• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.371-379
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• 2012

Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

• Journal of IKEEE
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• v.23 no.2
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• pp.425-430
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• 2019

This work describes the design and characterization of a X-band power amplifier (PA) monolithic microwave integrated circuit (MMIC) using a $0.25{\mu}m$ gate length gallium nitride (GaN) high electron mobility transistor (HEMT) technology. The developed X-band power amplifier MMIC has small signal gain of over 22.7 dB and saturated output power of 43.02 dBm (20.04 W) over the entire band of 9 to 10 GHz. Maximum saturated output power is a 43.84 dBm (24.21 W) at 9.5 GHz. Its power added efficiency (PAE) is 41.0~51.24% and the chip dimensions are $3.7mm{\times}2.3mm$, generating the output power density of $2.84W/mm^2$. The developed GaN power amplifier MMIC is expected to be applied in a variety of X-band radar applications.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.679-690
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• 2005

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, f($x_1,{\cdots},\;x_n$) a multilinear polynomial in n non-commuting variables over K, a $\in$ R. Supppose that, for any $x_1,{\cdots},\;x_n\;\in\;I,\;a[d(f(x_1,{\cdots},\;x_n)),\;f(x_1,{\cdots},\;x_n)]$ = 0. If $[f(x_1,{\cdots},\;x_n),\;x_{n+1}]x_{n+2}$ is not an identity for I and $$S_4(I,\;I,\;I,\;I)\;I\;\neq\;0$$, then aI = ad(I) = 0.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.857-866
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• 2009

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.5
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• pp.430-433
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• 2017

This paper presents a S/C/X-band LNA MMIC with resistive feedback structure in 0.25 um GaN HEMT process. The GaN devices have advantages as a high output power device having high breakdown voltage, energy band gap and stability at high temperature. Since the receiver using the GaN device with high linearity can be implemented without a limiter, the noise figure of the receiver can be improved and the size of receiver module can be reduced. The proposed GaN LNA MMIC based on 0.25 um GaN HEMT device is achieved the gain of > 15 dB, the noise figure of < 3 dB, the input return loss of > 13 dB, and the output return loss of > 8 dB in the S/C/X-band. The current consumption of GaN LNA MMIC is 70 mA with the drain voltage 20 V and the gate voltage -3 V.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.