• Management Science and Financial Engineering
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• v.7 no.1
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• pp.27-39
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• 2001

The multi-projective model considers attributes and the relationships among attributes called projections. The critical features of the multi-projective model are the way of relating attributes in the description of the system, the way of reasoning incomplete projections, and the determination of connected patterns between projection. In order to get a full picture of the system, we build a set of projections. The multi-projective model can be thought of as projections of a multi-dimensional reality onto simplified “model space”. The multi-projective database modeling approach used in this paper unified the ideas and terminology of various database models. Most importantly, the multi-projective modeling is presented as a tool of database design in the relational and other database models.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.493-505
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• 2000

We discuss the class of projective systems whose supports are the complement of the union of two linear subspaces in general position. We express the weight enumerators of the codes generated by these projective systems using two simplex codes corresponding to given linear subspaces. We also prove these codes are uniquely determined upto equivalence by their weight enumerators.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.1-14
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• 2002

This paper treats the history of the fundament of projective geometry Especially we introduce the essence of the framework of Karl Chirstian von Staudt's ‘Geometrie der Lage’. Von Staudt used axiomatical method to bum the system of the projective geometry, and proved the fundamental theorem of projective geometry. And he handled imaginary elements (or the first time in synthetic projective geometry.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.7
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• pp.943-951
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• 1995

In this paper the projective controls, previously derived to preserve the dynamic modes of a state-feedback reference system, are extended to allow the preservation of the modes of a general output-feedback reference system. In general, the extension allows projective controls to be used as a controller approximation technique, where a reduced-order controller is designed to approximate the closed-loop behavior of the higher-order reference controller. This extension is useful if the best available reference control for the system is an output-feedback control. An example shows that the increased design freedom of proposed design method allows the stabilization of a given plant using a lower-order controller than the projective controls with state-feedback reference.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.689-699
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• 2001

We discuss the class of projective systems whose supports are the complement of the union of three linear subspaces in general position. We proves these codes are uniquely dtermined up to equivalence by their weight enumerators. Our result is a generalization of the result given in [1].

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.391-394
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• 2005

In this paper, we present an approach that is able to reconstruct 3 dimensional metric models from un-calibrated images acquired by a freely moved camera system. If nothing is known of the calibration of either camera, nor the arrangement of one camera which respect to the other, then the projective reconstruction will have projective distortion which expressed by an arbitrary projective transformation. The distortion on the reconstruction is removed from projection to metric through self-calibration. The self-calibration requires no information about the camera matrices, or information about the scene geometry. Self-calibration is the process of determining internal camera parameters directly from multiply un-calibrated images. Self-calibration avoids the onerous task of calibrating cameras which needs to use special calibration objects. The root of the method is setting a uniquely fixed conic(absolute quadric) in 3D space. And it can make possible to figure out some way from the images. Once absolute quadric is identified, the metric geometry can be computed. We compared reconstruction image from calibrated images with the result by self-calibration method.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.229-232
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• 2005

In this paper, an image-based "approach-align -grasp" visual servo control design is proposed for the problem of object grasping, which is based on the binocular stand-alone system. The basic idea consists of considering a vision system as a specific sensor dedicated a task and included in a control servo loop, and we perform automatic grasping follows the classical approach of splitting the task into preparation and execution stages. During the execution stage, once the image-based control modeling is established, the control task can be performed automatically. The proposed visual servoing control scheme ensures the convergence of the image-features to desired trajectories by using the Jacobian matrix, which is proved by the Lyapunov stability theory. And we also stress the importance of projective invariant object/gripper alignment. The alignment between two solids in 3-D projective space can be represented with view-invariant, more precisely; it can be easily mapped into an image set-point without any knowledge about the camera parameters. The main feature of this method is that the accuracy associated with the task to be performed is not affected by discrepancies between the Euclidean setups at preparation and at task execution stages. Then according to the projective alignment, the set point can be computed. The robot gripper will move to the desired position with the image-based control law. In this paper we adopt a constant Jacobian online. Such method describe herein integrate vision system, robotics and automatic control to achieve its goal, it overcomes disadvantages of discrepancies between the different Euclidean setups and proposes control law in binocular-stand vision case. The experimental simulation shows that such image-based approach is effective in performing the precise alignment between the robot end-effector and the object.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.463-476
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• 2006

It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

• The KIPS Transactions:PartB
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• v.17B no.3
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• pp.183-188
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• 2010

A factorization-based 3D reconstruction system is realized to recover 3D scene from an image sequence. The image sequence is captured from uncalibrated perspective camera from several views. Many matched feature points over all images are obtained by feature tracking method. Then, these data are supplied to the 3D reconstruction module to obtain the projective reconstruction. Projective reconstruction is converted to Euclidean reconstruction by enforcing several metric constraints. After many triangular meshes are obtained, realistic reconstruction of 3D models are finished by texture mapping. The developed system is implemented in C++, and Qt library is used to implement the system user interface. OpenGL graphics library is used to realize the texture mapping routine and the model visualization program. Experimental results using synthetic and real image data are included to demonstrate the effectiveness of the developed system.