The Feyn-structure of Yangian symmetry by Florian Loebbert, Harshad Mathur

“…Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. …”
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Water level monitoring by using magnetic optical sensor by Jonatan Daniel Morales Arrieta, Jesus Vargas Ortiz, Jesús Patricio Ordaz Oliver, Juan Carlos González Islas, Omar Samperio Vázquez

“…Firstly, mathematical modeling of the water level measurement in a tank using differential equations is described. This system comprises a printed circuit board (PCB), a novel float mechanism, an optical sensor, a microcontroller, and a visualization stage. …”
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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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A quantitative analysis of Koopman operator methods for system identification and predictions by Zhang, Christophe, Zuazua, Enrique

“…It is based on the so-called Koopman operator, which uses the well-known link between differential equations and linear transport equations. Data-driven methods recover specific finite-dimensional approximations of the Koopman operator, which can be understood as a transport operator. …”
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Analysis of non scalar control problems for parabolic systems by the block moment method by Boyer, Franck, Morancey, Morgan

“…We also deduce estimates on the cost of controllability when the final time goes to the minimal null control time.We illustrate how the method works on a few examples of such abstract controlled systems and then we deal with actual coupled systems of one dimensional parabolic partial differential equations. Our strategy enables us to tackle controllability issues that seem out of reach by existing techniques.…”
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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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Mathematical Modelling of Cholera Transmission incorporating Media Coverage. by Muhereza, Obed

“…The model was thereafter analyzed using the stability theory of differential equations. The basic reproduction number Ra, was derived using the next generation matrix approach. …”
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A computational role of blood nanofluid induced by a stenosed artery with porous medium and thermophoretic particle deposition effects by Shivalila Hangaragi, N. Neelima, N. Beemkumar, Ankur Kulshreshta, Umair Khan, Noreen Sher Akbar, Mohammad Kanan, Mona Mahmoud

“…Based on these assumptions, the governing equations are formulated and transformed into a system of ordinary differential equations using appropriate similarity transformations. …”
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How Do Diabetes Models Measure Up? A Review of Diabetes Economic Models and ADA Guidelines by Lindsay Govan, Olivia Wu, Robert Lindsay, Andrew Briggs

“…There are four main types of models: Markov-based cohort, Markov-based microsimulations, discrete-time microsimulations, and continuous time differential equations. All models were long-term diabetes models incorporating a wide range of compilations from various organ systems. …”
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Chemical effects on ecological interactions within a model-experiment loop by Lamonica, Dominique, Charles, Sandrine, Clément, Bernard, Lopes, Christelle

“…We modelled the dynamics of the three species and their interactions using a mechanistic model based on coupled ordinary differential equations. The main processes occurring in this three-species microcosm were thus formalized, including growth and settling of algae, growth of duckweeds, interspecific competition between algae and duckweeds, growth, survival and grazing of daphnids, as well as cadmium effects. …”
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Randomized radial basis function neural network for solving multiscale elliptic equations by Yuhang Wu, Ziyuan Liu, Wenjun Sun, Xu Qian

“…Ordinary deep neural network (DNN)-based methods frequently encounter difficulties when tackling multiscale and high-frequency partial differential equations. To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic equations. …”
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Displacement of hydrocarbon liquids by water using the models of zonally heterogeneous deformable formations by Marat Ya. Khabibullin, Rustem I. Suleymanov, Razifa R. Stepanova, Alina Az. Gizzatullina, Arsen M. Khabibullin

“…It is known that the motion of two-phase hydrocarbon systems in deformable reservoirs is represented by complex nonlinear partial differential equations. An analytical solution of such equations is possible only with the use of special approaches. …”
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Direct and Indirect Protection with Pediatric Quadrivalent Live-Attenuated Influenza Vaccination in Europe Estimated by a Dynamic Transmission Model by Laetitia Gerlier, Judith Hackett, Richard Lawson, Sofia Dos Santos Mendes, Catherine Weil-Olivier, Markus Schwehm, Martin Eichner

“…**Methods:** A deterministic, age-structured, dynamic model was used to simulate influenza transmission across 14 European countries, comparing current vaccination coverage using a quadrivalent inactivated vaccine (QIV) to a scenario whereby vaccination coverage was extended to 50% of 2–17 year-old children, using QLAIV. Differential equations described demographic changes, exposure to infectious individuals, recovery and immunity dynamics. …”
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