Robust pareto multiobjective optimum design of FG-Beam under moving mass by Moein Abdollah-Salimi, Nader Nariman-Zadeh, Reza Ansari

“…By substituting terms of energy into the Lagrange equation, differential equations of motion are obtained. Displacement fields as a function of time and x-coordinate are calculated by means of the numerical solution of the above-mentioned equations. …”
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Investigation of properties of system of automatic control of liquid-propellant rocket propulsion system with integrating regulator by I. A. Kyzmenko, A. B. Yakovlev

“…There are obtained differential equations describing the operation of the comparison element, the throttle valve, the hydraulic amplifier, and the processes in the gas generator. …”
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Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes by Maria Guadalupe Vazquez-Peña, Cruz Vargas-De-León, Jorge Velázquez-Castro

“…The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. …”
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Steady Three-Dimensional MHD Mixed Convection Couple Stress Flow of Hybrid Nanofluid with Hall and Ion Slip Effect by Ali Rehman, Waris Khan, Ebenezer Bonyah, Samsul Ariffin Abdul Karim, Ahmed Alshehri, Ahmed M. Galal

“…To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. …”
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On the possibility of controlling the temperature of gases and liquids in a transportation system by local cooling or heating with account salt deposition by Evgeny L. Pankratov

“…The model is based on an analytical solution of partial differential equations with nonlinearity and variation of their coefficients in space and time. …”
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Simple Ion Transfer at Liquid|Liquid Interfaces by L. J. Sanchez Vallejo, J. M. Ovejero, R. A. Fernández, S. A. Dassie

“…We describe numerical simulations implementing different approaches for solving the differential equations associated with the mass transport and charge transfer. …”
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Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency by Anup Kumar, Bhupendra K. Sharma, Bandar Almohsen, Laura M. Pérez, Kamil Urbanowicz

“…The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. …”
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Mathematical analysis of Lassa fever epidemic with real data by Adnan Aslam, Takasar Hussain, Muhammad Ozair, Arfah Hafeez, Wedad Albalawi, Mohammed Zakarya, Nadir Omer

“…Seven dimensional mathematical model is considered as the system of ordinary differential equations. First, we compute the equilibrium point in which no disease exists then, after finding the reproduction number, both types of stabilities, local and global, of this equilibrium point is discussed. …”
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What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics? by Aditya S. Khanna, Dobromir T. Dimitrov, Steven M. Goodreau

“…We construct models from each class, usingordinary differential equations and exponential random graph models,respectively. …”
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Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository by Claudia Siqueira da Silveira, Antonio Carlos Marques Alvim, Jose de Jesus Rivero Oliva

“…Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. …”
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Hydromagnetic Flow of Two Immiscible Couple Stress Fluids through Porous Medium in a Cylindrical Pipe with Slip Effect by Punnamchandar Bitla, Yitagesu Daba Kore

“…The resulting differential equations governing the flow in the two regions are converted to nondimensional forms using appropriate dimensionless variables. …”
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Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 by S. V. Bolokhov, V. D. Ivashchuk

“…The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. …”
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Application of fluid dynamics in modeling the spatial spread of infectious diseases with low mortality rate: A study using MUSCL scheme by Nnaji Daniel Ugochukwu, Kiogora Phineas Roy, Onah Ifeanyi Sunday, Mung’atu Joseph, Aguegboh Nnaemeka Stanley

“…By treating susceptible, infected, and treated population densities as fluids governed by a system of partial differential equations, the study simulates the epidemic’s spatial dynamics. …”
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Modeling and 1 : 1 Internal Resonance Analysis of Cable-Stayed Shallow Arches by Jiangen Lv, Zhicheng Yang, Xuebin Chen, Quanke Wu, Xiaoxia Zeng

“…Firstly, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equations. Secondly, the multiple scales method (MSM) is used to derive the modulation equations of the system under external excitation of the shallow arch. …”
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Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion by Luis Rabelo, Mario Marin, Petros Xanthopoulos, Carlos Arellano Lennox, Pedro Coiduras, Bernardo Campos, Luz Andrade, Ricardo Collins, Erwin Atencio, Daryelis Pitty

“…This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. …”
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Forecasting Crude Oil Consumption in China Using a Grey Prediction Model with an Optimal Fractional-Order Accumulating Operator by Huiming Duan, Guang Rong Lei, Kailiang Shao

“…In this paper, we study the grey-extended SIGM model, which is directly estimated with differential equations. This model has high simulation and prediction accuracies and is one of the important models in grey theory. …”
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Theoretical Analysis and Experimental Validation on Galloping of Iced Transmission Lines in a Moderating Airflow by Bing Huo, Xuliang Li, Fujiang Cui, Shuo Yang

“…Galloping of an iced transmission line subjected to a moderating airflow has been analysed in this study, and a new form of galloping is discovered both theoretically and experimentally. The partial differential equations of the iced transmission line are established based on the Hamilton theory. …”
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Reconstruction of self-oscillating systems with delay time modulation by Ponomarenko, Vladimir Ivanovich, Prokhorov, Mihail Dmitrievich

“…The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. …”
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Computational Role of Autocatalytic Chemical Reaction in the Dynamics of a Ternary Hybrid Nanofluid Past a Rotating Stretching Surface by Shreedevi Madiwal, N. B. Naduvinamani, J. K. Madhukesh, Umair Khan, Anuar Ishak, Raman Kumar, Md Irfanul Haque Siddiqui

“…The governing equations are transformed into the system of ordinary differential equations (ODEs) and numerically tackled with the help of the Runge–Kutta–Fehlberg 4th 5th (RKF45) order scheme. …”
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On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria by Alma Mašić, Hermann J. Eberl

“…In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable.The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. …”
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