• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.563-571
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• 1997

In this paper we define CR(completely reachable), MICR(minimal cyclic refinement)and MACR(maximal cyclic refinement)-Modules. We have obtained equivalent statements for minimal cyclic submodule and maximal cyclic submodule. Also we have obtained necessary and sufficient conditions for a module M with MICR to be cyclic or strongly cyclic.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.1-9
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• 1998

In this paper we define CR(completely reachable), MICR(minimal cyclic refinement) and MACR(maximal cyclic refinement)-Modules. We have obtained equivalent statements for minimal cyclic submodule and maximal cyclic submodule. Also, we have obtained necessary and sufficient conditions for a module M with MICR to be cyclic or strongly cyclic.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.679-687
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• 2005

In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.223-234
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• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• Nuclear Engineering and Technology
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• v.56 no.6
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• pp.2352-2366
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• 2024

Reinforced concrete (RC) shear walls with precast steel-concrete composite modular (PSCCM) are strongly recommended in the structural design of nuclear power plants due to the need for a large number of process pipeline crossings and industrial construction. However, the effect of the PSCCM on the mechanical behavior of the whole RC shear wall is still unknown and has received little attention. In this study, three 1:3 scaled specimens, one traditional shear wall specimen (TW) and two shear wall specimens with the PSCCM (PW1, PW2), were designed and investigated under cyclic loadings. The failure mode, hysteretic curve, energy dissipation, stiffness and strength degradations were then comparatively investigated to reveal the effect of the PSCCM. Furthermore, numerical models of the RC shear wall with different PSCCM distributions were analyzed. The results show that the shear wall with the PSCCM has comparable mechanical properties with the traditional shear wall, which can be further improved by adding reinforced concrete constraints on both sides of the shear wall. The accumulated energy dissipation of the PW2 is higher than that of the TW and PW1 by 98.7 % and 60.0 %. The failure of the shear wall with the PSCCM is mainly concentrated in the reinforced concrete wall below the PSCCM, while the PSCCM maintains an elastic working state as a whole. Shear walls with the PSCCM arranged in the high stress zone will have a higher load-bearing capacity and lateral stiffness, but will suffer a higher risk of failure. The PSCCM in the low stress zone is always in an elastic working state.