• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권1호
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• pp.91-110
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• 2015

본 연구는 초등수학 영재교육 대상자들이 원주율 개념에 대해서 어떻게 이해하고 있는지를 살펴보고자 하였다. 이를 위해 원주율 계산 방법의 역사 발달 단계를 토대로 세 가지 과제를 개발한 후 6학년 영재교육 대상자 12명을 대상으로 적용하여 그 반응을 분석하였다. 연구결과, 학생들은 '원주율 = 3.14'라는 사고의 고착화로 인하여 원주율의 개념, 근사성, 무한성을 제대로 이해하지 못하였으며, 원주율과 원주율의 근삿값을 혼동하는 오류를 보였다. 또한 학생들은 원주율을 '(원주) ${\div}$ (지름)'의 대수적인 식으로 이해하려는 성향이 강하였으며, 원주율의 상수성과 무한성을 깊이 있게 이해하고 있는 학생은 극히 적었다. 반면에 과제에 대한 토론 활동은 학생들이 원주율의 근사성에 대한 아이디어를 발견할 수 있는 기회를 제공하였다. 이상의 결과를 종합하여, 초등학교에서의 원주율 지도와 관련하여 원주율을 원의 지름을 단위길이로 원의 둘레를 측정하여 얻을 수 있는 값으로 도입할 것과 공학적 도구 등을 이용하여 직관적인 방법을 통해 이해하도록 할 것, 원주율 개념이 가지는 본질적인 의미를 이해할 수 있도록 다양한 상황을 통해 도입할 것을 제안하였다.

• 한국수학사학회지
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• 제24권3호
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• pp.13-21
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• 2011

칸토르에 의해서 과학적으로 불가침의 영역이었던 무한이 실무한으로 정의되고 무한의 논리가 성립될 수 있었다. 칸토르의 무한수학과 무한신학을 통하여, 이 연구에서는 수학과 물리 세계와 관련된 실무한의 의미를 고찰하고, 모든 실무한을 넘어서는 절대무한으로서의 신의 속성이 함의하는 의미를 논의한다.

• 대한수학회지
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• 제54권5호
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• 한국군사과학기술학회지
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• 제13권3호
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• pp.503-510
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• 2010

The quick variation of the canister wall temperature causes the modification of the shape of canister wall. This paper is the possibility of adoption and the error analysis about the transient heat flux method. The commercial code(Fluent Ver6.2.16) was employed for the calculation of surface temperature in the case of steady and unsteady heat flux condition. Based the surface temperature variation and surface material property, transient heat flux method can calculate the surface heat flux. In the case of steady heat flux condition, the error is about 2%, and in the case of unsteady heat flux condition, the error is about 3.6%. With the unsteady heat flux condition, the time which reach the maximum surface heat flux is almost same between the numerical analysis and transient heat flux method.

• Journal of Mechanical Science and Technology
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• 제17권8호
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• pp.1120-1132
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• 2003

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular. integral equations for edge and temperature dislocation distribution functions are constructed and solved numeric-ally, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.

• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.453-470
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• 2018

We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.

• 전기의세계
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• 제29권7호
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• pp.471-477
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• 1980

This paper deals with a modified Kalman filter. An approaching horizon with a suitable initial condition will be considered, which is a little different from the classical Kalman filter. It will be shown in this paper that the new filter with approaching horizons is not only easy to computer but also possesses asymptotic stability properties. Thus this new estimatoris an excellent compromise between the ease of computation and the strict sense of optimality. When this estimator is used for the standard problem, the error covariance bound has been obtained. It is shown that the new estimator can be used as a suboptimal estimator which has a stability property. It is also demonstrated that the steady state Kalman filter can be obtained from the moving horizon estimator by taking the horizon parameter as infinity.

• 충청수학회지
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• 제37권1호
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• 한국표면공학회지
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• 제50권2호
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• pp.98-107
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• 2017

Pd-based membranes have been widely used in hydrogen purification and separation due to their high hydrogen diffusivity and infinite selectivity. However, it has been difficult to fabricate thin and dense Pd-based membranes on a porous stainless steel(PSS) support. In case of a conventional PSS support having the large size of surface pores, it was required to use complex surface treatment and thick Pd coating more than $6{\mu}m$ on the PSS was required in order to form pore free surface. In this study, we could fabricate thin and dense Pd membrane with only $3{\mu}m$ Pd layer on a new PSS support manufactured by metal injection molding(MIM). The PSS support had low surface roughness and mean pore size of $5{\mu}m$. Pd membrane were prepared by advanced Pd sputter deposition on the modified PSS support using fine polishing and YSZ vacuum filling surface treatment. At temperature $400^{\circ}C$ and transmembrane pressure difference of 1 bar, hydrogen flux and selectivity of $H_2/N_2$ were $11.22ml\;cm^{-2}min^{-1}$ and infinity, respectively. Comparing with $6{\mu}m$ Pd membrane, $3{\mu}m$ Pd membrane showed 2.5 times higher hydrogen flux which could be due to the decreased Pd layer thickness from $6{\mu}m$ to $3{\mu}m$ and an increased porosity. It was also found that pressure exponent was changed from 0.5 on $6{\mu}m$ Pd membrane to 0.8 on $3{\mu}m$ Pd membrane.

• 한국콘텐츠학회논문지
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• 제11권1호
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• pp.56-64
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• 2011

스트림데이터는 무한하고 연속적인 특성을 지니고 있기 때문에 전체 데이터를 기반으로 빈발 항목 집합을 탐사하는 것은 어렵다. 이 때문에 데이터의 특성과 사용자의 특성을 반영한 특수한 데이터마이닝 방법이 필요하다. 이 논문에서는 사용자가 최근에 발생한 데이터에 더 많은 관심이 있다는 특성을 반영하여 빈발 항목을 탐사하는 FIMWB 방법을 제안한다. FIMWB는 과거 데이터의 발생 시점과 현재 시점과의 시간 간격에 따라 가변적인 가중치를 배치에 부여하여 최신 데이터에 더 많은 관심과 중요성을 반영한다. FP-Digraph는 FIMWB를 통해 탐사된 빈발 항목으로 그래프를 구성하여 빈발 항목 집합을 탐사한다. 실험 결과로 FIMWB 방법이 불필요한 항목의 생성을 감소시키고 트리기반(FP-Tree)의 빈발 항목 집합 탐사에 비해 제안하는 FP-Digraph 방법이 스트림 데이터 환경에 더 적합함을 알 수 있다.