Adaptive Fuzzy Tracking Control for a Class of Uncertain Nonlinear Time-Delayed Systems with Saturation Constrains by Yu-Jun Zhang, Li-Bing Wu, Hong-Yang Zhao, Xiao-Dong Hu, Wen-Yu Zhang, Dong-Ying Ju

“…First, the mean value theorem is employed to deal with the nonaffine term with input nonlinearity. …”
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On a class of functions unifying the classes of Paatero, Robertson and others by S. Bhargava, S. Nanjunda Rao

“…A consequence of these basic theorems is a theorem for this class Mkλ(α,β,b,c) which unifies some earlier results concerning the radii of convexity of functions in the class Vkλ(β) of Moulis and those concerning the radii of starlikeness of functions in the classes Uk of Pinchuk and U2(β) of Robertson etc. …”
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Two-scale convergence analysis and numerical simulation for periodic Kirchhoff plates by Zhiwei Huang, Xiaomiao Zeng, Chen Wang, Chongren Liu

“…Besides, the well-posedness analysis of the PDE is verified by the Lax-Milgram theorem, and the reasonability of the two-scale asymptotic expansion solution by the AHM is mathematically verified through the proof of two-scale convergence. …”
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Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model by Yang Ding, Jing-liang Dong, Tong-lin Yang, Zhong-ping Wang, Shuang-xi Zhou, Yong-qi Wei, An-ming She

“…Nowadays, the probability statistics method based on Bayes’ theorem is widely used for evaluating the damage of bridge, that is, Bayesian inference. …”
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Mitigation of epidemics in contact networks through optimal contact adaptation by Mina Youssef, Caterina Scoglio

“…Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. …”
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Event-Trigger Reinforcement Learning-Based Coordinate Control of Modular Unmanned System via Nonzero-Sum Game by Yebao Liu, Tianjiao An, Jianguo Chen, Luyang Zhong, Yuhan Qian

“…The stability of the closed-loop system is verified via Lyapunov’s theorem. Experiment results demonstrate the validity of the proposed method. …”
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High Performance GPU-Based Fourier Volume Rendering by Marwan Abdellah, Ayman Eldeib, Amr Sharawi

“…Relying on the Fourier projection-slice theorem, this technique operates on the spectral representation of a 3D volume instead of processing its spatial representation to generate attenuation-only projections that look like X-ray radiographs. …”
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Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades by Van Binh Phung, Anh Tuan Nguyen, Hoang Minh Dang, Thanh-Phong Dao, V. N. Duc

“…The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. …”
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Climate Predictions: The Chaos and Complexity in Climate Models by D. T. Mihailović, G. Mimić, I. Arsenić

“…The concept in modeling of climate, as a complex system, seen through Gödel’s theorem and Rosen’s definition of complexity and predictability is discussed. …”
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Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion by Gervásio Annes Degrazia, Michel Stefanello, Felipe Denardin Costa, Luís Gustavo Nogueira Martins, Otávio Costa Acevedo

“… An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. …”
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Bifurcation Analysis of a Discrete Basener–Ross Population Model: Exploring Multiple Scenarios by A. A. Elsadany, A. M. Yousef, S. A. Ghazwani, A. S. Zaki

“…These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. …”
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Global Multi-Phase Path Planning Through High-Level Reinforcement Learning by Babak Salamat, Sebastian-Sven Olzem, Gerhard Elsbacher, Andrea M. Tonello

“…The results validate our method's convergence guarantees using Lyapunov’s stability theorem and underscore its computational advantages.…”
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Computational Study of a Fractional-Order HIV Epidemic Model with Latent Phase and Treatment by Sana Abdulkream Alharbi, Nada A. Almuallem

“…We derive some results from the fixed-point theorem and Ulam–Hyers stability. Ultimately, the obtained numerical simulation results are in agreement with the analytical outcomes obtained from the model analysis. …”
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Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data. by Subhankar Dutta, Hana N Alqifari, Amani Almohaimeed

“…In the Bayesian technique, prior information about the LED parameters is used to estimate the posterior distribution of the parameters, which is derived using Bayes' theorem. The model's reliability is determined by computing the posterior predictive distribution of the survival or hazard functions. …”
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Prediction Model of Mining Subsidence Parameters Based on Fuzzy Clustering by Fei Cheng, Jun Yang, Ziwen Zhang, Jingliang Yu, Xuelian Wang, Yongdong Wu, Zhengyi Guo, Hui Li, Meng Xu

“…Through the analysis of the main geological and mineral characteristics of mining subsidence, the geological and mineral characteristics are simplified according to the third similar theorem. The feature equation is obtained by using the equation analysis method and dimension analysis method. …”
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Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach by Jing-jing Liu, Tie-lin Chen, Chang-ling Xie, Jian-hua Tian, Yu-xin Wei

“…First, the model of calculating the function expression of the detaching surface for the collapsing block is formed in the framework of the upper bound theorem of limit analysis and the extremum principle. …”
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Interferometric Dynamic Measurement: Techniques Based on High-Speed Imaging or a Single Photodetector by Yu Fu, Giancarlo Pedrini, Xide Li

“…In these applications, various physical quantities need to be measured in any instant and the Nyquist sampling theorem has to be satisfied along the time axis on each measurement point. …”
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Time-Dependent Reliability Analysis of RC Deep Beams considering Linear/Nonlinear Creep and Shrinkage Using ANFIS Network and MCS by Seyed Bahram Beheshti Aval, Mohsen Ghabdian

“…In the nonlinear range, creep was taken into account by the affinity hypothesis theorem to consider the effect of high-level sustained loading. …”
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Thermodynamic Phase Transition and Joule Thomson Adiabatic Expansion for dS/AdS Bardeen Black Holes with Consistent 4D Gauss-Bonnet Gravity by Hossein Ghaffarnejad, Elham Ghasemi, Emad Yaraie, Mohammad Farsam

“…Instead of the work \cite{1} given by Glaven and Lin in which in according to the Lovelock theorem it is not applicable for all types of 4-dimensional curved spacetimes of Einstein Gauss Bonnet gravity, authors of the work \cite{2} applied breakdown of diffeomorphism property to present a consistentEinstein-Gauss-Bonnet gravity theory in 4-dimensions. …”
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PERFORMANCE REQUIRED FOR COMMON-USE COMPONENTS OF COMPUTER NETWORKS by BOLUN, Ion

“…Based on Jackson’s partitioning theorem and considering the linear dependence of the costs of channels, routers, and servers on their performance, a simplified analytical model for these components of the network is defined. …”
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