• East Asian mathematical journal
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• v.25 no.4
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• pp.433-440
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• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.

• Journal of the Korean Ceramic Society
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• v.30 no.6
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• pp.441-448
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• 1993

The Ba1-xSrxTiO3 thin films deposited on ITO-coated glass substrate at 55$0^{\circ}C$ by rf magnetron sputtering method have individual preferential orientations as a function of composition (X=0, 0.25, 0.5, 0.75, 1) due to the stress relief interactions among the intrinsic compressive stress, thermal tensile stress adn extrinsic compressive stress (compressive stress in case of BaTiO3(Tc=12$0^{\circ}C$) and Ba0.75Sr0.25TiO3(Tc=57$^{\circ}C$)). This behavior also appears on the (BaSr)TiO3 thin films (X=0.5) deposited on ITO-coated glass substrate at deposition temperature between 35$0^{\circ}C$ and 55$0^{\circ}C$. The composition of Ba1-xSrxTiO3 thin films deposited on ITO-coated glass substrate at 55$0^{\circ}C$ is close to stoichiometry (1.009~1.089 in A/B ratio), but the compositional deviation from a stoichiometry is larger as SrTiO3 is added. The morphology of Ba1-xSrxTiO3 thin films is very similar for over all substrate temperatures, and the roughness due to the differences of cluster size is the smallest at X=0.25.

• Bulletin of the Korean Chemical Society
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• v.15 no.7
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• pp.541-545
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• 1994

A series of samples of the ${Ca_xEu_{1-x}FeO_{3-y}$ (x=0.00, 0.25, 0.50, 0.75, and 1.00) system has been prepared at $1,250^{\circ}C$ under an atmospheric air pressure. X-ray diffraction analysis of the solid solution assigns the structure of the compositions of x=0.00, 0.25, 0.50, and 0.75 to the orthoferrite-type orthorhombic system, and that of x=1.00 to the brownmillerite-type orthorhombic one. The mole ratios of $Fe^{4+}$ ion in the solid solutions or ${\tau}$ values were determined by the Mohr's salt analysis and nonstoichiometric chemical formulas of the system were formulated from x, ${\tau}$, and y values. From the result of the Mossbauer spectroscopy, the coordination and magnetic property of the iron ion are discussed. The electrical conductivities are measured as a function of temperature. The activation energy is minimum at the composition of x=0.25. The conduction mechanism can be explained by the hopping of electrons between the mixed valences of $Fe^{3+}\;and\;Fe^{4+}$ ions.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.313-318
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• 2012

The power inequality ${\prod}_{k=1}^{N}\;{x}_{k}^{x_{k}}\;{\geq}\;{\prod}_{k=1}^{N}\;{p}_{k}^{x_{k}}$ holds for the points $(x_1,{\ldots},x_N),(p_1,{\ldots},p_N)$ of the simplex. We show this using the analytic method combining Frostman's density theorem with the strong law of large numbers.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.201-215
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $f(x+y+z+w)\;+\;2f(x)\;+\;2f(y)\;+\;2f(z)\;+\;2f(w)\;-\;f(x+y)\;-\;f(x+z)\;-\;f(x+w)\;-\;f(y+z)\;-\;f(y+w)\;-\;f(z+w)=0$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.159-170
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• 2012

In this paper, we investigate the stability of a bi-Jensen functional equation $2{f}(\frac{x+y}{2},\;z)-f(x,\;z)-f(y,\;z)=0$, $2{f}(x,\;\frac{y+z}{2})-f(x,\;y)-f(x,\;z)=0$ in the spirit of P.G$\breve{a}$vruta.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.11
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• pp.1311-1316
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• 2014

To be used in a transmitter of a satellite transponder of this paper, X band 25W power amplifier module, a part constituting of high-power amplifier is transmitted to the equipment for transmitting to geostationary communications satellites(36,000Km distance). PAM consisted a total of four power amplifier module has a high output characteristic of the high-output amplifier is used in the ground station. Used in conjunction with the structured type power amplifier module is composed of Serial Combining Structure. This PAM(Power Amplifier Module) configured by combining the circuit with the power amplifier, 10 MMIC chips and the Al2O3 thin film substrate using a Hybrid Technique of power amplifier module, was implemented at X band PAM(Power Amplifier Module) of 25W grade.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2012.05a
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• pp.333-333
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• 2012

In this study, we investigated morphology of nanotube and micropore on the Ti-25Nb-xHf alloys with Hf contents after anodization. Ti-25Nb-xHf ternary alloys contained from (0~15) wt.% Hf contents were manufactured by vacuum arc-melting furnace. The obtained ingots were homogenized in an argon atmosphere at $1000^{\circ}C$ for 12h and then water quenching. The specimens were cut from ingots to 3mm thickness and first ground and polished using SiC paper (grades from 100 to 2000). 2steps anodization treatments on Ti-25Nb-xHf alloys were carried out at room temperature for experiments. Micro-pore formation was performed in Ca+P mixed solution at 265V for 3min. After that, nanotube formation was in 1M $H_3PO_4$ electrolytes containing 0.8wt.% NaF solutionat 10V for 120min. Morphologies of micropore and nanotube depended on the Hf content in Ti-25Nb-xZr ternary system.