• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.353-355
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• 1988

The properites of Zn-diffusion in III-V ternary alloy semiconductor $In_{1-x}Ga_{x}p$, which was grown by the temperature gradient solution (TGS) method, have been investigated. The composition, x, dependence of the Zn-diffusion coefficient at $850^{\circ}C$ and the activation energy for Zn-diffusion into $In_{1-x}Ga_{x}p$ were found to be $D850^{\circ}C$(x)= $3.935{\times}10^{-8}exp(-6.84{\cdot}x)$, and $E_{A}(x)=1,28+2,38{\cdot}x$, respectively. From this study, we confirm that the Zn-diffusion in $In_{1-x}Ga_{x}p$ was explainable with the diffusion mechanisms of the interstitial-substitutional, which was widely accepted mechanisms in the III-V binary semiconductors.

• Journal of Magnetics
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• v.14 no.1
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• pp.1-6
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• 2009

The magnetic properties of ${Bi_x}{Ca_{1-x}}{MnO_3}$ for x = 0.12, 0.13, 0.14, 0.15, and 0.16 were examined by measuring magnetic susceptibility, resistivity and electron magnetic resonance at different temperatures. ${Bi_x}{Ca_{1-x}}{MnO_3}$ showed complicated magnetic structure that varies with temperature and composition, particularly around Bi composition x. 0.15. The aim of this study was to determine how the magnetic and physical properties of ${Bi_x}{Ca_{1-x}}{MnO_3}$ change in this region. In addition, first principles calculations of the magnetic phase of ${Bi_x}{Ca_{1-x}}{MnO_3}$ for x = 0, 0.125, 0.25 were carried out, and the spin state, electric and magnetic characteristics are discussed.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.185-192
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• 2003

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.163-167
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• 2008

This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that $X\;{\in}\;W\;EI ({\alpha})$, if and only if $\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent or $\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And also we establish that $X\;{\in}\;W\;EI({\alpha})$, if and only if $\frac {X_{U(n+1)}\;-\;X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.701-713
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• 2004

We obtain the Hyers-Ulam-Rassias stability of a betatype functional equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)+ \lambda(x,y)$ with a restricted domain and the stability in the sense of R. Ger of the equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)$ with a restricted domain in the following settings: $g(\varphi(x),\phi(y))-\psi(x,y)g(s,y)-\lambda(x,y)$\mid$\leq\varepsilon(x,y)$ and $\frac{g(\varphi(x),\phi(y))}{\psi(x,y),g(x,y)}-1 $\mid$ \leq\epsilon(x,y)$.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.715-720
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• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.99-105
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• 2022

The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations (a) 2T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ + xⁿyⁿT(xⁿ) (b) 3T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ+xⁿT(yⁿ)xⁿ+xⁿyⁿT(xⁿ) for every x, y ∈ R. Further, few extensions of these results are also presented in the framework of *-ring.

• Journal of Sericultural and Entomological Science
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• v.16 no.2
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• pp.147-155
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• 1974

The purpose of this study is to find out influence of reeling conditions on the denier control of raw silk for automatic silk reeling machine. The results obtained are as follows： 1. Effect of groping end part temperature (X$_1$) (1) Average size Y＝0.02945X$_1$＋18.27 (2) Size range Y＝0.04224X$_1$＋2.99 (3) Size deviation Y＝0.01667X$_1$－0.13 (4) Maximum deviation of size Y＝0.04657X$_1$－0.929 (5) Quality of raw silk Y＝－0.07055X$_1$＋10.082. Effect of silk reeling bath temperature (X$_2$) (1) Average size Y＝0.0334X$_2$＋19.08 (2) Size range Y＝0.016X$_2$＋5.24 (3) Size deviation Y＝0.0014X$_2$＋1.05 (4) Maximum deviation of size Y＝0.0206X$_2$＋1.59 3. Effect of silk reeling velocity(X$_3$) (1) Size range Y＝0.01797X$_3$＋3.95 (2) Size deviation Y＝0.00327X$_3$＋0.845 (3) Maximum deviation of size Y＝0.00905X$_3$＋1.50 (4) Quality of raw silk Y＝－0.03232X$_3$＋8.62