• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.319-324
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• 2006

Let K be a finite cyclic extension of $k=\mathbb{F}_q(T)$ of prime degree ${\ell}$. Let ${\tilde{\mathcal{C}}}l_{K,{\ell}}$ be the Sylow ${\ell}$-subgroup of the ideal class group ${\tilde{\mathcal{C}}}l_K$ of $\mathcal{O}_K$. The structure of ${\tilde{\mathcal{C}}}l_{K,{\ell}}$ as $\mathbb{Z}_{\ell}[G]$/<$N_G$>-module is determined the dimensions $${\lambda}_i\;:=dim_{\mathbb{F}_{\ell}}({\tilde{\mathcal{C}}}l_{K,{\ell}}^{({\sigma}-1)^{i-1}}/{\tilde{\mathcal{C}}}l_{K,{\ell}}^{({\sigma}-1)^i})$$ for $i{\geq}1$. In this paper we investigate the dimensions ${\lambda}_1$ and ${\lambda}_2$.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.437-442
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• 2005

In studying injective covers, the modules C such that Hom(E, C) = 0 and $Ext^1$(E, C) = 0 for all injective module E play an important role because of Wakamatsu's lemma. If C is a module over the ring k[[x, y]] with k a field, the class of these modules C contains the class $\={D}$ of all direct summands of products of modules of finite length ([3, Theorem 2.9]). In this paper we show that every module over any commutative ring has a $\={D}$-preenvelope.

• Education of Primary School Mathematics
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• v.4 no.2
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• pp.139-150
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• 2000

The objectives of the current study are first, to compare and analyze the two different teaching methods of elementary mathematics in the traditional method and in the constructivists view, and, second, thereby to reveal possible problems of the present teaching practice and to suggest some guidelines to solve those problems.The results of this research are as follows: First, longer time was spent to reach the target pont of class because the class was a little bit disturbed and noisy due to a large amount of student activities in the beginning of the class in the constructive view. Second, in the class in the constructive view, the teacher should be able to respond appropriately to the situation where the students were cognitively. And the teachers sufficient preparation for the class was found essential to have the students reach the target point by themselves through identifying children`s minds. Third, the class in the constructivists view provide the teaching environment were the teacher could evaluate each students ability accurately and study progress of the class. And fourth, finally, it was not easy for the teacher to pay attention individually to each student in the current situation of large class, The effort to have more concern for students seems to contribute to opening student`s closed minds and to forming positive attitudes toward mathematics.

• The korean journal of orthodontics
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• v.27 no.2
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• pp.197-208
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• 1997

Class III malocclusion patients can be approached with many different types of treatment methods, and thus, each patient's problems must be accurately evaluated to allow selection of the best possible treatment method. Cephalometric analysis is an essential part of diagnosis and treatment planning of orthodontic patients, and it would certainly be helpful if reliable cephalometric guidelines could be set. The author divided 482 Class III malocclusion patients(253 males and 229 females) into fourgroups according to different types of treatment methods they have received to correct imbalance between upper and lower jaws: 1) orthopedic appliance (face mask & RPE), 2) camouflage treatment with fixed appliance, 3) surgical-orthodontic treatment, 4) cross-bite correction with removable plates/ functional appliance. Cephalometric values at the time of first clinical examination were compare among the four groups. Cephalometric analysis indicates the following results: 1)the amounts of antero-posterior and vertical skeletal discrepancies and dental compensation were greatest in surgery group 2) SNB, Wits, distance from Nasion Perpendicular Plane to point a facial angle, facial convexity, and APDI were greater in orthopedic appliance group than fixed appliance(camouflage) group, but there was no statistical difference 3) removable plates/ functional appliance group showed least amounts of skeletal discrepancies and dental compensation with statistical significance.

• Clean Technology
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• v.16 no.3
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• pp.220-228
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• 2010

Four Keggin-type heteropolyacids, $H_nXM_{12}O_{40}$(X = P and Si, M = W and Mo) that were substituted with heteroatom and polyatom were applied to the dehydration reaction of fructose to 5-hydroxymethylfurfural (HMF). The results showed that the acid became stronger when the heteroatom and polyatom were substituted with P and W than the cases of Si and Mo, respectively. However, the amount of acidic sites increased with the decrease in the acid strength, resulting in the change of the catalytic activity of heteropolyacids in the dehydration reaction. The experimental results revealed that four different heteropolyacids produced similar amounts of HMF via the dehydration reaction of fructose due to the counterbalancing effect between the amount of active sites, which is related to the catalytic activity of heteropolyacids, and the softness of polyanion. In addition, it was observed that the prepared heteropolyacids showed good structural stability after heat treatment at $200^{\circ}C$.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.353-359
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• 2017

Starting from a t-norm T, it is possible to construct a class of new t-norms, so-called T-generalized t-norm. The purpose of this paper is to describe some properties of this class of generalized t-norms. An algebraic structure as well as a binary relation among t-norms are also investigated. Some open problems are discussed as well.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.483-493
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• 2013

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1255-1267
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• 2020

The class of isotropic almost complex structures, J_𝛿,𝜎, define a class of Riemannian metrics, g_𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g_𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J_𝛿,𝜎.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.8C
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• pp.772-781
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• 2009

This paper proposes a novel algorithm for the efficient classification and retrieval of medical images. After color and edge features are extracted from medical images, these two feature vectors are then applied to a multi-class Support Vector Machine, to give membership vectors. Thereafter, the two membership vectors are combined into an ensemble feature vector. Also, to reduce the search time, Correlated Categories Vector is proposed for similarity matching. The experimental results show that the proposed system improves the retrieval performance when compared to other methods.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.545-551
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• 2008

Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\rho$(R[x]) = ($\rho$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.