• Bulletin of the Korean Chemical Society
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• v.11 no.3
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• pp.235-238
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• 1990

Complexes of the type[Co(T)(L-pro)], where T is the quadridentate $N_2O_2$-type ligand, N,N'-dimethylethylenediamine-N,N'-diacetate or N,N'-dimethylethylenediamine-N,N'-di-$\alpha$-butyrate, have been prepared. The complexes were separated into the two stereoisomers, $\Delta$-s-cis-[Co(T)(L-pro)] and $\Lambda$-s-cis-[Co(T)(L-pro)]. They were characterized by their proton magnetic resonance, absorption and circular dichroism spectra, elemental analyses.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.261-271
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• 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 $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.445-506
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the s-th power of the positive divisors of N and ${\sigma}_{s,r}(N;m)={\sum_{d{\mid}N\\d{\equiv}r\;mod\;m}}\;d^s$ with $N,m,r,s,d{\in}\mathbb{Z}$, $d,s$ > 0 and $r{\geq}0$. In a celebrated paper [33], Ramanuja proved $\sum_{k=1}^{N-1}{\sigma}_1(k){\sigma}_1(N-k)=\frac{5}{12}{\sigma}_3(N)+\frac{1}{12}{\sigma}_1(N)-\frac{6}{12}N{\sigma}_1(N)$ using elementary arguments. The coefficients' relation in this identity ($\frac{5}{12}+\frac{1}{12}-\frac{6}{12}=0$) motivated us to write this article. In this article, we found the convolution sums $\sum_{k<N/m}{\sigma}_{1,i}(dk;2){\sigma}_{1,j}(N-mk;2)$ for odd and even divisor functions with $i,j=0,1$, $m=1,2,4$, and $d{\mid}m$. If N is an odd positive integer, $i,j=0,1$, $m=1,2,4$, $s=0,1,2$, and $d{\mid}m{\mid}2^s$, then there exist $u,a,b,c{\in}\mathbb{Z}$ satisfying $\sum_{k& lt;2^sN/m}{\sigma}_{1,i}(dk;2){\sigma}_{1,j}(2^sN-mk;2)=\frac{1}{u}[a{\sigma}_3(N)+bN{\sigma}_1(N)+c{\sigma}_1(N)]$ with $a+b+c=0$ and ($u,a,b,c$) = 1(Theorem 1.1). We also give an elementary problem (O) and solve special cases of them in (O) (Corollary 3.27).

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.213-225
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• 2023

For every n ≥ 2, let ℝⁿ_‖·‖ be Rn with a norm ‖·‖ such that its unit ball has finitely many extreme points more than 2n. We devote to the description of the sets of extreme and exposed points of the closed unit balls of 𝓛(²ℝⁿ_‖·‖) and 𝓛_𝒮(²ℝⁿ_‖·‖), where 𝓛(²ℝⁿ_‖·‖) is the space of bilinear forms on ℝⁿ_‖·‖, and 𝓛_𝒮(²ℝⁿ_‖·‖) is the subspace of 𝓛(²ℝⁿ_‖·‖) consisting of symmetric bilinear forms. Let 𝓕 = 𝓛(²ℝⁿ_‖·‖) or 𝓛_𝒮(²ℝⁿ_‖·‖). First we classify the extreme and exposed points of the closed unit ball of 𝓕. We also show that every extreme point of the closed unit ball of 𝓕 is exposed. It is shown that ext B_{𝓛𝒮(²ℝⁿ‖·‖)} = ext B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖) and exp B_{𝓛𝒮(²ℝⁿ‖·‖)} = exp B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖), which expand some results of [18, 23, 28, 29, 35, 38, 40, 41, 43].

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.

• Bulletin of the Korean Chemical Society
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• v.26 no.8
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• pp.1190-1196
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• 2005

Halopyrroles, N-substituted 2-halopyrroles were prepared by halogenation of N-substituted pyrroles with NBS, NCS, or surfuryl chloride. N-Substituted 3-halopyrroles were synthesized by acid-catalyzed thermal and photochemical isomerization reactions of N-substituted 2-halopyrroles. Both the thermal and photochemical reactions were acid-catalyzed. For the acid-catalyzed isomerization, a mechanism of [1,3] bromine shift followed by deprotonation is operated. For the acid-catalyzed photoisomerization, an excited triplet state of 2-protonated N-benzyl-2-halopyrrole produces an intermediate N-substituted pyrrole complex with halonium ion which is equilibrated with N-substituted pyrrole plus halonium ion, and then the halonium ion newly adds to 3-position of N-substituted pyrrole followed by deprotonation to afford N-benzyl-3-halopyrrole.

• Nuclear Engineering and Technology
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• v.18 no.2
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• pp.92-96
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• 1986

The $^{93}Nb(n,n\alpha)^{89m}Y$, $^{93}Nb(n,{\alpha})^{90m}Y$ and $^{93}Nb(n,2n)^{92m}Nb$ cross sections at a neutron energy of 14.6 MeV have been measured relative to the $^{27}Al(n,p)^{27}Mg$ and $^{27}Al(n,{\alpha})^{24}Na$ cross sections. A small accelerator utilizing $T(D,n)^4He$ reaction was used as a neutron source and the neutron energy spread is about 0.4MeV at the sample. All induced activities were measured with a 70cc HPGe detector in the same geometry.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.967-986
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• 2017

We give the necessary condition for an operator defined on a cartesian product of $c_0(\mathcal{X})$ spaces to be summing or dominated and we show that for the multiplication operators this condition is also sufficient. By using these results, we show that ${\Pi}_s(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_s(l^m_2{\mid}m{\in}\mathbb{N})$ for s > 2 or a copy of $1_s(l^m_1{\mid}{\in}\mathbb{N})$, for any $l{\leq}S$ < ${\infty}$. Also ${\Delta}_{s_1,{\ldots},s_n}(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}$ if ${\upsilon}_n(s_1,{\ldots},s_n){\leq}2$ or a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}(l^m_2{\mid}m{\in}\mathbb{N})$ if 2 < ${\upsilon}_n(s_1,{\ldots},s_n)$, where ${\frac{1}{{\upsilon}_n(s_1,{\ldots},s_n})}={\frac{1}{s_1}}+{\cdots}+{\frac{1}{s_n}}$. We find also the necessary and sufficient conditions for bilinear operators induced by some method of summability to be 1-summing or 2-dominated.

• Tribology and Lubricants
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• v.4 no.2
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• pp.36-43
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• 1988

Titanium carbide(TiC) and titanium nitride(TiN) flims were deposited on $Si_3N_4$-TiC composite cutting tools by chemical vapor deposition(CVD) using $TiCl_4-CH_4-H_2$ and $TiCl_4-H_2-N_2$ gas mixtures, respectively. The nonmetal to metal ratio of deposit increases with increasing $m_{C/Ti}$(mole ratio of CH$_4$ to TiCl$_4$ in the input) for TiC coatings and $m_{N/Ti}$(mole ratio of N$_2$ to TiCl$_4$ in the input) for TiN coatings. The nearly stoiahiometric films could be obtained under the deposition condition of $m_{C/Ti}$ between 1.15 and 1.61 for TiC, and that of $m_{N/Ti}$ between 25 and 28 for TiN. Also maximum microhardness of the coatings can be obtained in these ranges. The interfacial region of TiC coatings on $Si_3N_4$-TiC ceramics is wider than that of TiN coatings according to Auger depth profile analysis, which indicates good interfacial bonding for TiC. Experimental results show that TiC coatings have an randomly equiaxed structure and Columnar structure with(220) preferred orientation can be obtained for TiN coatings. And, multilayer coatings have a dense and equiaxed structure.

• Korean Journal of Plant Taxonomy
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• v.39 no.1
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• pp.42-47
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• 2009

In this study, the somatic chromosome of 14 taxa of Korean Galium L. were investigated. Among them were a few taxa for which the somatic chromosome number was determined for the first time. The somatic chromosome numbers of Korean Galium L. were 2n = 22, 24, 44, 48, 66, 72, 77, 88 and so basic chromosome numbers were x = 11 or 12. Those taxa having the basic chromosome number x = 11 showed polyploidy, including diploid, tetraploid, heptaploid, and octoploid. Tetraploid and hexaploid can be observed in those taxa with the basic number x = 12. The eleven taxa reported 11 for the first time are G. spurium var. echinospermon (Wallr.) Hayek (2n = 44), G. gracilens (A. Gray) Makino (2n = 22), G. pogonanthum Franch. & Sav. (2n = 22, 44), G. trachyspermum A. Gray (2n = 22, 44), G. japonicum (Maxim.) Makino & Nakai (2n = 77), G. trifloriforme Kom. (2n = 44), G. dahuricum Turcz. var. dahuricum (2n = 48, 72), G. dahuricum var. tokyoense (Makino) Cufod. (2n = 22), G. kinuta Nakai & Hara (2n=66), G. verum var. trachycarpum for. nikkoense (Nakai) Ohwi (2n = 44), G. verum var. asiaticum for. pusillum (Nakai) M. Park (2n = 44). The taxa with the same chromosome numbers as previously reported ones were G. boreale L. (2n=22) and G. verum var. asiaticum Nakai for. asiaticum (2n = 44). The chromosome number of G. trifidum L. (2n = 22) was different from the previous report. Two infraspecific taxa of G. dahuricum showed differences in their basic chromosome numbers (x = 11 for G. dahuricum Turcz. var. dahuricum and x = 12 for var. tokyoense (Makino) Cufod. The somatic chromosome number for G. dahuricum Turcz. var. dahuricum was found to be 2n = 48 (tetraploid) or 72 (hexaploid), while that of G. dahuricum var. tokyoense (Makino) Cufod. was found to be 2n = 22 (diploid). Therefore, basic chromosome numbers for members of the genus Galium can be used as valuable characters in delimiting infrageneric sections and investigating interspecific relationships.