• 대한수학회논문집
• /
• 제20권1호
• /
• pp.107-116
• /
• 2005

We show an algorithm to draw the famous picture of Kleinian modular group PSL(2, $\mathbb{Z}$), which appears in describing the moduli space of elliptic curves.

• 대한수학회논문집
• /
• 제20권2호
• /
• pp.259-273
• /
• 2005

In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.

• East Asian mathematical journal
• /
• 제38권3호
• /
• pp.321-329
• /
• 2022

For an ample divisor A of birational type on a singular del Pezzo surface S of degree 4 with A₁-singularity, we show that the affine cone of S defined by A is flexible

• 대한수학회지
• /
• 제52권4호
• /
• pp.853-868
• /
• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2007년도 추계학술대회논문집
• /
• pp.834-839
• /
• 2007

This paper investigates the distortion of magnetic field of a brushless DC (BLDC) motor due to deformed rubber magnet. Global or local deformation of rubber magnet in the BLDC motor is mathematically modeled by using the Fourier series. Distorted magnetic field is calculated by using the finite element method, and unbalanced magnetic force are calculated by using the Maxwell stress tensor. The first harmonic deformation in the global deformation of rubber magnet generates the first harmonic driving frequency of the unbalanced magnetic force, and the rest harmonic deformations of rubber magnet except the harmonic deformation with multiple of common divisor of pole and slot introduces the driving frequencies with multiple of slot number ${\pm}1$ to the unbalanced magnetic force. However, the harmonic deformation with multiple of common divisor of pole and slot does not generate unbalanced magnetic force due to the rotational symmetry. When the rubber magnet is locally deformed, the unbalanced magnetic force has the first harmonic driving frequency and the driving frequencies with multiples of slot number ${\pm}1$.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제48권1호
• /
• pp.81-91
• /
• 2009

This paper focuses on two problems in the 10th grade mathematics, the rational zero theorem and the content(the integer divisor) of a polynomial Among 138 students participated in the problem solving, 58 of them (42 %) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 %) consider the rational zero theorem is a mathematical fake(false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggests that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic(or primitive) polynomial as ail answer.

• 대한수학회지
• /
• 제56권4호
• /
• pp.869-915
• /
• 2019

Let H be a Krull monoid with class group G such that every class contains a prime divisor. Then every nonunit $a{\in}H$ can be written as a finite product of irreducible elements. If $a=u_1{\cdot}\;{\ldots}\;{\cdot}u_k$ with irreducibles $u_1,{\ldots},u_k{\in}H$, then k is called the length of the factorization and the set L(a) of all possible k is the set of lengths of a. It is well-known that the system ${\mathcal{L}}(H)=\{{\mathcal{L}}(a){\mid}a{\in}H\}$ depends only on the class group G. We study the inverse question asking whether the system ${\mathcal{L}}(H)$ is characteristic for the class group. Let H' be a further Krull monoid with class group G' such that every class contains a prime divisor and suppose that ${\mathcal{L}}(H)={\mathcal{L}}(H^{\prime})$. We show that, if one of the groups G and G' is finite and has rank at most two, then G and G' are isomorphic (apart from two well-known exceptions).

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.93-107
• /
• 2005

Based on the recently developed ABS algorithm for solving linear Diophantine equations, we present a special ABS algorithm for solving such equations which is effective in computation and storage, not requiring the computation of the greatest common divisor. A class of equations always solvable in integers is identified. Using this result, we discuss the ILP problem with upper and lower bounds on the variables.

• 호남수학학술지
• /
• 제34권1호
• /
• pp.63-76
• /
• 2012

In this paper, we present the convolution sum ${\sum}_{m<n/8}{\sigma}_1(2m){\sigma}_1(n-8m)$ evaluated for all $n{\in}\mathbb{N}$.

• 대한수학회지
• /
• 제42권6호
• /
• pp.1279-1285
• /
• 2005

Here we generalize previous work by Eisenbud-Harris and Farkas in order to prove that certain Brill-Noether divisors on the moduli space of curves have distinct supports. From this fact we deduce non-trivial regularity results for a higher co dimensional Brill-Noether locus and for the general $\frac{g+1}{2}$-gonal curve of odd genusg.