• 대한수학회지
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• 제56권1호
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• pp.169-181
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• 2019

In [9], Geramita, Harbourne, and Migliore find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a linear star configuration in ${\mathbb{P}}^n$ n of any codimension r. In [8], Geramita, Galetto, Shin, and Van Tuyl extend the result on a general star configuration in ${\mathbb{P}}^n$ but for codimension 2. In this paper, we find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a general star configuration in ${\mathbb{P}}^n$ of any codimension r using a matroid configuration in [10]. This generalizes both the result on a linear star configuration in ${\mathbb{P}}^n$ of codimension r in [9] and the result on a general star configuration in ${\mathbb{P}}^n$ of codimension 2 in [8].

• 대한수학회지
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• 제58권2호
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• pp.283-308
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• 2021

In [30] the author finds a graded minimal free resolution of the 2-nd order symbolic power of a star configuration in ℙn of any codimension r. In this paper, we find that of any m-th order symbolic power of a star configuration in ℙn of codimension 2, which generalizes the result of Galetto, Geramita, Shin, and Van Tuyl in [15, Theorem 5.3]. Furthermore, we extend it to the m-th order symbolic power of a star configuration in ℙn of any codimension r for m = 3, 4, which also generalizes the result of Biermann et al. in [1, Corollaries 4.6 and 5.7]. We also suggest how to find a graded minimal free resolution of the m-th order symbolic power of a star configuration in ℙn of any codimension r for m ≥ 5.

• 충청수학회지
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• 제28권1호
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• pp.119-125
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• 2015

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

• 대한수학회지
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• 제56권3호
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• pp.645-667
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• 2019

It has been little known when an Artinian point quotient has the strong Lefschetz property. In this paper, we find the Artinian point star configuration quotient having the strong Lefschetz property. We prove that if ${\mathbb{X}}$ is a star configuration in ${\mathbb{P}}^2$ of type s defined by forms (a-quadratic forms and (s - a)-linear forms) and ${\mathbb{Y}}$ is a star configuration in ${\mathbb{P}}^2$ of type t defined by forms (b-quadratic forms and (t - b)-linear forms) for $b=deg({\mathbb{X}})$ or $deg({\mathbb{X}})-1$, then the Artinian ring $R/(I{\mathbb_{X}}+I{\mathbb_{Y}})$ has the strong Lefschetz property. We also show that if ${\mathbb{X}}$ is a set of (n+ 1)-general points in ${\mathbb{P}}^n$, then the Artinian quotient A of a coordinate ring of ${\mathbb{X}}$ has the strong Lefschetz property.

• 대한수학회지
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• 제49권2호
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.53-57
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• 1998

Star tracker placement configuration is proposed and the properness of the placement configuration is verified for star tracker's sun avoidance angle requirement. Precision attitude determination system is successfully designed using a gyro-star tracker inertial reference system for a candidate LEO spacecraft. Elaborate kalman filter formulation for a spacecraft is proposed for covariance analysis. The covariance analysis is performed to verify the capability of the proposed attitude determination system. The analysis results show that the attitude determination error and drift rate error are good enough to satisfy the mission of a candidate spacecraft.

• 대한수학회지
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• 제55권4호
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• pp.763-783
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• 2018

In this paper, we study an Artinian point-configuration quotient having the SLP. We show that an Artinian quotient of points in $\mathbb{p}^n$ has the SLP when the union of two sets of points has a specific Hilbert function. As an application, we prove that an Artinian linear star configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ and $\mathbb{Y}$ are linear starconfigurations in $\mathbb{p}^2$ of type s and t for $s{\geq}(^t_2)-1$ and $t{\geq}3$. We also show that an Artinian $\mathbb{k}$-configuration quotient $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP if $\mathbb{X}$ is a $\mathbb{k}$-configuration of type (1, 2) or (1, 2, 3) in $\mathbb{p}^2$, and $\mathbb{X}{\cup}\mathbb{Y}$ is a basic configuration in $\mathbb{p}^2$.

• 한국추진공학회지
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• 제27권1호
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• pp.17-26
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• 2023

Star 형상을 갖는 추진제 그레인은 다양한 면적 선도가 가능하고, 제작이 용이하여 실제 고체 추진제 로켓에 유용하게 적용될 수 있다. 그러나, 설계와 관련한 형상 변수가 많고 연소 말기 슬리버가 존재하므로, 해석 비용이 저렴한 일반적인 단일 최적화 기법으로는 최적 설계가 성공하기 어렵다. 본 연구에서는 활용성과 설계 성공률을 높이기 위해 데이터베이스를 사용하여 star 그레인을 설계하는 기법을 제안하였다. 제안된 방법에서는 성능 변수를 정의하고, 데이터베이스를 구축한 후 요구조건을 만족하는 해를 탐색한다. 제안된 방법을 적용하여 다양한 종류의 연소 면적 선도를 갖는 star 그레인의 설계를 수행하고, 설계 방법의 타당성을 검증하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.209-214
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• 2019

We investigate all kinds of the Hilbert function of the Artinian quotient of the coordinate ring of a linear star configuration in ${\mathbb{P}}^n$ of type (n+1) (or (n+1)-general points in ${\mathbb{P}}^n$), which generalizes the result [7, Theorem 3.1].

• 충청수학회지
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• 제25권3호
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• pp.553-562
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• 2012

It has been proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ for $3{\leq}t{\leq}9$ and $3{\leq}t{\leq}s$ has generic Hilbert function. We extend the condition to $t$ = 10, so that it is true for $3{\leq}t{\leq}10$, which generalizes the result of [7].