• Advances in materials Research
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• 제4권1호
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• pp.31-44
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• 2015

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• 한국수학사학회지
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• 제25권3호
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• pp.1-14
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• 2012

구장산술이래 동양의 전통 수학은 유리수체를 기본으로 이루어져 있다. 따라서 방정식의 무리수해는 허용되지 않으므로 근사해를 구하는 방법은 방정식론에서 매우 중요한 과제가 되었다. 중국의 사료에 나타나는 근사해에 관한 역사를 먼저 기술하고, 이를 조선산학에 나타나는 근사해에 관한 사료와 비교한다. 조선의 근사해에 대한 이론은 박율(1621 - 1668) 의 산학원본 (算學原本) 과 조태구 (趙泰耉, 1660-1723) 의 주서관견(籌書管見)에 이미 정립되었다. 중국의 이론과 달리 두 산학자 모두 근사해의 오차에 관심을 가지고 더 좋은 근사해를 구하는 방법을 얻어내었음을 밝힌다.

• 대한원격탐사학회지
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• 제14권2호
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• pp.137-148
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• 1998

본 논문에서 고해상도 위성영상의 정밀 기하학적 보정에 대하여 기술한다. 일반적으로 GCP로부터 영상과 기준 지도 사이의 다하식을 유도하는 polynomial warping 방법인 경우 원하는 정확도를 얻기위해 영상 전체를 골고루 분포된 많은 GCP를 요구하게 된다. 하지만 제안되는 알고리즘은 위성-센서-궤도-지구 간의 기하학적 모델을 바탕으로 2-3개의 GCP만으로도 전체 영상을 매우 정확히 보정할 수 있다. 개발된 알고리즘은 GCP를 순차적으로 사용하여 부정확한 초기 궤도 및 자세 정보를 정밀하게 추정하고 이러한 추정은 Kalman filter를 사용하여 이루어진다. 이 알고리즘은 현재 우리별 3호의 전처리 소프트웨어에 통합되어 구현되어 있으며 앞으로 우리별 3호 영상뿐 아니라 다목적실용위성 영상의 정밀 기하학적 보정에 사용될 예정이다.

• 대한수학회보
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• 제51권1호
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• pp.77-82
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• 2014

We prove that if ${\mid}a_1{\mid}$ is large and ${\mid}a_0{\mid}$ is small enough, then every approximate zero of power series equation ${\sum}^{\infty}_{n=0}a_nx^n$=0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, $a_nz^n$ + $a_{n-1}z^{n-1}$ + ${\cdots}$ + $a_1z$ + $a_0$ = 0 for a given integer n > 1.

• International Journal of Control, Automation, and Systems
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• 제6권3호
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• pp.378-385
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• 2008

This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems without delays. To get the spectral factorization, we apply the reorganized innovation approach. The calculation of spectral factorization comes down to two Riccati equations with the same dimension as the original systems.

• Steel and Composite Structures
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• 제7권6호
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• pp.441-456
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• 2007

In literature for thin-walled sections with L, [, +, I, and ${\Box}$- shapes the approximate torsion equations for stiffness are used which were proposed by Bach (Hsu 1984), p.30. New formulae for torsional stiffness of bars with L, [, +, I, and ${\Box}$ cross section valid not only for thin-walled sections are presented in this paper. These formulae are obtained by appropriate polynomial approximation of stiffness results obtained by means of method of fundamental solutions. On the base of obtained results the validity of Bach's formulae are verified when cross section is not thin-walled.

• Structural Engineering and Mechanics
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• 제76권1호
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• pp.129-139
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• 2020

In this piece of work, carbon nanotubes motion equations are framed by Kelvin's method. Employment of the Kelvin's method procedure gives birth to the tube frequency equation. It is also exhibited that the effect of frequencies is investigated by varying the different index of polynomial function. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported and these frequency curves are higher than that of clamped-free curves. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes.

• 한국전산유체공학회지
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• 제20권4호
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• pp.44-50
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• 2015

The computational efficiency of flow simulations with Multi-resolution analysis (MRA) was enhanced via the boundary treatment of the computational domain. In MRA, an adaptive dataset to a solution is constructed through data decomposition with interpolating polynomial and thresholding. During the decomposition process, the basis points of interpolation should exceed the boundary of the computational domain. In order to resolve this problem, the weight coefficients of interpolating polynomial were adjusted near the boundaries. By this boundary treatment, the computational efficiency of MRA was enhanced while the numerical accuracy of a solution was unchanged. This modified MRA was applied to two-dimensional steady Euler equations and the enhancement of computational efficiency and the maintenance of numerical accuracy were assessed.

• 대한전기학회논문지
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• 제41권3호
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• pp.300-310
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• 1992

This paper deals with the problem of robust pole-assignment control for linear systems with structured uncertainty. It considers two cases whose colsed-loop characteristic equations are presented as a family of interval polynomial and polytopic polynomial family respectively. We propose a method of finding the pole-placement region in which the fixed gain controller guarantees the required damping ratio and stability margin despite parameter perturbation. Some results of Kharitonov like stability and two kinds of transformations are included. As an illustrative example, we show that the proposed method can apply effectivly to the single magnet levitation system including some uncertainties (mass, inductance etc.).

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권11호
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• pp.5324-5337
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• 2017

In this paper, we investigate the feasibility of interference alignment(IA) in signal space in the scenario of multiple cell and multiple user cellular networks, as the feasibility issue is closely related to the solvability of a multivariate polynomial system, we give the mathematical analysis to support the constraint condition obtained from the polynomial equations with the tools of algebraic geometry, and a new distribute IA algorithm is also provided to verify the accessibility of the constraint condition for symmetric system in this paper. Simulation results illustrate that the accessibility of the constraint condition is hold if and only if the degree of freedom(DoF) of each user can be divided by both the transmit and receive antenna numbers.