Presenting a one-objective optimization model to determine the reliability of the components of a coherent system by Elham Basiri

“…Purpose: In this paper, the amount required to increase the reliability of the components of a coherent system is determined so that the cost of this increase is minimized and the reliability of the whole system is not less than the predetermined value.Methodology: In this research, after introducing the objective and constraint functions in the optimization problem, the Lagrange method is used and then the problem is solved by presenting an algorithm. …”
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Pulmonary nocardiosis in a fat-tailed sheep by Reza Kheirandish, Masoud Sami, Reza Ghanbarpour, Soodeh Alidadi

“…Microscopically, the nodules consisted of foci of pyogranulomatous inflammation with the presence of macrophages, multinucleated (langhans- type) giant cells and eosinophilic amorphous material with rosette-shape configurations (Splendore-Hoeppli reaction). …”
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The Dynamical Behavior of a Rigid Body Relative Equilibrium Position by T. S. Amer

“…The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. …”
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Vibration Suppression Method of a Hydraulic Flexible Manipulator based on the System of Piezoelectric Feedback Driven by Luo Tianhong, Miao Changbin, Xu Xiangyang, Ma Xiangyu, Li Fuying

“…In order to suppress the vibration in the end of large double-link hydraulic flexible manipulator,taking the heavy load hydraulic flexible mechanical arm as the study object and aiming at the end of arm movement in the process of vibration phenomenon,by the servo-hydraulic system-Euler Bernoulli model,Lagrange equation and Jacobian matrix,a piezoelectric feedback driven system control method is designed,through the end of the robot arm equipped with sensitive piezoelectric transmitter,piezoelectric actuators and inversion control design methods,the movement of servo hydraulic cylinder vibration,the hydraulic cylinder with manipulator friction and manipulator rod elastic vibration influence of the hydraulic flexible manipulator end vibration are studied. …”
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Mycobacterium bovis tuberculosis in a neonatal holstein calf by Mehmet Burak Ateş, Mustafa Kemal Çiftçi, Ertan Oruç, Ayşe Çelebi, Gökhan Akçakavak

“…Histopathologically, exudative lesions that extensive caseification necrosis and calcification with diffuse inflammatory cells and Langhans type giant cells without fibrous capsule were seen in the lung parenchyma. …”
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Multiple normalized solutions to the nonlinear Schrödinger–Poisson system with the $L^2$-subcritical growth by Siwei Wei, Kaimin Teng

“…In this paper, we study the existence of multiple normalized solutions to the following Schrödinger–Poisson system with general nonlinearities: \begin{equation*} \begin{cases} -\varepsilon^2\Delta u+V(x)u+\phi u=f(u)+\lambda u & \hbox{in $\mathbb{R}^3$,} \\ -\varepsilon^2\Delta\phi=u^2& \hbox{in $\mathbb{R}^3$,}\\ \int_{\mathbb{R}^3}|u|^2{\rm d}x=\varepsilon^3 a^2,\ \end{cases} \end{equation*} where $\varepsilon$, $a>0$, $\lambda\in\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V(x):\mathbb{R}^3 \rightarrow [0,\infty)$ is a continuous function, and $f$ is a differentiable function satisfying $L^2$-subcritical growth. …”
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Prediction of Horizontal Pneumatic Conveying of Large Coal Particles Using Discrete Phase Model by Daolong Yang, Ge Li, Yanxiang Wang, Qingkai Wang, Jianping Li, Qianqian Huang, Youtao Xia, Qian Li

“…In order to predict the horizontal pneumatic conveying of large coal particles, the coupling methods based on the Euler–Lagrange approach and discrete phase model (DPM) have been used for the simulated research. …”
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Transient Dynamic Response of Delaminated Composite Rotating Shallow Shells Subjected to Impact by Amit Karmakar, Kikuo Kishimoto

“…In this paper a transient dynamic finite element analysis is presented to study the response of delaminated composite pretwisted rotating shallow shells subjected to low velocity normal impact. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. …”
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Suspended Load Path Tracking Control Strategy Using a Tilt-Rotor UAV by M. A. Santos, B. S. Rego, G. V. Raffo, A. Ferramosca

“…Initially, the equations of motion for the multibody mechanical system are derived from the load’s perspective by means of the Euler-Lagrange formulation, in which the load’s position and orientation are chosen as degrees of freedom. …”
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FAULT DIAGNOSIS NEW METHOD OF ROLLING BEARING BASED ON ADAPTIVE REDUNDANT LIFTING SCHEME PACKET by XIAO ShunGen, SONG MengMeng, LAI LianFeng

“…Aiming at feature identification of weak signal for rolling bearing fault,an adaptive redundant lifting scheme packet（ ARLSP） diagnostic method of undecimated operation was proposed to solve the faults distortion that caused by traditional wavelet packet or lifting wavelet transform using sample operation.ARLSP was based on the principle of lifting scheme.Initial undecimated prediction and update operator were calculated by Lagrange interpolating subdivision,and then constructed an ARLSP decomposition and reconstruction algorithm.Simulation signals were tried out by denoising and anti frequency aliasing,results show that ARLSP method was superior to the traditional wavelet packet in denoising capabilities,and there are no frequency aliasing.Moreover,taking an experiment on an asynchronous motor,the vibration signals of the rolling bearings 6205 under conditions of no fault,the inner ring fault,outer ring fault and rolling fault were measured.ARLSP method has been successfully used to extract characteristic frequency and frequency multiplication for various faults,and has got a higher diagnostic accuracy than traditional wavelet packet.…”
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Multiperiod Telser’s Safety-First Portfolio Selection with Regime Switching by Chuangwei Lin, Huiling Wu

“…Referring to Tchebycheff inequality, we modify Telser’s safety-first model to the case that aims to maximize the expected terminal wealth subject to a constraint where the upper bound of the disaster probability is less than the risk control level. By the Lagrange multiplier technique and the embedding method, we study in detail the existence of the optimal strategy and derive the closed-form optimal strategy. …”
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DYNAMIC CHARACTERISTICS OF ROTOR-BEARING SYSTEM AND EVOLUTION OF BEARING WEAR (MT) by WEI Lai, HOU XiangLin, ZHANG Yu, FU XueYan

“…Taking the rotor system supported by angular contact ball bearing as the research object, the dynamic model of rotor bearing system is established by using Lagrange equation. Based on the Archard wear model, the calculation model of wear depth of bearing raceways considering lubrication effects is presented. …”
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An Asymmetrical Mixed Higher-Order Discontinuous Galerkin Time Domain Method for Electromagnetic Scattering from the Plasma Sheath around a Hypersonic Vehicle by Jirong Guo, Yiping Han

“…In this study, a detailed computational model was reconstructed with the high-order Lagrange grids for the nonuniform plasma flow region and the high-order Serendipity grids for the homogeneous medium region. …”
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Development of a Driving Cycle for Fuzhou Using K-Means and AMPSO by Minrui Zhao, Hongni Gao, Qi Han, Jiaang Ge, Wei Wang, Jue Qu

“…First, bad data in the original dataset are preprocessed, the time-series standard smoothing algorithm is used to smoothen the data, and Lagrange’s interpolation is used to realize data interpolation. …”
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Design of Bionic Bird Jumping Mechanism for Autonomous Take-off and Landing Based on the Micro-platform by Zhang Chunpeng, Shao Weiping, Hao Yongping

“…In order to improve the imitation of lower limbs, a parallelogram like lower limb leg mechanism is designed, and the kinematic equation of lower limb mechanism is established by combining the spatial D-H expression method. Based on the Lagrange equation, the dynamic equation of the lower limb mechanism is established. …”
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Energy-efficient resource allocation scheme for device-to-device communication underlaying LTE-A uplink by Zheng-cang ZHU, Ji-hong ZHAO, Rui TANG, Hua QU, Lu-yao WANG, Zhao-xin CAO

“…To cope with the co-channel interference between cellular links and device-to-device (D2D) links concurrently transmitting with the long term evolution-advanced (LTE-A) uplink spectrum,a joint resource allocation scheme was pro-posed to maximize the global energy efficiency of D2D links.The above problem can be decomposed into the power control subproblem and the channel assignment subproblem.Specifically,the power control subproblem can be optimally solved with the help of Dinkelbach method and Lagrange duality.Based on the above results,the channel assignment subproblem turns out to be the set packing problem which was generally NP-hard problem,Therefore,a heuristic algo-rithm was further devised to achieve a tradeoff between performance and complexity.Simulations show that the proposed joint resource allocation scheme outperforms the ones where only single resource variable is optimized,and it achieves the polynomial-time complexity at only minor performance loss when compared to the global optimum.…”
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Automatic Parking Trajectory Planning Based on Warm Start Nonlinear Dynamic Optimization by Hongbin Ren, Yaqi Niu, Yunong Li, Lin Yang, Hongliang Gao

“…The obstacle avoidance constraints were transformed into continuous, smooth nonlinear constraints using the Lagrange dual function. This approach enables the determination of a globally optimal parking path while satisfying vehicular kinematic constraints. …”
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Vibration Behaviour Analysis and Vibration Suppression Studies of the Space Robot by Tian Yong, Yue Xiang, Feng Yan, Jiang Binzhang

“…Then, a rigid-soft coupled dynamic model that combined the flexible motion model with the Lagrange method was established. Using the dynamic model, the factors influencing the vibration behaviour of space robots were analysed. …”
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Power Control Algorithm Based on a Cooperative Game in User-Centric Unmanned Aerial Vehicle Group by Yuexia Zhang, Pengfei Zhang

“…The algorithm helps to establish a downlink power control model of the UUAVG, construct a product of the signal to interference noise ratio function of each user as a utility function of the cooperative game, and deduce the optimal power control scheme using the Lagrange function. This scheme reduces the interference of the service unmanned aerial vehicle (UAV) to edge users and improves the communication quality of all the users as well as the throughput of the entire system. …”
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A Direct Eigenanalysis of Multibody System in Equilibrium by Cheng Yang, Dazhi Cao, Zhihua Zhao, Zhengru Zhang, Gexue Ren

“…This paper presents a direct eigenanalysis procedure for multibody system in equilibrium. The first kind Lagrange’s equation of the dynamics of multibody system is a set of differential algebraic equations, and the equations can be used to solve the equilibrium of the system. …”
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