Fluid-Induced Nonlinear Vibration of a Cantilevered Microtube with Symmetric Motion Constraints by Yong Guo

“…The Galerkin method is applied to produce a set of ordinary differential equations. The effect of the internal material length scale parameter on the critical flow velocity is investigated. …”
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Solving the Linear 1D Thermoelasticity Equations with Pure Delay by Denys Ya. Khusainov, Michael Pokojovy

“…We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. …”
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An Analysis of the Cluster-Detecting Property of the BCM Neuron by Lawrence Udeigwe

“…By exploring the qualitative behaviors of an underlying system of differential equations, we present a rigorous mathematical analysis of this cluster-detecting property. …”
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A New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators by Zhaoxia Chen, Xiong You, Xin Shu, Mei Zhang

“…In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta (RK) methods by introducing frequency-depending weights in the update. …”
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Mean-periodic functions by Carlos A. Berenstein, B. A. Taylor

“…Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. …”
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Derivation of Equations for Flexible Multibody Systems in Terms of Quasi-Coordinates from the Extended Hamilton’s Principle by L. Meirovitch

“…In this article, hybrid (ordinary and partial) differential equations for flexible multibody systems are derived in terms of quasi-coordinates directly from the extended Hamilton's principle. …”
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The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals by Nurlybek A. Ispulov, Abdul Qadir, Marat K. Zhukenov, Talgat S. Dossanov, Tanat G. Kissikov

“…In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.…”
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Three-dimensional guidance control for vehicle convoy and interception by Yihua Dong, Yuefen Tan, Jingang Zhao, Wencheng Wang

“…Based on the differential equations for the range, the pitch angle and the yaw angle between successive vehicles, the deviated pursuit and the proportional navigation are proposed to derive decentralized control strategy for vehicle convoy and interception control. …”
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Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space-Time Fractional Equations by Huitzilin Yépez-Martínez, Ivan O. Sosa, Juan M. Reyes

“…The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.…”
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Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers by Zhaolin Jiang, Yanpeng Gong, Yun Gao

“…Circulant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant and g-circulant matrices with the sum and product of Fibonacci and Lucas numbers. …”
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A synthesized view of the CSF-blood barrier and its surgical implications for aging disorders by Birra Taha, Robert McGovern, Cornelius Lam, Cornelius Lam

“…We briefly review the mathematical framework for CSF transport as described by a set of well-studied partial differential equations. Moreover, we describe the major contributors of CSF flow through both diffusive and convective forces beginning at the molecular level and extending into macroscopic clinical observations. …”
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Calculation of Wall Heat Conductivity under Non-Symmetric Boundary Conditions by R. I. Yesman

“…Advancing of phase transformation front along cross-section is considered with the purpose to take into account phase and chemical transformations in high-impact coatings and the Dirac δ-function is applied in this case.While stating a problem nonlinear boundary conditions and differential equations of heat transfer with due account of thermal and physical characteristics dependence on temperature have been used in the paper. …”
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On a Perturbed Risk Model with Time-Dependent Claim Sizes by Longfei Wei, Jia Hao, Shiyu Song, Zhenhua Bao

“…We study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. Integro-differential equations and Laplace transforms satisfied by the Gerber–Shiu functions are obtained. …”
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Three-loop ladder diagrams with two off-shell legs by Ming-Ming Long

“…We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical regions. …”
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Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems by Hammad Khalil, Mohammed Al-Smadi, Khaled Moaddy, Rahmat Ali Khan, Ishak Hashim

“…The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. …”
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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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Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy by Haiyang Wang, Zhen Wu

“…We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. …”
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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. …”
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Vibrations of Plates and Shells with Attached Mass by L. U. Sultanov, I. R. Garifullin

“…The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. …”
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A Mathematical Model For The Population Dynamics Of Disease Transmiting Vectors in Particular Female Anopheles Mosquitoes. by Turyamusiima, Richard

“…The mosquito free equilibrium and endemic equilibrium have been determined by setting system of ordinary differential equations to zero. Basic reproduction has been determined using the next generation matrix management analyzed. …”
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