• 한국수학사학회지
• /
• 제26권4호
• /
• pp.245-257
• /
• 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.

• 제어로봇시스템학회논문지
• /
• 제14권8호
• /
• pp.774-778
• /
• 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.

• 한국산림과학회지
• /
• 제67권1호
• /
• pp.52-59
• /
• 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
• /
• 제33권1호
• /
• pp.83-102
• /
• 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.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2017년도 제48회 춘계학술대회논문집
• /
• pp.675-678
• /
• 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.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 제38회 하계학술대회
• /
• pp.477-478
• /
• 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.

• 한국학교수학회논문집
• /
• 제3권2호
• /
• pp.59-67
• /
• 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.

• 한국학교수학회논문집
• /
• 제16권4호
• /
• pp.841-862
• /
• 2013

이 연구는 2007 개정 교육과정의 '기하와 벡터' 교과에서 다루어지는 벡터와 내적 개념을 분석하여 그 특징을 기술함으로써 벡터와 내적 개념 지도의 교수학적 시사점을 얻는데 목적을 두었다. 이를 위해 '기하와 벡터' 교육과정에서 다루어지는 벡터와 내적 개념 분석을 위한 세부 관점을 Tall(2002a; Tall, 2004b)과 Watson et al.(2003; Watson, 2002)에 기초하여 5가지로 추출하고, 이렇게 추출된 세부 관점을 토대로 '기하와 벡터' 교육과정 및 교육과정해설서, '기하와 벡터' 교과서 10종 모두에서 다루어지는 벡터와 내적 개념의 특징을 분석하였다. 이로부터 벡터와 내적 개념 형성과 관련된 교육과정상의 이슈를 구체화하였으며 이에 비추어 '기하와 벡터' 교과서에서 벡터 단원의 내용을 전개하는 방식과 관련된 시사점을 논의하였다.

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제30권11호
• /
• pp.1072-1079
• /
• 2003

본 논문은 점층적으로 대규모 문서 분류를 할 수 있는 새로운 클러스터링 알고리즘에 대한 것으로, 고차원의 대규모 문서 집합에 대한 클러스터링을 수행하는 spherical k-means (SKM) 알고리즘과 점층적인 방식으로 클러스터링을 수행하는 퍼지(fuzzy) ART(adaptive resonance theory) 신경망의 특징을 이용하였다. 즉, SKM의 벡터 공간 모델과 개념벡터를 토대로 퍼지 ART의 경계변수의 개념을 결합한 것이다. 제시하는 알고리즘은 점층적 클러스터링의 지원과 함께 최적의 클러스터 수를 자동으로 결정할 뿐 아니라 이상치(outlier)와 노이즈(noise)에 의한 overfitting의 문제도 해결하였다. 또한 생성된 클러스터들의 질을 평가할 수 있는 응집도를 측정하는 목적 함수의 값에 있어서도 CLASSIC3 데이타 집합으로 실험한 결과 기존의 SKM에 비해 평균 8.04%의 향상된 응집도를 나타냈다.

• Structural Engineering and Mechanics
• /
• 제14권6호
• /
• pp.679-698
• /
• 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.