Physics-Informed Denoising Model for Dynamic Data Recovery of Power Systems by Jian Li, Guoqiang Lu, Yongbin Li, Dongning Zhao, Huaiyuan Wang, Yucheng Ouyang

“…In light of the poor interpretability exhibited by traditional machine learning (ML) methods in denoising, a physics-informed denoising model (PIDM) for dynamic data recovery is proposed. The differential equations of physical models in power systems are employed to guide the training of PIDM. …”
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Novel computations of the time-fractional chemical Schnakenberg mathematical model via non-singular kernel operators by Abdul Hamid Ganie, Fatemah Mofarreh, N. S. Alharthi, Adnan Khan

“…The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractional-order nonlinear differential equations that arise in related fields of engineering and science.…”
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Two-phase Agrawal hybrid nanofluid flow for thermal and solutal transport fluxes induced by a permeable stretching/shrinking disk by Hatem Gasmi, Muhammad Waqas, Umair Khan, Aurang Zaib, Anuar Ishak, Imtiaz Khan, Ali Elrashidi, Mohammed Zakarya

“…Through the utilization of similarity ansatz, the governing partial differential equations are simplified into a class of ordinary differential (similarity) equations. …”
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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. …”
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FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
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MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA by Matheus Dias Carvalho, Ricardo de Carvalho Falcão, Antonio Marcos de Oliveira Siqueira

“…This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. …”
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Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. …”
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Stochastic Diffusive Modeling of CO₂ Emissions with Population and Energy Dynamics by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Hisham M. Al-Khawar, Yasir Nawaz

“…A novel numerical scheme, an extension of the Euler-Maruyama algorithm, is proposed to solve stochastic time-dependent partial differential equations governing the model. The scheme's consistency and stability are rigorously analyzed in the mean square sense. …”
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CALCULATION OF STATIC PARAMETERS OF SILICON DIODE CONTAINING δ-LAYER OF TRIPLE-CHARGED POINT DEFECTS IN SYMMETRIC p–n-JUNCTION by N. A. Poklonski, A. I. Kovalev, N. I. Gorbachuk, S. V. Shpakovski

“…It was assumed that the cross-section for v-band hole capture on t-defects is greater than the cross-section for c-band electron capture on t-defects.The system of stationary nonlinear differential equations, which describe in the drift-diffusion approximation a migration of electrons and holes in semiconductors, is solved numerically. …”
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Accelerating and decelerating flow of radiatively Casson fluid between two permeable disks under convective boundary conditions by A. Naeem, Z. Abbas, M.Y. Rafiq

“…Jacobi elliptic sine square function is used to derive the solution of non-linear differential equations by transforming the equations into an elliptic integral form and then by using a change of variables which simplifies the governing equations so that the solution can be derived easily. …”
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Characterising the scale-up and performance of antiretroviral therapy programmes in sub-Saharan Africa: an observational study using growth curves by Benjamin Bigelow, Stéphane Verguet

“…We developed two ordinary differential equations models, the Gompertz and logistic growth models, that allowed for the estimation of summary parameters related to scale-up and rates of change in ART coverage. …”
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Evidence of Exponential Speed-Up in the Solution of Hard Optimization Problems by Fabio L. Traversa, Pietro Cicotti, Forrest Sheldon, Massimiliano Di Ventra

“…Then, we solve its associated nonlinear ordinary differential equations numerically, towards the equilibrium points. …”
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Causal models and prediction in cell line perturbation experiments by James P. Long, Yumeng Yang, Shohei Shimizu, Thong Pham, Kim-Anh Do

“…Next we present Cellbox, a recently proposed system of ordinary differential equations (ODEs) based model that obtained the best prediction performance on a Melanoma cell line perturbation data set (Yuan et al. in Cell Syst 12:128–140, 2021). …”
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Spatially Distributed Morphogen Production and Morphogen Gradient Formation by Arthur D. Lander, Qing Nie, Frederic Y. M. Wan

“…Partial differential equations and auxiliaryconditions governing the activities of the morphogen Dpp in Drosophila wingimaginal discs were formulated and analyzed as Systems B, R, and C in[7][9][10]. …”
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Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source by V. S. Malyar, A. V. Malyar

“…The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. …”
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Simulation modeling tools in training environmental science students by А. G. Kot, A. B. Achasov, O. Yu. Seliverstov, V. G. Karpov

“…Students are encouraged to create and investigate the "Predator Prey" model, which is based on the Volterra-Lotka system of differential equations. The model describes the dynamics of predator and prey populations in a closed and stationary system. …”
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On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method by Sadegh Tavakoliyan, Mohamad Najar, Parham Memarzadeh, Tadeh Zirakian

“…The finite point method (FPM) is a numerical, mesh-free technique for solving differential equations, particularly in fluid dynamics. While the FPM has been previously applied in solid mechanics to analyze plates under in-plane loading, there remains a notable scarcity of research exploring the out-of-plane analysis of elastic plates using this method. …”
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Entropy Analysis of Carreau Nanofluid Flow in the Presence of Joule Heating and Viscous Dissipation Past Unsteady Stretching Cylinder by Eshetu Haile Gorfie, Gizachew Bayou Zegeye, Gurju Awgichew Zergaw

“…The governing partial differential equations are transformed into first‐order initial value problems by similarity transformation and linearization. …”
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An Evolutionary Game Model of a Regional Logistics Service Supply Chain Complex Network in a Blockchain Environment by Guangsheng Zhang, Zhaomin Zhang

“…The stability theorem of differential equations is employed to elucidate the inherent decision-making mechanisms present in the game. …”
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Investigation of natural convection heat transfer in MHD fluid within a hexagonal cavity with circular obstacles by Mohammad Dehghan Afifi, Ali Jahangiri, Mohammad Ameri

“…The finite element method is employed to solve the governing partial differential equations of the system. This research focuses on the impact of innovative geometry, variations in Rayleigh and Hartmann numbers on flow patterns, temperature distribution and concentration fields. …”
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