An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis by Hashem Saberi Najafi, Sayed Arsalan Sajjadi, Hossein Aminikhah

“…In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution. …”
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Isolated tubercular dacryoadenitis in a non-immunocompromised healthy adult by Ajax Jossy, N Kaviyapriya, Nirupama Kasturi, Sree J Rekha

“…The patient had an elevated erythrocyte sedimentation rate, and incisional biopsy showed granulomatous inflammation with Langhan's giant cells suggestive of a tubercular etiology. …”
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Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams by Ramazan-Ali Jafari-Talookolaei, Maryam Abedi

“…The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. …”
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A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel by Hashim M. Alshehri, Aziz Khan

“…Our numerical results are based on the Lagrange polynomial interpolation. We observe that the model of fractional order has the same behavior of the solutions as the integer order existing model.…”
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New Applications of a Kind of Infinitesimal-Operator Lie Algebra by Honwah Tam, Yufeng Zhang, Xiangzhi Zhang

“…Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. …”
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Observability and uniqueness theorem for a coupled hyperbolic system by Boris V. Kapitonov, Joel S. Souza

“…We obtain the inverse inequality by the Lagrange multiplier method under certain conditions.…”
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Measuring Hemoglobin Levels in the Optic Disc of Parkinson’s Disease Patients Using New Colorimetric Analysis Software by Maria Pilar Bambo, Elena Garcia-Martin, Maria Satue, Susana Perez-Olivan, Silvia Alayon, Marta Gonzalez-Hernandez, Vicente Polo, Jose Manuel Larrosa, Manuel Gonzalez-De la Rosa

“…OCT examinations and one photograph of the optic disc were performed. The Laguna ONhE (“optic nerve hemoglobin”; Insoft SL, Tenerife, Spain) software was used to analyze the Hb level on the acquired optic disc photographs. …”
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A predefined-time radial basis function (RBF) neural network tracking control method considering actuator faults for a new type of spraying robot by J. Zhao, J. Zhao, Y. Li, Y. Li, Y. Li, B. Pei, Z. Yu, Z. Dong

“…Combined with the Euler–Lagrange dynamics model of the two-joint manipulator, a nonsingular PRC controller is designed according to the uncertainty in model parameters and external interference. …”
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Geodesic Effect Near an Elliptical Orbit by Alina-Daniela Vîlcu

“…O'Connell (1970, 1975) in a different setting, using the tools of Newtonian mechanics and the Euler-Lagrange equations.…”
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Willmore-Like Tori in Killing Submersions by Manuel Barros, Óscar J. Garay, Álvaro Pámpano

“…The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. …”
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Motion Planning of Compliant Parallel Robot by Tian Hao, Yu Yueqing

“…The research on motion planning of the parallel robot with compliant joints is carried out.According to the characteristics of compliant joint,the system analysis model is built.The dynamics equation is obtained based on Lagrange method.To guarantee the smooth running of the system and suppress the rate of speed of inertia force,the trapezoidal and S-curve velocity planning method are used for motion planning.The motion planning algorithms of linear and circular trajectories are given.The simulation results show that the motion planning method is effective.…”
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Comparison of Analytical Solution of DGLAP Equations for... by Neelakshi N. K. Borah, D. K. Choudhury, P. K. Sahariah

“…The DGLAP equation for the nonsinglet structure function F 2 N S ( x , t ) at LO is solved analytically at low x by converting it into a partial differential equation in two variables: Bjorken x and t    ( t = l n ( Q 2 / Λ 2 ) and then solved by two methods: Lagrange’s auxiliary method and the method of characteristics. …”
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Hierarchical Sliding Mode Algorithm for Athlete Robot Walking by Van Dong Hai Nguyen, Xuan-Dung Huynh, Minh-Tam Nguyen, Ionel Cristian Vladu, Mircea Ivanescu

“…The dynamic equations are determined by Euler-Lagrange method. A new method based on hierarchical sliding mode for controlling postures is also introduced. …”
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Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum by Luca Collini, Rinaldo Garziera, Kseniia Riabova, Mariya Munitsyna, Alessandro Tasora

“…The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. …”
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Balans, Moderasyon, ak Varyete by Isabel Valentin-Oquendo

“…Piramid sa a gen twa mesaj ladann: balans, moderasyon, ak varyete. This document is FCS8721-Hai, one of a series of the Department of Family, Youth, and Community Sciences, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. …”
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Joint bandwidth and power allocation algorithm in cognitive radio network with consideration of utility and fairness by Ji-lei YAN, Jian-dong LI, Lin-jing ZHAO, Quan DONG

“…A unified utility function was designed to adapt to different types of services and an optimization problem was formulated based on the network utility maximization model.By applying the Lagrange duality method,a distributed joint bandwidth and power allocation algorithm was proposed.Simulation results show that this algorithm can effectively allocate proper resources to various types of secondary users.It can not only maximize the total utility of all secondary users but also maintain the utility fairness among them.…”
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Balans, Moderasyon, ak Varyete by Isabel Valentin-Oquendo

“…Piramid sa a gen twa mesaj ladann: balans, moderasyon, ak varyete. This document is FCS8721-Hai, one of a series of the Department of Family, Youth, and Community Sciences, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. …”
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Incidencia de la frontera entre las poblaciones autóctonas americanas: El caso de Argentina y Chile by Miguel-Héctor Fernández-Carrión

“…La Historiografía, metodología y tipología de fronteras intenta completar una laguna existente sobre esta materia. La importancia de elaborar científicamente un método, es que todos los investigadores en un futuro puedan aplicar las mismas terminologías para referirse a unos supuestos iguales o semejantes, y además posibilita la clasificación tipológica de las fronteras tratadas en cada supuesto.…”
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Dynamics Modeling of the Crank-group Driving Mechanism with Clearance by Yan Weiliang, Cao Jujiang, Wang Yuqi, Wu Yao

“…The crank- group driving mechanism is a kind of under- actuated mechanism with redundant characteristics,aiming at the characteristics of mechanism,selecting continuous contact model for the joint clearance,the dynamics model of the basic structural unit- double crank mechanism with clearance is set up by the second kind Lagrange equation. Then,assume that the inertia force direction of no quality rod pointing to truss connecting rod,the derivation from the unit to the whole is carried out,and the dynamics model of the crank- group driving mechanism with clearance is established.…”
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Combining Laplace transform and Variational iteration method for solving singular IVPs and BVPs of Lane–Emden type equation by Mohamed H. Jassim, Waleed Mohammed Al-Hayani

“…Initially, this method requires calculating the lagrange multiplayer, and after its value was calculated, it was found to be equal , this method is applying on several problems and the results were improved using Padé approximations, the results were compared with the exact solution by calculating the absolute error value between them. …”
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