• 대한수학회지
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• 제49권2호
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• pp.379-394
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• 2012

Given an almost complex structure ($\mathbb^{C}^m$, J), $m\geq2$, that is defined by setting $\theta^{\alpha}=dz^{\alpha}+a_{\beta}^{\alpha}d\bar{z}^{\beta}$, ${\alpha}=1,\ldots$,m, to be (1, 0)-forms, we find conditions on ($a_{\beta}^{\alpha}$) for the existence of holomorphic functions an classify the almost complex structures by type ($\nu$,q). Then we determine types for several examples in $\mathbb{C}^2$ and $\mathbb{C}^3$ including the natural almost complex structure on $S^6$.

• 대한수학회보
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• 제40권1호
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• pp.149-157
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• 2003

Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,＋,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable $C^{r}$ manifold is affine. Let f : X ${\longrightarrow}$ Y be a definable $C^1$ map between definable $C^1$ manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < ${\gamma}$ < $\infty$, then every definable $C^{s}$ manifold admits a unique definable $C^{r}$ manifold structure up to definable $C^{r}$ diffeomorphism.

• Journal of the Optical Society of Korea
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• 제12권2호
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• pp.65-68
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• 2008

The miniband structure of a quantum dot lattice based on GaN/AlN nanowire arrays has been investigated using the finite element method and Floquet theorem. The quantum dot modes and the quantum wire modes in the nanowire arrays were graphically verified. The optimum geometries of GaN/AlN quantum wire arrays were investigated by using a correlation between the width of nanowires and the separation of the minibandgap which is to be larger than the thermal energy at room temperature.

• 자원ㆍ환경경제연구
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• 제11권2호
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• pp.195-210
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• 2002

In this paper, we present a nonrenewable resource model including environmental pollution stock as a state variable to analyze the dynamic structure of environmental tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost for environmental pollution stock is the same as that of the costate variable for environmental pollution stock. We did this by applying the theorem, Continuous Dependence on Initial Conditions (Coddington and Levinston, 1985, pp. 22~27), to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of environmental tax to be imposed over time. In addition, we also identified that the costate variable for environmental pollution stock is solely due to the disutility effect.

• 대한수학회논문집
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• 제34권3호
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• pp.991-1004
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• 2019

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.743-765
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• 2019

Conceptual and procedural knowledge of integration is necessary not only in calculus but also in real analysis, complex analysis, and differential geometry. However, students show not only focused understanding of procedural knowledge but also limited understanding on conceptual knowledge of integration. So they are good at computation but don't recognize link between several concepts. In particular, Riemann sum is helpful in solving applied problem, but students are poor at understanding structure of Riemann sum. In this study, we try to investigate understanding on conceptual and procedural knowledge of integration and to analyze errors. Conducting experimental class of Riemann sum, we investigate the understanding of Riemann sum structure and so present the implications about improvement of integration teaching.

• 한국수학사학회지
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• 제28권6호
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• pp.301-310
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• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.793-807
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• 2015

Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method.

• 전자공학회논문지SC
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• 제46권3호
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• pp.8-14
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• 2009

본 논문은 성능 향상을 위하여 IMC 제어 구조를 갖는 PID 제어기 설계를 제안했다. 내부 모델은 최종값 정리와 유전자 알고리즘을 이용하여 2차의 지연시간을 갖는 모델로 동정 하였다. 그리고 제어기 파라미터 값은 성능지수 (IAE, ITAE)값이 최소가 되도록 내부 모델과 수치적 계산에 의해서 자동 동조된다. 시뮬레이션을 통하여 다양한 공정에 대하여 본 논문에서 새롭게 제안된 방법이 기존의 방법보다 우수함을 확인 할 수 있었다.

• Advances in aircraft and spacecraft science
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• 제6권6호
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• pp.479-495
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• 2019

Periodic cellular core structures included in sandwich panels possess good stiffness while saving weight and only lately their potential to act as passive vibration filters is increasingly being studied. Classical homogeneous honeycombs show poor vibracoustic performance and only by varying certain geometrical features, a shift and/or variation in bandgap frequency range occurs. This work aims to investigate the vibration filtering properties of the AUXHEX "hybrid" core, which is a cellular structure containing cells of different shapes. Numerical simulations are carried out using two different approaches. The first technique used is the harmonic analysis with commercially available software, and the second one, which has been proved to be computationally more efficient, consists in the Wave Finite Element Method (WFEM), which still makes use of finite elements (FEM) packages, but instead of working with large models, it exploits the periodicity of the structure by analysing only the unit cell, thanks to the Floquet-Bloch theorem. Both techniques allow to produce graphs such as frequency response plots (FRF's) and dispersion curves, which are powerful tools used to identify the spectral bandgap signature of the considered structure. The hybrid cellular core pattern AUXHEX is analysed and results are discussed, focusing the investigation on the possible spectral bandgap signature heritage that a hybrid core experiences from their "parents" homogeneous cell cores.