• Journal of the Korean Ceramic Society
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• v.25 no.5
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• pp.502-508
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• 1988

The $\alpha$ to $\beta$ phase transformation of $\alpha$-Si3N4 whisker and related microstructural changes have been investigated. When only $\alpha$-Si3N4 whisker was heat treated in the range 1650~175$0^{\circ}C$, the $\alpha$ to $\beta$ phase transformation occured. In this case, it eas suggested that the oxygen content in $\alpha$-Si3N4 whisker affected the transformation behavior. Although $\alpha$-Si3N4 whisker with Si was heat treated under the same condition, however, the variation of $\beta$- fraction had a similar tendency with heat treating time. Therfore, it was considered that the oxygen content in $\alpha$-Si3N4 whisker affected the transformation behavior dominently rather than the content of added Si. The added $\beta$ phase did not affect the transformation behaviro of $\alpha$-Si3N4 whisker.

• Journal of the Korean Ceramic Society
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• v.34 no.9
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• pp.957-962
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• 1997

Dicalcium silicate has many polymorphs according to temperature. $\beta$-dicalcium silicate which exists in cement is stabilized by minor components drived from raw materials regardless of temperature, such as high temperature and room temperature. K2O, SO3 and B2O3 are effective stabilizers for $\beta$-dicalcium silicate at room temperature. B2O3 was the most effective stabilizer. Transformation from $\beta$ to ${\gamma}$ phase causes dicalcium silicate to change volume, resulting in dusting phenomenon. When B2O3 was used the phase transformation is the least than any other stabilizers. In addition, the starting temperature of quenching influences phases transformation : low temperature of quenching presented much phase transformation and decreased size of parameter of $\beta$-dicalcium silicate.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.591-599
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• 2009

For given ${\alpha},{\omega}\;{\in}\;{\mathbb{R}}$ and ${\beta}$ > 1, let $T_{{\beta},{\alpha},{\omega}}$ be the skew-product transformation on the torus, [0, 1) ${\times}$ [0, 1) defined by (x, y) ${\longmapsto}\;({\beta}x,y+{\alpha}x+{\omega})$ (mod 1). In this paper, we give a criterion of ergodicity and weakly mixing for the transformation $T_{{\beta},{\alpha},{\omega}}$ when the natural extension of the given ${\beta}$-transformation can be viewed as a generalized baker's transformation, i.e., they flatten and stretch and then cut and stack a two-dimensional domain. This is a generalization of theorems in [10].

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.867-879
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• 2012

For ${\beta}$ > 1, let $T_{\beta}$ : [0, 1] ${\rightarrow}$ [0, 1) be the ${\beta}$-transformation. We consider an invariant $T_{\beta}$-orbit closure contained in a closed interval with diameter 1/${\beta}$, then define a function ${\Xi}({\alpha},{\beta})$ by the supremum such $T_{\beta}$-orbit with frequency ${\alpha}$ in base ${\beta}$, i.e., the maximum value in $T_{\beta}$-orbit closure. This paper effectively determines the maximal domain of ${\Xi}$, and explicitly specifies all possible minimal intervals containing $T_{\beta}$-orbits.

• The Korean Journal of Ceramics
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• v.3 no.3
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• pp.208-212
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• 1997

Shear-induced phase transformation behavior of chemically stabilized $\beta$-cristobalite was studied by the fiber push-out technique. To obtain the critical grain size for phase transformation, the hot-pressed polycrystalline $\beta$-cristobalite, which was used as the interphase between fiber and matrix, was annealed at $1300^{\circ}C$ for 10h. Two types of fibers, mullite and sapphire fiber, were used in this study. Debonding between mullite fiber and cristobalite interphase occurred at a critical load of 230 MPa. Static friction and fiber sliding were continuously followed by debonding. Shear-induced transformation induced cracks in the cristobalite interphase at the debonding stage. In the case of the sapphire fiber, the debonding occurred at a lower load of 180 MPa due to the residual stress in the interface caused by the difference in thermal expansion coefficients between the fiber and the cristobalite interphase. The load was insufficient for shear-induced phase transformation.

• The Korean Journal of Mycology
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• v.17 no.1
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• pp.27-30
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• 1989

F. velutipes Leu 2 gene (${\beta}-isopropylmalate$ dehydrogenase gene) was used for transformation of P. florida leucine requiring auxotrophic mutant P101. Transformation frequency was very low but the transformed colony can grow on minimal medium very slowly. Transformation was identified by Southern hybridization and reverse transformation into E. coli using chromosome DNA isolated from transformed P. florida.

• Korean Journal of Materials Research
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• v.12 no.5
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• pp.375-381
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• 2002

N-type ${\beta}-FeSi_2$ with a nominal composition of $Fe_{0.98}Co_{0.02}Si_2$ powders has been produced by mechanical alloying process and consolidated by vacuum hot pressing. As-milled powders were of metastable state and fully transformed to ${\beta}-FeSi_2$ phase by subsequent isothermal annealing. However, as-consolidated $Fe_{0.98}Co_{0.02}Si_2$ consisted of untransformed mixture of ${\alpha}-Fe_2Si_ 5$ and $\varepsilon$-FeSi phases. Isothermal annealing has been carried out to induce the transformation to a thermoelectric semiconducting ${\beta}-FeSi_2$ phase. The transformation behavior of ${\beta}-FeSi_2$ was investigated by utilizing DTA, a modified TGA under magnetic field, SEM, and XRD analyses. Isothermal annealing at $830^{\circ}C$ in vacuum led to the thermoelectric semiconducting ${\beta}-FeSi_2$ phase transformation, but some residual metallic $\alpha$ and $\varepsilon$ phases were unavoidable even after prolonged annealing. Thermoelectric properties were remarkably improved by isothermal annealing due to the transformation from metallic $\alpha$ and $\varepsilon$ phases to semiconducting phases.

• The Korean Journal of Ceramics
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• v.3 no.2
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• pp.116-123
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• 1997

A chemically stabilized $\beta$-cristobalite, which is stabilized by stuffing cations of $Ca^{2+}$ and $Al^{3+}$, was prepared by a solution-polymerization route employing Pechini resin or PVA solution as a polymeric carrier. The polymeric carrier affected the crystallization temperature, morphology of calicined powder, and particle size distribution. In case of the polyvinyl alcohol (PVA) solution process, a fine $\beta$-cristobalite powder with a narrow particle size distribution (average particle size : 0.3$\mu\textrm{m}$) and a BET specific surface area of 72 $\m^2$/g was prepared by an attrition-milling for 1 h after calcination at 110$0^{\circ}C$ for 1h. Wider particle size distribution and higher specific surface area were observed for the $\beta$-cristobalite powder derived from Pechini resin. The cubie(P1-to-tetraganalb) phase transformation in polynystalline $\beta$-cristobalite was induced at approximately 18$0^{\circ}C$. Like other materials showing transformation toughening, a critical size effect controlled the $\beta$-to-$\alpha$ transformation. Densifed cristobalite sample had some cracks in its internal texture after annealing. The cracks, occurred spontaneoulsy on cooling, were observed in the sample with an average grain sizes of 4.0 $\mu\textrm{m}$ or above. In case of the sintered cristobalite having a composition of CaO.$2Al_2O_3$.40SiO$_2$, small amount of amorphous phase and slow grain growth during annealing were observed. Shear stress-induced transformation was also observed in ground specimen. Cristobalite having a composition of CaO.2Al2O3.80SiO2 showed a more sensitive response to shear stress than the CaO.$2Al_2O_3$.40SiO$_2$ type cristobalite. Shear-induced transformation resulted in an increase of volume about 13% in $\alpha$-cristobalite phase on annealing for above 10 h in the case of the former composition.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• Korean Journal of Materials Research
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• v.11 no.12
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• pp.1068-1073
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• 2001

An n-type iron$silicide(Fe_{0.98}Co_{0.02}Si_2)$has been produced by mechanical alloying process and consolidated by vacuum hot pressing. Although as-milled powders after 120 hours of milling did not show an alloying progress,${\beta}-FeSi_2$phase transformation was induced by isothermal annealing at$830{\circ}C$for 1 hour, and the fully transformed${\beta}-FeSi_2$phase was obtained after 4 hours of annealing. Near fully dense specimen was obtained after vacuum hot pressing at$ 1100{\circ}C$with a stress of 60MPa. However, as-consolidated iron silicides were consisted of untransformed mixture of ${\Alpha}-Fe_2Si_5$and ${\varepsilon-FeSi$phases. Thus, isothermal annealing has been carried out to induce the transformation to a thermoelectric semiconducting${\beta}-FeSi_2$phase. The condition for${\beta}-FeSi_2$transformation was investigated by utilizing DTA, SEM, and XRD analysis. The phase transformation was shown to be taken place by a vacuum isothermal annealing at$830{\circ}C$and the transformation behaviour was investigated as a function of annealing time. The mechanical properties of${\beta}-FeSi_2$materials before and after isothermal annealing were characterized in this study.