Backward Anticipated Social Optima: Input Constraints and Partial Information by Shujun Wang

“…Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by <i>anticipated</i> backward stochastic differential equations (ABSDE) in which the <i>terminal</i> instead of the <i>initial</i> condition is specified and the anticipated terms are involved. …”
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A simple model of carcinogenic mutations with time delay and diffusion by Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk

“…In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. …”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations.…”
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Dynamic Characteristics of a Cylindrical Roller Bearing with Cage Cracks by Yang Yang, Xiaoye Qi, Yongjie Wang, Meiling Wang, Baogang Wen, Jingyu Zhai

“…The derived dynamic differential equations of cylindrical roller bearings were solved by means of the modified Newton–Raphson iterative algorithm and the BDF predictive correction algorithm with automatic variable order and step length. …”
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MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition by B. R. Rout, S. K. Parida, S. Panda

“…The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. …”
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Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method by Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, E. M. Mohamed

“…Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. …”
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Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment by Brandy Rapatski, Juan Tolosa

“…We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact.…”
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From the Guest Editors by Carlos Castillo-Chávez, Christopher Kribs Zaleta, Yang Kuang, Baojun Song

“…Those of us who met the field of mathematical biology as a well-developed,flourishing, and rewarding discipline owe much to those who made it so.This special issue of Mathematical Biosciences and Engineering isdedicated to two such pioneers: Fred Brauer and Karl Hadeler.Since retrospectives of both men have been published in other venues [1, 2], we will only summarize their contributions briefly here.Fred Brauer obtained his Ph.D. from MIT in 1956 under Norman Levinson,and during a long tenure at the University of Wisconsin he co-wrote severaltexts on ordinary differential equations that have become classics.His research entered mathematical biology first through early studies inpredator-prey systems and harvesting, both with and without delays.He then moved into mathematical epidemiology, and the text he co-authoredwith Carlos Castillo-Chavez in both these areas earlier this decade isalready in wide use.For more information please click the “Full Text” above.…”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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AI-assisted discovery of quantitative and formal models in social science by Julia Balla, Sihao Huang, Owen Dugan, Rumen Dangovski, Marin Soljačić

“…By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. …”
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Fuzzy Networked Control Systems Design Considering Scheduling Restrictions by H. Benítez-Pérez, A. Benítez-Pérez, J. Ortega-Arjona, O. Esquivel-Flores

“…Therefore, it is necessary to study the behavior of the delays as well as the integration into differential equations of these bounded delays. The related time delays needs to be known a priory but from a dynamic real-time behavior. …”
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A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method by H. T. Cho, A. S. Cornell, Jason Doukas, T.-R. Huang, Wade Naylor

“…We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. …”
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Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive by Ruili Huo, Yichen Liu, Peng Wu, Hai Fang, Weiqing Liu, Ding Zhou

“…The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. …”
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Mathematical analysis of a model for glucose regulation by Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała

“…Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). …”
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A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation by Muhammad Abid, Madiha Bibi, Nasir Yasin, Muhammad Shahid

“…Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. …”
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Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model by Guiyun Liu, Baihao Peng, Xiaojing Zhong, Xuejing Lan

“…In this paper, nodes are divided into five states according to the residual energy and infection level, and the differential equations are constructed to describe the evolution of nodes. …”
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Conciliating accuracy and efficiency to empower engineering based on performance: a short journey by Chinesta, Francisco, Cueto, Elias

“…The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. …”
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Hopf Bifurcation, Cascade of Period-Doubling, Chaos, and the Possibility of Cure in a 3D Cancer Model by Marluci Cristina Galindo, Cristiane Nespoli, Marcelo Messias

“…We study a cancer model given by a three-dimensional system of ordinary differential equations, depending on eight parameters, which describe the interaction among healthy cells, tumour cells, and effector cells of immune system. …”
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Impact of a block structure on the Lotka-Volterra model by Clenet, Maxime, Massol, François, Najim, Jamal

“…The model consists of n coupled differential equations linking the abundances of n different species. …”
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