• Advances in nano research
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• 제7권5호
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• pp.311-324
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• 2019

The present study aims to evaluate the nonlinear and post-buckling behaviors of orthotropic graphene sheets exposed to end-shortening strain by implementing a semi-Galerkin technique, as a new approach. The nano-sheets are regarded to be on elastic foundations and different out-of-plane boundary conditions are considered for graphene sheets. In addition, nonlocal elasticity theory is employed to achieve the post-buckling behavior related to the nano-sheets. In the present study, first, out-of-plane deflection function is considered as the only displacement field in the proposed technique, which is hypothesized by an appropriate deflected form. Then, the exact nonlocal stress function is calculated through a complete solution of the von-Karman compatibility equation. In the next step, Galerkin's method is used to solve the unknown parameters considered in the proposed technique. In addition, three different scenarios, which are significantly different with respect to concept, are used to satisfy the natural in-plane boundary conditions and completely attain the stress function. Finally, the post-buckling behavior of thin graphene sheets are evaluated for all three different scenarios, and the impacts of boundary conditions, polymer substrate, and nonlocal parameter are examined in each scenario.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.157-169
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• 2020

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 충청수학회지
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• 제19권1호
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• pp.101-110
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• 2006

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

• 충청수학회지
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• 제31권2호
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• pp.255-268
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• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권3호
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• pp.129-145
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• 2017

In this paper, we establish lower estimates for the modulus of the non-tangential derivative of the holomorphic functionf(z) at the boundary of the unit disc. Also, we shall give an estimate below |f''(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_0{\neq}0$.

• 대한수학회보
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• 제51권3호
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• pp.803-812
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• 2014

Let ${\mathcal{S}}^0_{\mathcal{H}}$ be the class of normalized univalent harmonic mappings in the unit disk. A subclass ${\mathcal{V}}^{\mathcal{H}}(k)$ of ${\mathcal{S}}^0_{\mathcal{H}}$, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in ${\mathcal{V}}^{\mathcal{H}}(k)$ are given.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.38.1-38
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• 2001

In this paper, the vibration suppression problem of an axially moving power transmission belt is investigated. The equations of motion of the moving belt is first derived by using Hamilton´s principle for systems with changing mass. The total mechanical energy of the belt system is considered as a Lyapunov function candidate. Using the Lyapunov second method, a nonlinear boundary control law that guarantees the uniform asymptotic stability is derived. The control performance with the proposed control law is simulated. It is shown that a boundary control can still achieve the uniform stabilization for belt systems.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.1-12
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• 2015

This paper is concerned with boundary value problems for systems of n-th order dynamic equations on time scales. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• 대한수학회보
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• 제34권1호
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)