• 한국수학사학회지
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• 제30권3호
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• 한국가구학회지
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• 제12권1호
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• pp.21-26
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• 2001

This study was carried out to get some basic information on mechanical properties of Platanus orientalis L. for the rational utilization of this wood. Relationship of anatomical characteristics with compression strength parallel to grain was analyzed using stepwise regression technique. All possible combination of 8 independent variables were regressed on compression strength parallel to grain. The summarized results in this study were as follows: 1. The compression strength parallel to grain increased with the increase of wood fiber length and wood fiber width. The strength, however, decreased with increase of number of pore per $\textrm{mm}^2$ and tangential diameter of pore. 2. The major factors affecting compression strength parallel to grain in heartwood were length of wood fiber and number of pore $per{\;}{\textrm{mm}^2}$ but width of wood fiber and length of vessel element were the important factors in sapwood.

• 제어로봇시스템학회논문지
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• 제17권3호
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• pp.236-240
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• 2011

The terminal sliding mode control schemes have been studied a lot since they can guarantee that the state error gets to zero in a finite time. However, the conventional terminal sliding surfaces have been designed using power function whose exponent is a rational number between 0 and 1, and whose numerator and denominator should be odd integers. It is clearly restrictive. Thus, in this paper, we propose a novel terminal sliding surface using power function whose exponent can be a real number between 0 and 1.

• 한국국방경영분석학회지
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• 제16권2호
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• pp.96-104
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• 1990

This paper concerns the problem of deciding the rational spare inventory levels for efficient use of a limited defence budget and, at the same time, for enhancing the operation rate of equipement/weapons in the army. The system we are concerned has a finite number of repairmen at each base and the depot. After repair job has completed, the repaired items are returned to the base where they have originated. For the system, we identify the distribution of the total number of failed items which belong to a base and develope a method to find spare inventory levels of repairable items at each base to satisfy a specified minimum fill rate.

• 대한수학회보
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• 제56권4호
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• 대한수학회지
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• 제56권6호
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• pp.1463-1474
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• 2019

Let C be a nonsingular projective curve of genus ${\geq}2$ over an algebraically closed field of characteristic 0. For a point P in C, the Weierstrass semigroup H(P) is defined as the set of non-negative integers n for which there exists a rational function f on C such that the order of the pole of f at P is equal to n, and f is regular away from P. A point P in C is referred to as a weak Galois-Weierstrass point if P is a Weierstrass point and there exists a Galois morphism ${\varphi}:C{\rightarrow}{\mathbb{p}}^1$ such that P is a total ramification point of ${\varphi}$. In this paper, we investigate the number of weak Galois-Weierstrass points of which the Weierstrass semigroups are generated by two positive integers.

• 대한수학회보
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• 제61권4호
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• pp.907-915
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• 2024

Let f be an integral quadratic form in k variables, F the Gram matrix corresponding to a ℤ-basis of ℤ^k. For r ∈ F^-1ℤ^k, a rational number n with f(r) ≡ n mod ℤ and a positive integer c, set N_f(n, r; c) := #{x ∈ ℤ^k/cℤ^k : f(x + r) ≡ n mod c}. Siegel showed that for each prime p, there is a number w depending on r and n such that N_f(n, r; p^ν+1) = p^k-1N_f(n, r; p^ν) holds for every integer ν > w and gave a rough estimation on the upper bound for such w. In this short note, we give a more explicit estimation on this bound than Siegel's.

• 대한조선학회논문집
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• 제52권2호
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• pp.119-124
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• 2015

The purpose of this research is a verification of the current equation for calculating equipment number and a suggesting a method for development of a rational new equation. The equation for calculating equipment number consists of total surface area of a ship that fluid resistance act on. Equipment number determines the specification of anchoring and mooring equipment such as anchor weight, anchor chains length and diameter, the number, length and breaking load of tow lines and mooring lines. The equation for equipment number calculation is basically derived considering x, y components of a wind and current force acting on a ship. But this equation is only based on a tanker, which was main type of ships when the equation was derived. Therefore, verification of the equation is required for other types of ships, such as container carrier, LNG carrier, etc. Therefore, in this research, we find out the equation for equipment number calculation should be revised for other types of ships especially the container carrier, by comparing wind and current force acting on a ship to holding force of an anchor and anchor chains, which are selected based on the equipment number.

• 대한수학교육학회지:수학교육학연구
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• 제22권1호
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• pp.53-68
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• 2012

본 연구는 아이들이 문장제 또는 수식 형태의 나눗셈의 결과를 여러 타입의 분수들-진분수, 가분수, 대분수-과 연관시키면서 분수가 가지는 여러 하위 개념 중 몫에 대한 개념 도식을 어떻게 구성해 가는지에 대하여 미국의 5학년 초등학생 네 명을 대상으로 이루어졌다. 실험 결과는 다음과 같았다. 균등분배 상황에서, 아이들은 나눗셈을 두 가지 방식으로 개념화하였다. 첫째, 아이들이 나눗셈을 통해 대분수 형태의 몫을 산출했을 경우, 이 대분수 형태의 몫은 진분수와 가분수 형태의 분수들을 부분-전체의 하위개념이 아니라 몫이라는 하위개념으로 이해하는데 개념적인 기초가 되었다. 둘째, 진분수 형태의 몫을 얻은 경우, 아이들은 그 몫을 곱셈구조의 예로 보려는 경향이 있었다. 즉, $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. 하지만, 장제법 계산은 소수 형태의 몫을 생산함으로써 아이들이 이 구조를 깨닫는 것을 어렵게 했다.

• International Journal of CAD/CAM
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• 제4권1호
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• pp.33-45
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• 2004

In this work, a rational procedure has been formulated for the selection of points approximating slice contours cut in LOM (Laminated Object manufacturing) with first order approximation. It is suggested that the number of points representing a slice contour can be 'minimised' or 'optmised' by equating the horizontal chordal deviation (HCD) to the user-defined surface form tolerance. It has been shown that such optimization leads to substantial reduction in slice height calculations and NC codes file size for cutting out the slices. Due to optimization, the number of contour points varies from layer to layer, so that points on successive layer contours have to be matched by four sided ruled surface patches and triangular patches. The technological problems associated with the cutting out of triangular patches have been addressed. A robust algorithm has been developed for the determination of slice height for optimum and arbitrary numbers of contour points with different strategies for error calculations. It has been shown that optimisation may even lead to detection and appropriate representation of elusive surface features. An index of optimisation has been defined and calculations of the same have been tabulated.