• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.313-325
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• 2009

We consider zero-divisor graphs with respect to primal, nonprimal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ringtheoretic properties of R and the graph-theoretic properties of ${\Gamma}_I(R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.555-567
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• 2007

We first find strongly 2-primal rings whose sub direct product is not (strongly) 2-primal. Moreover we observe some kinds of ring extensions of (strongly) 2-primal rings. As an example we show that if R is a ring and M is a multiplicative monoid in R consisting of central regular elements, then R is strongly 2-primal if and only if so is $RM^{-1}$. Various properties of (strongly) 2-primal rings are also studied.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• Journal of Digital Contents Society
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• v.15 no.3
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• pp.347-355
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• 2014

The general octree structure is common for various applications including computer graphics, geometry information analysis and query. Unfortunately, the general octree approach causes duplicated sample data and discrepancy between sampling and representation positions when applied to sample continuous spatial information, for example, signed distance fields. To address these issues, some researchers introduced the dual octree. In this paper, the weakness of the dual octree approach will be illustrated by focusing on the fact that the dual octree cannot access some specific continuous zones asymptotically. This paper shows that the primal tree presented by Lefebvre and Hoppe can solve all the problems above. Also, this paper presents a three-dimensional primal tree traversal algorithm based the Morton codes which will help to parallelize the primal tree method.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• Animal Bioscience
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• v.34 no.1
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• pp.127-133
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• 2021

Objective: This study was conducted to evaluate the correlation between body size traits, carcass traits, and primal cuts in Hanwoo steers. Methods: Sixty-one beef carcasses were classified for conformation and primal cut weight. Additionally, carcass weight, fat thickness, carcass dimensions, and longissimus muscle area were determined to complement the grading. Results: The average live weight and cold carcass weight were 759 and 469 kg, respectively. The mean carcass meat, fat, and bone proportions were 551, 298, and 151 g/kg, respectively. Primal cuts weights showed significant positive correlations (p<0.001) of 0.42 to 0.82 with live weight, carcass weight, and longissimus muscle area and a significant negative correlation with carcass fat (without shank, -0.38 to -0.10). Primal cut weights were positively correlated (p<0.01) with carcass length (0.41 to 0.77), forequarter length (0.33 to 0.57), 6th lumbar vertebrae-heel length (0.33 to 0.59), 7th cervical vertebrae carcass breadth (0.35 to 0.58), 5th to 6th thoracic vertebrae breadth (0.36 to 0.65), 7th to 8th thoracic vertebrae girth (0.38 to 0.63), and coxae girth (0.34 to 0.56) and non-significantly related to cervical vertebrae length and coxae thickness. Conclusion: There was a high correlation among live weight, carcass weight, longissimus muscle area, carcass length, 7th cervical vertebrae carcass breadth, 5th to 6th thoracic vertebrae breadth, and 7th to 8th thoracic vertebrae girth of the primal cuts yield. The correlation between fat and primal cut yields was highly significant and negative. Carcass length and 7th to 8th thoracic vertebrae girth, appear to be the most important traits affecting primal cut yields.

• Food Science of Animal Resources
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• v.35 no.6
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• pp.859-866
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• 2015

To determine chemical components and meat quality traits related to palatability of 10 primal cuts, 25 Hanwoo carcasses were selected from 5 carcasses × 5 quality grades and used to obtain proximate data and meat quality characteristics. Significant differences (p<0.05) in chemical component and meat quality were found among the 10 primal cuts. The highest fat content was found in the kalbi, followed by dungsim, yangjee, chaekeut, ansim, abdari, suldo, moksim, udun, and satae. Protein and moisture contents in the 10 primal cuts were in reverse order of fat content. Moksim had the highest drip loss % and cooking loss % than all other primal cuts while kalbi showed the lowest (p<0.05) percentage of drip and cooking loss. Ansim had the longest sarcomere length but the lowest shear force values than all other cuts (p<0.05). The highest (p<0.05) score for overall acceptability was observed in ansim. Moksim, udun, abdari, and satae were rated the lowest (p<0.05) in overall acceptability among the 10 primal cuts from Hanwoo carcasses. In conclusion, ansim, dungsim, chaekeut, and kalbi had the highest overall acceptability due to their higher fat contents and lower shear force values.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.457-466
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• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.5
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• pp.801-810
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• 2004

The Primal-Dual Interior-Point (PDIP) method is currently one of the fastest emerging topics in optimization. This method has become an effective solution algorithm for large scale nonlinear optimization problems. such as the electric Optimal Power Flow (OPF) and natural gas and electricity OPF. This study describes major theoretical developments of the PDIP method as well as practical issues related to implementation of the method. A simple quadratic problem with linear equality and inequality constraints

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.927-938
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• 2011

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.