• Title, Summary, Keyword: dual modules

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EXTENSIONS OF DRINFELD MODULES OF RANK 2 BY THE CARLITZ MODULE

  • Woo, Sung-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.251-257
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    • 1995
  • In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

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ON DUAL ZARISKI TOPOLOGY OVER GRADED COMULTIPLICATION MODULES

  • Abu-Dawwas, Rashid;Alshehry, Azzh Saad
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.11-18
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    • 2021
  • In this article, we deal with Zariski topology on graded comultiplication modules. The purpose of this article is obtaining some connections between algebraic properties of graded comultiplication modules and topological properties of dual Zariski topology on graded comultiplication modules.

A Study on the Implementation of a Control System with Dual Structure and Its Reliability Analysis (이중구조를 갖는 제어시스템의 구현과 신뢰도 분석에 관한 연구)

  • ;;;Zeung Nam Bien
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.9
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    • pp.1351-1363
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    • 1990
  • In this paper, a reliable control system structured with dual CPU modules and dual I/O modules is implemented as a means of achieving a highly reliable fault tolerant control system. For this, faults in the system modules are first examined, and a fault detection technique consisting of self diagnostic, comparison process, and exception processing is applied. Self diagnostic is used to locate which components in the modules have been failed, while comparison process is to cmpare control outputs computed by both CPU modules and protect the plant from malfunction by blocking failed control outputsin advance. Finally exception processing is used to determine the faults that are not detected immediately by the self diagnostic and comparison process, e.g. bus error processing when acknowledge signal for data transfer is not activeted in the I/O modules. Also reliability analysis is conducted for the discrete time Markov model with dual structure. It is shown quantitatively that the reliability is improved in the control system with dual structure in comparison with a system with single module structure.

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A study on the control system with dual structure to enhance its reliability (제어 시스템의 신뢰도 향상을 위한 이중화 구조 연구)

  • 박세화;문봉채;김병국;변증남
    • 제어로봇시스템학회:학술대회논문집
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    • pp.773-778
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    • 1990
  • In this paper, a reliable control system structured with dual CPU modules and dual I/O modules is implemented as a means of achieving a highly reliable fault tolerant control system. For this, faults in the system modules are first examined, and a fault detection technique consisting of self diagnostic, comparison process, and exception processing is applied. Also reliability analysis is conducted for the discrete time Markov model with dual structure. It is shown quantitatively that the reliability is improved in the control system with dual structure in comparison with a system with single module structure.

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GORENSTEIN WEAK INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE

  • Gao, Zenghui;Ma, Xin;Zhao, Tiwei
    • Journal of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1389-1421
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    • 2018
  • In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

EXTENSIONS OF t-MODULES

  • Woo, Sung-Sik
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.361-367
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    • 1994
  • An elliptic module is an analogue of an elliptic curve over a function field [D]. The dual of an elliptic curve E is represented by Ext(E, $G_{m}$) and the Cartier dual of an affine group scheme G is represented by Hom(G, G$G_{m}$). In the category of elliptic modules the Carlitz module C plays the role of $G_{m}$. Taguchi [T] showed that a notion of duality of a finite t-module can be represented by Hom(G, C) in a suitable category. Our computation shows that the Ext-group as it stands is rather too "big" to represent a dual of an elliptic module.(omitted)

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Module Multilevel-Clamped Composited Multilevel Converter (M-MC2) with Dual T-Type Modules and One Diode Module

  • Luo, Haoze;Dong, Yufei;Li, Wuhua;He, Xiangning
    • Journal of Power Electronics
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    • v.14 no.6
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    • pp.1189-1196
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    • 2014
  • A modular multilevel-clamped composited multilevel converter ($M-MC^2$) is proposed. $M-MC^2$ enables topology reconfiguration, power device reuse, and composited clamping. An advanced five-level converter ($5L-M-MC^2$) is derived from the concept of $M-MC^2$. $5L-M-MC^2$ integrates dual three-level T-type modules and one three-level neutral point clamped module. This converter can also integrate dual three-level T-type modules and one passive diode module by utilizing the device reuse scheme. The operation principle and SPWM modulation are discussed to highlight converter performance. The proposed $M-MC^2$ is comprehensively compared with state-of-the-art five-level converters. Finally, simulations and experimental results are presented to validate the effectiveness of the main contributions of this study.