• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.603-613
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• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.

• Nuclear Engineering and Technology
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• v.19 no.3
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• pp.169-179
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• 1987

The change of material J-R (J-T) curve with crack extension and J-calculation method was investigated to give experimental and analytical method for reliable J-R (J-T) curve, which was adapted recently as a tool for instability analysis of Nuclear Pressure Vessel. Experiments were carried out by Single Specimen Unloading Compliance Method using 1/2"T, Compact-Tension Type fracture mechanic specimens which were the same size and material as domestic nuclear pressure vessel material surveillance specimens. The results revealed that crack extension up to 25~30% of initial uncracked ligament and JD (Deformation theory J) calculation method, currently being used in NUREG-0744, could give rather reliable material J-R (J-T) curve than the small crack extension and JM (Modified J) calculation method. But as JM results more or less higher J at instability, the application of JM should be considered regarding to the problem of power plant availability.lity.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.37-45
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• 2007

Let X, Y be vector spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for a cubic function $f:X{\rightarrow}Y$ satisfies $$r^3f(\frac{\Sigma_{j=1}^{n-1}x_j+2x_n}{r})+r^3f(\frac{\Sigma_{j=1}^{n-1}x_j-2x_n}{r})+8\sum_{j=1}^{n-1}f(x_j)=2f{\sum_{j=1}^{n-1}}x_j)+4{\sum_{j=1}^{n-1}}(f(x_j+x_n)+f(x_j-x_n))$$ for all $x_1,{\cdots},x_n{\in}X$.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.951-959
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• 1994

A sequence ${X_j : j \geq 1}$ of random variables is said to be pairwise positive quadrant dependent (pairwise PQD) if for any real $r-i,r_j$ and $i \neq j$ $$ P{X_i > r_i,X_j > r_j} \geq P{X_i > r_i}P{X_j > r_j} $$ (see [8]) and a sequence ${X_j : j \geq 1}$ of random variables is said to be associated if for any finite collection ${X_{i(1)},...,X_{j(n)}}$ and any real coordinatewise nondecreasing functions f,g on $R^n$ $$ Cov(f(X_{i(1)},...,X_{j(n)}),g(X_{j(1)},...,X_{j(n)})) \geq 0, $$ whenever the covariance is defined (see [6]). Instead of association Cox and Grimmett's [4] original central limit theorem requires only that positively linear combination of random variables are PQD (cf. Theorem $A^*$).

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.4
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• pp.488-503
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• 1999

The present paper considers the constraint effect on J-R curves under the two-parameter $J-A_2$ controlled crack growth within a certain amount of crack extension. Since the parameter $A_2$ in $J-A_2$ three-term solution is independent of applied loading under fully plasticity or large-scale defor-mation $A_2$ is a proper constraint parameter uring crack extension. Both J and $A_2$ are used to char-acterize the resistance curves of ductile crack growth using J as the loading level and $A_2$ are used to char-acterize the resistance curves of ductile crack growth using J as the loading level and A2 as a con-straint parameter. Approach of the constraint-corrected J-R curve is proposed and a procedure of transferring the J-R curves determined from standard ASTM procedure to non-standard speci-mens or real cracked structures is outlined. The test data(e.g. initiation toughness JIC and tearing modulus $T_R$) of Joyce and Link(Engineer-ing Fracture Mechanics 1997, 57(4) : 431-446) for single-edge notched bend[SENB] specimen with from shallow to deep cracks is employed to demonstrate the efficiency of the present approach. The variation of $J_{IC}$ and $T_R$ with the constraint parameter $A_2$ is obtained and a con-straint-corrected J-R curves is constructed for the test material of HY80 steel. Comparisons show that the predicted J-R curves can very well match with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension. Finally the present constraint-corrected J-R curve is used to predict the crack growth resistance curves for different fracture specimens. over a reasonably large amount of crack extension. Finally the present constraint-corrected J-R curve is used to predict the crack growth resistance curves for different fracture specimens. The constraint effects of specimen types and specimen sizes on the J-R curves can be easily obtained from the constrain-corrected J-R curves.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• Journal of Welding and Joining
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• v.15 no.4
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• pp.178-186
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• 1997

The purpose of this study is to evaluate the J-R curve characteristics for the 5083 aluminum alloy weldment by the load ratio analysis. The results of the load ratio analysis are compared with those of the J-R curve which are obtained by the ASTM unloading compliance method. The crack length calculated by the load ratio analysis is agrees well with the measured final crack length. The slope of the exponential J-R curve estimated by the load ratio analysis is slightly smaller than that by the ASTM unloading compliance method. The exponential correlation of the J-R curve for the 5083 aluminum alloy base metal by the load ratio analysis is J = 93.88 ${\Delta}{\alpha}^{0.375}$. That for the weld metal and HAZ is J = 69.87 ${\Delta}{\alpha}^{0.389}$ and J = 70.59 ${\Delta}{\alpha}^{0.359}$ respectively. The J-R curve obtained by the ASTM unloading compliance method is overpredicted and should be offsetted due to the initial negative crack. On the other hand, the load ratio analysis method can evaluate the J-R curve by only load displacement curve without particular crack measurement equipment.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.161-169
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• 2012

Let R be a commutative Noetherian ring and I, J be ideals of R. We introduced the notion of (I; J)-cominimax R-modules. For an integer $n$ and an R-module M, let $H^i_{I,J}(M)$ be an (I; J)-cominimax R-module for all $i<n$. The J-minimaxness of some Ext modules of $H^n_{I,J}(M)$ is investigated. Among of the obtaining results, there is a generalization of the main result of [1].

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.812-815
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• 2002

The shape of K-R curve for an ideally brittle material is flat because the surface energy is an unvaried material property. However, the K-R curve can take on a variety of shapes when nonlinear material behavior accompanies fracture. By the way, a general metallic material is nonlinear, structural steel is such. Therefore, the J-R curve form J-integral value instead of K parameters can be used to evaluate elastic-plastic materials with flaws in terms of ductile fracture that can be significant to design. In this paper, R-curve behaviors form K and J parameter is considered for the precise assessment of fracture analysis, in case of JS-SS400 steels.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.653-657
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• 2014

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.