RESEARCH CONCAVE CIRCULAR HOLE TEMPLATE LINEAR VARIABLE THICKNESS STIFFNESS AND STRENGTH THEORIES by LI ShaoJie

“…This paper studies linear variable thickness circular aperture concave template theory of stiffness and strength calculation.First,set up mechanical model:Template for circular concave,outside the perimeter fixed; center has a round hole,inside the perimeter free,outside under uniformly distributed vertical load.Secondly,the establishment of mathematical model:Derivation of concave template in the axisymmetric condition,ordinary differential equation with variable coefficients of elastic curved surface,and gives the mathematical expressions of boundary conditions.Again,in view of the differential equation boundary value problem,the displacement method and the Matlab algorithm,it is concluded that the deflection of concave template function,and establish the stiffness calculation condition of concave template.Then,determine the concave template on the bending moment and the maximum bending moment and stress,so as to establish a concave template strength calculation conditions.Finally,numerical examples.This paper presents the function solutions,to change law of control concave template section variable parameters.In this way,not only highlight the interdependent relationship between the quantity of each,and optimization,and discussion and application.The result is suitable for uniform,continuous,isotropic material artifacts.Because in the process of calculation and data processing with error,so the formula is similar.…”
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A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method by Abdelhalim Ebaid, Nwaf Al-Armani

“…Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. …”
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Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough by ZHOU Bin

“…Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. …”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation by Kenneth L. Jones, Xiaogui He, Yunkai Chen

“…An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. …”
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Noether symmetries, solutions and conserved quantities of a new (3+1)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion: Multi-analytical ap... by Oke Davies Adeyemo

“…In addition, the equation is reduced to its corresponding nonlinear ordinary differential equation using a plane wave transformation. …”
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…Instead of solving the partial differential equation, we can find the optimal conditions for which the surface is the extremal of the Dirichlet functional. …”
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Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification by Li-Qun Chen, Hu Ding, C.W. Lim

“…The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. …”
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Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation by F. Waffo Tchuimmo, J. B. Gonpe Tafo, A. Chamgoue, N. C. Tsague Mezamo, F. Kenmogne, L. Nana

“…The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. …”
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Data-driven model discovery and model selection for noisy biological systems. by Xiaojun Wu, MeiLu McDermott, Adam L MacLean

“…Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. …”
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The analysis of modyficated mono equation by Donatas Švitra, Renata Retkutė

“… The differential equation with dalay: Ń(t) = α (N(t - h))/(1 +(N(t-h)/K)n) - βN(t),  n > 1 is proposed to model blood cells dynamics. …”
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Approximation of Analytic Functions by Chebyshev Functions by Soon-Mo Jung, Themistocles M. Rassias

“…We solve the inhomogeneous Chebyshev's differential equation and apply this result for approximating analytic functions by the Chebyshev functions.…”
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Logic Structure of Means Used for Higher Dynamic Stability of Power Transmission Systems by G. E. Pospelov

“…The paper contains a proposal for classification of means used for higher dynamic stability of power transmission systems on the basis of a differential equation of generator rotor motion which makes possible to estimate efficiency of these means.…”
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Steady Three-Dimensional MHD Mixed Convection Couple Stress Flow of Hybrid Nanofluid with Hall and Ion Slip Effect by Ali Rehman, Waris Khan, Ebenezer Bonyah, Samsul Ariffin Abdul Karim, Ahmed Alshehri, Ahmed M. Galal

“…To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. …”
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Machine learning to identify environmental drivers of phytoplankton blooms in the Southern Baltic Sea by Maximilian Berthold, Pascal Nieters, Rahel Vortmeyer-Kley

“…We employed generalized additive mixed models to characterize similar blooming patterns and trained an artificial neural network within the Universal Differential Equation framework to learn a differential equation representation of these pattern. …”
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On Oscillations of Solutions of Third-Order Dynamic Equation by Gro Hovhannisyan

“…We are proving the new oscillation theorems for the solutions of third-order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. …”
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Approximate controllability of neutral functional differential system with unbounded delay by Jong Yeoul Park, Sang Nam Kang

“…We consider a class of control systems governed by the neutral functional differential equation with unbounded delay and study the approximate controllability of the system. …”
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An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

“…An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.…”
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About the location of some quasipolinomial roots by Donatas Švitra, Ingrida Sirvydaitė

“…The same research is carried out for a differential equation with delay of neutral type appearing in mathematical ecology. …”
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The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour by Georg Wehowar, Erika Hausenblas

“…Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function.…”
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