• 충청수학회지
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• 제34권4호
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• pp.335-343
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• 2021

In this article, we investigate the finiteness of Auslander Index when a ring A has not necessarily a canonical module, or a Gorenstein module. We also study the relations between column invariants and row invariants.

• 대한수학회보
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• 제57권3호
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• pp.803-813
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• 2020

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂_R M^∗ → Hom_R(Hom_R(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and Extⁱ_R(M, M) = 0 (i ⩾ 1), then M is projective.

• Korean Journal of Mathematics
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• 제7권1호
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• 호남수학학술지
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• 제28권4호
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• pp.533-541
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• 2006

let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.

• 대한수학회보
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• 제49권5호
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• pp.989-996
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• 2012

Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper we study the amalgamated duplication ring $R{\bowtie}I$ which is introduced by D'Anna and Fontana. It is shown that if R is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonical module), then $R{\bowtie}I$ is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when $R{\bowtie}I$ is generically quasi-Gorenstein. In addition, it is shown that $R{\bowtie}I$ is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is approximately Gorenstein, then $R{\bowtie}I$ is approximately Gorenstein.

• 대한수학회보
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• 제57권2호
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• pp.275-280
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• 2020

Let (R, m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that β_R(I, R) denotes the constant value of depth_R(R/Iⁿ) for n ≫ 0. In this paper we introduce the new notion γ_R(I, R) and then we prove the following inequalities: β_R(I, R) ≤ γ_R(I, R) ≤ dim R - cd(I, R) ≤ dim R/I. Also, some applications of these inequalities will be included.

• 한국반도체및디스플레이장비학회:학술대회논문집
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• 한국반도체및디스플레이장비학회 2007년도 춘계학술대회
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• pp.230-233
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• 2007

A system of anodic process of aluminum thin film has implemented for nanofabrication. The manufactured equipment consists of three main parts: chiller, reaction bath and power supply. The chiller module consists of refrigeration compressor, copper tube and coolant with a thermostat. The reaction bath has kept in same temperature as a thermodynamic canonical ensemble system during the anodic reaction process. The magnetic bar has stirred oxalic acid in bath for uniform reaction. The DC power supply has applied into two electrodes, aluminum for anode and platinum for cathode in the oxalic acid. The anodization process results in the formation of nanoporous thin films.

• 한국정보통신학회논문지
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• 제21권3호
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• pp.568-577
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• 2017

WAVE 시스템에서는 통신 보안 기능을 지원하기 위해 IEEE Std 1609.2 규격이 정의되었다. IEEE Std 1609.2에서는 자동차 통신에서의 보안 서비스 및 관리 메시지의 구조를 ASN.1으로 정의하였다. 또한 이 메시지 구조를 COER 방식으로 인코딩하도록 하고 있다. 본 논문에서는 IEEE Std 1609.2에 정의된 보안 메시지를 처리하는 IEEE Std 1609.2 메시지 인코더/디코더를 설계 및 구현하였다. 설계된 인코더/디코더는 IEEE Std 1609.2 메시지 구조에 부합하는 C 언어 데이터 구조의 메시지를 생성하는 모듈, 메시지 인코더 모듈, 메시지 디코더 모듈로 구성되며, 리눅스 환경에서 구현되었다. 또한 구현된 인코더/디코더의 수행 속도를 측정하여 그 성능을 분석하였다.

• 대한수학회지
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• 제39권1호
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• Molecules and Cells
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• 제41권9호
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• pp.842-852
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• 2018

Notch signaling is an evolutionarily conserved pathway and involves in the regulation of various cellular and developmental processes. Ligand binding releases the intracellular domain of Notch receptor (NICD), which interacts with DNA-bound CSL [CBF1/Su(H)/Lag-1] to activate transcription of target genes. In the absence of NICD binding, CSL down-regulates target gene expression through the recruitment of various corepressor proteins including SMRT/NCoR (silencing mediator of retinoid and thyroid receptors/nuclear receptor corepressor), SHARP (SMRT/HDAC1-associated repressor protein), and KyoT2. Structural and functional studies revealed the molecular basis of these interactions, in which NICD coactivator and corepressor proteins competitively bind to ${\beta}-trefoil$ domain (BTD) of CSL using a conserved ${\varphi}W{\varphi}P$ motif (${\varphi}$ denotes any hydrophobic residues). To date, there are conflicting ideas regarding the molecular mechanism of SMRT-mediated repression of CSL as to whether CSL-SMRT interaction is direct or indirect (via the bridge factor SHARP). To solve this issue, we mapped the CSL-binding region of SMRT and employed a 'one- plus two-hybrid system' to obtain CSL interaction-defective mutants for this region. We identified the CSL-interaction module of SMRT (CIMS; amino acid 1816-1846) as the molecular determinant of its direct interaction with CSL. Notably, CIMS contains a canonical ${\varphi}W{\varphi}P$ sequence (APIWRP, amino acids 1832-1837) and directly interacts with CSL-BTD in a mode similar to other BTD-binding corepressors. Finally, we showed that CSL-interaction motif, rather than SHARP-interaction motif, of SMRT is involved in transcriptional repression of NICD in a cell-based assay. These results strongly suggest that SMRT participates in CSL-mediated repression via direct binding to CSL.