• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.113-129
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• 2010

Inclusion and exclusion is used in many papers to count certain objects exactly or asymptotically. Also it is used to derive the Bonferroni inequalities in probabilistic area [6]. Inclusion and exclusion on finitely many types of properties is first used in R. Meyer [7] in probability form and first used in the paper of McKay, Palmer, Read and Robinson [8] as a form of counting version of inclusion and exclusion on two types of properties. In this paper, we provide a proof for inclusion and exclusion on finitely many types of properties in counting version. As an example, the asymptotic number of general cubic graphs via inclusion and exclusion formula is given for this generalization.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-257
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• 1995

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.11-30
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• 2004

Access Control is one of essential branches to provide system's security. Depending on what standards we apply, in general, there are Role-based access control, History-based access control. The first is based on subject's role, The later is based on subject's history. In fact, RBAC has been implemented, we are using it by purchasing some orders through the internet. But, HBAC is so complex that there will occur some errors on the system. This is more and more when HBAC is used with other access controls. So HBAC's formalization and model which are general enough to encompass a range of policies in using more than one access control model within a given system are important. To simplify these, we design the mathematical model called non-access structure. This Non-access structure contains to historical access list. If it is given subjects and objects, we look into subject grouping and object relation, and then we design Non-access structure. Then we can determine the permission based on history without conflict.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.627-639
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• 2011

Hopf corings are dened in this work as coring objects in the category of algebras over a commutative ring R. Using the Dieudonn$\'{e}$ equivalences from [7] and [19], one can associate coring structures built from the Hopf algebra $F_p[x_0,x_1,{\ldots}]$, p a prime, with Hopf ring structures with same underlying connected Hopf algebra. We have that $F_p[x_0,x_1,{\ldots}]$ coring structures classify thus Hopf ring structures for a given Hopf algebra. These methods are applied to dene new ring products in the Hopf algebras underlying known Hopf rings that come from connective Morava ${\kappa}$-theory.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.809-823
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• 2020

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.41-55
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• 2001

The purpose of this study was to compare and analyze the curricula of kindergarten and elementary school and to present a plan for connecting the two curricula. The curricula emphasized mathematical thinking and problem solving instead of fragmentary knowledge and adopted the streamed curriculum based on children’s ability and interest. And both of them consisted of number and operation, geometry, measurement, statistics, and put emphasis on activity such as real life experience, play, manipulation of concrete objects, and communication. However, there are some kinds of differences between them, because the kindergarten curriculum is not included in the common curriculum, from 1st grade to 10th grade. Thus, this study recommended several ideas based. Thus, this study recommended several ideas based on theories to connect the mathematics curricula of kindergarten and elementary school.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2531-2533
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• 2002

In this paper, we evaluate feasibility of an object-oriented method in a distributed real-time control environment through the prediction of delay expected. We adopt CAN as the distributed network and the application layer of the CAN is composed of client/server communication model of COM and surroundings for the support of real-time capability of the COM. Mathematical models formalizing delays which are predicted to invoke in the COM architecture are proposed. Sensors and actuators which are widely used in distributed network-based systems are represented by COM objects in this paper. It is expected that the mathematical models can be used to protect distributed network-based systems from violation of real-time features by the COM.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.833-847
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• 2016

We are interested in the problem of finding the Hausdorff distance between two objects in ${\mathbb{R}}^2$, or in ${\mathbb{R}}^3$. In this paper, we develop an algorithm for computing the Hausdorff distance between two ellipses in ${\mathbb{R}}^3$. Our algorithm is mainly based on computing the distance between a point $u{\in}{\mathbb{R}}^3$ and a standard ellipse $E_s$, equipped with a pruning technique. This algorithm requires O(log M) operations, compared with O(M) operations for a direct method, to achieve a comparable accuracy. We give an example,and observe that the computational cost needed by our algorithm is only O(log M).

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.107-130
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• 2004

A $JB^{*}-triple$ is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ can be defined in a canonical way. If A is also the dual of some Banach space $A_{*}$, then A is said to be a JBW triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, }holds. On $JBW^{*}-triples$, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual $A_{*}$ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.