• 충청수학회지
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• 제23권4호
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• pp.679-689
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• 2010

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.

• 한국수학교육학회지시리즈A:수학교육
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• 제56권4호
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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.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.547-550
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• 2001

Through matched filtering synthetic aperture radar (SAR) produces high-resolution imagery from data collected by a relative small antenna. While the impulse response obtained by the matched filter approach produces the best achievable signal-to-noise ratio, large sidelobes must be reduced to obtain higher-resolution SAR images. So, many enhancement methods of SAR imagery have been proposed. As a deconvolution method, the phase-extension inverse filtering is based on the characteristics of the matched filtering used in SAR imaging. It improves spatial resolution as well as effectively suppresses the sidelobes with low computational complexity. In the phase-extension inverse filtering, the impulse response is obtained from simulation with a point target. But in a real SAR environment, for example ERS-1, the impulse response is distorted by many non-ideal factors. So, in the phase-extension inverse filtering for a real SAR processing, the magnitudes of the frequency transfer function have to be compensated to produce more desirable results. In this paper, an estimation method to obtain a more accurate impulse response from a real SAR image is studied. And a compensation scheme to produce better performance of the phase-extension inverse filtering is also introduced.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권2호
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• pp.643-661
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• 2018

This paper proposes a novel algorithm for lane detection based on inverse perspective transformation and Kalman filter. A simple inverse perspective transformation method is presented to remove perspective effects and generate a top-view image. This method does not need to obtain the internal and external parameters of the camera. The Gaussian kernel function is used to convolute the image to highlight the lane lines, and then an iterative threshold method is used to segment the image. A searching method is applied in the top-view image obtained from the inverse perspective transformation to determine the lane points and their positions. Combining with feature voting mechanism, the detected lane points are fitted as a straight line. Kalman filter is then applied to optimize and track the lane lines and improve the detection robustness. The experimental results show that the proposed method works well in various road conditions and meet the real-time requirements.

• 대한수학회보
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• 제40권2호
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• pp.289-300
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• 2003

We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.

• Korean Journal of Mathematics
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• 제12권1호
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• pp.55-65
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• 2004

Let $h_e(y)$, $h_o(y)$ denote the limits of the sequences {$^{2n}x$}, {$^{2n+1}x$}, respectively. From these two functions, we obtain a function $y=p(x)$ as an inverse function of them. Several differential properties of $y=p(x)$ are induced.

• Structural Engineering and Mechanics
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• 제45권4호
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• pp.471-494
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• 2013

In this paper, identification of isotropic and orthotropic linear elastic material constitutive parameters has been demonstrated by a FEA-free energy-based inverse analysis method. An important feature of the proposed method is that it requires no finite element (FE) simulation of the tested material. Full-field displacements calculated using digital image correlation (DIC) are used to compute DIC stress fields enforcing the equilibrium condition and DIC strain fields using interpolation functions. Boundary tractions and displacements are implicitly recast into an objective function that measures the energy residual of external work and internal elastic strain energy. The energy conservation principle states that the residual should be zero, and so minimizing this objective function inversely identifies the constitutive parameters. Synthetic data from simulated testing of isotropic materials and orthotropic composite materials under 2D plane stress conditions are used for verification of the proposed method. When identifying the constitutive parameters, it is beneficial to apply loadings in multiple directions, and in ways that create non-uniform stress distributions. The sensitivity of the parameter identification method to noise in both the measured full-field DIC displacements and loadings has been investigated.

• KIEE International Transactions on Power Engineering
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• 제5A권4호
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• pp.403-411
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• 2005

At present, the Cournot model is one of the most commonly used theories to analyze the gaming situation in an oligopoly type market. However, several problems exist in the successful application of this model to the electricity market. The representative one is obtaining the inverse demand curve able to be induced from the relationship between market price and demand response. In the Cournot model, each player offers their generation quantity to obtain maximum profit, which is accomplished by reducing their quantity compared with available total capacity. As stated above, to obtain the probable Cournot equilibrium to reflect the real market situation, we have to induce the correct demand function first of all. Usually the correlation between price and demand appears over the long-term through statistical data analysis (for example, regression analysis) or by investigating consumer utility functions of several consumer groups classified as residential, industrial, and commercial. However, the elasticity has a tendency to change continuously according to the total market demand size or the level of market price. Therefore it should be updated as the trading period passes by. In this paper we propose a method for inducing and updating this price elasticity of demand function for more realistic market equilibrium.

• 대한기계학회논문집A
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• 제21권2호
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• pp.281-287
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• 1997

In the conventional inverse modeling method for on-line modeling of the secondary path transfer function, the signal to noise ratio between the arbitrary random signal and the plant noise have to keep at -10 - -20 dB. For these reasons, the modeling can't be exactly implemented by the conventional method alone and the convergence time for modeling becomes too long. In this study, by combining the conventional inverse modeling method with an adaptive line enhancer, or with an adaptive noise canceller, a rigorous transfer functions of secondary path modeling and the control of a primary noise have been implemented simultaneously.