• Korean Journal of Microbiology
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• v.29 no.1
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• pp.69-73
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• 1991

The chromosome of Fusarium species during the vegetatve nuclear divisions in hyphae were observed by use of HCl-Giemsa technique on light microscope. The haploid chromosome number of Fusarium anthophilum 7472 was n=7, n=6 in F. anthophilum 7481 and n=6 in F. oxysporum 7500. The haploid chromosome number was 7 in F. napiforme 6129 and F. napiforme 6144. Those of F. caucasicum F. caucasicum ATCC 18791 and F. aquaeductuum ATCC 15612 were n=5. F. coeruleum ATCC 20088 was n=6, n=8 in F. camptoceras ATCC 16065 and n=7 in F. sambucinum NRRL 13451. From these results and previous papers, it may be concluded that the basic haploid chromosome number of the genus Fusarium is n=4.

• Journal of the Korean Society of Clothing and Textiles
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• v.21 no.4
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• pp.710-717
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• 1997

An investigation made of fabric strength & elongation and the lock stitch seam strength & elongation by stitch density (N1.5; 26 stitches/3 cm, N2.0; 19 stitches/3 cm, N2.5; 14 stitches/3cm) depending on methods of. sample prepariation (angle variations of unseamed sample and overlapping way of seamed sample) It found maximum stitch density that results of the seam strength test was highist in each angle of bias. The results obstained were as follows: 1. As the results of fabric strength and elongation tests as a function of angle of bias, breaking strength were that warp and weft angles (0$^{\circ}$, 90$^{\circ}$) were much higher than bias angles (20$^{\circ}$, 30$^{\circ}$, 45$^{\circ}$, 60$^{\circ}$) . And otherwise breaking elongation were that 45$^{\circ}$ angle of bias were highest and were that the warp & weft way were lower. 2. As the results of the seam strength tests by the stitch density under samples of same angles, the maximum stitch density were those; under 0$^{\circ}$/0$^{\circ}$, 60$^{\circ}$/60$^{\circ}$:F1, F2-N2.0, F3-N1.5, under 20$^{\circ}$/20$^{\circ}$, 30$^{\circ}$/30$^{\circ}$, 45$^{\circ}$/45$^{\circ}$: F1-N2.5, F2-N2.0, F3-N1.5, under 90$^{\circ}$/90$^{\circ}$: F1, F2, F3-N1.5. 3. As the results of the seam strength tests by the stitch density under samples of symmetry angles, the maximum stitch density were those; under 20$^{\circ}$/-20$^{\circ}$, 30$^{\circ}$/-30$^{\circ}$, 60$^{\circ}$/-60$^{\circ}$: F1, F3-N1.5, F2-N2.0, under 45$^{\circ}$/-45$^{\circ}$: F1, F2-N2.0, F3-N1.5.

• YAKHAK HOEJI
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• v.35 no.3
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• pp.231-235
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• 1991

Compounds of the structure of -4,9-dione are known to have an antibacterial activity against Gram-positive bacteria. New kinds of 2-amino-$\alpha$-cyano-$\alpha$-ethoxycarbonyl-niethyl)-1,4-naphthoquino ne was reacted with some alkylamines(methylamine, ethylamine, ethanolarnine, isopropylamine, cyclohexylamine, benzylamine) to yield 2-amino-3-ethoxycarbonyl-N-alkyl-4,9-diones.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.244-248
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• 2012

F-Measure is one of the external measures for evaluating the validity of clustering results. Though it has clear advantages over other widely used external measures such as Purity and Entropy, F-Measure has inherently been less sensitive than other validity measures. This insensitivity owes to the definition of F-Measure that counts only most influential portions. In this research, we present $F_n$-Measure, an external cluster evaluation measure based on F-Measure. $F_n$-Measure is so sensitive that it can detect their difference in the cases that F-Measure cannot detect the difference in clustering results. We compare $F_n$-Measure to F-Measure for a few clustering results and show which measure draws better result based upon homogeneity and completeness.

• Journal of the Mineralogical Society of Korea
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• v.15 no.2
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• pp.95-103
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• 2002

The object of this study was to interpret the ralationship between expandability (% $S_{XRD}$), MacEwan crystallite thickness ( $N_{CSD}$), and mean fundamental particle thickness ( $N_{F}$ ) in illite-semctite mixed layer (I-S), quantitatively. This interpretation was extracted from comparison of two structural models (MacEwan crystallite model and fundamental particle model) of I-S mixed layers. In I-S structure, % $S_{XRD}$, $N_{CSD}$, and $N_{F}$ are not independent parameters but are related to each others by particular geometric relations. % $S_{XRD}$ is dependent on $N_{CSD}$ by short-stack effect, whereas, % $S_{XRD}$ and $N_{F}$ have relation to smectite interlayer number (Ns)=( $N_{F-}$1)/(100%/% $S_{XRD-}$ $N_{F}$ . Therefore, % $S_{XRD}$ and $N_{F}$ should satisfy a specific physical condition, 1< $N_{F}$ <100%/% $S_{XRD}$, because $N_{s}$ is positive. Based on this condition, this study suggested % $S_{XRD}$ vs $N_{F}$ diagram which can be used to interpret % $S_{XRD}$, $N_{F}$ , $N_{S}$ , and ordering, quantitatively. The diagram was examined by XRD data for I-S samples from Ceumseongsan volcanic complex, Korea. I-S samples showed that $N_{F}$ departs from the physical upper-limit ( $N_{F}$ =100%/% $S_{XRD}$) with decrease in % $S_{XRD}$. This phenomenon may happen due to decrease of stacking-capability of fundamental particles with their thickening.g.s with their thickening.g.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.293-299
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• 2005

Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.935-942
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• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.