• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1905-1914
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• 2013

Let D be an integral domain with quotient field K, M a torsion-free D-module, X an indeterminate, and $N_v=\{f{\in}D[X]|c(f)_v=D\}$. Let $q(M)=M{\otimes}_D\;K$ and $M_{w_D}$={$x{\in}q(M)|xJ{\subseteq}M$ for a nonzero finitely generated ideal J of D with $J_v$ = D}. In this paper, we show that $M_{w_D}=M[X]_{N_v}{\cap}q(M)$ and $(M[X])_{w_{D[X]}}{\cap}q(M)[X]=M_{w_D}[X]=M[X]_{N_v}{\cap}q(M)[X]$. Using these results, we prove that M is a strong Mori D-module if and only if M[X] is a strong Mori D[X]-module if and only if $M[X]_{N_v}$ is a Noetherian $D[X]_{N_v}$-module. This is a generalization of the fact that D is a strong Mori domain if and only if D[X] is a strong Mori domain if and only if $D[X]_{N_v}$ is a Noetherian domain.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.2 no.2 s.3
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• pp.97-101
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• 2003

A MMIC (monolithic microwave integrated circuit) mixer chip using the Schottky diode of an InGahs/CaAs p-HEMT process has been developed for the receiver down converter of Ku-band. A different approach to the MMIC mixer structure is applied for reducing the chip size by the exchange of ports between If and LO. This MMIC covers with RF (14.0 - 14.5 GHz) and If (12.252 - 12.752 GHz). According to the on-wafer measurement, the miniature (3.3X3.0 m) MMIC mixer demonstrates conversion loss below 9.8 dB, RF-to-IF isolation above 23 dB, LO-to-IF isolation above 38 dB, respectively.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.5A
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• pp.743-750
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• 2000

In this paper, low-power block filtering architecture for digital If down sampler and up sampler is proposed. Software radio technology requires low power and cost effective digital If down and up sampler. Digital If down sampler and up sampler are accompanied with decimation filter and interpolation filter, respectively. In the proposed down sampler architecture, it is shown that the parallel and low-speed processing architecture can be produced by cancellation of inherent up sampler of block filter and down sampler. Proposed up sampler also utilizes cancellation of up sampler and inherent down sampler of block filtering structure. The proposed architecture is compared with the conventional polyphase architecture.

• Information and Communications Magazine
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• v.19 no.11
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• pp.85-108
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• 2002

향후 다양한 무선 통신 규격들의 통합 수용을 위한 SDR (Software Defined Radio) 기술이IMT-2000 이후의 4세대 이동 통신 시스템을 위한 핵심 기술로써 심각하게 고려되고 있다. 이에 부응하여 SDR기반의 멀티모드용 통신 시스템을 구성하기 위한 주요 기술로서 디지털 IF 기술에 대한 필요성이 급속도로 고조되고 있는 상황이다. 최근 ABC/DAC 및 범용 디지털 신호처리 소자들의 고속화 및 고성능화로 인해 If (Intermediate Frequency) 대역과 기저대역 신호들 간의 직접 디지털 변환의 구현이 현실화되고 있다. 사용자의 관점에서 국지적으로 상용화되고 있거나 장래에 출현할 다양한 이동 통신 시스템 규격들 및 이에 대해 사업자들에게 할당되는 주파수 대역들이 서로 다른 점을 고려할 때, 이종 시스템 혹은 사업자들에게 할당된 주파수 대역에 구애받지 않고 언제 어디서나 자유롭게 무선 채널을 엑세스하고 또한 특정 채널을 임의로 선택하기 위한 디지털 If기술의 실현이 필수적이다 이러한 SDR기반 디지털 If 기술은 소프트웨어적으로 재구성 가능한 하드웨어 구조를 요구하며, 특정 이동 통신 규격의 물리 계층만을 지원하는 무선 인터페이스가 아닌 다중이동 통신 모드를 지원할 수 있는 유연성이 가미된 채널화 알고리즘이 필요하게 된다. 따라서 디지털 If기술은 무선 인터페이스 처리 부분, 즉 주파수 상 하향 변환 및 채별 선택 조합을 용도에 맞게 단일의 하드웨어 플렛폼 상에서 고속 디지털 신호처리 알고리즘을 기반으로 동작하기 위한 기능을 필연적으로 요구한다. 본 논문에서는 향후 SDR 기반의 기지국 및 단말기 운영 및 구생 모델을 제시하며, 디지털 If에 대한 필요성 및 동작 원리, 그리고 요소 기능들에 대한 구체적인 동작 원리 및 디지털 If와 더불어 활용 가능한 기술에 대하여 논의한다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.2
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• pp.227-231
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• 2004

A MMIC (Monolithic Microwave Integrated Circuit) mixer chip using the schottky diode of InGaAs/CaAs p-HEMT process has been developed for receiver down converter of Ka-band. A different approach of MMIC mixer structure is applied for reducing the chip size by the exchange of ports between IF and LO. This MMIC covers with RF (30.6∼31.0㎓)and IF (20.8∼21.2㎓). According to the on-wafer measurement, the MMIC mixer with miniature size of 3.0mm1.5mm demonstrates conversion loss below 7.8㏈, LO-to-RF isolation above 27㏈, LO-to-IF isolation above 19㏈ and RF-to-IF isolation above 39㏈, respectively.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.83-94
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• 2016

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and $Im({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$, if and only if a module M is semi N-injective and $Ker({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$. Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Im({\alpha}{\beta}){\subseteq}^{\oplus}N$, if and only if a module M is direct N-injective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Ker({\beta}{\alpha}){\subseteq}^{\oplus}M$. The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1041-1057
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• 2019

Let ${\Gamma}$ be a nonzero commutative cancellative monoid (written additively), $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}$ $R_{\alpha}$ be a ${\Gamma}$-graded integral domain with $R_{\alpha}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma}$, and $S(H)=\{f{\in}R{\mid}C(f)=R\}$. In this paper, we study homogeneously divisorial domains which are graded integral domains whose nonzero homogeneous ideals are divisorial. Among other things, we show that if R is integrally closed, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is an h-local $Pr{\ddot{u}}fer$ domain whose maximal ideals are invertible, if and only if R satisfies the following four conditions: (i) R is a graded-$Pr{\ddot{u}}fer$ domain, (ii) every homogeneous maximal ideal of R is invertible, (iii) each nonzero homogeneous prime ideal of R is contained in a unique homogeneous maximal ideal, and (iv) each homogeneous ideal of R has only finitely many minimal prime ideals. We also show that if R is a graded-Noetherian domain, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is a divisorial domain of (Krull) dimension one.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.273-286
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• 2023

In this paper we show that if T ∈ L(X) and S ∈ L(X) is a Riesz operator commuting with T and X_S(F) ∈ Lat(S), where F = {0} or F ⊆ ℂ ⧵ {0} is closed then T|X_S(F) and T|X_T(F) + S|X_S(F) share the local spectral properties such as SVEP, Dunford's property (C), Bishop's property (𝛽), decomopsition property (𝛿) and decomposability. As a corollary, if T ∈ L(X) and Q ∈ L(X) is a quasinilpotent operator commuting with T then T is Riesz if and only if T + Q is Riesz. We also study some spectral properties of Riesz operators acting on Banach spaces. We show that if T, S ∈ L(X) such that TS = ST, and Y ∈ Lat(S) is a hyperinvarinat subspace of X for which 𝜎(S|Y ) = {0} then 𝜎_*(T|Y + S|Y ) = 𝜎_*(T|Y ) for 𝜎_* ∈ {𝜎, 𝜎_loc, 𝜎_sur, 𝜎_ap}. Finally, we show that if T ∈ L(X) and S ∈ L(Y ) on the Banach spaces X and Y and T is similar to S then T is Riesz if and only if S is Riesz.