• 대한수학회논문집
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• 제35권2호
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• pp.469-480
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• 2020

Let R be a commutative ring with identity and M a unital R-module. We give a new generalization of exact sequences called e-exact sequences. A sequence $0{\rightarrow}A{\longrightarrow[20]^f}B{\longrightarrow[20]^g}C{\rightarrow}0$ is said to be e-exact if f is monic, Imf ≤_e Kerg and Img ≤_e C. We modify many famous theorems including exact sequences to one includes e-exact sequences like 3 × 3 lemma, four and five lemmas. Next, we prove that for torsion-free module M, the contravariant functor Hom(-, M) is left e-exact and the covariant functor M ⊗ - is right e-exact. Finally, we define e-projective module and characterize it. We show that the direct sum of R-modules is e-projective module if and only if each summand is e-projective.

• 대한수학회논문집
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• 제38권1호
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• pp.21-38
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• 2023

Let R be a commutative ring with identity. Let R be an integral domain and M a torsion-free R-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari [1], and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor T or and Ext, and study some properties of them.

• 대한수학회보
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• 제35권2호
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• pp.363-374
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• 1998

We investigate relationships of E-depths and T-codepths of modules in s short exact exact sequence. We give E-depths and T-codepths of some modules.

• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.453-458
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• 2006

It is well known fact for the iid data that the limiting standard errors of sample autocorrelations are all unity for all time lags and they are asymptotically independent for different lags (Brockwell and Davis, 1991). It is also usual practice in time series modeling that this fact continues to be valid for white noise series which is a sequence of uncorrelated random variables. This paper contradicts this usual practice for white noise. We consider a sequence of martingale differences which belongs to white noise time series and derive exact joint asymptotic distributions of sample autocorrelations. Some implications of the result are illustrated for conditionally heteroscedastic time series.

• Korean Journal of Mathematics
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• 제20권3호
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• pp.307-314
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• 2012

Let M be a left R-module and R be a ring with unity, and $S=\{0,2,3,4,{\ldots}\}$ be a submonoid. Then $M[x^{-s}]=\{a_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ is an $R[x^s]$-module. In this paper we show some properties of $M[x^{-s}]$ as an $R[x^s]$-module. Let $f:M{\rightarrow}N$ be an R-linear map and $\overline{M}[x^{-s}]=\{a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ and define $N+\overline{M}[x^{-s}]=\{b_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}b_0{\in}N,\;a_i{\in}M}$. Then $N+\overline{M}[x^{-s}]$ is an $R[x^s]$-module. We show that given a short exact sequence $0{\rightarrow}L{\rightarrow}M{\rightarrow}N{\rightarrow}0$ of R-modules, $0{\rightarrow}L{\rightarrow}M[x^{-s}]{\rightarrow}N+\overline{M}[x^{-s}]{\rightarrow}0$ is a short exact sequence of $R[x^s]$-module. Then we show $E_1+\overline{E_0}[x^{-s}]$ is not an injective left $R[x^s]$-module, in general.

• 대한수학회보
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• 제47권4호
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• pp.693-699
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• 2010

In this paper we show that the flat property of a left R-module does not imply (carry over) to the corresponding inverse polynomial module. Then we define an induced inverse polynomial module as an R[x]-module, i.e., given an R-linear map f : M $\rightarrow$ N of left R-modules, we define $N+x^{-1}M[x^{-1}]$ as a left R[x]-module. Given an exact sequence of left R-modules $$0\;{\rightarrow}\;N\;{\rightarrow}\;E^0\;{\rightarrow}\;E^1\;{\rightarrow}\;0$$, where $E^0$, $E^1$ injective, we show $E^1\;+\;x^{-1}E^0[[x^{-1}]]$ is not an injective left R[x]-module, while $E^0[[x^{-1}]]$ is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN = 0. We show inj $dim_R$ N = n implies inj $dim_{R[x]}$ N = n + 1 by using the induced inverse polynomial modules and their properties.

• 대한수학회보
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• 제57권5호
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• pp.1319-1334
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• 2020

In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if R^g_𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if R_e is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.

• 호남수학학술지
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• 제2권1호
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• pp.13-18
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• 1980

모든 기호(記號)는 G.E Bredon의 저(著) Sheaf Theory의 기호(記號)를 따른다. A가 torsion free이며 elementary sheaf이라 하자. 그리고 L을 injective L-module이라 하자 $dim_{\varphi}X<{\infty}$이라면 support의 $family{\varphi}$와 locally subset z에 대하여 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{\varphi}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-p}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ 이며 support의 family c와 compact subset z에 대하여도 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{c}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-y}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ A가 elementary이면 locally closed z와 z에서 closed인 $z^{\prime}$ 그리고 $z^{\prime\prime}=z-z^{\prime}$에 대하여 exact sequence ⋯⋯${\rightarrow}H^{z^{\prime}}_{p}\;(X:A){\rightarrow}H^{z}_{p}(X:A){\rightarrow}H^{z^{\prime\prime}}_{p}\;(X:A){\rightarrow}$⋯⋯ 가 존재(存在)한다.

• 말소리와 음성과학
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• 제2권3호
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• pp.115-124
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• 2010

The current study investigated the role of acoustic correlates of domain-initial strengthening in lexical segmentation of a non-native language. In a series of cross-modal identity-priming experiments, native Korean listeners heard English auditory stimuli and made lexical decision to visual targets (i.e., written words). The auditory stimuli contained critical two word sequences which created temporal lexical ambiguity (e.g., 'mill#company', with the competitor 'milk'). There was either an IP boundary or a word boundary between the two words in the critical sequences. The initial CV of the second word (e.g., [$k_{\Lambda}$] in 'company') was spliced from another token of the sequence in IP- or Wd-initial positions. The prime words were postboundary words (e.g., company) in Experiment 1, and preboundary words (e.g., mill) in Experiment 2. In both experiments, Korean listeners showed priming effects only in IP contexts, indicating that they can make use of IP boundary cues of English in lexical segmentation of English. The acoustic correlates of domain-initial strengthening were also exploited by Korean listeners, but significant effects were found only for the segmentation of postboundary words. The results therefore indicate that L2 listeners can make use of prosodically driven phonetic detail in lexical segmentation of L2, as long as the direction of those cues are similar in their L1 and L2. The exact use of the cues by Korean listeners was, however, different from that found with native English listeners in Cho, McQueen, and Cox (2007). The differential use of the prosodically driven phonetic cues by the native and non-native listeners are thus discussed.

• 한국HCI학회:학술대회논문집
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• 한국HCI학회 2009년도 학술대회
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• pp.482-486
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• 2009

기존의 음악 플레이어들은 녹음 되거나 디지털적으로 캡쳐 된 음악정보를 재생 하여 사용자들이 "한 방향"으로의 수동적인 감상을 가능하게 하였다. 본 논문에서는 mp3나 wav 로 형태로 실제로 연주 되고 녹음 된 음악에서의 특정 음표의 시간적인 위치를 찾아내는 알고리즘을 소개 하도록 한다. 찾아내고자 하는 음표의 악보를 이용하면, 우선 주어진 녹음 된 음악 파일에서의 해당 음표의 위치를 시간적인 순서대로 예측 할 수 있다. 그러나, 연주/녹음된 음악은 악보에 나와 있는 대로 연주 되지 않고 대부분 시간적으로 혹은 심지어 내용적으로 변화가 있게 마련이다. 따라서 추가적인 분석을 통하여 음표의 정확한 위치를 찾아나가게 되고, 그 위치로부터 이러한 예측 및 교정작업 (prediction/correction)을 계속적으로 수행하게 된다. 이러한 부가적인 정보를 이용하여 사용자가 음표의 위치에 (즉 리듬에) 기반한 인터액션을 통하여 실제 음악을 연주하는 듯 한 사용자 경험을 줄 수 있다.