• Journal of the Korean Mathematical Society
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• v.56 no.1
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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].

• Journal of the Korean Mathematical Society
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• v.58 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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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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• 1998.10a
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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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 $\mathbb{p}^2$.

• Journal of the Korean Society of Propulsion Engineers
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• v.27 no.1
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• pp.17-26
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• 2023

The star-shaped propellant grain can be used for designing burning surface areas with various profiles and are easy to manufacture, so it can be usefully applied to actual solid rocket motors. However, since there are many design-related configuration variables and slivers at the end of combustion, it is difficult to achieve an optimal design using a general optimization technique. In this study, the new method for designing star grains using a database was proposed to increase usability and success rate of optimization design. In the proposed method, a solution that satisfies the requirements is obtained after defining the performance variables, constructing the database. By applying the proposed method, the design of star grains with various profiles of the burning surface area was performed, and the validity of the design method was confirmed.

• The Pure and Applied Mathematics
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• v.26 no.3
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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].

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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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].