• Research in Mathematical Education
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• v.7 no.1
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• pp.59-67
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• 2003

In linear algebra course, the theory of vector space is usually presented in a very formal setting, which causes severe difficulties to many students. In this study, the effect of teaching the theory of vector space in linear algebra from the geometrical point of view on students' learning was investigated. It was found that the teaching of the theory of vector space in linear algebra from the geometrical point of view increases the meaningful loaming since it increases the visualization.

• Research in Mathematical Education
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• v.18 no.4
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• pp.289-305
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• 2014

The current mathematical education calls for a learning environment from the constructionism perspective that actively creates mathematical objects. This research first analyzes JavaMAL's expression 'move' that enables students to express the agent's behavior constructively before they learn vector as a formal concept. Since expression 'move' is based on a coordinate, it naturally corresponds with the expression of vectors used in school mathematics and lets students take an embodied approach to the concept of vector. Furthermore, as a design tool, expression 'move' can be used in various activities that include vector structure. This research studies the educational significance entailed in JavaMAL's expression 'move'.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.319-335
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• 2011

We classify equivariant topoligical complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

• International Journal of Advanced Culture Technology
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• v.10 no.1
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• pp.42-46
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• 2022

To cultivate talented people with creative and convergent thinking skills to live in the era of the 4th industrial revolution, the national curriculum of Korea is gradually emphasizing convergence education and software education. To meet the demands of the times, this paper suggests subject-convergent teaching-learning materials for educating core principles of Support Vector Machines, especially targeting elementary learners. Based on analysis of the national curriculum, achievement standards of three subjects are integrated. After printable worksheets for traditional face-to-face classes had developed, they were transformed to online interactive worksheets for non-face-to-face classes. The teaching-learning materials are expected to promote the growth of the learners' academic motivation and knowledge.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• The Mathematical Education
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• v.29 no.1
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• pp.63-68
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• 1990

Let M be a differentiable manifold, TM its tangent bundle and FM its frame bundle. The theory of complete lifts and Horizontal lifts to FM of vector fields on M ahs been studied by many authors. Tn this paper, vertical lifts of functions vector fields md 1-forms on M to FM are studied.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.237-251
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• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.569-581
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• 2011

Let a finite group R act smoothly on a closed manifold M. We assume that R acts freely on M except a union of closed submanifolds with codimension at least two. Then, we show that there exists an isomorphism between equivariant topological complex vector bundles over M and nonequivariant topological complex vector orbibundles over the orbifold M/R. By using this, we can classify nonequivariant vector orbibundles over the orbifold especially when the manifold is two-sphere because we have classified equivariant topological complex vector bundles over two sphere under a compact Lie group (not necessarily effective) action in [6]. This classification of orbibundles conversely explains for one of two exceptional cases of [6].

• Journal of Information Processing Systems
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• v.15 no.2
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• pp.422-432
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• 2019

A hybrid kernel function of support vector machine is proposed to improve the classification performance of power quality disturbances. The kernel function mathematical model of support vector machine directly affects the classification performance. Different types of kernel functions have different generalization ability and learning ability. The single kernel function cannot have better ability both in learning and generalization. To overcome this problem, we propose a hybrid kernel function that is composed of two single kernel functions to improve both the ability in generation and learning. In simulations, we respectively used the single and multiple power quality disturbances to test classification performance of support vector machine algorithm with the proposed hybrid kernel function. Compared with other support vector machine algorithms, the improved support vector machine algorithm has better performance for the classification of power quality signals with single and multiple disturbances.