• Honam Mathematical Journal
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• v.45 no.2
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• pp.269-284
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• 2023

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct-projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure-direct-projective. We give applications of some of the results to comodule categories.

• 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.

• 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.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.9-17
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• 2002

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.189-212
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• 2006

Let $F^{\alpha}G$ be a twisted group algebra with basis ${{\mu}g|g\;{\in}\;G}$ and $P\;=\;{C_g|g\;{\in}\;G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{\alpha}G$ generated by all class sums $\sum\limits{_{x{\in}C_g}}\;{\mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{\alpha}G$ and in $F^{\alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\alpha-spherical$ functions as characters of projective class algebras.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.329-337
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• 2016

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.9
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• pp.3177-3195
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• 2014

In many moving object detection problems of an aerial video, accurate and robust stabilization is of critical importance. In this paper, a novel accurate image alignment algorithm for aerial electronic image stabilization (EIS) is described. The feature points are first selected using optimal derivative filters based Harris detector, which can improve differentiation accuracy and obtain the precise coordinates of feature points. Then we choose the Delaunay Triangulation edges to find the matching pairs between feature points in overlapping images. The most "useful" matching points that belong to the background are used to find the global transformation parameters using the projective invariant. Finally, intentional motion of the camera is accumulated for correction by Sage-Husa adaptive filtering. Experiment results illustrate that the proposed algorithm is applied to the aerial captured video sequences with various dynamic scenes for performance demonstrations.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.921-934
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• 2019

The object of the present paper is to study generalized pseudo-projectively symmetric manifolds and Einstein generalized pseudo-projectively symmetric manifolds. Finally, the existence of generalized pseudo-projectively symmetric manifolds have been proved by two non-trivial examples.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• Journal of Korean Society for Geospatial Information Science
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• v.10 no.2 s.20
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• pp.49-56
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• 2002

Many users of 3D virtual city are Utilize a texture image for the cognition of real object. In this study, building's facet images were achieved by a digital camera and adjusted its distortion by use of the 2D projective transformation method. After then, Images are mapped to a 3D building model by means of the OpenGL. Application program is able to offer an automation solution to construction process of the 3D virtual city.