Introduction:PDT is one of the most promising approaches for tumor treatment,while a delivery system is typically required for hydrophobic photosensitizers.However,the nonspecific distribution and leakage of photosensitizers could lead to insufficient drug accumulation in tumor sites.Methods:An engineered ferritin was generated for site-specific conjugation of Ce6 to obtain a leaking-proof delivery system,and a ferrimagnetic core was biomineralized in the cavity of ferritin,resulting in a fluorescent ferrimagnetic ferritin nanoplatform(MFtn-Ce6).The distribution and tumor targeting of MFtn-Ce6 can be detected by magnetic resonance imaging(MRI)and fluorescence imaging(FLI).Results:MFtn-Ce6 showed effective dual-modality MRI and FLI.A prolonged in vivo circulation and increased tumor accumulation and retention of photosensitizer was observed.The time-dependent distribution of MFtn-Ce6 can be precisely tracked in real time to find the optimal time window for PDT treatment.The colocalization of ferritin and the iron oxide core confirms the high stability of the nanoplatform in vivo.The results showed that mice treated with MFtn-Ce6 exhibited marked tumor-suppressive activity after laser irradiation.Conclusion:The ferritin-based leaking-proof nanoplatform can be used for the efficient delivery of the photosensitizer to achieve an enhanced therapeutic effect.This method established a general approach for the dual-modality imagingguided tumor delivery of PDT agents. 展开更多
关键词 PROOF distribution RETENTION
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Block Verification Mechanism Based on Zero-Knowledge Proof in Blockchain
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作者 Jin Wang Wei Ou +3 位作者 Osama Alfarraj Amr Tolba Gwang-Jun Kim Yongjun Ren 《Computer Systems Science & Engineering》 SCIE EI 2023年第5期1805-1819,共15页
Since transactions in blockchain are based on public ledger verification,this raises security concerns about privacy protection.And it will cause the accumulation of data on the chain and resulting in the low efficien... Since transactions in blockchain are based on public ledger verification,this raises security concerns about privacy protection.And it will cause the accumulation of data on the chain and resulting in the low efficiency of block verification,when the whole transaction on the chain is verified.In order to improve the efficiency and privacy protection of block data verification,this paper proposes an efficient block verification mechanism with privacy protection based on zeroknowledge proof(ZKP),which not only protects the privacy of users but also improves the speed of data block verification.There is no need to put the whole transaction on the chain when verifying block data.It just needs to generate the ZKP and root hash with the transaction information,then save them to the smart contract for verification.Moreover,the ZKP verification in smart contract is carried out to realize the privacy protection of the transaction and efficient verification of the block.When the data is validated,the buffer accepts the complete transaction,updates the transaction status in the cloud database,and packages up the chain.So,the ZKP strengthens the privacy protection ability of blockchain,and the smart contracts save the time cost of block verification. 展开更多
关键词 Blockchain privacy protection zero-knowledge proof smart contract
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Blockchain-Based Cognitive Computing Model for Data Security on a Cloud Platform
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作者 Xiangmin Guo Guangjun Liang +1 位作者 Jiayin Liu Xianyi Chen 《Computers, Materials & Continua》 SCIE EI 2023年第12期3305-3323,共19页
Cloud storage is widely used by large companies to store vast amounts of data and files,offering flexibility,financial savings,and security.However,information shoplifting poses significant threats,potentially leading... Cloud storage is widely used by large companies to store vast amounts of data and files,offering flexibility,financial savings,and security.However,information shoplifting poses significant threats,potentially leading to poor performance and privacy breaches.Blockchain-based cognitive computing can help protect and maintain information security and privacy in cloud platforms,ensuring businesses can focus on business development.To ensure data security in cloud platforms,this research proposed a blockchain-based Hybridized Data Driven Cognitive Computing(HD2C)model.However,the proposed HD2C framework addresses breaches of the privacy information of mixed participants of the Internet of Things(IoT)in the cloud.HD2C is developed by combining Federated Learning(FL)with a Blockchain consensus algorithm to connect smart contracts with Proof of Authority.The“Data Island”problem can be solved by FL’s emphasis on privacy and lightning-fast processing,while Blockchain provides a decentralized incentive structure that is impervious to poisoning.FL with Blockchain allows quick consensus through smart member selection and verification.The HD2C paradigm significantly improves the computational processing efficiency of intelligent manufacturing.Extensive analysis results derived from IIoT datasets confirm HD2C superiority.When compared to other consensus algorithms,the Blockchain PoA’s foundational cost is significant.The accuracy and memory utilization evaluation results predict the total benefits of the system.In comparison to the values 0.004 and 0.04,the value of 0.4 achieves good accuracy.According to the experiment results,the number of transactions per second has minimal impact on memory requirements.The findings of this study resulted in the development of a brand-new IIoT framework based on blockchain technology. 展开更多
关键词 Blockchain Internet of Things(IoT) blockchain based cognitive computing Hybridized Data Driven Cognitive Computing(HD2C) Federated Learning(FL) Proof of Authority(PoA)
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A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture
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作者 Mike Remer 《Journal of Applied Mathematics and Physics》 2023年第8期2216-2220,共5页
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An... This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true. 展开更多
关键词 -3(-n) - 1 Remer Conjecture 3n + 1 Collatz Conjecture Comparative Analysis PROOF Natural Numbers Integer Sequences Factorial Processes Par-tial Differential Equations Bounded Values Collatz Conjecture Collatz Algo-rithm Collatz Operator Collatz Compliance And Mathematical Conjectures
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A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma
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作者 Cassie Lu 《数学计算(中英文版)》 2023年第2期1-6,共6页
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo... This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question. 展开更多
关键词 Brouwer’s Fixed Point Theorem Sperner’s Lemma PROOF
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核的分解与极大广义Bochner-Riesz平均 被引量:1
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作者 陆善镇 《Chinese Quarterly Journal of Mathematics》 CSCD 1989年第1期23+16-22,16-22,共8页
设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(... 设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。 展开更多
关键词 RIESZ satisfying MAXIMAL 数学季刊 proof ARGUMENT kernel implies INEQUALITY uniquely
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一类积分-微分方程解的有界性 被引量:1
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作者 孟繁伟 《Chinese Quarterly Journal of Mathematics》 CSCD 1989年第2期102+94-101,94-101,共9页
本文研究了积分-微分方程解的有界性质。给出了方程(A)所有解有界的判別准则,同时也研究了方程(A)解的渐近性质。给出了方程(A)所有解当t→∞时趋向于有穷极限的充分条件。
关键词 解的有界性 积分-微分方程 渐近性质 有穷 proof BOUNDEDNESS INEQUALITY 数学季刊 satisfied quasi
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Goldbach数的例外集合(Ⅲ)
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作者 陈景润 刘健民 《Chinese Quarterly Journal of Mathematics》 CSCD 1989年第1期15+1-14,1-14,共15页
本文把能表成两个奇素数之和的偶数称为Goldbach数,以E(x)记作不超过x的非Goldbach数的数目,并且证明了E(x)=O(x^(0.95)
关键词 奇素数 INTEGER GOLDBACH LEMMA proof 陈景润 数学季刊 LETTER notes 石西
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R上向量场的一个几何性质
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作者 韩茂安 《Chinese Quarterly Journal of Mathematics》 CSCD 1989年第1期24-31,共8页
本文讨论n维空间上的向量场在其奇点附近的几何性质,主要结果如下列定理所述。定理考虑n维微分系统 x=X(x),x∈R^n (E) 设X∈C^1(R^n),X(0)=0,L=DX(0)。 (Ⅰ) 假定0为(E)的双曲奇点,则下列三点等价: (ⅰ) 矩阵L的所有特征根为实数; (ⅱ)... 本文讨论n维空间上的向量场在其奇点附近的几何性质,主要结果如下列定理所述。定理考虑n维微分系统 x=X(x),x∈R^n (E) 设X∈C^1(R^n),X(0)=0,L=DX(0)。 (Ⅰ) 假定0为(E)的双曲奇点,则下列三点等价: (ⅰ) 矩阵L的所有特征根为实数; (ⅱ) 对(E)的任何解X(t)≠0,只要limx(t)=0(当t→+∞或-∞时),则极限limx(t)/||x(t)||存在; (ⅲ) 对x(E)的任何解x(t)≠0,只要limx(t)=0(当t→+∞或-∞时),则极限lim(x′(t)/||x′(t)||)存在。 (Ⅱ) 如果L的特征值均为实数且不为零,则有: 当limx(t)=0时,有lim(x(t)/||x(t)||=-lim(x′(t)/||x′(t)||); 当limx(t)=0时,有lim(x(t)/||x(t)||)=lim (x′(t)/||x′(t)||) 展开更多
关键词 双曲奇点 几何性质 向量场 微分系统 特征根 SINGULAR ANSWER 数学季刊 茂安 proof
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