• Honam Mathematical Journal
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• v.44 no.2
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• pp.259-270
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• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.

• Journal of computational fluids engineering
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• v.18 no.3
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• pp.26-33
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• 2013

In the present study, unsteady flow simulations of a variable geometry nozzle were conducted using a two-dimensional flow solver based on hybrid unstructured meshes. The variable geometry nozzle is used to achieve efficient performances of aircraft engines at various operating conditions. To describe the motion of the variable geometry nozzle, an algebraic method based on the basis decomposition of normal edge vector was used for the deformation of viscous elements. A ball-vertex spring analogy was used for inviscid elements. The aerodynamic data were obtained for a range of nozzle pressure ratios, and the validations were made by comparing the present results with available experimental data. The unsteady nozzle flows were simulated with an oscillating diverging section and a converging-diverging section. It was found that the nozzle performances are influenced by the nozzle exit flow characteristics, mass flow rate, as well as unsteady effects. These unsteady effects are shown to behave differently depending on the frequency of the nozzle motion.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.3
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• pp.305-319
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• 2000

Numerical solution lot frictional contact problems of nonlinearly deformable bodies having large deformation is presented. The contact conditions on the possible contact points are expressed by using the contact error vector, and the iterative scheme is used to reduce the contact error vector monotonically toward zero. At each iteration the solution consists of two steps : The first step is to revise the contact force by using the contact error vector given by the previous geometry, and the second step is to compute the displacement and the contact error vector by solving the equilibrium equation with the contact force given at the first step. Convergence of the iterative scheme to the correct solution is analyzed, and the numerical simulations we performed with a rigid-plastic membrane and a nonlinear elastic beam.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.5
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• pp.857-859
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• 2015

In this letter, we consider a directional routing protocol that reduces the duplicated packets for AODV-based flooding in the course of establishing the end-to-end route in the multi-hop maritime ad-hoc networks. We propose an adaptive means of reducing the routing overhead subject to the node density and the target probability of successful routing that is analyzed by the stochastic geometry.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.519-533
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• 2007

In this paper we study a equality $\frac{1}{h_a}+\frac{1}{h_b}+\frac{1}{h_c}=\frac{1}{r}$ which contains altitudes and radius of inscribed circle of triangle. We search some paths for proving the equality, and find out 9 proof method of the equality which is related with descriptive geometry, coordinate geometry, and vector geometry.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.125-138
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• 2011

We give some characterizations of non-existence of lightlike hypersurfaces of an indefinite space form. Some geometric objects for the induced Ricci tensor to be symmetric are studied.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.119-125
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• 1998

We determine the possible types of Chern classes of rank 2 stable bundles (mod Picard groups) on the Enriques surfaces and their covering K3 surfaces.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.809-818
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• 2013

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.841-862
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• 2013

This study analyzed issues in the mathematics curriculum concerning the cognitive development of the vector and inner product concepts in the light of Tall's and Watson's research(Tall, 2004a; Tall, 2004b; Watson et al., 2003; Watson, 2002). Some suggestions in teaching the vector and inner product concepts were elaborated in the terms of these analyses. First, the position vector needs to be represented by an arrow on the coordinate system in order to introduce the component form of a vector represented by a directed line segment. Second, proofs of the vector operation law should be carried out by symbolic manipulations based on the algebraic concept of a vector in the symbolic world. Third, it is appropriate that the inner product is defined as $\vec{a}{\cdot}\vec{b}=a_1b_1+a_2b_2$ (when, $\vec{a}=(a_1,a_2)$, $\vec{b}=(b_1,b_2)$) when it comes to considering the meaning of the inner product relevant to vector space in the formal world. Cognitive growth of concepts of the vector and inner product can be properly induced through revising explanation methods about the concepts in the curriculum in the basis of the above suggestions.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.573-594
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• 2014

Capacity of making assessment items among teacher's assessment competency is essential element in validity and reliability of assessment. Errors in test items on the formal and content aspects can be a big stumbling block to derive a correct evaluation result. Through this assessment, the positive feedback can not be derived. In this study, By analyzing midterm and final 60 exam papers for geometry and vector in 45 high Schools of Seoul GyeonggiIncheon area, We argue error items and improvements on the formal and content aspect the paper-based assessment of mathematics. Through this, Our intention is to improve the skills of teachers for making assessment items.