• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.49-57
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• 2010

It is shown that for a derivation $$f(x_1{\cdots}x_{j-1}x_jx_{j+1}{\cdots}x_k)=\sum_{j=1}^{k}x_{1}{\cdots}x_{j-1}x_{j+1}{\cdots}x_kf(x_j)$$ on a unital $C^*$-algebra $\mathcal{B}$, there exists a unique $\mathbb{C}$-linear *-derivation $D:{\mathcal{B}}{\rightarrow}{\mathcal{B}}$ near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• 전기의세계
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• v.28 no.4
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• pp.53-63
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• 1979

Interface recombination velocity in $Al_{x}$G $a_{1-x}$ As-GaAs and $Al_{0.85}$, G $a_{0.15}$ As-GaA $s_{1-y}$S $b_{y}$ heterojunction systems is studied as a function of lattice mismatch. The results are applied to the design of highly efficient III-V heterojunction solar cells. A horizontal liquid-phase epitaxial growth system was used to prepare p-p-p and p-p-n $Al_{x}$G $a_{1-x}$ As-GaA $s_{1-y}$S $b_{y}$-A $l_{x}$G $a_{1-x}$ As double heterojunction test samples with specified values of x and y. Samples were grown at each composition, with different GaAs and GaAs Sb layer thicknesses. A method was developed to obtain the lattice mismatch and lattice constants in mixed single crystals grown on (100) and (111)B oriented GaAs substrates. In the AlGaAs system, elastic lattice deformation with effective Poisson ratios .mu.$_{eff}$ (100=0.312 and .mu.$_{eff}$ (111B) =0.190 was observed. The lattice constant $a_{0}$ (A $l_{x}$G $a_{1-x}$ As)=5.6532+0.0084x.angs. was obtained at 300K which is in good Agreement with Vegard's law. In the GaAsSb system, although elastic lattice deformation was observed in (111) B-oriented crystals, misfit dislocations reduced the Poisson ratio to zero in (100)-oriented samples. When $a_{0}$ (GaSb)=6.0959 .angs. was assumed at 300K, both (100) and (111)B oriented GaAsSb layers deviated only slightly from Vegard's law. Both (100) and (111)B zero-mismatch $Al_{0.85}$ G $a_{0.15}$As-GaA $s_{1-y}$S $b_{y}$ layers were grown from melts with a weight ratio of $W_{sb}$ / $W_{Ga}$ =0.13 and a growth temperature of 840 to 820 .deg.C. The corresponding Sb compositions were y=0.015 and 0.024 on (100) and (111)B orientations, respectively. This occurs because of a fortuitous in the Sb distribution coefficient with orientation. Interface recombination velocity was estimated from the dependence of the effective minority carrier lifetime on double-heterojunction spacing, using either optical phase-shift or electroluminescence timedecay techniques. The recombination velocity at a (100) interface was reduced from (2 to 3)*10$^{4}$ for y=0 to (6 to 7)*10$^{3}$ cm/sec for lattice-matched $Al_{0.85}$G $a_{0.15}$As-GaA $s_{0.985}$S $b_{0.015}$ Although this reduction is slightly less than that expected from the exponential relationship between interface recombination velocity and lattice mismatch as found in the AlGaAs-GaAs system, solar cells constructed from such a combination of materials should have an excellent spectral response to photons with energies over the full range from 1.4 to 2.6 eV. Similar measurements on a (111) B oriented lattice-matched heterojunction produced some-what larger interface recombination velocities.ities.ities.s.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• The Korean Journal of Ceramics
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• v.2 no.2
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• pp.76-82
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• 1996

PLZT ceramics having two nominal compositions, $Pb_{1-3x/2}La_xV_{x/2}(Zr_{03}Ti_{03})O_3$ and $Pb_{1-x}La_x(Zr_{0.2}Ti_{0.5})_{1-x/4}V_{x/4}O_3$ (V: vacancy) with x=0.00~0.30, were prepared. The physical, structural, and dielectric properties were investigated by X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and measurements of bulk density and dielectric constant. The two series with A-stie and B-site vacancies showed different physical, structural, dielectric properties, and, specially, Curie temperature. In comparison to PLZT with B-site vacancies, PLZT with A-site vacancies showed high Curie temperatures and low maxima of dielectric constant. Consequently, it is evident that the properties of PLZT ceramics depend on the vacancy formula adopted as a batch composition in preparation.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Proceedings of the Korean Magnestics Society Conference
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• 1994.10a
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• pp.42-43
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• 1994

• Journal of the Korean Magnetics Society
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• v.6 no.4
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• pp.218-224
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• 1996

The magnetic properties and crystallization behaviors of $Fe_{83-x}Al_{x}Nb_{5}B_{12}(X=1~5at%)$ alloys were investigated. The $Fe_{80}Al_{3}Nb_{5}B_{12}$ alloy was developed a very good soft magnetic material with ultra-fine grain structure in Fe-Al-Nb-B system alloys. When 1 at% of Cu was added in Fe-Al-Nb-B alloy, the soft magnetic properties were found to improve significantly through the reduction of the grain size upto about 6~7 nm at $450^{\circ}C$. The magnetic properties of the $Fe_{79}Al_{3}Nb_{5}B_{12}Cu_{1}$ alloy were as follows : ${\mu}_{eff}(1\;kHz)=26,000,\;B_{10}=1.45\;T,\;H_{c}=25\;mOe,\;P_{c}(100\;kHz,\;0.2\;T)=55\;W/kg$, respectively.

• Journal of the Korean Magnetics Society
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• v.7 no.6
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• pp.293-298
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• 1997

$Fe_5Si_Xb_{5-x}$ (x=0, 1, 2, 3) powders were prepared by mechanical alloying, and their phases and magnetic properties were investigated by using XRD, TEM, Mossbauer spectroscopy and VSM. Starting elements are incorporated into $\alpha$-Fe in the early stage of mechanical alloying, and the stable phases are formed as the milling proceeds. After the annealing at 80$0^{\circ}C$ for 2 hours, it is found that the FeB and $Fe_2B$ phases coexist for the $Fe_5B_5$(x=0) composition. By substituting Si for B, the formation of $Fe_2B$ phase is restricted and the $Fe_5SiB_2$, $Fe_2Si_{0.4}B_{0.6}$ and paramagnetic phase begin to appear. The FeB phase has wide range of hyperfine magnetic field because it is not fully crystallized on the annealing at 800 $^{\circ}C$. On the contrary, others have good crystalline phases and show well-defined hyperfine magnetic field. Magnetic saturation is highest for the $Fe_5B_5$ composition where the amount of the $Fe_2B$ phase in large.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Proceedings of the Korean Magnestics Society Conference
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• 2004.12a
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• pp.241-242
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• 2004