Online vibration state identification of multi-rigid-body system based on self-healing model by Guoyu Wang, Yang Tian, Chunming Hou, Kewei Tong

“…Firstly, considering the influence of the joint surface, the Lagrange method is used to establish the mechanical model of the multi-rigid-body system. …”
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Resource allocation for multi-conductor power-cable carrier communications systems by XU Zhi-qiang1, ZHAI Ming-yue1, ZHAO Yu-ming2

“…Owing to the limitation of lagrange multiplier method used to solve the resource allocation problem with cross-interfere, linear transformation was applying for the transmitting signal and its correlative parameters to decouple channels’ cross-interfere and decompose the complicated allocation problem into multiple simple equivalent channel optimization problems. …”
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Impact-Rubbing Dynamics of Rotor with Hollow Shaft and Offset Discs Based on MDOF Timoshenko Beam Theory by Guofang Nan, Xia Yao, Jingya Yao, Chao Wang

“…Compared with the traditional approach, the novel method can obtain more data to satisfy the need of engineering. The Lagrange equation is adopted to derive the equations of motion for the rotor system, and the Newmark-β method is applied to solve the equations. …”
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Antibiogram profile of escherichia coli isolated from migratory birds by Ferdaus Mohd. AltafHossain, Md. Mukter Hossain, Md. Taslim Hossain

“…<b>Aim:</b> The aim of the study was to conduct the in vitro antibiotic susceptibility test of Escherichia coli isolated from the migratory birds available in winter season at Hakaluki Haor (lagoon) of Bangladesh<p> <b>Materials and Methods:</b> A total of 100 Escherichia coli strains were isolated and subjected for in vitro antibiotic susceptibility test. …”
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RESEARCH ON ROBUST VIBRATION CONTROL OF PLANE SINGLE ARM FLEXIBLE BEAM BASED ON μ SYNTHESIS by GONG ChiKun, WEI BingSheng, YUAN LiPeng

“…Firstly, by hypothetical modal method described elastic deformation, and using Lagrange equation established the dynamic model. Secondly, considering the parameter uncertainty andmodeling perturbation of load mass and structural damping, by using linear fractional transformation and weighting function established mixed uncertainty model. …”
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CoLR: Classification-Oriented Local Representation for Image Recognition by Tan Guo, Lei Zhang, Xiaoheng Tan, Liu Yang, Zhiwei Guo, Fupeng Wei

“…The CoLR model is efficiently solved by Augmented Lagrange Multiplier (ALM) scheme based on a variable splitting strategy. …”
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Trajectory Planning of Energy Consumption Optimal Redundant Manipulators with Constraints by Yuanfei Zhou, Haitao Tang

“…The dynamics of the redundant manipulator are modeled based on lagrange dynamics， and the motion trajectory is constructed using the uniform quintic B-spline function. …”
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Parasite Fauna of the Blackbelly Garter Snake (<i>Thamnophis melanogaster</i>) in Central Mexico by Frida S. Silva-Trejo, Petra Sánchez-Nava, Armando Sunny, Crystian Sadiel Venegas-Barrera, Javier Manjarrez

“…In this work, the metazoans that parasitize the snake <i>Thamnophis melanogaster</i> in Laguna de Cuitzeo, Michoacán, were identified, and their infection parameters were calculated to determine the factors that determine the presence of the metazoan species found. …”
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Research and Improvement of Flexible Micro-positioning Platform with a Three-dimensional Bridge-type Amplification Mechanism by Zhao Zhiquan, Zhu Xijing, Li Jing, Cui Jiajun

“…By applying the strain energy theory, the second theorem of Castigliano, and Lagrange's theorem, the static and dynamic mathematical models of the micro-positioning platform were established. …”
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Study on dynamics characteristic on combination misalignment and rubbing of the dual-rotor system by YAO Xia, NAN Guofang, LI Yao, QIU Xuewen

“…The misalignment of the dual-rotor system for the aero-engine will lead to abnormal increase of the vibration which results in the rotor-stator rubbing and affects the safty and stability of the rotor operation.The dual-rotor system was taken as the research object.Considering the combination misalignment-rubbing fault, the dynamic model of the rotor system is established based on the lumped mass method.The differential equation of the system motion was established according to the Lagrange equation, and the Range-Kutta method was used to solve it.The influence mechanism of the key parameters such as the speed, the misalignment angle and the coupling misalignment on the nonlinear dynamic characteristics of the system was studied.The results show that the system presents complex dynamic characteristics such as periodic, multi-periodic, quasi-periodic and chaotic motion with the increase of the rotor’s speed.When the speed is in the range of 1 500-2 200 rad/s, the system switches between periodic 2 motion and chaotic state through multiple paroxysmal bifurcations and paroxysmal inverted bifurcations.There are nonlinear phenomena such as jump in the bifurcation diagram of the vibration response with the change of the parallel misalignment of the coupling.As the misalignment angle of the bearing increases, the chaotic interval of the high speed decreases, and the stable periodic motion interval increases.…”
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Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction by Chenfei Shao, Chongshi Gu, Zhenzhu Meng, Yating Hu

“…Another contribution of the proposed model is that the actual elastic modulus at each monitoring point can be back-calculated. Moreover, with a Lagrange polynomial interpolation, we can obtain the distribution field of elastic modulus, rather than gaining one value for the whole dam in previous studies. …”
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Design and Simulation of a Combined Displacement Amplification Mechanism by Xueyuan Rong, Hong Zhou, Chunlin Guan

“…The dynamics model and the inherent frequency of the mechanism are established by Lagrange dynamics equation， the finite element simulation method is performed to verify the correctness of models. …”
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Principle of Virtual Work as Foundational Framework for Metamaterial Discovery and Rational Design by dell’Isola, Francesco, Misra, Anil

“…The principle of virtual work provides the necessary framework for development of theories that can lead to novel metamaterials, as it was the unifying principle which allowed the French-Italian School, headed by D’Alembert, Lagrange and Gabrio Piola, to found modern continuum mechanics. …”
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English Perceptions and Representations of Venetian Chromatic Variations by Anne GEOFFROY

“…These attempts at understanding colours need to be linked to the uniqueness of the Venetian environment and to the quality of light in the lagoon where refraction is a daily phenomenon. Although Venetian colours have traditionally been associated to painting, they also belong to the texture of the city itself as exemplified in marbles and mosaics. …”
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A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer by Esam Y. Salah, Bhausaheb Sontakke, Ahmed A. Hamoud, Homan. Emadifar, Atul Kumar

“…The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. Finally, the model was simulated using the Mathematica software, and through the figures, we found that the components of the model approach the equilibrium point, which indicates the stability of the model at the equilibrium point. …”
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A Simulation Model for a Hybrid-Electric Craft in Restricted Waters by Francesco Mauro, Ubaldo la Monaca, Alberto Marinò, Vittorio Bucci

“…This work presents a simulation model for a small passenger craft that will operate in the Grado Lagoon. The model combines the hydrodynamic issues of manoeuvring and propulsion in restricted water with the simulation of the electric loads and capacity of the energy storage system installed onboard. …”
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RIS-assisted terahertz frequency band vehicle network capacity optimization by Fatang CHEN, Xiaoling LIU, Dan WANG, Ruofan ZHANG

“…In order to alleviate the spectrum scarcity and capacity limitation of the current wireless system, the terahertz frequency band was introduced and the reconfigurable intelligent surface (RIS) was used for auxiliary communication to construct a downlink vehicle network.Considering the constraints of limited total system power, QoS constraints of cellular mobile users, and randomness constraints of vehicle and user locations, a hybrid optimization model was established for optimal power allocation and optimal deployment of RIS with the aim of maximizing the total rate of vehicle users.Based on the balance method, linear transformation method, and element elimination method, the original NP-hard problem was transformed into a convex optimization problem with complex correlation constraints and multivariate coupling.The inner layer iteration was based on the Lagrange multiplier method to solve the optimal power allocation, and the outer layer iteratively solved the optimal deployment of RIS based on a improved genetic algorithm.The simulation results show that rationally deploying the number and distribution density of RIS nodes based on optimal power allocation can save costs while achieving a higher target total capacity.…”
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Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation by Shu-Li Mei, De-Hai Zhu

“…Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount. …”
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Stochastic User Equilibrium Assignment in Schedule-Based Transit Networks with Capacity Constraints by Wangtu Xu, Lixin Miao, Wei-Hua Lin

“…When the capacity constraint of the transit line segment is reached, we show that the Lagrange multipliers of the mathematical programming problem are equivalent to the equilibrium passenger overload delay in the congested transit network. …”
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Numerical Research of the Water Entry of Hyperelastic Spheres Within Low Froude Numbers by L. Zhang, R. Xie, H. Jia

“…The water-entry process of solid and hollow hyperelastic spheres was numerically simulated using the arbitrary Lagrange–Euler method, based on the finite element analysis software LS-DYNA. …”
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