• Korean Journal of Materials Research
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• v.31 no.12
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• pp.682-689
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• 2021

NbC, HfC, TaC, and their solid solution ceramics have been identified as the best materials for ultrahigh-temperature ceramics. However, their structural stability and elastic properties are mostly unclear. Thus, we investigated structure and elastic properties of (Nb_1-xTa_x)C and (Nb_1-xHf_x)C solid solutions via ab initio calculations. Our calculated results show that the stability of (Nb_1-xTa_x)C and (Nb_1-xHf_x)C increases with the increase of Hf and Ta content, and (Nb_1-xHf_x)C is more stable than (Nb_1-xTa_x)C at the same content of Hf and Ta. The lattice constants decrease with increasing of Hf and Ta content. (Nb_1-xTa_x)C and (Nb_1-xHf_x)C carbides are mechanically stable and brittle. Bulk modulus of (Nb_1-xTa_x)C increases with increasing Ta content. In contrast, bulk modulus of (Nb_1-xHf_x)C decreases with increasing Hf content. Hardness of solid solutions shows the highest values at the (Nb_0.25Ta_0.75)C and (Nb_0.75Hf_0.25)C. In particular, (Nb_0.75Hf_0.25)C shows the highest hardness for the current system. The results indicate that the overall mechanical properties of (Nb_1-xHf_x)C solid solutions are superior to those of (Nb_1-xTa_x)C solid solutions. Therefore, controlling the Hf and Ta element and content of the (Nb_1-xTa_x)C and (Nb_1-xHf_x)C Solid solution is crucial for optimizing the material properties.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.113-124
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• 2005

For a Tychonoff space X, C(X) is a Riesz-space. It is well known that C(X) is order-Cauchy complete if and only if X is a quasi~F space and that if X is a compact space and QF(X) is a minimal quasi-F cover of X, then the order- Cauchy completion of C(X) is isomorphic to C(QF(X)). In this paper, we investigate motivations and historical backgrounds of the definition for quasi-spaces and the construction for minimal quasi-F covers.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.503-507
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• 2006

Let X be a Tychonoff space and ${\sum}(X)$ the set of all the subrings of C(X) that contain $C^*(X)$. For any A(X) in ${\sum}(X)$ suppose $_{{\upsilon}A}X$ is the largest subspace of ${\beta}X$ containing X to which each function in A(X) can be extended continuously. Let us write A(X) ~ B(X) if and only if $_{{\upsilon}A}X=_{{\upsilon}B}X$, thereby defining an equivalence relation on ${\sum}(X)$. We have shown that an A(X) in ${\sum}(X)$ is isomorphic to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence class if and only if there exists a subspace T of ${\beta}X$ with the property that A(X)={$f{\in}C(X):f^*(p)$ is real for each $p$ in T}, $f^*$ being the unique continuous extension of $f$ in C(X) from ${\beta}X$ to $\mathbb{R}^*$, the one point compactification of $\mathbb{R}$. As a consequence it follows that if X is a realcompact space in which every $C^*$-embedded subset is closed, then C(X) is never isomorphic to any A(X) in ${\sum}(X)$ without being equal to it.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.65-70
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• 2001

We obtained the sum of two curvature ($C_x+C_y$) in toric lens which two toroidal surface is the right angle each other. $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$ and the sum of two curvature ($C_a+C_b$) in toric lens about the cross angle. $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$ and claculated the parameter S, C, ${\theta}$ of a combination power in toric lens of the cross angle including surface curvature ($C_x$, $C_y$) values. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1009-1018
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• 1997

Observing that for any $\beta_c$-Wallman functor $A$ and any Tychonoff space X, there is a cover $(C_1(A(X), X), c_1)$ of X such that X is $A$-disconnected if and only if $c_1 : C_1(A(X), X) \longrightarrow X$ is a homeomorphism, we show that every Tychonoff space has the minimal $A$-disconnected cover. We also show that if X is weakly Lindelof or locally compact zero-dimensional space, then the minimal G-disconnected (equivalently, cloz)-cover is given by the space $C_1(A(X), X)$ which is a dense subspace of $E_cc(\betaX)$.

• Journal of Sericultural and Entomological Science
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• v.36 no.1
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• pp.8-25
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• 1994

The study was conducted to obtain the genetic information on heterosis and combining ability of the quantitative characters for F1 hybrid breeding in silkworms. Six parental varieties and each set of 30 diallel crosses in F1's were used as materials, and bred on the randomized complete block design with three replications. Fourteen characters were observed with the twenty samples in each tray. The data were analyzed for (1) heterosis and combining ability in F1 hybrid. The heterosis in the weight and the length of cocoon showed positively high at 24.51%, and 23.4%, respectively and the weight of the whole cocoon as well as the weight of the whole cocoon layer showed a siginificant heterosis ranging from 15.56% to 15.71% and from 17.14% to 19.01%, but the fifth and the total instar period showed negative heterosis. It was found that the combination between, C70XRomogua and N9 X Romogua showed highly a negative heterosis on the fifth instar period and for the cocoon weight. The female of N9+Sansuian and the male of Romogua X Sansurian have a high heterosis effect, on the cocoon shell weight, and Sansurian X Romogua(reciprocal) on the length and the weight of cocoon filament with no regard to sexuality. The significant maternal and cytoplasmic effect on heterosis of the cocoon weight and the cocoon shell weight were observed with the combinations, N9 X C5, N63 X C70 and on the length of the cocoon filament with the combinations, Sansurian X N63, Sansurian X C5, Sansurian X C70 and N9 X C70, N63 X C70 on the weight of cocoon filament. As mean squared of GCA, SCA and RCA were significant with these combining ability for all characters resulted from additive and non-additive altogether and there is a significant difference between reciprocals. Sansurian showed a negative GCA effect on the fifth and total larval duration, but the higher positive GCA effects took places with varieties N9 and C5 on the length, width, weight of cocoon, cocoon shell weight, percentage of cocoon shell weight, length and weight of cocoon filament, percentage of raw-silk with no regard to both generations and silkworm sexuality. The values of SCA between the cross combinations varied generation-wise and sex-wise. It was shown that SCA value for the fifth instar period was highly negative for Sansurian X C70, Romogua X C70, Sansurian X C5, Romogua X C5, but it was positive effect on the cocoon weight, cocoon shell weight with N9 X C5, and C70 X Sansurian, on the length of cocoon filament with N9 X C5, Romogua X Sansurian on the weight of cocoon filament between Romogua and N63 and on the percentage of raw-silk between the combination of Sansurian X Romoga.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1047-1059
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• 1999

Let $C(X)(C_{K}(X))$ denote the hyperspace of all nonempty closed connected subsets (subcontinua) of a locally compact Haus-dorff space X with the Fell topology. We prove that the following statements are equivalent: (1) X is locally connected. (2) C(X) is locally connected,. (3) C(X) is locally connected at each $E{\in}C_{k}(X).(4) C_{k}(X)$ is locally connected.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.913-919
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• 2014

We investigate the relationships between the space X and the hyperspaces concerning admissibility and connectedness im kleinen. The following results are obtained: Let X be a Hausdorff continuum, and let A, $B{\in}C(X)$ with $A{\subset}B$. (1) If X is c.i.k. at A, then X is c.i.k. at B if and only if B is admissible. (2) If A is admissible and C(X) is c.i.k. at A, then for each open set U containing A there is a continuum K and a neighborhood V of A such that $V{\subset}IntK{\subset}K{\subset}U$. (3) If for each open subset U of X containing A, there is a continuum B in C(X) such that $A{\subset}B{\subset}U$ and X is c.i.k. at B, then X is c.i.k. at A. (4) If X is not c.i.k. at a point x of X, then there is an open set U containing x and there is a sequence $\{S_i\}^{\infty}_{i=1}$ of components of $\bar{U}$ such that $S_i{\longrightarrow}S$ where S is a nondegenerate continuum containing the point x and $S_i{\cap}S={\emptyset}$ for each i = 1, 2, ${\cdots}$.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.449-452
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• 1998

We have studied the oxidatio nrte of $Si_{1-x}Ge_{x}$ epitaxial layer grown by MBE(molecular beam epitaxy). Oxidation were performed at 700.deg. C, 800.deg. C, 900.deg. C, and 1000.deg. C. After the oxidation, the results of AES(auger electron spectroscopy) showed that Ge was completely rejected out of the oxide and pile up at $SiO_{2}/$Si_{1-x}Ge_{x}$ interface. It is shown that the presence of Ge at the $SiO_{2}$/$Si_{1-x}Ge_{x}$ interface changes the dry oxidation rate. The dry oxidation rate was equal to that of pure Si regardless of Ge mole fraction at 700.deg. C and 800.deg.C, while it was decreased at both 900.deg. C and 1000.deg.C as the Ge mole fraction was increased. The ry oxidation rates were reduced for heavy Ge concentration, and large oxidation time. In the parabolic growth region of $Si_{1-x}Ge_{x}$ oxidation, The parabolic rate constant are decreased due to the presence of Ge-rich layer. After the longer oxidation at the 1000.deg.C, AES showed that Ge peak distribution at the $SiO_{2}$/$Si_{1-x}Ge_{x}$ interface reduced by interdiffusion of silicon and germanium.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.299-302
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• 1994

Throughout this paper, let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$ /(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued (resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.(omitted)