• Korean Journal of Mathematics
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• v.17 no.2
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.409-425
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• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.6
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• pp.1010-1019
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• 1994

It is shown that there exists a nonlinear mapping which transforms image features and their changes to the desired camera motion without measuring of the relative distance between the camera and the object. This nonlinear mapping can eliminate several difficulties occurring in computing the inverse of the feature Jacobian as in the usual feature-based visual feedback control methods. Instead of analytically deriving the closed form of this mapping, a Fuzzy Membership Function-based Neural Network (FMFNN) incorporating a Fuzzy-Neural Interpolating Network is used to approximate the nonlinear mapping. Several FMFNN's are trained to be capable of tracking a moving object in the whole workspace along the line of sight. For an effective implementation of the proposed FMF network, an image feature selection process is investigated. Finally, several numerical examples are presented to show the validity of the proposed visual servoing method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.28B no.9
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• pp.739-746
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• 1991

This paper develops a modified multilayer perceptron architecture which speeds up learning as well as the net's mapping accuracy. In Phase I, a cluster partitioning algorithm like the Kohonen's self-organizing feature map or the leader clustering algorithm is used as the front end that determines the cluster to which the input data belongs. In Phase II, this cluster selects a subset of the hidden layer nodes that combines the input and outputs nodes into a subnet of the full scale backpropagation network. The proposed net has been applied to two mapping problems, one rather smooth and the other highly nonlinear. Namely, the inverse kinematic problem for a 3-link robot manipulator and the 5-bit parity mapping have been chosen as examples. The results demonstrate the proposed net's superior accuracy and convergence properties over the original backpropagation network or its existing improvement techniques.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.9
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• pp.1710-1718
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• 2015

Selected mapping (SLM) is an effective scheme to reduce the peak to average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system. For data recovery, the receiver needs to know the side information (SI) on the scrambling sequence selected by the transmitter. In this paper, a new SLM scheme is proposed, which can reduce implementation complexity substantially by allowing the receiver to recover the data without SI. In the proposed SLM method, the concept of virtual channel corresponding to the convolution of the multipath channel and the inverse discrete fourier transform (IDFT) of the scrambling sequence is assumed. The receiver can recover the data without SI by using the virtual channel estimated with pilot signals. It is shown by simulation that the proposed SLM has PAPR reduction and BER performances similar to the previous SLM schemes while it can reduce implementation complexity substantially.

• East Asian mathematical journal
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• v.36 no.5
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• pp.571-581
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• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2154-2159
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• 2005

This paper presents the kinematic analysis of two robots, an exoskeleton type master robot and a human like slave robot with two arms. Two robots are designed and built to be equivalent as motion following robots. The operator wears the exoskeleton robot to generate motions, then the slave robot is required to follow after the motion of the master robot. However, different kinematic configuration yields position mismatches of the end-effectors. To synchronize motions of two robots, kinematic analysis of mapping is analyzed. The forward and inverse kinematics have been simulated and the corresponding experiments are also conducted to confirm the proposed mapping analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.874-879
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• 1992

It is shown that there exists a nonlinear mappping which transforms features and their changes to the desired camera motion without measurement of the relative distance between the camera and the part, and the nonlinear mapping can eliminate several difficulties encountered when using the inverse of the feature Jacobian as in the usual feature-based visual feedback controls. And instead of analytically deriving the closed form of such a nonlinear mapping, a fuzzy membership function (FMF) based neural network is then proposed to approximate the nonlinear mapping, where the structure of proposed networks is similar to that of radial basis function neural network which is known to be very useful in function approximations. The proposed FMF network is trained to be capable of tracking moving parts in the whole work space along the line of sight. For the effective implementation of proposed IMF networks, an image feature selection processing is investigated, and required fuzzy membership functions are designed. Finally, several numerical examples are illustrated to show the validities of our proposed visual servoing method.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.1085-1088
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• 1999

This paper presents a method for soccer scene analysis and coordinate transformation from scene to ground model using a priori knowledge. First, the ground and spectator regions are separated, and various objects are extracted from the separated ground region. Second, an affine model is used for mapping the object positions on the soccer image into the position on the ground model. Problems regarding holes arising from mapping processing are solved using inverse mapping instead of a usual interpolation method. Experiments are performed on a PC using about 100 RGB images acquired at 240＊640 resolution and 3∼5 frames per second.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.491-502
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• 2000

The disjoint union of mapping class groups g,1 gives us a braided monoidal category so that it gives rise to a double loop space structure. We show that there exists a natural twist in this category, so it gives us a ribbon category. We show that there exists a natural twist in this category, so it gives us a ribbon category. We explicitly express this structure by showing how the twist acts on the fundamental group of the surface Sg,l. We also make an explicit description of this structure in terms of the standard Dehn twists, as well as in terms of Wajnryb's Dehn twists. We show that the inverse of the twist g for the genus g equals the Dehn twist along the fixed boundary of the surface Sg,l.