• Advances in nano research
• /
• 제9권2호
• /
• pp.69-82
• /
• 2020

In this paper, a new explicit analytical formula is derived for the critical buckling load of Double Walled Carbon Nanotubes (DWCNTs) embedded in Winkler elastic medium without taking into account the effects of the nonlocal parameter, which indicates the effects of the surrounding elastic matrix combined with the intertube Van der Waals (VdW) forces. Furthermore, we present a model which predicts that the critical axial buckling load embedded in Winkler, Pasternak or Kerr elastic medium under axial compression using the nonlocal Donnell shell theory, this model takes into account the effects of internal small length scale and the VdW interactions between the inner and outer nanotubes. The present model predicts that the critical axial buckling load of embedded DWCNTs is greater than that without medium under identical conditions and parameters. We can conclude that the embedded DWCNTs are less susceptible to axial buckling than those without medium.

• Bulletin of the Korean Chemical Society
• /
• 제7권3호
• /
• pp.224-228
• /
• 1986

A nonlinear theory is presented for the fluctuations of intermediates in the Brusselator near the critical point caused by diffusion. The method used is the two time scaling method different from the conventional method in the sense that a slight nonlinear effect is included in the initial time region where the linear approximation is conventionally valid. The result obtained by the nonlinear theory shows that fluctuations close to the critical point approach the value of a stable steady state or deviate infinitely from an unstable steady state, as time goes to infinity, while the linear theory gives approximately time-independent fluctuations. A brief discussion is given for the correlation at a time between fluctuating intermediates when the system approaches a stable steady state.

• 논리연구
• /
• 제13권2호
• /
• pp.1-26
• /
• 2010

이 글은 고 김영정 교수의 비판적 사고 이론을 비판적으로 검토하는 것이 목적이다. 그는 비판적 사고의 기본 속성은 능동적 반성성이고, 비판적 사고가 지향하는 주요 특성은 심층성, 다각성, 영역 전이성이라고 정의한다. 그리고 그는 비판적 사고 개념이 창의성 개념과 연결될 수 있는 가능성을 모색하여, 비판-창의적 사고라는 개념을 제시한다. 나는 이런 정의의 한계를 지적하면서도, 비판-창의적 사고를 향상시킬 방법이 가능하다고 주장하겠다.

• 호남수학학술지
• /
• 제27권4호
• /
• pp.609-619
• /
• 2005

We are concerned with the multiplicity of solutions of the nonlinear elliptic equation with Dirichlet boundary condition. We reveal the existence of m solutions of the nonlinear elliptic equation by a critical point theory, under some condition.

• Proceedings of the Jangjeon Mathematical Society
• /
• 제20권2호
• /
• pp.183-191
• /
• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• Bulletin of the Korean Chemical Society
• /
• 제12권4호
• /
• pp.403-406
• /
• 1991

Light scattering phenomena are discussed for a nonpolar binary liquid mixture composed of an optically active solute and an optically nonactive solvent in the critical region, using the Fisher theory. Comparing them with those in the case that the Ornstein-Zernike theory is satisfied, the appropriate analytic results are obtained and discussed.

• 한국정밀공학회지
• /
• 제19권8호
• /
• pp.84-91
• /
• 2002

This paper analyzes the subsurface stress at the spherical contact using Hamilton equation, and with that data, calculates the fatigue limit under the variations of friction coefficient using fatigue theory. After rough surface being made, this paper figures out the random load generated by contacting to the rough surface, analyzes the stress of its subsurface, and calculates the fatigue limit of the rough surface using fatigue theory. The three parts of the fatigue theory are applied, which are critical plane theory, stress invariant theory and mesoscopic theory.

• Korean Journal of Mathematics
• /
• 제17권4호
• /
• pp.461-471
• /
• 2009

Let ${\Omega}$ be a bounded subset of $R^n$ with smooth boundary and H be a Sobolev space $W_0^{1,2}({\Omega})$. Let $I{\in}C^{1,1}$ be a strongly definite functional defined on a Hilbert space H. We investigate the conditions on which the functional I satisfies the Palais-Smale condition. Palais-Smale condition is important for determining the critical points for I by applying the critical point theory.

• Korean Journal of Mathematics
• /
• 제19권4호
• /
• pp.481-493
• /
• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Korean Journal of Mathematics
• /
• 제17권1호
• /
• pp.67-76
• /
• 2009

We show the existence of at least two nontrivial solutions for a class of the systems of the nonlinear elliptic equations with Dirichlet boundary condition under some conditions for the nonlinear term. We obtain this result by using the variational linking theory in the critical point theory.