• Journal of applied mathematics & informatics
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• v.2 no.1
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• pp.59-83
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• 1995

In this paper, we proved the set of points which are the vertices of the n-gon in $mathbb{P}^2(n\geq3$)$ has the Uniform Position Property and what the graded free resolutions of the ideals of k-configurations in $mathbb{P}^3$ are.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1001-1015
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• 2011

In this article we study the problem to determine all occurring Betti diagrams of varieties $X{\subset}\mathbb{P}^r$ of almost minimal degree, i.e. deg(X) = codim(X; $\mathbb{P}^r$)+2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim$(X,\mathbb{P}^r){\leq}8$.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.487-497
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• 2008

Buchsbaum and Eisenbud showed that every Gorenstein ideal of grade 3 is generated by the submaximal order pfaffians of an alternating matrix. In this paper, we describe a method for constructing a class of type 3, grade 3, perfect ideals which are not Gorenstein. We also prove that they are algebraically linked to an even type grade 3 almost complete intersection.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.387-398
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• 2014

In this paper, we give a structure theorem for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection of grade 3 and a Gorenstein ideal of grade 3 geometrically linked by a regular sequence. We also present the Hilbert function of a Gorenstein ideal of grade 4 induced by a Gorenstein matrix f.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.389-401
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• 2002

We give an upper bound for the degrees of the nonvanishing homology modules of the Schur complex L$\sub$λ/${\mu}$/ø in terms of the depths of the determinantal ideals of ø). Using this fact, we obtain the acyclic theorem for L$\sub$λ/ø and the information concerning the support of the homology modules of L$\sub$λ/${\mu}$/ø.

• Imaging Science in Dentistry
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• v.47 no.2
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• pp.75-86
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• 2017

Purpose: The purpose of this study was to apply a newly developed free software program, at low cost and with minimal time, to evaluate the quality of dental and maxillofacial cone-beam computed tomography (CBCT) images. Materials and Methods: A polymethyl methacrylate (PMMA) phantom, CQP-IFBA, was scanned in 3 CBCT units with 7 protocols. A macro program was developed, using the free software ImageJ, to automatically evaluate the image quality parameters. The image quality evaluation was based on 8 parameters: uniformity, the signal-to-noise ratio (SNR), noise, the contrast-to-noise ratio (CNR), spatial resolution, the artifact index, geometric accuracy, and low-contrast resolution. Results: The image uniformity and noise depended on the protocol that was applied. Regarding the CNR, high-density structures were more sensitive to the effect of scanning parameters. There were no significant differences between SNR and CNR in centered and peripheral objects. The geometric accuracy assessment showed that all the distance measurements were lower than the real values. Low-contrast resolution was influenced by the scanning parameters, and the 1-mm rod present in the phantom was not depicted in any of the 3 CBCT units. Smaller voxel sizes presented higher spatial resolution. There were no significant differences among the protocols regarding artifact presence. Conclusion: This software package provided a fast, low-cost, and feasible method for the evaluation of image quality parameters in CBCT.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.221-230
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• 1988

In the microcomputer-based velocity control for an electro-hydraulic servo system, the effects of control methods and control hardware on the performance of the system were investigated. Experiments were carried out with PID and deadbeat controllers using 8 or 16 bit microprocessor and 8 or 12 bit A/D and D/A converters. It is found that the transient response of the system is better with PID controller than with deadbeat controller. When the number of bits of the microprocessor and converters are small, it is also found that amplitude quantization due to limited word-length gives significant effects on transient responses of the system. Analytically predicted step responses are in good agreement with experimental ones.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.99-124
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• 2017

The structure theorems [3, 6, 21] for the classes of perfect ideals of grade 3 have been generalized to the structure theorems for the classes of perfect ideals linked to almost complete intersections of grade 3 by a regular sequence [15]. In this paper we obtain structure theorems for two classes of Gorenstein ideals of grade 4 expressed as the sum of a perfect ideal of grade 3 (except a Gorenstein ideal of grade 3) and an almost complete intersection of grade 3 which are geometrically linked by a regular sequence.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.