• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.507-512
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• 1993

In this paper we discuss the nonlinear motion of a conservative two-link arm using first integrals, which includes one integral constant. In the analysis of the motion, the constant plays important role. First, we give some discussion on the free motion by focusing on the integral constant. As the result, the free motion can be classified into two types-the one is oscillation and the other is rotation. Second, we discuss the forced motion of the arm actuated only at the second joint. We take the first integral in a more general form, and show that the forced motion of the second link can be expressed as a variation of the integral constant. Also, the characteristic of the forced motion actuated by arbitrary constant torques is discussed.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.3
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• pp.20-29
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• 2008

In this paper, we propose a do-interlacing algorithm using integral projection-based motion estimation considering Region Of Interest(ROI). The proposed motion estimation method finds the motion of the given ROI accurately with low computational cost. In order to incorporate the motion estimation in do-interlacing, an entire image is first segmented into multiple ROIs according to the temporally predicted block-wise motion types and spatial positions. Then, motion vectors of respective ROIs are obtained by the integral projection method. In this paper, totally five ROIs, one for the global motion and four for the local motions, are made, and therefore, five motion vectors are produced for each field. By using the estimated motion vectors, motion compensation is performed for increasing the vortical resolution of the converted frames. Finally, do-interlaced frames are obtained by effectively combining the results of motion compensation and stable intra-field do-interlacing according to the reliability of motion compensation. Experimental results show that the proposed algorithm provides better image quality than existing algorithms in both subjective and objective measures.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• The Mathematical Education
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• v.56 no.4
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• pp.387-405
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• 2017

The purpose of this study is to investigate the change of students 'perception and expression about the motion of object following distance function $={x \atop 3}$ and distance function $y=\frac{x^3}{3}+3$ according to the necessity of research on students' perception and expression about integral constant. In this paper, we present the recognition and the expression of the difference of the constant in the relationship between the distance function and the speed function of the students, while examining the process of constructing the speed function and the inverse process of the distance function. This provides implications for the relationship between the derivative and the indefinite integral corresponding to the inverse process. In particular, in a teaching experiment, a constructive activity was performed to analyze the motion of two distance functions, where the student had a difference of the constant term. At this time, the students used the expression 'starting point' for the constants in the distance function, and the motion was interpreted by using the meaning. This can be seen as a unique 'students' mathematics' in the process of analyzing the motion of objects. These scenes, in introducing the notion of the relation between differential and indefinite integral, it is beyond the comprehension of the integral constant as a computational procedure, so that the learner can understand the meaning of the integral constant in relation to the motion of the object. It is expected that it will be a meaningful basic research on the relationship between differential and integral.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.13-20
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• 2010

We proposed a new technique to perform fast video stabilization using integral image in this article. In the proposed technique, it evaluate local and global motion by the block matching using the generated integral image for each frame and compensate the motion like jitter. We made the various experimental jitter patterns to evaluate the effectiveness of the proposed technique and evaluated stabilization capability and execution time with the existing ones. Through the experiment, we found that the execution time of proposed technique was faster than that of existing techniques and the compensation of jitter was well done.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.475-489
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• 2011

In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x) = $\hat{v}$(($g_1,x)^{\sim}$,..., $(g_n,x)^{\sim}$) defined on a very general function space $C_{a,b}$[0,T]. We also present a change of scale formula for function space integrals of such cylinder functionals.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.