Probing levitodynamics with multi-stochastic forces and the simple applications on the dark matter detection in optical levitation experiment by Xi Cheng, Ji-Heng Guo, Wenyu Wang, Bin Zhu

“…., assuming that all of these forces adhere to the fluctuation-dissipation theorem. The ratio of total damping to the stochastic damping coefficient distinguishes the levitodynamics from cases involving only one single stochastic force. …”
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Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics by Lifang Guo, Salha Alshaikey, Abeer Alshejari, Muhammad Din, Umar Ishtiaq

“…Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result.…”
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Haar Wavelet Method for Nonlinear Vibration of Functionally Graded CNT-Reinforced Composite Beams Resting on Nonlinear Elastic Foundations in Thermal Environment by Jianyu Fan, Jin Huang

“…The convergence and comparison studies are carried out, and the results indicate that the numerical rate of convergence of the proposed method is in agreement with the convergence theorem, and good accuracy of the present results is observed. …”
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A Sensor Positioning Scheme with High Accuracy in Nonuniform Wireless Sensor Networks by Junho Park, Hyuk Park, Dong-ook Seong, Jaesoo Yoo

“…And a density probability scheme based on the central limit theorem and normal distribution theory has been proposed to improve the location accuracy in nonuniform sensor network environments. …”
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State-of-the-art survey of smart contract verification based on formal methods by Wenbo ZHANG, Simin CHEN, Lifei WEI, Wei SONG, Dongmei HUANG

“…Smart contract represents an essential application scenario of blockchain technology.Smart contract technology improves programmability and scalability of blockchain, and has broad development prospects.However, a series of security incidents caused a great number of economic losses and weakened users’ confidence in the Ethereum platform.The security of smart contract has become a critical problem that restricts the further development of smart contract.Defects in smart contract code may cause serious consequences and cannot be modified once deployed, it is especially important to verify the correctness of smart contract in advance.In recent years, researchers have obtained many achievements in verification of smart contract, but there is a lack of systematic summary of these research results.Therefore, some basic principles of Ethereum were introduced, including the transaction, gas mechanism, storage and programming language.Eight common types of vulnerabilities in smart contract were summarized and their causes were explained.Some real security events were reviewed and some examples of vulnerability codes were presented.Then, the research work on automatic verification of smart contract based on symbolic execution, model checking and theorem proving was classified and summarized.Three open-source automated tools were selected, including Mythril, Slither and Oyente.And experiments were implemented to evaluate and compare the three tools from the aspects of efficiency, accuracy and the types of vulnerability can be detected.Furthermore, related review articles were surveyed, and the advantages of this paper compared with these works were summarized.The critical problems in the vulnerability detection technology of smart contract were also summarized and the direction of future research was proposed at last.…”
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Impact of moving target on underwater positioning by using state measurement by Tippireddy Srinivasa Reddy, Rajeev Arya

“…The absorption losses generated due to the spillover effect cause false measurements of the moving target. Theorem 1 describes the genesis of these absorption losses and their consequences in UAWSN. …”
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Investigation of reactive power referring to recent studies of time-averaged stored energy density by Jiangwei Chen, Jiacheng Qiu

“…This work may be helpful to establish a bridge between electrical power theory and Poynting’s theorem, deepen the understanding of reactive power, and improve electrical power theory.…”
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Coalgebraic Structure of Genetic Inheritance by Jianjun Tian, Bai-Lian Li

“…We also put forward certain theoremsthat state the relationship between gametic coalgebra and gameticalgebra. By Brower's theorem in topology, we prove the existenceof equilibrium state for the in-evolution operator.…”
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Digital technology and artificial intelligence issues in scientific works by A. N. Timokhovich, E. G. Samokhodkina, E. V. Samokhodkin, A. A. Elzon

“…The main semantic units, reflecting different aspects of the research field are digitalization; artificial intelligence (additional semantic units: knowledge representation, theorem proving, computer vision, robotics, machine learning, multi-agent systems, artificial intelligence tools); neural networks (additional semantic units: learning with a teacher, learning without a teacher, input data); strong or general artificial intelligence, weak or applied artificial intelligence; Marusya voice assistant, Alisa voice assistant, Siri voice assistant, Bixby voice assistant, Google Assistant; speech recognition, fingerprint recognition, human face identification. …”
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Analysis of Face Stability during Excavation of Double-O-Tube Shield Tunnel by Yuyou Yang, Qinghong Zhou, Hongan Li, Xuegang Huang, Xiaoming Tu

“…Then by means of the kinematic theorem of limit analysis, the numerical results were obtained, and a design chart was provided. …”
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Compressed Sensing Based Apple Image Measurement Matrix Selection by Ying Xiao, Wanlin Gao, Ganghong Zhang, Han Zhang

“…Compressed sensing based apple image sampling method makes a breakthrough to the limitation of the Nyquist sampling theorem. By investigating the matrix measurement signal, the method can project a higher dimensional signal to a low-dimensional space for data compression and reconstruct the original image using less observed values. …”
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An applied noise model for scintillation-based CCD detectors in transmission electron microscopy by Christian Zietlow, Jörg K. N. Lindner

“…The Poisson noise, arising from the quantized nature of the beam electrons, gets correlated by this convolution, which allows to reconstruct the detector PSF based on the Wiener–Khinchin theorem and the Pearson correlation coefficients under homogeneous illumination conditions. …”
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The radiation from ultrafast point dipoles, moving uniformly near chiral media by V. N. Kadantsev

“…Using the generalized reciprocity theorem for media characterized by the Hermitian permittivity tensor, we consider the transient and Cherenkov radiation excited by a uniformly moving bunch of charged particles when it crosses (or moves along) the interface of media, one of which is an optically active gyrotropic medium. …”
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A Novel Model-Free Intelligent Proportional-Integral Supertwisting Nonlinear Fractional-Order Sliding Mode Control of PMSM Speed Regulation System by Peng Gao, Xiaodong Lv, Huimin Ouyang, Lei Mei, Guangming Zhang

“…Moreover, the stability of the proposed hybrid MF-iPI-ST-NLFOSMC strategy is proved by the Lyapunov stability theorem and fractional-order theory. Finally, the simulations and comparison results verify that the hybrid MF-iPI-ST-NLFOSMC strategy proposed in this paper has better performance than the other model-free controllers in terms of the static characteristic, dynamic characteristic, and robustness.…”
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Novel solutions and stability of quaternion differential equations: symmetry and asymmetry analyses using matrix representation and Lyapunov methods by Prasantha Bharathi Dhandapani, Anthony Raj Abraham, Hijaz Ahmad, Taha Radwan

“…This result is likely due to the matrix representation strategy and the use of the Picard–Lindelöf theorem, which is an important consequence of traditional ordinary differential equations (ODE) formulations. …”
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Phantom hairy black holes and wormholes in Einstein-bumblebee gravity by Chikun Ding, Changqing Liu, Yuehua Xiao, Jun Chen

“…We first find that the Lorentz violation (LV) effect can change the so-called black hole no-hair theorem and these scalar fields can give a hair to a black hole. …”
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Periodic solutions for a class of perturbed sixth-order autonomous differential equations by Chems Eddine Berrehail, Amar Makhlouf

“…Findings – All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results. …”
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A simplified kinetic model for the tropospheric ozone cycle by J. K. Conceição, T. S. F. Alves, E. M. D. Moya, S. A. Pozza, D. S. Rodrigues

“…To study it, the Center Manifold Theorem was used to determine its stability. As for the results, our analytical calculations demonstrate the asymptotic local stability of the steady state, which was also numerically corroborated. …”
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A Novel Modeling Technique for the Forecasting of Multiple-Asset Trading Volumes: Innovative Initial-Value-Problem Differential Equation Algorithms for Reinforcement Machine Learni... by Mazin A. M. Al Janabi

“…This paper provides some crucial parameters for the assessment of the trading volumes of multiple-asset portfolio(s) during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed-form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half-life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. …”
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Water Flow Parameters on the Symmetry Axis and Extreme Line of Current by O. A. Burtseva, M. S. Alexandrova

“…By introducing dimensionless complexes on the basis of π-theorem, the formula for the length of inertial front of the water flow at its spreading from a rectangular pipe into a wide diverting channel is derived. …”
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