• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.407-418
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• 2019

In this paper, we study conformal transformations between special class of Finsler metrics named C-reducible metrics. This class includes Randers metrics in the form $F={\alpha}+{\beta}$ and Kropina metric in the form $F={\frac{{\alpha}^2}{\beta}}$. We prove that every conformal transformation between locally dually flat Randers metrics must be homothetic and also every conformal transformation between locally dually flat Kropina metrics must be homothetic.

• Korean Journal of Materials Research
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• v.13 no.5
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• pp.292-296
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• 2003

In an attempt to enhance phase transformation and homogenization of Mn-doped $FeSi_2$, mechanical alloying of elemental powders was applied. Cold pressing and sintering in vacuum were carried out to produce a dense microstructure, and then isothermal annealing was employed to induce a phase transformation to the $\beta$-$FeSi_2$semiconductor. Phase transitions in this alloy system during the process were investigated by using XRD, EDS and SEM. As-milled powders after 100 h of milling were shown to be metastable state. As-sintered iron silicides consisted of untransformed mixture of $\alpha$-$Fe_2$$Si_{5}$and $\varepsilon$-FeSi phases. $\beta$-$FeSi_2$phase transformation was induced by subsequent isothermal annealing at $830^{\circ}C$, and near single phase of $\beta$-$FeSi_2$was obtained after 24 h of annealing. Thermoelectric properties in terms of Seebeck coefficient, and electrical conductivity were evaluated and correlated with phase transformation. Seebeck coefficient electrical resistivity and hardness increased with increasing annealing time due to $\beta$ phase transformation.

• Applied Microscopy
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• v.25 no.3
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• pp.90-98
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• 1995

In the Fe-Si system, a mixture of a($Fe_{2}Si_5$) - and ${\epsilon}$(FeSi)-composition powders was sintered and heat-treated subsequently at various temperatures and time to get thermoelectric ${\beta}$-phase($FeSi_2$) compacts. The different transformational sequences depending on the heat treating temperature were found through the investigation into phase transformation and microstructural development. That is, a rapid eutectoid decomposition of ${\alpha}{\to}{\beta}+Si$ occurred together with a accompanying slow reaction between the dispersed Si formed by above decomposition and the preexisted ${\epsilon}$ phase at temperatures below $830^{\circ}C$. The unreacted Si and the micropores formed due to the density change upon the transformation coarsened as heat treating time elapsed. At temperatures above $880^{\circ}C$, however, transformation was proceeded by a peritectoid reaction of ${\alpha}+{\epsilon}{\to}{\beta}$. It took at least 200min. to achieve 90% volume fracion of transformed ${\beta}$ phase, and the growth of micro-pores was also observed in this transformational sequence with prolonged heat treating time.

• Korean Journal of Materials Research
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• v.10 no.9
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• pp.636-641
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• 2000

The effects of Fe and V content on the characteristics of $\beta$ to $\alpha$ phase transformation for Zr-0.8Sn alloys were studied by optical and transmission electron microscopy. With increasing V content, $\beta{\rightarrow}\alpha+\beta$ transformation temperature decreased, thus allowing the width of $\alpha$-lath to be fine air-cooled Zr-0.8Sn-xV alloys. The width of $\alpha$-lath, however, was slightly increased with Fe content. While the $\beta$ to $\alpha$ transformed microstructures of water-quenched Zr-0.8Sn, Zr-0.8Sn-0.1Fe, Zr-0.8Sn-0.2Fe, Zr-0.8Sn-0.4Fe, Zr-0.8Sn-0.1V and Zr-0.8Sn-0.2V were mainly slipped martensite, that of water-quenched Zr-0.8Sn-0.4V was predominantly twinned martensite. The transition of slipped martensite to twinned martensite in Zr-0.8Sn-Xv was thought to be due to the decrease of $M_S$ temperature.

• Proceedings of the KIEE Conference
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• 2001.07c
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• pp.1433-1435
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• 2001

The mechanical and phase transformation of the cold isostatically pressed $\beta$-SiC ceramic were investigated as a function of the sintering temperature. The result of phase analysis revealed 6H, 4H, 3C and phase transformation between 3C and 4H showed over 2000$^{\circ}C$ and the $\beta$ ${\rightarrow}$ $\alpha$ phase transformation was in saturation at 2200$^{\circ}C$. The relative density and the mechanical properties of $\alpha$-SiC ceramic was increased with increased sintering temperature. The flexural strength showed the highest value of 230 MPa at 2200$^{\circ}C$. This reason is because crack was propagated through surface flaw. The fracture toughness showed the highest value of 4.2 $MPa{\cdot}m^{1/2}$ at 2200$^{\circ}C$.

• Horticultural Science & Technology
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• v.18 no.6
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• pp.797-801
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• 2000

The present study was conducted to improve the efficiency of transformation mediated by Agrobacterium tumefaciens in hot pepper. Both regeneration ratio and transformation frequency after the cocultivation with A. tumefaciens were affected by inoculation time and artificial wounding. Transformation frequency was increased over 50% by combining artificial wounding with 120 s of inoculation treatment. Confirmation for the transformation of regenerated shoots was carried out by histochemical ${\beta}$-glucuronidase assay and polymerase chain reaction analysis using npt II primer.

• Mycobiology
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• v.31 no.1
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• pp.42-45
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• 2003

For transformation of Pleurotus ostreatus, two novel vectors, pPhKM1 and pPhKM2, were constructed, using the regulatory sequences of the P. sajor-caju $\beta$-tubulin gene(TUB1) and the ble gene encoding phleomycin binding protein. pPhKM1 contains ble fused to the TUB1 promoter and the Schizophyllum commune GPD terminator. pPhKM2 contains ble fused to the promoter and terminator regions of P. sajor-caju TUB1. To confirm phleomycin-resistance activity, each vector was cotrans-formed with pTRura3-2 into the P. ostreatus homokaryotic $ura^-$ strain. The transforming DNA was stably integrated into the genomic DNA. Subsequently, phleomycin resistance was conferred on wild-type dikaryotic P. ostreatus by transformation with pPhKM1 or pPhKM2. This transformation system generated stable phleomycin-resistant transformants.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Natural Product Sciences
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• v.14 no.4
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• pp.269-273
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• 2008

Microbial transformation of isoxanthohumol (1), a prenylated flavanone from hops, has resulted in the production of a pair of glucosylated derivatives. The structures of these compounds were elucidated to be (2S)-5-methoxy-8-prenylnaringenin 7-O-${\beta}$-D-glucopyranoside (2) and (2R)-5-methoxy-8-prenylnaringenin 7-O-${\beta}$-Dglucopyranoside (3) based on the spectroscopic analyses.