• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1215-1229
• /
• 2020

Let D be an integral domain and S a multiplicative subset of D. An ascending chain (I_k)_k∈ℕ of ideals of D is said to be S-stationary if there exist a positive integer n and an s ∈ S such that for each k ≥ n, sI_k ⊆ I_n. As a generalization of domains satisfying ACCP (resp., ACC on ∗-ideals) we define D to satisfy S-ACCP (resp., S-ACC on ∗-ideals) if every ascending chain of principal ideals (resp., ∗-ideals) of D is S-stationary. One of main results of this paper is the Hilbert basis theorem for an integral domain satisfying S-ACCP. Also we investigate the class of such domains D and we generalize some known related results in the literature. Finally some illustrative examples regarding the introduced concepts are given.

• Kyungpook Mathematical Journal
• /
• v.63 no.1
• /
• pp.123-129
• /
• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• Korean Journal of Materials Research
• /
• v.9 no.8
• /
• pp.849-853
• /
• 1999

In the study, superconducting properties of $Bi_2$-x(sub)$LSr_2$Ca(sub)1+x(sub)$LCu_2$O(sub)8+d (x(sub)L=0, 0.05, 0.1, 0.2) films prepared by the LPE method was investigated. The peak decompositions of Sr3d and Ca2p XPS spectra, together with the EPMA results, elucidated the occupancies of Bi, Sr and Ca atoms on the SrO- and Ca-layers. The lattice parameter c monotonically increased with increasing x(sub)L for $0\leq$x(sub)L$\leq$0.2. The superconducting critical temperature T(sub)c showed a maximum value around x(sub)L=0.1. The x(sub)L dependence of the superconducting critical temperature T(sub)c and the lattice parameter c are explained by the changes of the excess oxygens in the BiO-layer. Since distribution and deficiency of the atoms in SrO-layer have influenced on superconducting properties and crystal structure.

• Journal of the Korean Ceramic Society
• /
• v.39 no.9
• /
• pp.813-817
• /
• 2002

Magnetoelectric(ME) laminate composites of $Pb(Mg_{1/3}Nb_{2/3})O_3-PbTiO_3 (PMN-PT)$ and Terfenol-D were prepared by sandwiching single crystals of PMN-PT between Terfenol-D disks. The magnetoelectric voltage coefficient (dE/dH) of the composite was determined to be 10.30 V/cm${\cdot}$Oe, at 1 kHz and under a dc magnetic bias of 0.4 T. The value of dE/dH is ∼80 times higher than either that of naturally occurring magnetoelectrics or artificially-grown magnetoelectric composites. This superior magnetoelectric voltage coefficient is attributed to the high piezoelectric voltage constant as well as the high elastic compliance of PMN-PT single crystal and the large magnetostrictive response of Terfenol-D.

• Korean Chemical Engineering Research
• /
• v.61 no.4
• /
• pp.627-634
• /
• 2023

Graphitic carbon nitride (g-C₃N₄) has attracted considerable attention since its discovery for its catalysis of water splitting to hydrogen and oxygen under visible light irradiation. However, pristine g-C₃N₄ confers only low photocatalytic efficiency and requires surface cocatalysts to reach moderate activity due to a lack of accessible surface active sites. Inspired by the high specific surface area and superior electron transfer of graphene, we developed a strongly coupled binary structure of graphene and g-C₃N₄ aerogel with 3D porous skeleton. The as-prepared 3D structure photocatalysts achieve a high surface area that favors efficient photogenerated charge separation and transfer, enhances the light-harvesting efficiency, and significantly improves the photocatalytic hydrogen evolution rate as well. The photocatalyst performance is observed to be optimized at the ratio 3:7 (g-C₃N₄:GO), leading to photocatalytic H₂ evolution of 16125.1 mmol. g^-1. h^-1 under visible light irradiation, more than 161 times higher than the rate achieved by bulk g-C₃N₄.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.571-594
• /
• 2022

Let D be an integral domain with quotient field K, Pic(D) be the ideal class group of D, and X be an indeterminate. A polynomial overring of D means a subring of K[X] containing D[X]. In this paper, we study almost Dedekind domains which are polynomial overrings of a principal ideal domain D, defined by the intersection of K[X] and rank-one discrete valuation rings with quotient field K(X), and their ideal class groups. Next, let ℤ be the ring of integers, ℚ be the field of rational numbers, and 𝔊f be the set of finitely generated abelian groups (up to isomorphism). As an application, among other things, we show that there exists an overring R of ℤ[X] such that (i) R is a Bezout domain, (ii) R∩ℚ[X] is an almost Dedekind domain, (iii) Pic(R∩ℚ[X]) = $\oplus_{G{\in}G_{f}}$ G, (iv) for each G ∈ 𝔊f, there is a multiplicative subset S of ℤ such that RS ∩ ℚ[X] is a Dedekind domain with Pic(RS ∩ ℚ[X]) = G, and (v) every invertible integral ideal I of R ∩ ℚ[X] can be written uniquely as I = XnQe11···Qekk for some integer n ≥ 0, maximal ideals Qi of R∩ℚ[X], and integers ei ≠ 0. We also completely characterize the almost Dedekind polynomial overrings of ℤ containing Int(ℤ).

• Bulletin of the Korean Chemical Society
• /
• v.30 no.8
• /
• pp.1899-1902
• /
• 2009

• Proceedings of the Korean Institute of Building Construction Conference
• /
• 2017.05a
• /
• pp.165-166
• /
• 2017

Corrosion of reinforcement is the main factors affecting the durability of reinforced concrete in the world which lead to the failure of structures of reinforced concrete buildings. In this research, mixed brucite(Mg(OH)₂) into ordinary portland cement paste in ratio of 5, 10 and 15% as a kind of CO₂ fixation material. Samples were exposed to an accelerated carbonation enslavement of 20% CO₂ concentration, 60% relative humidity, and a temperature of 20℃ until tested at 3d, 7d, 14d and 28d. After 28d CO₂ accelerated curing, in the paste containing MH megnesian calcite was found by XRD and SEM-EDX. Meanwhile, paste containing Mg(OH)₂ exhibit the better pore distribution than ordinary portland cement paste and relatively good compressive strength.

• Korean Journal of Mathematics
• /
• v.28 no.3
• /
• pp.539-554
• /
• 2020

A set {a₁, a₂, …, a_m} of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two elements in the set decreased by one is a perfect square. In this paper, we find a solution of Pellian equations which is constructed by D(-1)-triples and using this result, we prove the extendibility of D(-1)-pair with some conditions.

• Korean Journal of Fisheries and Aquatic Sciences
• /
• v.56 no.3
• /
• pp.331-340
• /
• 2023

To estimate the biological reference points, suitable for fisheries management of sandfish Arctoscopus japonicas in the East Sea of Korea, we simulated the yield-per-recruit (Y/R) from age 0 to 6 (0-2,555 days). The stimulation was based on two instantaneous natural mortality conditions: size-dependent (M_t, d^-1) and constant (M_cons, d^-1); Subsequently, the biological reference points of the two mortality conditions was compared. M_t decreased from 0.0075 d^-1 to 0.0018 d^-1 depending on growth, and M_cons remained constant at 0.0011 d^-1 for all ages. Our Y/R model showed that the maximum yield of M_cons was 14 times higher than that of the M_t. The length at first capture to maximize the harvest at the F_0.1 points of the two natural mortality conditions was L_c,t=10.2 cm (TL) and L_c,cons=17 cm (TL). We concluded that M_t was more suitable for estimating M than M_cons; this is because L_c,t showed minimal difference from the current fishing regulations (11 cm, TL), and M_t reflected more biological characteristics than M_cons. We suggest that 10.2 cm and 0.8 as the suitable length at first capture and corresponding age, respectively for efficient fisheries management of sandfish.