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NHR-200-II is a small integrated pressurized water reactor with 200 MW core thermal power. The core heat is transferred to two independent intermediate circuits via fourteen in-vessel primary heat exchangers (PHE), and the heat in the intermediate circuits is transferred to feedwater by two steam generators (SG) in the two intermediate circuits respectively. A passive residual heat removal (PRHR) branch is connected to each intermediate circuit to remove core decay heat under postulated accidents. During normal operation, PRHR branches are isolated by valves while SG branches in intermediate circuits are open. The valves in PRHR branches will be opened and the isolation valves of SG branches will be closed during decay heat removal scenarios. The decay heat removal capacity of NHR-200-II PRHRS could be seriously deteriorated once the isolation valves for SG branches fail to close, which was confirmed in a scaled integral test loop previously. Current understanding of PRHRS's thermal- hydraulic characteristics with possible isolation failure in SG branches is limited. In this paper, the NHR-200-II PRHRS is modeled with RELAP5 considering the case of success and fail to isolate SG branches. A series of numerical simulations are carried out to study the impact of various parameters, such as the initial temperature, the size of the intermediate circuits' header, and the initial flow direction in the intermediate circuits. Oscillatory flow is found when SG branches fail to be isolated under certain parameters combinations. An improved PRHRS design is purposed to eliminate possible flow oscillations, and the purposed improved design are tested by numerical simulations. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with center Z(R), central closure RC, right Martindale quotient ring Qr, F a left generalized derivation and I a nonzero right ideal of R which is semiprime as a ring. We proved in this article that if one of the following conditions holds: (i) F(x o y) ± x o y = 0 (ii) F(xy) ± xy ∈ Z(R) (iii) F(x)F(y) ± xy ∈ Z(R) (iv) F([x,y]) = ±[F(x), y] (v) F(x o y) = ±(F(x) o y) for all x, y ∈ I, then R is commutative or there exists q ∈Qr(RC) such that F(x) = qx for all x ∈ R. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring with characteristic different from two and L a noncentral square-closed Lie ideal of R. Suppose that R admits a multiplicative generalized derivation (F; d) satisfying d(L) ⊂ L. In the present paper, we shall prove that d is commuting on L if one of the following conditions holds: (i)F([x, y]) = ±[x, d(y)] (ii)F(x o y) = ±(x o d(y)) (iii)F([x, y]) = ±(F(y)x) (iv)F([x, y]) = ±(F(x)y) (v)F(x o y) = ±(F(y)x) (vi) F(x o y) = ±(F(x)y) for all x, y 2 L. [ABSTRACT FROM AUTHOR]

Let M be a prime Γ-ring, I a nonzero ideal, θ an automorphism and d a θ-derivation of M. In this article we have proved the following result: (1) If d([x, y]α) = ±([x, y]α) or d((x o y)α) = ±((x o y)α) for all x, y ε I;α ε Γ, then M is commutative. (2) Under the hypothesis dθ = θd and Char M, 2, if (d(x) o d(y))α = 0 or [d(x),d(y)]α = 0 for all x, y 2 I;α α Γ, then M is commutative. (3) If d acts as a homomorphism or an antihomomorphism on I, then d = 0 or M is commutative. Moreover, an example is given to demonstrate that the primeness imposed on the hypothesis of the various results is essential. [ABSTRACT FROM AUTHOR]

Let M be a prime Γ-ring, I a nonzero ideal, θ an automorphism and dd a θ-derivation of MM. In this article we have proved the following result: (1) If d([x,y]α)=±([x,y]α) or d((xoy)α)=±((xoy)α) for x,y∈I;α∈Γ, then M is commutative. (2) Under the hypothesis dθ=θd and CharM ≠ 2, if (d(x) o d(y))α=0 or [d(x),d(y)]α=0 for all x,y∈I;α∈Γ, then M is commutative. (3) If dd acts as a homomorphism or an anti-homomorphism on I, then d=0 or M is commutative. Moreover, an example is given to demonstrate that the primeness imposed on the hypothesis of the various results is essential. [ABSTRACT FROM AUTHOR]

Let R be a prime ring, I a nonzero ideal of R, and a ε R. Suppose that σ is a nontrivial automorphism of R such that af{(σ(x 0 y))n - (x 0 y)m} = 0 or a{(σ([x; y]))n - ([x; y])m} = 0 for all x,y ε I, where n and m are fixed positive integers. We prove that if char(R) > n + 1 or char(R) = 0, then either a = 0 or R is commutative. [ABSTRACT FROM AUTHOR]

Let R be a ring, S a nonempty subset of R and d a derivation on R. A mapping $f:R\longrightarrow R$ is called commuting on S if [ f( x), x] = 0 for all x ∈ S. In this paper, our purpose is to produce commutativity results for rings and show that if R is a 2-torsion free semiprime ring and I a nonzero ideal of R, then a derivation d of R is commuting on I if one of the following conditions holds: (i) d( x) ∘ d( y) = x ∘ y (ii) d( x) ∘ d( y) = − ( x ∘ y) (iii) d( x) ∘ d( y) = 0 (iv) [ d( x), d( y)] = − [ x, y] (v) d( x) d( y) = xy (vi) d( x) d( y) = − xy (vii) d( x) d( y) = yx (viii) d( x) d( x) = x for all x, y ∈ I. Further, if d( I) ≠ 0, then R has a nonzero central ideal. Finally, some examples are given to demonstrate that the restrictions imposed on the hypotheses of the various results are not superfluous. [ABSTRACT FROM AUTHOR]