Redundancy-Reduction-Based Hierarchical Design in Synchronization of Multi-Agent Systems by Haoyi Que, Zhaowen Xu, Hongye Su

“…The approach could be separated into two main steps: the first is a method of network partition that reduces the trivial interaction, which does not affect the information traversal, and the second involves applying the time-dependent functional approach of Lyapunov to give global exponential conditions, under the criteria for the synchronization of multiple agents, with a lower conservatism of the decision variables compared to some other results, so that the information available could fully benefit from the actual discrete-time communication pattern. Both mathematical proofs and numerical example evidence are presented to demonstrate the effectiveness of the implemented approach. …”
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A heuristic solution to Fermat's last theorem by Sóstenes Rônmel da Cruz, Cleomacio Miguel da Silva, Agrinaldo Jacinto do Nascimento Júnior

“…As a result, many mathematical proofs have been generated for different values of n. …”
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Logic-Based Security Architecture for Systems Providing Multihop Communication by Iman Almomani, Eman Al-Banna, Mousa AL-Akhras

“…The key advantage of LBSA is that it enables a security protocol to prove its correctness mathematically. Mathematical proofs provided by LBSA cover more cases that usually cannot be covered exhaustively by simulation tools. …”
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Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks by Rutishauser, Ueli, Douglas, Rodney J., Slotine, Jean-Jacques E

“…We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. …”
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Integer and Fractional-Order Sliding Mode Control Schemes in Wind Energy Conversion Systems: Comprehensive Review, Comparison, and Technical Insight by Irfan Sami, Shafaat Ullah, Laiq Khan, Ahmed Al-Durra, Jong-Suk Ro

“…This paper will provide insight for the researcher working in the WECS and will serve them in the selection and exploration of the most appropriate control schemes for quality wind power extraction. The concise mathematical proofs of the IOSMC, FOSMC and their variants will also serve the researchers in selecting the relevant sliding surfaces control laws for their research tasks. …”
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Toward Trusted IoT by General Proof-of-Work by Chih-Wen Hsueh, Chi-Ting Chin

“…We reintroduce GPoW with more mathematic proofs so that PoPT can be optimal and describe how PoPT can be realized with simulation results, mining examples and synchronization scenario toward trusted IoT.…”
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Single-stage DNA splicing system via Yusof-Goode approach by Wen Li, Lim

“…In addition, the characteristics of rule are investigated by providing mathematical proofs. Based on the characteristics of rule, some theorems and lemmas have been formulated to predict the number types of single-stage splicing language of Y-G splicing system. …”
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Impact of Unprepared Competence and Difficulty in Competence of Mathematics Teachers During Online Learning by Jitu Halomoan Lumbantoruan, Hendrikus Male

“…Teachers have no self-constructed modules, difficulty writing symbols and mathematical proofs online. Students provide an assessment of teacher competence online, from 100% of respondents 80% disagree with pedagogic and 90% disagree with professional competence. …”
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Inverse methods and integral-differential model demonstration for optimal mechanical operation of power plants – numerical graphical optimization for second generation of tribology... by Casesnoves Francisco

“…Then, the authors propose the development of programming optimization and mathematical proofs-algorithms of the integral-differential model for various models. …”
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Optimizations for Computing Relatedness in Biomedical Heterogeneous Information Networks: SemNet 2.0 by Anna Kirkpatrick, Chidozie Onyeze, David Kartchner, Stephen Allegri, Davi Nakajima An, Kevin McCoy, Evie Davalbhakta, Cassie S. Mitchell

“…The unsupervised learning algorithm for rank aggregation (ULARA), which ranks concepts with respect to the user-specified target, was reconstructed using derived mathematical proofs of correctness and probabilistic performance guarantees for optimization. …”
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A privacy-preserving scheme with multi-level regulation compliance for blockchain by Wangjing Jia, Tao Xie, Baolai Wang

“…In conclusion, the scheme demonstrates strong privacy by relying on mathematical proofs through zk-SNARKs to ensure security while comprehensively safeguarding content. …”
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TJET: Ternary Join-Exit-Tree Based Dynamic Key Management for Vehicle Platooning by Xu, Chang, Lu, Rongxing, Wang, Huaxiong, Zhu, Liehuang, Huang, Cheng

“…Moreover, we also analyze the capacities and activation conditions of join tree and exit tree based on strict mathematical proofs. Detailed security analysis show that our proposed TJET holds desirable security properties including forward security, backward security, and resistance to key control. …”
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Consistency of circuit lower bounds with bounded theories by Jan Bydzovsky, Jan Krajicek, Igor C. Oliveira

“…Motivated by this and related questions about the interaction between mathematical proofs and computations, we investigate circuit complexity from the perspective of logic. …”
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Assembly Sequence Planning for Rectangular Modular Robots with Accessibility Constraints by Anelize Zomkowski Salvi, Henrique Simas

“…Original implementation results and mathematical proofs for the three novel ASPs are also presented. …”
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New Security Proofs and Complexity Records for Advanced Encryption Standard by Orhun Kara

“…For instance, the consensus on the security of AES is not based on formal mathematical proofs but on intensive cryptanalysis over its reduced rounds spanning several decades. …”
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DD-KARB: data-driven compliance to quality by rule based benchmarking by Mohammad Reza Besharati, Mohammad Izadi

“…In addition to the approaches such as formal methods, mathematical proofs, and logical evaluations, benchmarking can be used for compliance assessment. …”
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Game Theory-Based Authentication Framework to Secure Internet of Vehicles with Blockchain by Manik Gupta, Rakesh Kumar, Shashi Shekhar, Bhisham Sharma, Ram Bahadur Patel, Shaily Jain, Imed Ben Dhaou, Celestine Iwendi

“…Formal and informal security analyses justify the framework’s credibility in more depth with mathematical proofs. A rigorous comparative study demonstrates that the suggested framework achieves greater security and functionality characteristics and provides lower transaction and computation overhead than many of the available solutions so far. …”
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The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry by David Nocar, George Grossman, Jiří Vaško, Tomáš Zdráhal

“…It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics.…”
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Transforming two-dimensional tensor networks into quantum circuits for supervised learning by Zhihui Song, Jinchen Xu, Xin Zhou, Xiaodong Ding, Zheng Shan

“…Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. …”
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On Indeterminacy of Interval Multiplicative Pairwise Comparison Matrix by Ting Kuo, Ming-Hui Chen

“…In addition to mathematical proofs, we present experimental results of computer simulations to corroborate our argument. …”
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