• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.779-787
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• 2017

Let m be the Lebesgue measure on ${\mathbb{C}}$ normalized to $m(D)=1,{\mu}$ be an invariant measure on D defined by $d_{\mu}(z)=(1-{\mid}z{\mid}^2)^{-2}dm(z)$. For $f{\in}L^1(D^n,m{\times}{\cdots}{\times}m)$, Bf the Berezin transform of f is defined by, $$(Bf)(z_1,{\ldots},z_n)={\displaystyle\smashmargin{2}{\int\nolimits_D}{\cdots}{\int\nolimits_D}}f({\varphi}_{z_1}(x_1),{\ldots},{\varphi}_{z_n}(x_n))dm(x_1){\cdots}dm(x_n)$$. We prove that if $f{\in}L^1(D^2,{\mu}{\times}{\mu})$ is radial and satisfies ${\int}{\int_{D^2}}fd{\mu}{\times}d{\mu}=0$, then for every bounded radial function ${\ell}$ on $D^2$ we have $$\lim_{n{\rightarrow}{\infty}}{\displaystyle\smashmargin{2}{\int\int\nolimits_{D^2}}}(B^nf)(z,w){\ell}(z,w)d{\mu}(z)d{\mu}(w)=0$$. Then, using the above property we prove n-harmonicity of bounded function which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.

• Journal of the Korean Chemical Society
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• v.41 no.6
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• pp.277-283
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• 1997

Platinum(II) complexes(where, $[Pt(L)_2X_2]$; L=isoxazole(isox), 3,5-dimethylisoxazole(3,5-diMeisox), 3-methyl,5-phenylisoxazole(3-Me,5-Phisox), and 4-amino-3,5-dimethylisoxazole(4-ADI); X=Cl, Br) with planar ligands are investigated on antitumor activity by MM2 and EHMO calculations. It was found that, the net atomic charges of the halogen atoms in all of cis-, trans-isomers are greater than that of the nitrogen with planar form, indicating that ionic character of Pt-X bond is greater than that of Pt-N. Also, the ${\sigma}MO$ energy level($E{\sigma}_{(Pt-X)}$) of the interaction between $d_{x2-y2}$ orbital of Pt atom and $p_x$ orbital of X found to be higher than that of between $d_{x2-y2}$ orbital of Pt atom and $p_x$ orbital of N about all the complexes. It is found that bond strength of between Pt and X atom is weaker than that of between Pt and N atom. The ${\sigma}MO$ energy level($E{\sigma}_{(Pt-X)}$) of trans- complexes found to be higher than that of cis- complexes, as a result of bond strength of Pt-X in cis- and trans-complexes, for all the complexes. The degree of dissociation of X atom in Pt-X bond for trans-complexes are related to antitumor activity and the logIA value of inhibitory activity coefficient(IA).

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.343-349
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• 2011

Let D be an integral domain, $D^w$ be the $w$-integral closure of D, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}c(f)_v=D\}$. In this paper, we introduce the concept of $t$-locally APVD. We show that D is a $t$-locally APVD and a UMT-domain if and only if D is a $t$-locally APVD and $D^w$ is a $PvMD$, if and only if D[X] is a $t$-locally APVD, if and only if $D[X]_{N_v}$ is a locally APVD.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.5
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• pp.621-627
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• 2011

In this paper, we analysed performance for on-wafer GaN HEMT using load-pull in X-band, and studied optimum impedance point based on analysis result. We suggested method of optimum performance device by analysis of optimum impedance for solid state device on-wafer condition before packaging. The measured device is gate length 0.25um, and gate width is 400um, 800um. device 400um is performed $P_{sat}$=33.16dBm, PAE=67.36%, Gain=15.16dBm, and device 800um is performed $P_{sat}$=35.91dBm, PAE=69.23%, Gain=14.87dBm.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.211-224
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• 2002

In this paper we show that if D is a continuous linear Jordan derivation on a Banach algebra A satisfying [[D($x^{n}$), $x^{n}$, $x^{n}$] $\in$ rad(A) for a positive integer n and for all x${\in}$A, then D maps A into rad(A).

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.8
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• pp.15-23
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• 1998

Single crystalline I $n_{x}$G $a_{1-x}$ N thin film was grwon by MOCVD on (001) sapphire substrate for the blue light emitting devices. A good quality of I $n_{0.13}$G $a_{0.87}$N/GaN heterostructure grwon above 700.deg. C was confiremed by various characterization techniques of AFM, RHEED and DC-XRD. Through PL measurement at room temperautre for the Si-Zn co-doped I $n_{x}$G $a_{a-x}$N/GaN structure grwon at 800.deg. C to obtain blue wavelength emission, 460-470 nm and 425 nm emission peak were observed, which are believed to be from donor-to-acceptor pair transition and band edge emission of In/x/G $a_{1-x}$ N, respectively. The result of PL measurement of the undoped MQW I $n_{x}$G $a_{1-x}$ N layer at low temperature confirmed that the strong MQW peak was resulted by exciton from the GAN barrier and carrier of DA pair confined into the well layer.ll layer.yer.r.

• 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.