• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.2
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• pp.628-646
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• 2016

This paper proposes a novel channel assignment scheme that is based on finite projective plane (FPP) theory. The proposed scheme involves using a Markov chain model to allocate N channels to N users through intermixed channel group arrangements, particularly when channel resources are idle because of inefficient use. The intermixed FPP-based channel group arrangements successfully related Markov chain modeling to punch through ratio formulations proposed in this study, ensuring fair resource use among users. The simulation results for the proposed FPP scheme clearly revealed that the defined throughput increased, particularly under light traffic load conditions. Nevertheless, if the proposed scheme is combined with successive interference cancellation techniques, considerably higher throughput is predicted, even under heavy traffic load conditions.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.591-600
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• 2020

A module M is called ss-semilocal if every submodule U of M has a weak supplement V in M such that U∩V is semisimple. In this paper, we provide the basic properties of ss-semilocal modules. In particular, it is proved that, for a ring R, _RR is ss-semilocal if and only if every left R-module is ss-semilocal if and only if R is semilocal and Rad(R) ⊆ Soc(RR). We define projective ss-covers and prove the rings with the property that every (simple) module has a projective ss-cover are ss-semilocal.

• East Asian mathematical journal
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• v.14 no.2
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• pp.259-268
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• 1998

In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.143-154
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• 2008

Lomp [9] has studied finitely generated projective modules over semilocal rings. He obtained the following: finitely generated projective modules over semilocal rings are semilocal. We shall give necessary and sufficient conditions for finitely generated modules to be semilocal modules. By using a lifting property, we also give characterizations of right perfect (semiperfect) rings. Our main results can be summarized as follows: (1) Let M be a finitely generated module. Then M has finite hollow dimension if and only if M is weakly supplemented if and only if M is semilocal. (2) A ring R is right perfect if and only if every flat right R-module is lifting and every right R-module has a flat cover if and only if every quasi-projective right R-module is lifting. (3) A ring R is semiperfect if and only if every finitely generated flat right R-module is lifting if and only if RR satisfies the lifting property for simple factor modules.

• 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.

• Journal of the Korea Society of Computer and Information
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• v.7 no.1
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• pp.20-26
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• 2002

Projective Maps let designers find out uncovered attributes which are unexposed by users' incomplete view at abstraction step, and design proper database for users' model This database keeps the original meaning and has a good structure to represent the real world precisely. Also, the database which is designed by using Projective Maps, resents a method which describes the real world by less projections to users.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.673-682
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• 2020

For the recently defined notion of strongly lifting modules, it has been shown that a direct sum is not, in general, strongly lifting. In this paper we investigate the question: When are the direct sums of strongly lifting modules, also strongly lifting? We introduce the notion of a relatively strongly projective module and use it to show if M = M1 ⊕ M2 is amply supplemented, then M is strongly lifting if and only if M1 and M2 are relatively strongly projective and strongly lifting. Also, we consider when an arbitrary direct sum of hollow (resp. local) modules is strongly lifting.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.259-267
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• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.27-43
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• 2022

The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane ℝℙ² are completely classified up to topological equivalence. A planar graph (i.e., embedded in the plane), admitting the one-sided fattening, is known to be a cactus boundary. For the graphs embedded in ℝℙ² admitting the one-sided fattening, unlike the planar graphs, a new building block appears: a bracelet along the Möbius band, which is not a connected summand of the oriented surfaces.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.