• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.8
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• pp.774-778
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• 2008

The inaccuracy of inertial sensors used in low cost IMU's limits the usage to ARS, at best. Sensor fusion technologies are widely used to overcome this problem. GPS is the most popular secondary sensor, but GPS alone cannot fully compensate the IMU errors in the initial alignment process and rectilinear flights. This paper presents a new concept of aiding the low cost IMU with the sun line of sight vector. The simulation and experimental results in this paper proves that aiding of INS/GPS with the sun line of sight vector increases the observability and improves accuracy remarkably.

• Journal of Korean Society of Forest Science
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• v.67 no.1
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• pp.52-59
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• 1984

A Gentan probability q(j) is the probability that a newly planted forest will be felled at age-class j. A future change in growing stock and yield of the forests can be predicted by means of this probability. On the other hand a state of the forests is described in terms of an n-vector whose components are the areas of each age-class. This vector, called age-class vector, flows in a n-1 dimensional simplex by means of $n{\times}n$ matrices, whose components are the age-class transition probabilities derived from the Gentan probabilities. In the simplex there exists a fixed point, into which an arbitrary forest age vector sinks. Theoretically this point means a normal state of the forest. To each age-class-transition matrix there corresponds a single normal state; this means that there are infinitely many normal states of the forests.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.675-678
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• 2017

In the present, various methods have been employed to obtain the lesser thrust loss. Numerical simulations have been carried out for optimizing the thrust vector control system. Thrust vector control based on coflowing shear layer is an effective method to control the primary jet direction in the absence of moving parts. Thrust vector in symmetric nozzles is acquired by secondary flow injections that result to boundary layer separation. The pressure in secondary flow inlet was varied to check the deflection angle of jet flow.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.477-478
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• 2007

This paper proposes a new concept of support vector machine (SVM) based voltage stability classifier using time-series phasor data. The classifier, based on a linear SVM, can provide very effective signals for identification of long-term voltage stability. In addition, the SVM output is applicable as an voltage stability indicator when an amount of corrective controls are performed just to make the system reach around at the maximum deliverable point.

• Journal of the Korean School Mathematics Society
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• v.3 no.2
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• pp.59-67
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• 2000

Two groups of students, who are the students in the natural science course of high school in Korea, learned the equation of figure in space (point, line, plane) to understand more effectively with two different textbooks. One group was taught with the textbook used now in most high schools and the other group was taught with the textbooks systematized by associating old concept with new concept. The results are as follows : 1) We need understand the basic concept of vector plainly and flexibly to apply it to the solution of problems. 2) It helps students understand new concepts how we should establish the concept about point, line and plane in space by applying the concept about those on XY plane, 3) It is very effective in understanding the new knowledge system more easily to analyze the existent concepts and to arrange them systematically for efficient understanding of new concepts. 4) The texts which consist of contents organized by basic concepts improve students' learning ability.

• 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 KIISE:Software and Applications
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• v.30 no.11
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• pp.1072-1079
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• 2003

This study is purported for suggesting a new clustering algorithm that enables incremental categorization of numerous documents. The suggested algorithm adopts the natures of the spherical k-means algorithm, which clusters a mass amount of high-dimensional documents, and the fuzzy ART(adaptive resonance theory) neural network, which performs clustering incrementally. In short, the suggested algorithm is a combination of the spherical k-means vector space model and concept vector and fuzzy ART vigilance parameter. The new algorithm not only supports incremental clustering and automatically sets the appropriate number of clusters, but also solves the current problems of overfitting caused by outlier and noise. Additionally, concerning the objective function value, which measures the cluster's coherence that is used to evaluate the quality of produced clusters, tests on the CLASSIC3 data set showed that the newly suggested algorithm works better than the spherical k-means by 8.04% in average.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.679-698
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• 2002

In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction concept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces.