• 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].

• 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.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.271-289
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• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

• 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.

• 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.

• Bulletin of the Korean Chemical Society
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• v.13 no.2
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• pp.184-187
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• 1992

Regeneration methods of oximes, hydrazones, and N,N-dimethylhydrazones to the related carbonyl compounds were effected using various dicarbonyl compounds which are activated with electron withdrawing substituents such as trifluoromethylated $\beta-diketones$, $\beta-acylpyruvates$, and $\alpha-diketones$ via an equilibrium exchange reaction. The chemical transformations of the dicarbonyl compounds in the exchange reaction were investigated by various spectroscopic methods.

• Journal of the Korean Society for Heat Treatment
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• v.23 no.5
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• pp.233-238
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• 2010

The phase transformations and the shape memory effect in In-rich Pb alloys and In rich-Sn alloys have been studied by means of X-ray diffractometry supplemented by metallographic observations. The alloys containing 12~15 at.%Pb transform from the ${\alpha}_2$ (fct) phase to the ${\alpha}_1$ (fct) phase by way of an intermediate phase (m phase) on cooling. The results of X-ray diffraction show that the metastable intermediate phase is observed both on cooling and heating, and has a face-centered orthorhombic (fco) structure. It is concluded that the ${\alpha}_1{\rightleftarrows}{\alpha}_2$ transformation is expressed by the ${\alpha}_1{\rightleftarrows}m{\rightleftarrows}{\alpha}_2$ transformation both on usual cooling and heating with the rate more than $8{\times}10^{-3}$ K/s. The $m{\rightleftarrows}{\alpha}_2$ transformation takes place with a mechanism involving macroscopic shear and are of diffusionless (martensitic) type. The temperature hysteresis in the two transformations is 10~13 K between the heating and cooling transformations. The alloys containing 0~11 at.%Sn are -phase solid solutions with a face centered tetragonal structure (c/a > 1) at room temperature, the axial ratio increasing continuously with tin content. The In-(11~15) at.%Sn alloys are mixtures of ${\alpha}$ and ${\beta}$ phases, the ${\beta}$ phase having a f. c. tetragonal structure (c/a < 1). The alloys containing more than 15 at.%Sn are ${\beta}$-phase solid solutions. The In-(12.9~15.0) at.%Sn alloys show a shape memory effect only when quenched to the temperature of liquid nitrogen, although their effect becomes weak and finally disappears after keeping at room temperature for a long time. The ${\beta}{\rightarrow}{\alpha}^{\prime}$ phase transformation is of the diffusionless (martensitic) type, and takes place between 330 K at 12.9 at.%Sn and 150 K at 14.5 at.%Sn. The hysteresis of transformation temperatures on heating and cooling is considerably large (29~40 K), depending on the composition. Both In-Pb and In-Sn alloys showed distinct the shape memory effects.

• Korean Journal of Pharmacognosy
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• v.33 no.3 s.130
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• pp.173-176
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• 2002

In search for the plant-derived antioxidant compound, it was found that the EtOAc, BuOH extracts obtained from the leaves parts of Oryza sativa L. which exhibited a significant antioxidant activity from 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical cleavage. Activity-guided fractionation on the basis of the inhibitory activity upon the 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical cleavage. and repeated column chromatography afforded several antioxidant compounds from Oryza sativa L. The structures and stereochemistry of these compounds were established on the basis of analysis of spectra and some chemical transformations as follows: 5,7-dihydroxy- 8-methoxyflavone, $acacetin-7-O-{\beta}-rutinoside$, $pectolinarigenin-7-O-{\beta}-rutinoside$. At antioxidant activity test for isolated three compounds, antioxidant activity was showed too.

• Journal of the Korean institute of surface engineering
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• v.36 no.2
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• pp.200-205
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• 2003

Thermoelectric p-type $Fe_{0.98}$ $Mn_{ 0.02}$$Si_2$ bulk specimens have been produced by mechanical alloying and consolidation by vacuum hot pressing. The subsequent isothermal annealing was not able to fully transform the mestastable as -milled powders into the $\beta$ $-FeSi_2$ phase, so that the obtained matrix consisted of not only thermoelectric semiconducting $\beta$-FeSi$_2$ but also some residual, untransformed metallic $\alpha$ $- Fe_2$$Si_{ 5}$ and $\varepsilon$-FeSi mixtures. Interestingly, $\beta$ - $FeSi_2$ was more easily obtained in the low density specimen when compared to the high density specimen. The oxidation at 700 and $800^{\circ}C$ in air led to the phase transformation of the above described iron - silicides and the formation of a thin silica surface layer.