• 대한수학회논문집
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• 제9권2호
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• pp.261-264
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• 1994

Throughout this paper, all rings are assumed to be commutative with identity. By a local ring (R, m), we mean a Noetherian ring R which has the unique maximal ideal m. By dim(R) we always mean the Krull dimension of R. Let I be an ideal in a ring R and t an indeterminate over R. Then the Rees algebra R[It] is defined to be(omitted)

• 대한수학회논문집
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• 제9권4호
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• 전자공학회논문지B
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• 제29B권1호
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• pp.1-10
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• 1992

This study presents a complete octree construction algorithm for 2D depth images obtained from orthogonal face views, which can represent 3D objects exactly. In constructing quadtree, optimal quadtree construction algorithm is applied to depth images for efficient use of memory and reduction of tree construction time. In addition, pseudo-octrees are constructed by using our proposed method, which construct pseudo-octrees according to the resolution value given in each node of constructed quadtree and mapping relation between quadrants and octants. Finally, a complete octree, which represents a 3D object, is constructed by volume intersection with each constructed pseudo-octree. The representation accuracy of a complete octree constructed by our algorithm is investigated by using a 3D display method and a volume ratio method for a complete octree.

• 대한교통학회:학술대회논문집
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• 대한교통학회 1996년도 제29회 학술발표회
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• pp.59-86
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• 1996

Current methods for evaluating unsignalized intersections, and estimating level-of-service (LOS) is determined from efficiency-based criteria such as little or no delay to very long delays. At present, similar procedures to evaluate intersections using safety-based criteria do not exist. The improvement of sight distances at intersections is the most effective way of improving intersection safety. However, a set of procedures is necessary to account for the limitations in current methodology. Such an approach would build upon such methods, but also account for: deficiencies in the current deterministic solution for the determination of intersection sight distances; opportunity for an accident and severity of an accident; and cost-effectiveness of attaining various levels of sight distances. In this research, a model that estimates the degree of safety at two-way stop-controlled intersections is described. Only crossing maneuvers are considered in this study because accidents caused by the crossing maneuvers are the dominate type among intersection accidents. Monte Carlo methods are used to estimate the hazard at an intersection as a function of roadway features and traffic conditions. Driver`s minimum gap acceptance in the crossing vehicles and headway distribution on the major road are used in the crossing vehicles and headway distribution on the major road are used in the model to simulate the real intersectional maneuvers. Other random variables addressed in the model are: traffic speeds; preception-reaction times of both drivers in the crossing vehicles and drivers in oncoming vehicles on the major road; and vehicles on the major roads. The developed model produces the total number of conflicts per year per vehicle and total potential kinetic energy per year per vehicle dissipated during conflicts as measurements of safety at intersections. Based on the results from the developed simulation model, desirable sight distances for various speeds were determined as 350 feet, 450 feet and 550 feet for 40 mph, 50 mph and 60 mph prevailing speed on the major road, respectively. These values are seven to eight percent less than those values recommended by AASHTO. A safety based level-of-service (LOS) is also developed using the results of the simulation model. When the total number of conflicts per vehicle is less than 0.05 at an intersection, the LOS of the intersection is `A' and when the total number of conflicts per vehicle is larger than 0.25 at an intersection, the LOS is `F'. Similarly, when the total hazard per vehicle is less than 350, 000 1b-ft2/sec2, the LOS is `F'. Once evaluation of the current safety at the intersection is complete, a sensitivity analysis can be done by changing one or more input parameters. This will estimate the benefit in terms of time and budget of hazard reduction based upon improving geometric and traffic characteristics at the intersection. This method will also enable traffic engineers in local governments to generate a priority list of intersection improvement projects.

• 대한수학회논문집
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• 제33권1호
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• pp.85-101
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• 2018

Let S be a polynomial ring over a field K, with a monomial order ${\prec}$, and let I be an unmixed graded ideal of S. In this paper we study two functions associated to I: The minimum distance function ${\delta}_I$ and the footprint function $fp_I$. It is shown that ${\delta}_I$ is positive and that $fp_I$ is positive if the initial ideal of I is unmixed. Then we show that if I is radical and its associated primes are generated by linear forms, then ${\delta}_I$ is strictly decreasing until it reaches the asymptotic value 1. If I is the edge ideal of a Cohen-Macaulay bipartite graph, we show that ${\delta}_I(d)=1$ for d greater than or equal to the regularity of S/I. For a graded ideal of dimension ${\geq}1$, whose initial ideal is a complete intersection, we give an exact sharp lower bound for the corresponding minimum distance function.

• 대한수학회논문집
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• 제23권4호
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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.

• 대한수학회보
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• 제49권4호
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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 $v_i=1$.

• 대한수학회보
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• 제54권1호
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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.

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.283-288
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• 2009

Let N be a zero-symmetric near-ring with identity and let ${\Gamma}(N)$ be a graph with vertices as elements of N, where two different vertices a and b are adjacent if and only if + = N, where is the ideal of N generated by x. Let ${\Gamma}_1(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set {n ${\in}$ N : = N} and ${\Gamma}_2(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set $N{\backslash}{\upsilon}({\Gamma}_1(N))$, where ${\upsilon}(G)$ is the set of all vertices of a graph G. In this paper, we completely characterize the diameter of the subgraph ${\Gamma}_2(N)$ of ${\Gamma}(N)$. In addition, it is shown that for any near-ring, ${\Gamma}_2(N){\backslash}M(N)$ is a complete bipartite graph if and only if the number of maximal ideals of N is 2, where M(N) is the intersection of all maximal ideals of N and ${\Gamma}_2(N){\backslash}M(N)$ is the graph obtained by removing the elements of the set M(N) from the vertices set of the graph ${\Gamma}_2(N)$.