• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.261-271
• /
• 2007

The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.529-538
• /
• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• Bulletin of the Korean Chemical Society
• /
• v.27 no.7
• /
• pp.1005-1008
• /
• 2006

The reaction of $AgClO_{4}$ with acyclic potential tridentate N,N,N',N',N''-pentamethyldiethylenetriamine (pmdeta) has given colorless crystals suitable for X-ray crystallography. The crystal structure ($P2_{1}$/n, a = 14.413(1) $\AA$, b = 25.270(2) $\AA$, c = 16.130(1) $\AA$, b = $103.012(1){^{\circ}}$, V = 5723.7(8) A$\AA^{3}$, Z = 4, R = 0.0349) has been solved and refined. Three silver(I) ions connect four pmdeta ligands to produce discrete complex of $[Ag_3(pmdeta)_4](ClO_4)_3$. A pmdeta ligand is bridged to three silver(I) ions, and three other pmdeta ligands are chelated to each silver(I) center in a tridentate mode. Thus, the product is a rare tri-nuclear silver(I) complex with two different chemical environments. $^{13}C$ NMR and $MAS\;^{13}$C NMR indicate that the tri-nuclear silver(I) complex is not rigid in solution. The contact angles and thermal analyses of the complex are measured and discussed.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.455-467
• /
• 2014

In this paper, we consider the additive set-valued functional equation $nf(\sum_{i=1}^{n}x_i)=\sum_{i=1}^{n}f(x_i){\oplus}\sum_{1{\leq}i&lt;j{\leq}n}f(x_i+x_j)$ where $n{\geq}2$ is an integer, and prove the Hyers-Ulam stability of the functional equation.

• Communications of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.39-46
• /
• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1071-1085
• /
• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.419-425
• /
• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.99-103
• /
• 2003

In this note we find the exact Probability distribution of d$\_$n, i/ the outdegree of the node i, in a random recursive tree with n nodes. For i = i$\_$n/ increasing as a linear function on n, we show that d$\_$n/,i$\_$n/ is asymptotically normal.

• Korean Journal of Plant Taxonomy
• /
• v.35 no.2
• /
• pp.99-114
• /
• 2005

Chromosome number, morphological variation and RAPD analysis were investigated to study on the speciation of Indigofera in Korea. Chromosome numbers of I. kirilowii (2n=16) and I. koreana (2n=32) are consistent with the previous reports. In this study tetraploid (2n=32) and hexaploid (2n=48) of I. grandiflora are newly observed. Indigofera grandiflora is distributed around Mt. Kaya area together with I. kirilowii and I. koreana. The former species has the larger sizes in plant height, leaves and flowers than the latter two and shows intermediate form between the two species in hairs on leaves and flowers which are one of the most important taxonomic characters in this group. In the RAPD analysis, I. grandiflora is similar to I. koreana than I. kirilowii but RAPD band patterns revealed difference between tetra- and hexaploid of the species. These results suggested that Korean endemic species of I. grandiflora (2n=16, 32, 48) might has multiple origin through polyploidization and/or hybridization between I. kirilowii (2n=16) and I. koreana (2n=32) around Mt. Kaya area where the latter two grow together.

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.475-491
• /
• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.