• Honam Mathematical Journal
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• v.21 no.1
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• pp.65-74
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• 1999

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.561-567
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.657-671
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• 2009

Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. In this paper we derive a class of the perfect ideals from a class of the complete matrices. From this we give a structure theorem for complete intersections of grade g > 3.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.09a
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• pp.27-30
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• 2001

Flow and transport at fracture intersections, and their effects on network scale transport, are investigated in three-dimensional random fracture networks. Fracture intersection mixing rules complete mixing and streamline routing are defined in terms of fluxes normal to the intersection line between two fractures. By analyzing flow statistics and particle transfer probabilities distributed along fracture intersections, it is shown that for various network structures with power law size distributions of fractures, the choice of intersection mixing rule makes comparatively little difference in the overall simulated solute migration patterns. The occurrence and effects of local flows around an intersection (local flow cells) are emphasized. Transport simulations at fracture intersections indicate that local flow circulations can arise from variability within the hydraulic head distribution along intersections, and from the internal no flow condition along fracture boundaries. These local flow cells act as an effective mechanism to enhance the nondiffusive breakthrough tailing often observed in discrete fracture networks. It is shown that such non-Fickian (anomalous) solute transport can be accounted for by considering only advective transport, in the framework of a continuous time random walk model. To clarify the effect of forest environmental changes (forest type difference and clearcut) on water storage capacity in soil and stream flow, watershed had been investigated.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.569-573
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• 1996

We study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, [I] = 0 in $A_{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, [P] = 0 in $A_{n-i}(R)$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1627-1654
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• 2017

We prove that in the parameter space of M-dimensional Fano complete intersections of index one and codimension two the locus of varieties that are not birationally superrigid has codimension at least ${\frac{1}{2}}(M-9)(M-10)-1$.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.401-415
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• 2020

It is well-known that if char𝕜 = 0, then an Artinian monomial complete intersection quotient 𝕜[x₁, …, x_n]/(x₁^a₁, …, x_n^a_n) has the strong Lefschetz property in the narrow sense, and it is decomposed by the direct sum of irreducible 𝖘𝖑₂-modules. For an Artinian ring A = 𝕜[x₁, x₂, x₃]/(x₁⁶, x₂⁶, x₃⁶), by the Schur-Weyl duality theorem, there exist 56 trivial representations, 70 standard representations, and 20 sign representations inside A. In this paper we find an explicit basis for A, which is compatible with the S₃-module structure.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.595-601
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• 1997

Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.625-634
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• 2024

The thrust of this paper is to extend the notion of Plithogenic vertex domination to the basic operations in Plithogenic product fuzzy graphs (PPFGs). When the graph is a complete PPFG, Plithogenic vertex domination numbers (PVDNs) of its Plithogenic complement and perfect Plithogenic complement are the same, since the connectivities are the same in both the graphs. Since extra edges are added to the graph in the case of perfect Plithogenic complement, the PVDN of perfect Plithogenic complement is always less than or equal to that of Plithogenic complement, when the graph under consideration is an incomplete PPFG. The maximum and minimum values of the PVDN of the intersection or the union of PPFGs depend upon the attribute values given to P-vertices, the number of attribute values and the connectivities in the corresponding PPFGs. The novelty in this study is the investigation of the variations and the relations between PVDNs in the operations of Plithogenic complement, perfect Plithogenic complement, union and intersection of PPFGs.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1485-1526
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• 2017

We show that birational rigidity of Mori fibre spaces is not open in moduli.