• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• Journal for History of Mathematics
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• v.30 no.3
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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.

• Journal of the Korea Furniture Society
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• v.12 no.1
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.3
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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.

• Journal of the military operations research society of Korea
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• v.16 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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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).

• Journal of the Korean Mathematical Society
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• v.56 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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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.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.2
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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.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.53-68
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• 2012

This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.