• Journal of the Korean Chemical Society
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• v.37 no.8
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• pp.765-772
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• 1993

Two-dimensional potassium tetratitanate ($K_2Ti_4O_9$) and three-dimensional potassium hexatitanate ($K_2Ti_6O_{13}$) fibers have been prepared by the combined method consisting of the flux melting (1150$^{\circ}C$)-slow cooling (cooling rate = 5$^{\circ}C$/h) process from the starting raw materials of $K_2CO_3$, and $TiO_2$ with the flux of $K_2MoO_4$. It was found that the fiber growth reaction is strongly dependent upon the mole ratio of flux (F) to raw material (R), which is 7 : 3 (F : R) as for the optimum growth condition. Relatively long fibers (average length ${\thickapprox}$ 4 mm) with a mixture of $K_2Ti_4O_9$ (major) and $K_2Ti_6O_{13}$ (minor) could be obtained when the reaction was carried out for the $K_2MoO_4-$K_2O{\cdot}4TiO_2$ (F : R = 7 : 3) system, but for the $K_2$MoO_4$-$K_2O{\cdot}6TiO_2$ (F : R = 7: 3) one, only the short fibers with ${\thickapprox}$ 2 mm long could be grown as the mixed phase of $K_2Ti_6O_{13}$ and $K_2Ti_4O_9$.

• Korean Journal of Medicinal Crop Science
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• v.13 no.3
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• pp.118-121
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• 2005

Karyotypes were established in seven Angelica species cultivated in Korea. The somatic chromosome numbers were 2n = 2x = 22 with the basic number of x = 11 in all Angelica plants examined. Their metaphase chromosomes ranged from 3.56 ${\mu}M$. to 8.91 x. in length. Distinctive Karyotypes were found in two species, A. tenuissima with all metacentries, K(2n) = 2x = 22m, and A. genuflexa with all subtelocentrics, K(2n) = 2x = 22st. Karyotype formulas of A. gigas, A. acutiloha, A. sinensis, A. decursiva and A. dahurica were K(2n) = 2x = 20m + 2sm, K(2n) = 2x = 12m + 10sm, K(2n) = 2x = 16m + 6sm, K(2n) = 2x = 18m + 4sm and K(2n) = 2x = 10m + 10sm + 2st, respectively. Cytological data showed that chromosomal polymorphisms within species were observed in Angelica plants compare to other regions.

• Journal of the Korean Chemical Society
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• v.39 no.1
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• pp.7-13
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• 1995

The crystal sructures of $X(Ca_{46}Al_{92}Si_{100}O_{384})$ and $Ca_{32}K_{28}-X(Ca_{32}K_{28}Al_{92}Si_{100}O_{384})$ dehydrated at $360^{\circ}C$ and $2{\times}10^{-6}$ Torr have been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd3 at $21(1)^{\circ}C.$ Their structures were refined to the final error indices, R_1=0.096,\;and\;R_2=0.068$ with 166 reflections, and R_1=0.078\;and\;R_2=0.056$ with 130 reflections, respectively, for which I > $3\sigma(I).$ In dehydrated $Ca_{48}-X,\;Ca^{2+}$ ions are located at two different sites opf high occupancies. Sixteen $Ca^{2+}$ ions are located at site I, the centers of the double six rings $(Ca(1)-O(3)=2.51(2)\AA$ and thirty $Ca^{2+}$ ions are located at site II, the six-membered ring faces of sodalite units in the supercage. Latter $Ca^{2+}$ ions are recessed $0.44\AA$ into the supercage from the three O(2) oxygen plane (Ca(2)-O(2)= $2.24(2)\AA$ and $O(2)-Ca(2)-O(2)=119(l)^{\circ}).$ In the structure of $Ca_{32}K_{28}-X$, all $Ca^{2+}$ ions and $K^+$ ions are located at the four different crystallographic sites: 16 $Ca^{2+}$ ions are located in the centers of the double six rings, another sixteen $Ca^{2+}$ ions and sixteen $K^+$ ions are located at the site II in the supercage. These $Ca^{2+}$ ions adn $K^+$ ions are recessed $0.56\AA$ and $1.54\AA$, respectively, into the supercage from their three O(2) oxygen planes $(Ca(2)-O(2)=2.29(2)\AA$, $O(2)-Ca(2)-O(2)=119(1)^{\circ}$, $K(1)-O(2)=2.59(2)\AA$, and $O(2)-K(1)-O(2)=99.2(8)^{\circ}).$ Twelve $K^+$ ions lie at the site III, twofold axis of edge of the four-membered ring ladders inside the supercage $(K(2)-O(4)=3.11(6)\AA$ and $O(1)-K(2)-O(1)=128(2)^{\circ}).$

• Applied Chemistry for Engineering
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• v.5 no.3
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• pp.478-500
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• 1994

The preparation of potassium hexatitanate whisker by flux method was investigated. In this study, 8 types synthesis of flux such as $V_2O_5$, $Bi_2O_3$, $B_2O_3$, $Pb_3O_4$, KCl, $K_4P_2O_7$, $K_2WO_4$ and $K_2MoO_4$ were tested to find a suitable flux for the synthesis of potassium hexatitanate whisker. Effects of various reaction variables such as reaction temperature, time, $TiO_2$ mole ratio to $K_2CO_3$, flux mole ratio to the mixture of $K_2CO_3$ and $TiO_2$, and slow-cooling treatment on the crystallization of potassium hexatitanate whisker were investigated. $K_2MoO_4$ and $K_2WO_4$ were better flux than others tested for the synthesis of potassium hexatitanate. In the presence of $K_2MoO_4$ or $K_2WO_4$ flux, the optimum condition for the synthesis of potassium hexatitanate whisker was that reaction temperature of $1000{\sim}1100^{\circ}C$, reaction time of 5 hours, $TiO_2$ mole ratio to $K_2CO_3$ of 6.0, and flux mole ratio to mixture ($K_2O+nTiO_2$) of 4.0. Slow-cooling treatment showed good effect on the growth of long fibrous potassium hexatitanate.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• The Korean Journal of Mycology
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• v.19 no.1
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• pp.66-73
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• 1991

Among 110 isolates of actinomycetes isolated from ginseng pathogen-suppressive soils, the three actinomycetes showing the effective controls to Fusarium solani or Cylindrocarpon destruc­tans causing ginseng root rots were identified according to their morphological, cultural and physio­logical characteristics on various culture media. Spore chains of K 6-2, S 2-1 and Y 2-2 were Spira (S), Retinaculum-apertum (RA) and Rectus-flexibilis (RF), respectively. Spore surfaces of K 6-2 were spiny, whereas S 2-1 and Y 2-2 were all smooth. Aerial mass colors of 3 isolates were gray series. As a result of various tests, they were identified as Streptomyces variabilis, Streptomyces virgi­niae and Streptomyces griseo/us, respectively.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04a
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• pp.697-699
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• 2002

임베딩은 어떤 연결망이 다른 연결망 구조에 포함 흑은 어떻게 연관되어 있는지를 알아보기 위해 어떤 특정한 연결망을 다른 연결망에 사상하는 것으로, 특정한 연결망에서 사용하던 여러 가지 알고리즘을 다른 연결망에서 효율적으로 이용할 수 있도록 한다. 본 논문에서는 2$^{2n-k}$ $\times$2$^{k}$ 토러스를 HCN(n,n)에 연장율 3에 임베딩 가능함을 보인다.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.591-603
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• 2006

For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.245-249
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• 2010

We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.