Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints by Moussa Kounta

“…In this situation the Hamilton-Jacobi-Bellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such cases V can be interpreted as a viscosity solution. …”
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Investigation of Subcombination Internal Resonances in Cantilever Beams by Haider N. Arafat, Ali H. Nayfeh

“…The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. …”
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Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays by Haijun Hu, Li Liu, Jie Mao

“…The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. …”
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Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach by Yonggui Kao, Hamid Reza Karimi

“…By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. …”
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Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model by Yuhong Wang, Shulin Yang, Wuyong Qian, Xiaozhong Li

“…Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). …”
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A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems by A. Karimi Dizicheh, F. Ismail, M. Tavassoli Kajani, Mohammad Maleki

“…In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. …”
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Research of the Transmission Error of Planetary Transmission System for Hub Motor by Chen Haoran, Qin Xunpeng, Zhang Jiang

“…Taking the planetary transmission system of hub motor as the research object,the kinematic differential equations of the system are established by considering the influence factors of time-varying mesh stiffness,meshing phase and equivalent mesh error,and the Runge-Kutta method is used to get the system transmission error. …”
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Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order by Yi Chai, Liping Chen, Ranchao Wu

“…By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. …”
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Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. …”
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Study on the Dynamics of Non-circular Planetary Gear Hydraulic Motor by Wei Shuang, Li Dianqi, Liu Guanghui

“…The dynamics differential equations are solved by using Runge-Kutta method. …”
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A Bright Entanglement and Squeezing Generated by an External Pumping Radiation in a Correlated Emission Laser by Chimdessa Gashu

“…The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. …”
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SEMI-ANALYTUCAL SOLUTION TO DYNAMIC ANALYSIS FOR PLOUGH SYSTEM by CHEN Hong Yue, ZHANG Kun, ZHANG Yu, MAO Jun, SONG Qiu Shuang

“…Dynamic model of plough system including three partial differential equations were solved with separation variables method. …”
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Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus by Yang Yan, Xiaohong Yu

“…Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. …”
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Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. …”
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Analysis of the Torsional Vibration Modeling and Rigidity Excitation of K-H-V Cycloid Steel Ball Transmission by Kong Xia, Zhang Jielu, Cai Yunlong

“…By analyzing the position relationships of each engagement force and the displacement relationships of each component,the governing differential equations of the system and the dimensionless equivalent engagement rigidities of each transmission disc are derived. …”
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Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet by Meysam Mohamadali, Nariman Ashrafi

“…Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. …”
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The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes by Peng Li, Chuancun Yin, Ming Zhou

“…Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. …”
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Review on Mathematical and Mechanical Models of the Vocal Cord by L. Cveticanin

“…The corresponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. …”
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Chemical Reaction Effect on Transient Free Convective Flow past an Infinite Moving Vertical Cylinder by Ashish Paul, Rudra Kanta Deka

“…The closed-form solutions of the dimensionless governing partial differential equations are obtained in terms of Bessel's functions and modified Bessel's functions by the Laplace transform technique. …”
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Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control by Robert Vrabel, Pavol Tanuska, Pavel Vazan, Peter Schreiber, Vladimir Liska

“…We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. …”
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