• 대한수학회보
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• 제61권2호
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• pp.433-450
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• 2024

Using a Reilly type integral formula due to Li and Xia [23], we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the 1-Bakry-Emery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.

• 대한수학회지
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• 제32권3호
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• pp.519-529
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• 1995

Let M be a compact smooth manifold of dimension n and let E be a flat (complet) vector bundle over M of rank r.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.133-137
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• 2023

Consider a Riemannian manifold M equipped with a metric g. In this article, we study a notion for statistical manifolds (M, g, ∇), which can have a nonzero torsion, abbreviated to SMT. Then it turns out that the tensor fields ∇g and ${\tilde{\nabla}}g$ obtained from two different SMT-connections are different.

• 대한수학회논문집
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• 제36권1호
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• pp.11-18
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• 2021

In this article, we deal with Zariski topology on graded comultiplication modules. The purpose of this article is obtaining some connections between algebraic properties of graded comultiplication modules and topological properties of dual Zariski topology on graded comultiplication modules.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.473-478
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• 2003

The purpose of this study is to model the seismic behavior of Welded Unreinforced Flange and Bolted (WUF-B) connections with post-Northridge details and evaluate the system performance of the builidings with WUF-B connections. For this purpose, based on test results, mathematical model of the connections were developed and compared with test results. This connection model take into account both panel zone deformation and connection fractures. Then, SAC Phase II 3 and 9-story buildings were modeled using the connection model developed in this study. From nonlinear static pushover analysis of the buildings, maximum strength, maximum roof drift, and so forth are investigated for the buildings with post-Northridge details. Analysis results were compared with those of buildings with pre-Northridge details and ductile connections with no fractures.

• Structural Engineering and Mechanics
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• 제9권3호
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• pp.241-256
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• 2000

The major sources of energy dissipation in steel frames with partially restrained (PR) connections are evaluated. Available experimental results are used to verify the mathematical model used in this study. The verified model is then used to quantify the energy dissipation in PR connections due to hysteretic behavior, due to viscous damping and at plastic hinges if they are formed. Observations are made for two load conditions: a sinusoidal load applied at the top of the frame, and a sinusoidal ground acceleration applied at the base of the frame representing a seismic loading condition. This analytical study confirms the general behavior, observed during experimental investigations, that PR connections reduce the overall stiffness of frames, but add a major source of energy dissipation. As the connections become stiffer, the contribution of PR connections in dissipating energy becomes less significant. A connection with a T ratio (representing its stiffness) of at least 0.9 should not be considered as fully restrained as is commonly assumed, since the energy dissipation characteristics are different. The flexibility of PR connections alters the fundamental frequency of the frame. Depending on the situation, it may bring the frame closer to or further from the resonance condition. If the frame approaches the resonance condition, the effect of damping is expected to be very important. However, if the frame moves away from the resonance condition, the energy dissipation at the PR connections is expected to be significant with an increase in the deformation of the frame, particularly for low damping values. For low damping values, the dissipation of energy at plastic hinges is comparable to that due to viscous damping, and increases as the frame approaches failure. For the range of parameters considered in this study, the energy dissipations at the PR connections and at the plastic hinges are of the same order of magnitude. The study quantitatively confirms the general observations made in experimental investigations for steel frames with PR connections; however, proper consideration of the stiffness of PR connections and other dynamic properties is essential in predicting the dynamic behavior.

• Kyungpook Mathematical Journal
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• 제20권1호
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• pp.53-58
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• 1980

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.197-206
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• 1988

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.207-212
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• 1988

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제31권3호
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• pp.257-277
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• 2017

본 연구의 주된 목적은 크게 두 가지로 나눌 수 있다. 첫째, 최근 수학적 모델링이 강조되는 상황에서 보로노이 다이어그램과 들로네 삼각분할을 주제로 영재교육을 위한 수학적 모델링 프로그램을 개발하는 것이다. 둘째, 본 연구에서 개발한 수학적 모델링 프로그램을 실제 영재교육 수업에 적용한 결과를 분석하여 수학적 모델링 수업을 설계하는 현직교사와 융합형 영재프로그램을 개발하는 영재교사에게 도움을 주고자 한다.