• 대한수학회보
• /
• 제41권1호
• /
• pp.137-145
• /
• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• 한국정보과학회논문지:시스템및이론
• /
• 제27권3호
• /
• pp.245-254
• /
• 2000

본 논문은 LOD 메쉬 생성을 위한 이산 곡률을 이용한 새로운 오차 척도를 제안한다. 메쉬의 간략화를 위한 이산 곡률은, 부드러운 곡면 추정의 과정 없이 꼭지점 중심의 표면각과 표면적, 이면각 등 의 기하학적 속성만을 이용하여 계산되는 곡률로서, 표면의 특징을 잘 표현하고 있다. 그러므로 이산 곡률에 기반한 새로운 이산 곡률 오차 척도는 원래 모델의 기하학적 형상을 최대로 유지하여 간략화 모델의 정확성을 증가 시키고, 전역 오차 척도로 사용될 수 있다. 또한, 본 논문에서는 LOD 모델을 간략화 비율이 아닌, 오차 척도를 기준으로 생성할 것을 제안한다. 왜냐 하면 LOD는 원래 모델과 각 단계의 간략화된 모델 사이의 근접도에 따라 나누어진 단계를 뜻하기 때문이다. 따라서 이산 곡률 오차 척도는 기존의 오차 척도에 비해 비교적 많은 수학적 연산이 필요하나, 각 단계의 LOD 모델이 원래 모델의 형상을 잘 유지하면서 간략화 비율이 아닌 상세도의 차이를 가지도록 효과적으로 LOD를 생성, 제어할 수 있다.

• 대한수학회보
• /
• 제42권1호
• /
• pp.75-85
• /
• 2005

In this paper, the visco-Da-Rios equation; (0.1) ($$\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}$$) is investigated on 3-dimensional complete orientable Riemannian manifolds. The global existence of solution is discussed by trans-forming (0.1) into a cubic nonlinear Schrodinger equation for complete orient able Riemannian 3-manifolds of constant curvature.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1551-1567
• /
• 2019

In this paper, Seiberg-Witten-like equations are written down on 3-manifolds. Then, it has been proved that the $L^2$-solutions of these equations are trivial on ${\mathbb{R}}^3$. Finally, a global solution is obtained on the strictly pseudoconvex CR-3 manifolds for a given constant negative scalar curvature.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
• /
• pp.768-771
• /
• 1997

Geometric probing addresses the problem of determining geometric aspects of a structure from the mathematics and results of a physical measuring device such as a probe. This paper presents a new algorithm to recognize the shape of an unknown object by using a robot hand with a force and torque sensor. The new algorithm is called S.E.P.(Shape Exploration Procedure) which finds the global shape of an unknown object. The proposed method is composed of three major parts, finding contact informations such as contact point, calculation of shape information such as curvature, and expression of global shape from these informations. Comparing with the conventional approaches, the advantages of the proposed method are explained and verified by conducting experiments with a 3-dof SCARA robot.

• Structural Engineering and Mechanics
• /
• 제66권4호
• /
• pp.543-555
• /
• 2018

Fiber Reinforced Polymer (FRP), which has a high strength to weight ratio, are now regularly used for strengthening of deficient reinforced concrete (RC) structures. While various researches have been conducted on FRP strengthening, an area that still requires attention is predicting the debonding failure load of prestressed FRP strengthened RC beams. Application of prestressing increases the capacity and reduces the premature failure of the beams largely, though not entirely. Few analytical methods are available to predict the failure loads under flexure failure. With this paucity, this research proposes a method for predicting debonding failure induced by intermediate crack (IC) for prestressed FRP-strengthened beams. The method consists of a numerical study on beams retrofitted with prestressed FRP in the tension side of the beam. The method applies modified Branson moment-curvature analysis together with the global energy balance approach in combination with fracture mechanics criteria to predict failure load for complicated IC-induced failure. The numerically simulated results were compared with published experimental data and the average of theoretical to experimental debonding failure load is found to be 0.93 with a standard deviation of 0.09.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.123-136
• /
• 2004

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.

• 한국지구과학회지
• /
• 제40권4호
• /
• pp.353-381
• /
• 2019

The general world model for homogeneous and isotropic universe has been proposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a (4+1)-dimensional space-time, and assume that the universe is spatially a 3-dimensional hypersurface embedded in the 4-dimensional space. The simultaneity for the entire universe has been specified by the global time coordinate. We define the line element as the separation between two neighboring events on the expanding universe that are distinct in space and time, as viewed in the world reference frame. The information that determines the kinematics of the geometry of the universe such as size and expansion rate has been included in the new metric. The Einstein's field equations with the new metric imply that closed, flat, and open universes are filled with positive, zero, and negative energy, respectively. The curvature of the universe is determined by the sign of mean energy density. We have demonstrated that the flat universe is empty and stationary, equivalent to the Minkowski space-time, and that the universe with positive energy density is always spatially closed and finite. In the closed universe, the proper time of a comoving observer does not elapse uniformly as judged in the world reference frame, in which both cosmic expansion and time-varying light speeds cannot exceed the limiting speed of the special relativity. We have also reconstructed cosmic evolution histories of the closed world models that are consistent with recent astronomical observations, and derived useful formulas such as energy-momentum relation of particles, redshift, total energy in the universe, cosmic distance and time scales, and so forth. The notable feature of the spatially closed universe is that the universe started from a non-singular point in the sense that physical quantities have finite values at the initial time as judged in the world reference frame. It has also been shown that the inflation with positive acceleration at the earliest epoch is improbable.

• 한국컴퓨터그래픽스학회논문지
• /
• 제14권4호
• /
• pp.19-25
• /
• 2008

본 논문에서는 지역 광원을 통해 음영 대비를 증가시켜 객체의 형태를 명확하게 나타낼 수 있는 셀 웨이딩 기법에 대하여 설명한다. 객체의 형태를 명확하게 나타내기 위하여, 본 논문은 가상의 지역 광원을 사용하여 입체감을 살리고 이를 통해 객체의 지역적 형태가 잘 나타나게 하였다. 또한 영역의 특성에 맞추어 형태를 자세히 묘사하기 위해 곡률과 세일리언시를 사용하여 영역의 복잡도와 중요도에 따라 음영 대비를 조절하였다. 이러한 기법은 광원의 위치와는 상관없이 객체의 전반적인 형태를 잘 표현할 수 있다.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
• /
• 제16권3호
• /
• pp.366-370
• /
• 2010

본 논문에서는 한 장의 2-D 이미지를 입력으로 받아 자동적으로 동양화처럼 보이는 그림으로 바꾸어 주는 비 사실적 랜더링(NPR) 시스템을 제안한다. 동양화의 선은 두께가 다양하고 끝이 갈라지는 특성이 있고, 농담의 변화를 주어 대상 물체의 입체감을 표현하는 경향이 있다. 본 논문에서는 이미지의 외곽선 추출을 바탕으로 curvature를 사용하여 선을 따라 변하는 두께를 가진 선을 생성한다. 또한 기존에 수채화 스타일에서 제안된 농담 표현방법과는 반대로 지역적인 세부표현을 증가시키고 광역적인 농담을 줄여준다. 본 논문은 외곽선 추출, 선 그리기를 통하여 다양한 두께의 선을 표현해 주는 방법과, 이미지의 필터링과 intensity 변환을 통한 농담을 표현하는 일련의 연속적인 방법을 제안하다.