• Korean Journal of Mathematics
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• v.26 no.4
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• pp.701-708
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• 2018

In this paper, seminormality and t-closedness in ring extensions involving amalgamated algebras are studied. Let $R{\subseteq}T$ be a ring extension with ideals $I{\subseteq}J$, respectively such that J is contained in the conductor of R in T. Assume that T is integral over R. Then it is shown that ($R{\bowtie}I$, $T{\bowtie}J$) is a seminormal (resp., t-closed) pair if and only if (R, T) is a seminormal (resp., t-closed) pair.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.3
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• pp.389-398
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• 2011

In this paper, the design and fabrication of a transmit/receive(T/R) module for Ka-band phased array radar is presented. A 5bit digital phase shifter and digital attenuator were used in common for both transmitter and receiver considering unique Ka-band characteristic. The circulator was excluded in the T/R module and was placed outside T/R module. The transmitting power per element antenna is designed to be about 1 W and the noise figure is designed to be below 8 dB. The designed T/R module RF part has a compact size of $5\;mm{\times}4\;mm{\times}57\;mm$. In order to implement the T/R module, MMICs used in T/R module was separately assessed before assembly of the designed T/R module. The transmitter of the fabricated T/R module shows about 1 W at 5 dBm unit module input power and the receiver shows a gain of about 20 dB and a noise figure of below 8 dB as expected in the design stage.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.167-169
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• 1999

Let R be a Noetherian domain. It is proved that $t$-dimR = 1 if and only if each (proper if R is not a valuation domain) $t$-linked overring D of R is of $t$-dimD = 1 if and only if each integrally closed $t$-linked overring of R is a Krull domain.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.621-626
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• 2001

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

• Journal of the Korean Chemical Society
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• v.46 no.2
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• pp.157-163
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• 2002

To identify RNA motifs interacting with $tRNA^{Val}$, a SELEX(Systematic Evolution of Ligands by Exponential Enrichment) was applied. Random DNA library which contains a region of ran-domized 48-mer oligonucleotide flanked by conserved sequ ence primers was transcribed into RNA pool using T7 RNA polymerase and RNA aptamers were selected with $tRNA^{Val}$ -immobilized affinity column through 14 rounds of SELEX. Some of the resulting aptamers contained a consensus sequence similar to the sequence in the loop regions of three rRNAs; C43GAAC47 sequence of 5S rRNA, G1491AAGU1495, G1379UUCC1383 sequence of 16S rRNA and C1064UUAG1068, G2110UGUA2114, C2480GACGG2485, A2600CAGU2604 sequence of 23S rRNA. These results suggest that $tRNA^{Val}$ can interact with 5S rRNA, 16S rRNA and 23S rRNA with variety in ribosome.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.