• Journal of the Korean Ceramic Society
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• v.32 no.3
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• pp.394-402
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• 1995

Electrical conductivity and thermoelectric power of the ferrous ferrite system of (Mg0.29-yMnyFe0.71)3-$\delta$O4 have been measured as function of the thermodynamic variables, cationic composition(y), temperature(T) and oxygen partial pressure(Po2) under thermodynamic equilibrium conditions at elevated temperatures. On the basis of the electrical properties-phase stability correlation, the stability regions of the ferrite spinel and its neighboring phases have been subsequently located in the log Po2 vs. y and log Po2 vs. 1/T planes in the ranges of 0 y 0.29, 1100 T/$^{\circ}C$ 1400 and 10-14 Po2/atm 1. The stability region, Δlog Po2(y, 1/T), of the ferrite spinel single phase widens with increasing Mn-content(y) and the boundaries of each region are linear against 1/T with negative slopes.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.1-12
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• 2016

This paper shows that the solutions to the perturbed differential system $y^{\prime}=f(t, y)+\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$ have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y).

• 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.20 no.1
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• pp.33-46
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• 2012

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation (0.1) $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+10f(x)+14f(-x)-3f(y)-3f(-y)$ for all $x$, $y$ with $x{\perp}y$, in non-Archimedean Banach spaces. Here ${\perp}$ is the orthogonality in the sense of R$\ddot{a}$tz.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.289-300
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• 2011

Let T(X) denote the semigroup (under composition) of transformations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = {${\alpha}\;{\in}\;T(X)\;:\;Y\;{\alpha}\;{\subseteq}\;Y$}. Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S($A^1$, A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.37-47
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• 2001

We present the general solution of the functional equation f(x$_1$y$_1$,x$_2$y$_2$) + f(x$_1$y$_1$(sup)-1,x$_2$) + f(x$_1$,x$_2$y$_2$(sup)-1) = f(x$_1$y$_1$(sup)-1,x$_2$y$_2$(sup)-1) + f(x$_1$y$_1$,x$_2$) + f(x$_1$,x$_2$y$_2$). Furthermore, we also prove the Hyers-Ulam stability of the above functional equation.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1651-1657
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• 2013

Let R be a prime ring, I a nonzero ideal of R, $d$ a derivation of R, $m({\geq}1)$, $n({\geq}1)$ two fixed integers and $a{\in}R$. (i) If $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx))^m=0$ for all $x,y{\in}I$, then either $a=0$ or R is commutative; (ii) If $char(R){\neq}2$ and $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx)){\in}Z(R)$ for all $x,y{\in}I$, then either $a=0$ or R is commutative.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1998.11a
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• pp.281-285
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• 1998

The microstructure and conduction characteristics of ZnO varistor fabricated in the range of 0.0 ~ 4.0mol% $Y_20_3$ were investigated. With increasing$Y_20_3$ content, distribution of spinel phase decreased, whereas Y-rich phase segregated to the nodal point increased, as a result, the average grain size decreased in the range of $20.0 ~ 4.8{\mu}m$. $Y_20_3$ content showing relatively good conduction characteristics was l.Omol%, then nonlinear exponent and leakage current was 55.3, 0.66mA.respectively.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.51 no.2
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• pp.82-86
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• 2002

A series of $Ni_xZn_yFe_{3-x-y}O_4$ films were prepared by spin-spray ferrite plating on glass substrates from aqueous solution at $90[^{\circ}C]$. The magnetic properties in terms of contents of Ni and Zn in the plated films are presented. All the films are polycrystalline with spinel structure. At x+y=0.58, the film presents preferential orientation. As composition of y in the films increases grain size and void in the films increases, while saturation magnetization and coercive force of the films decrease.