• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• 대한수학회논문집
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• 제32권4호
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• pp.789-803
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• 2017

Let $K={\mathbb{Q}}({\alpha})$ be a cubic field where ${\alpha}$ is an algebraic integer such that $disc_K({\alpha})$ is square-free. In this paper we will classify the structure of the unit group of the quotient ring ${\mathcal{O}}_K/A$ for each non-zero ideal A of ${\mathcal{O}}_K$.

• 대한수학회보
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• 제26권2호
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• East Asian mathematical journal
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• 제37권5호
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• pp.613-617
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• 2021

Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number H_d(f) of K of discriminant d is the ratio of class numbers 𝒪_K and 𝒪_f, where 𝒪_K is the ring of integers of K and 𝒪_f is the order of conductor f given by ℤ + f𝒪_K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number H_d(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

• 디지털융복합연구
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• 제13권12호
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• pp.117-124
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• 2015

빅데이터로 인해 통계분석에 대한 수용이 증대되면서 구조방정식모형과 같은 진보된 2세대 분석방법의 필요성이 증가하고 있다. 본 연구는 다양한 연구 분야에서 이용되는 구조방정식모형 중 부분최소제곱모형(PLS-SEM)을 적용하는데 있어 오픈 소프트웨어인 R의 활용방법에 대해서 제안하고자 한다. R은 GNU 프로젝트의 일부로서 무료이고, 빅데이터를 포함한 통계분석에 강력하면서도 유용한 도구이다. 이에 부분최소제곱모형의 대표적인 통계패키지인 SmartPLS와 본 연구가 제안하는 R을 활용하여 측정모형의 집중타당성, 판별타당성, 내적일관성을 분석하고, 구조 모형의 경로계수 및 조절효과를 분석하여 결과를 각각 비교 분석하였다. 분석결과 R은 측정모형과 구조모형에서 모두 SmartPLS와 동일한 결과를 나타내었고, 향후 상용 통계패키지를 대체할 수 있는 강력한 도구임을 확인하였다.

• Journal of Animal Science and Technology
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• 제62권3호
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• pp.321-333
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• 2020

Beef quality is influenced by the fattening period. Therefore, meat metabolomics profiles from the different fattening periods (e.g., short-term vs. long-term) were analyzed for identify potential indicators using nuclear magnetic resonance. Additionally, blood, free fatty acid, sensory, and mineral compositions in Korean steers were determined. Blood, free fatty acid, and mineral concentrations showed significant differences between short-term and long-term groups that were fed different diets. However, there were no sensory differences in the two fattening groups. Additionally, the metabolic profiles of meats were clearly separated based on multivariate orthogonal partial least square discriminant analysis. Six metabolites of variable importance in the projection plot were identified and showed high sensitivity as candidate markers for meat characteristics. In particular, lactate, carnosine, and creatine could be directly linked to scientific indicators of the fattening stage (31 vs. 28 mo) of meat. Our findings suggest that the metabolomics approach could be a powerful method for the detection of novel signatures underlying the managing period of beef.