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LOCALIZATION PROPERTY AND FRAMES

  • HA, YOUNG-HWA;RYU, JU-YEON
    • 호남수학학술지
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    • 제27권2호
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    • pp.233-241
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    • 2005
  • A sequence $\{f_i\}^{\infty}_{i=1}$ in a Hilbert space H is said to be exponentially localized with respect to a Riesz basis $\{g_i\}^{\infty}_{i=1}$ for H if there exist positive constants r < 1 and C such that for all i, $j{\in}N$, ${\mid}{\mid}{\leq}Cr^{{\mid}i-j{\mid}}$ and ${\mid}{\mid}{\leq}Cr^{{\mid}i-j{\mid}}$ where $\{{\tilde{g}}_i\}^{\infty}_{i=1}$ is the dual basis of $\{g_i\}^{\infty}_{i=1}$. It can be shown that such sequence is always a Bessel sequence. We present an additional condition which guarantees that $\{f_i\}^{\infty}_{i=1}$ is a frame for H.

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THE GENERAL LINEAR GROUP OVER A RING

  • Han, Jun-Cheol
    • 대한수학회보
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    • 제43권3호
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    • pp.619-626
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    • 2006
  • Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

STABILITY OF s-VARIABLE ADDITIVE AND l-VARIABLE QUADRATIC FUNCTIONAL EQUATIONS

  • Govindan, Vediyappan;Pinelas, Sandra;Lee, Jung Rye
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제29권2호
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    • pp.179-188
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    • 2022
  • In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

ON PC-CLOSED SETS

  • Ekici, Erdal;Tunc, A. Nur
    • 충청수학회지
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    • 제29권4호
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    • pp.565-572
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    • 2016
  • In this paper, the concept of $PC^{\star}$-closed sets is introduced. $PC^{\star}$-closed sets contain $pre^*_I$-open and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and weakly $I_{rg}$-closed sets.

SYSTEMS OF DERIVATIONS ON BANACH ALGEBRAS

  • Lee, Eun-Hwi
    • 대한수학회논문집
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    • 제12권2호
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    • pp.251-256
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    • 1997
  • We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

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NOTE ON GOOD IDEALS IN GORENSTEIN LOCAL RINGS

  • Kim, Mee-Kyoung
    • 대한수학회보
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    • 제39권3호
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    • pp.479-484
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    • 2002
  • Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S:sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp :sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

APPROXIMATION OF CUBIC MAPPINGS WITH n-VARIABLES IN β-NORMED LEFT BANACH MODULE ON BANACH ALGEBRAS

  • Gordji, Majid Eshaghi;Khodaei, Hamid;Najati, Abbas
    • 대한수학회보
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    • 제48권5호
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    • pp.1063-1078
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    • 2011
  • Let M = {1, 2, ${\ldots}$, n} and let V = {$I{\subseteq}M:1{\in}I$}. Denote M\I by $I^c$ for $I{\in}V$. The goal of this paper is to investigate the solution and the stability using the alternative fixed point of generalized cubic functional equation $ \sum\limits_{I{\in}V}f(\sum\limits_{i{\in}I}a_ix_i-\sum\limits_{i{\in}I^c}a_ix_i)=2{^{n-2}{a_1}}\sum\limits_{i=2}^na_i^2[f(x_1+x_i)+f(x_1-x_i)]+2{^{n-1}{a_1}(a^2_1-\sum\limits_{i=2}^2a^2_i)f(x_1)$ in ${\beta}$-Banach modules on Banach algebras, where $a_1,{\ldots},a_n{\in}\mathbb{Z}{\backslash}\{0\}$ with $a_1{\neq}={\pm}1$ and $a_n=1$.

하수관거정비사업에서 침입수.유입수 성과지표 활용을 위한 통계적 방법론에 관한 연구 (Statistical Methods for the Use of Infiltration and Inflow as Performance Index in Sewer Rehabilitation Works)

  • 김형준;박규홍
    • 상하수도학회지
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    • 제24권5호
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    • pp.617-628
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    • 2010
  • The operation performance of sewer rehabilitation projects conducted with Build-Transfer- Lease contract in Korea will be evaluated using the index of infiltration and inflow (I/I). Though I/I obtained at the fourth year should be initially evaluated based on the I/I values observed for the previous three years after the completion of sewer construction, the concrete methodology have not been proposed to rely on the so called 'performance evaluation committee'. This study suggests two statistical methodology to evaluate the I/I performance; the confidence interval method and the hypothesis-testing method. Assumed ten I/I values in each year for 20 years are used in this study. Two cases are analyzed and compared; case I to use as control data all I/I values for all years obtained before the evaluation year and case II to use I/I values for only 3 years before the evaluation year. As a result, case II tends to have relatively higher scores than case I, reflecting the low mean I/I values at the initial years.

지능형 I/O구조를 갖는 RAID 시스템의 성능 향상을 위한 연구 (A Study for High Performance of Intelligent I/O Architecture of RAID System)

  • 최귀열;박계원
    • 한국정보통신학회논문지
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    • 제10권11호
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    • pp.1989-1995
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    • 2006
  • RAID는 디스크 배열 상에 데이터를 이중으로 저장하거나 패리티를 사용하는 기법으로 디스크에 장애가 일어났을 경우 이를 복구하는 구조로 되어 있다. 본 논문에서는 지능형 I/O 구조를 갖는 고성능 I/O 서브시스템에서 CPU로부터 대부분 I/O 작업 부하를 줄이고 동시 에 I/O 성능을 향상시키는 방안에 대하여 연구한다. 지능형 I/O 장치의 디스크 스케줄링 디자인에 관한 초당 MB 처리율, 최대 I/O 응답시간 등의 실험 통하여 새로운 스케줄링 기법 에 의해 성능을 개선한다.

COLOCALIZATION OF GENERALIZED LOCAL HOMOLOGY MODULES

  • Hatamkhani, Marziyeh
    • 대한수학회보
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    • 제59권4호
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    • pp.917-928
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    • 2022
  • Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension rI(M, N) and artinianness dimension aI(M, N) of M, N with respect to I by rI(M, N) = inf{i ∈ ℕ0 : HIi(M, N) is not representable} and aI(M, N) = inf{i ∈ ℕ0 : HIi(M, N) is not artinian} and we show that aI(M, N) = rI(M, N) = inf{rIR𝔭 (M𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{aIR𝔭 (M𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩t>0ItN is artinian we prove that inf{i : HIi(M, N) is not minimax}=inf{rIR𝔭 (M𝔭,𝔭N) : 𝔭 ∈ Spec(R)\Max(R)}.