• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.149-167
• /
• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.839-853
• /
• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.405-432
• /
• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• Convergence Security Journal
• /
• v.5 no.3
• /
• pp.93-97
• /
• 2005

MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic partial differential equations. Apparently, however, it has shown entropy violations under small discontinuity. This non-physical shock grows fast and eventually all the meaningful information of the solution disappears. Some modifications of MacCormack's methods follow ideas of central schemes with an advantage of second order accuracy for space and conserve the high order accuracy for time step also. Numerical results are shown to perform well for the one-dimensional Burgers' equation and Euler equations gas dynamic.

• Geomechanics and Engineering
• /
• v.31 no.6
• /
• pp.623-635
• /
• 2022

This paper presents the re-evaluation of existing piezocone penetration test (CPTu)-based shear wave velocity (V_s) equations through their application into well-documented data obtained at nine sites in six countries. The re-evaluation indicates that the existing equations are appropriate to use for any specific soil, but not for various types of clays. Existing equations were adjusted to suit all nine clays and show that the correlations between the measured and predicted V_s values tend to improve with an increasing number of parameters in the equations. An adjusted equation, which comprises a CPTu parameter and two soil properties (i.e., effective overburden stress and void ratio) with the best correlation, can be converted into a CPTu-based equation that has two CPTu parameters and depth by considering the effect of soil cementation. Then, the developed equation was verified by application to each of the nine soils and nine other worldwide clays, in which the predicted V_s values are comparable with the measured and the stochastically simulated values. Accordingly, the newly developed CPTu-based equation, which is a time-saving and economical method and can estimate V_s indirectly for any type of naturally deposited clay, is recommended for practical applications.

• Structural Engineering and Mechanics
• /
• v.90 no.6
• /
• pp.601-610
• /
• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• Steel and Composite Structures
• /
• v.51 no.4
• /
• pp.457-471
• /
• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.836-839
• /
• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.183-193
• /
• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• Journal for History of Mathematics
• /
• v.36 no.1
• /
• pp.1-17
• /
• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.