• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.137-148
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• 2013

In this paper, we study the Lie-generalized Fibonacci sequence and the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We derive several interesting properties of the Lie-Fibonacci sequence and relationship between them. We also give a couple of sufficient conditions for the existence of the integral points on the hyperbola $\mathfrak{h}^a:x^2-axy+y^2=1$ and $\mathfrak{h}_k:x^2-axy+y^2=-k$ ($k{\in}\mathbb{Z}_{>0}$). To list all the integral points on that hyperbola, we find the number of elements of ${\Omega}_k$.

• Structural Engineering and Mechanics
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• 제55권4호
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• pp.785-799
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

• 충청수학회지
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• 제15권1호
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

• 대한수학회보
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• 제27권2호
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• pp.165-172
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• 1990

In this paper, we study a method which speeds up the convergence of monotone iterations and give some numerical examples of the types (2) and (3). In [2] this method has been applied to a system of hyperbolic differential equations with initial and boundary conditions.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2010년도 추계학술대회 논문집
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• pp.257-258
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• 2010

• Wind and Structures
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• 제26권6호
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• pp.355-367
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• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Advances in nano research
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• 제4권4호
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• pp.251-264
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• 2016

In this paper, a simple and refined nonlocal hyperbolic higher-order beam theory is proposed for bending and vibration response of nanoscale beams. The present formulation incorporates the nonlocal scale parameter which can capture the small scale effect, and it considers both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness without employing shear correction factor. The highlight of this formulation is that, in addition to modeling the displacement field with only two unknowns, the thickness stretching effect (${\varepsilon}_z{\neq}0$) is also included in the present model. By utilizing the Hamilton's principle and the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale beam are reformulated. Verification studies demonstrate that the developed theory is not only more accurate than the refined nonlocal beam theory, but also comparable with the higher-order shear deformation theories which contain more number of unknowns. The theoretical formulation proposed herein may serve as a reference for nonlocal theories as applied to the static and dynamic responses of complex-nanobeam-system such as complex carbon nanotube system.

• 대한수학회보
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• 제39권1호
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• pp.113-121
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• 2002

We construct lots of non-self similar fractal sets called generalized Markov attractors for a given (hyperbolic) iterated function system and calculated bounds of their Hausdorff dimensions.

• 대한수학회지
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• 제50권1호
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• pp.173-187
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• 2013

This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.

• 한국지반환경공학회 논문집
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• 제13권2호
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• pp.19-26
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• 2012

본 연구에서는 연약지반 중 선행하중재하 공법을 적용한 6개 지역과 연직배수 공법을 적용한 6개 지역을 대상으로 압밀침하 특성을 비교하였다. Asaoka방법, 쌍곡선방법, Hoshino방법의 장래 예측 침하량 기법을 이용하여 압밀침하량을 예측하고, 실제 계측 침하량과 비교하였으며, 종합적으로 Asaoka방법에 의해 예측된 장래침하량이 쌍곡선방법이나 Hoshino방법에 비해 예측 정확도가 높게 평가되었다. 연직배수공법을 적용한 지역에서는 Asaoka방법이 침하량 예측 정확도가 다른 방법에 비해 높게 평가된다고 알려진 것과는 다르게 세 방법 모두 비슷한 정확도를 나타내었다. 또한 연구대상지역의 지반개량 전후의 확인조사를 통해 N치의 변화, 토층의 물리적, 역학적 특성을 조사하였으며, 개량 후 물성치는 개선되고, 침하량 크기와 관계되는 역학적 특성들은 개선되었다. 또한, 토질의 강도는 증가한 것을 확인하였으며, 침하량과 관계되는 물성치의 변화가 큰 것으로 나타났다.