• Title/Summary/Keyword: exact sequence

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GRADED w-NOETHERIAN MODULES OVER GRADED RINGS

  • Wu, Xiaoying
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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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 Rg𝔪 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 Re 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.

POSTNIKOV SECTIONS AND GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

  • Lee, Kee-Young
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.393-401
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    • 2004
  • In this paper, we apply the concept of the group \ulcorner(X,A) of self pair homotopy equivalences of a CW-pair (X, A) to the Postnikov system. By using a short exact sequence related to the group of self pair homotopy equivalences, we obtain the following result: for any Postnikov section X$\sub$n/ of a CW-complex X, the group \ulcorner(X$\sub$n/, A) of self pair homotopy equivalences on the pair (X$\sub$n/, X) is isomorphic to the group \ulcorner(X) of self homotopy equivalences on X. As a corollary, we have, \ulcorner(K($\pi$, n), M($\pi$, n)) ≡ \ulcorner(M($\pi$, n)) for each n$\pi$1, where K($\pi$,n) is an Eilenberg-Mclane space and M($\pi$,n) is a Moore space.

ON THE PROPERTIES OF LOCAL HOMOLOGY GROUPS OF SHEAVES

  • PARK, WON-SUN
    • Honam Mathematical Journal
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    • v.2 no.1
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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.

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TATE-SHAFAREVICH GROUPS AND SCHANUEL'S LEMMA

  • Yu, Hoseog
    • Honam Mathematical Journal
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    • v.39 no.2
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    • pp.137-141
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    • 2017
  • Let A be an abelian variety defined over a number field K and let L be a finite Galois extension of K. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Let $Res_{L/K}(A)$ be the restriction of scalars of A from L to K and let B be an abelian subvariety of $Res_{L/K}(A)$ defined over K. Assuming that III(A/L) is finite, we compute [III(B/K)][III(C/K)]/[III(A/L)], where [X] is the order of a finite abelian group X and the abelian variety C is defined by the exact sequence defined over K $0{\longrightarrow}B{\longrightarrow}Res_{L/K}(A){\longrightarrow}C{\longrightarrow}0$.

A Study on Flame and Smoke Detection Method of a Tunnel Fire (터널 화재의 화염 및 연기 검출 기법 연구)

  • Lee, Jeong-Hun;Lee, Byoung-Moo;Han, Dong-Il
    • Proceedings of the IEEK Conference
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    • 2008.06a
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    • pp.1027-1028
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    • 2008
  • In this paper, we proposed image-processing technique for automatic real-time fire and smoke detection in tunnel fire environment. To minimize false detection of fire in tunnel we used motion information of video sequence. And this makes it possible to detect exact position of event in early stage with detection, test, and verification procedures. In addition, by comparing false detection elimination results of each step, we have proved the validity and efficiency of proposed algorithm.

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Turbulent Flow through a Square Straight and Curved Duct with Reynolds Stress Models (정사각 직관과 $180^{\circ}$ 곡관내 난류유동의 레이놀즈응력모형 적용)

  • Chun, Kun-Ho;Choi, Young-Don
    • Proceedings of the KSME Conference
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    • 2000.04b
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    • pp.771-776
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    • 2000
  • Fine grid calculations are reported for the developing turbulent flow in a straight duct and a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=R_c/H_H=3.357$ and a bend angle of 180 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

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Identification of a Cellular Protein Interacting with Murine Retrovirus Gag Polyproteins

  • Choi, Wonja
    • Journal of Microbiology
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    • v.34 no.4
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    • pp.311-315
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    • 1996
  • The retroviral Gag polyprotein directs the assembly of virion particles and plays an important role in some events after entry into a host cell. The Gag polyprotein of a virus mixture is responsible for inducing murine acquired immunodeficiency syndrome (MAIDS) when injected into susceptible strains of mice. In order to identify the host cellular proteins which interact with the MAIDS virus Gag proteins and possibly mediate the function of the Gag proteins, mouse T-cell leukemic cDNA expression library was screened using the yeast GAL4 two hybrid system. Of 11 individual positive clones, the clone Y1 was selected for the study of protein-protein interaction. Its DNA sequence revealed that it was an exact match to the murine SH3 domain-containing protein SH3P8. It is expressed as 2.4 kbp transcripts in testis at higher levels and in various tissues tested at lower levels. Glutathione S-transferase-Y1 fusion protein binds tightly to $Pr60^{def-gag}$ as well as $Pr65^{eco-gag}$.

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An Efficient Video Indexing Method using Object Motion Map in compresed Domain (압축영역에서 객체 움직임 맵에 의한 효율적인 비디오 인덱싱 방법에 관한 연구)

  • Kim, So-Yeon;No, Yong-Man
    • The Transactions of the Korea Information Processing Society
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    • v.7 no.5
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    • pp.1570-1578
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    • 2000
  • Object motion is an important feature of content in video sequences. By now, various methods to exact feature about the object motion have been reported[1,2]. However they are not suitable to index video using the motion, since a lot of bits and complex indexing parameters are needed for the indexing [3,4] In this paper, we propose object motion map which could provide efficient indexing method for object motion. The proposed object motion map has both global and local motion information during an object is moving. Furthermore, it requires small bit of memory for the indexing. to evaluate performance of proposed indexing technique, experiments are performed with video database consisting of MPEG-1 video sequence in MPEG-7 test set.

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An experimental study on the Ground deformation caused by sea-dike construction (방조제 축조에 따른 지반의 변형에 관한 실험연구)

  • 김성필
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.42 no.5
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    • pp.78-83
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    • 2000
  • When a sea-dike is constructed on soft soils, it is much difficult to calculate ground deformation caused by forced displacements. In this study , a series of laboratory model tests have been performed to investigate the ground deformation under a constructed sea-dike on soft soils. Construction sequence of sea-dike embankment was assumed such as constructed by quarry first and followed by soils adjacent to quarry embankment. as test data and displacement in subsoils have been analyzed, it seems that deformation is caused by general shear failure. the shape of ground deformation caused by forced displacements was well defined be parabola . Upon comparing profiles and depth of forced displacement from the model test to those based on stress-baring capacity method commonly used, it has been found that deformation prediction using stress-bearing capacity method was not exact at the edge of loading.

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Analysis of Multicarrier DS/DPSK Systems with Single Tone Interference Rejection (단일톤 간섭제거를 위한 다단반송파 DS/DPSK 시스템의 성능분석)

  • 엄종선;김동인
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.22 no.4
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    • pp.761-770
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    • 1997
  • Narrowband signals can be treated like a single tone interference at the receiver which demodulates wideband signals spectrum overlaid at the same frequency band. In this paper, the single tone interference is effectively suppressed by the use of a multicarrier DPSK direct-sequence(DS) spread spectrum(SS) with maximal-ratio(MR) combining instead of notch filter, which is hard to implement. A noncoherent DPSK system is considered because it is more realizable and does not require any complicate phase tracking, compared with a single carrier system subject to a constraint system bandwidth, and their performance comparisons are validated through simulation. We also propose a suboptimal-ratio(SR) combining which yields uniform and tight low bound on the performance of the MR combining, and then system parameters re optimized by theoretically evaluating the low bound, since an exact analysis appears intractable.

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