• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1279-1287
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• 2022

A partition of n is complete if every positive integer from 1 to n can be represented by the sum of its parts. The concept of complete partitions has been extended in several ways. In this paper, we consider the number of k-relaxed r-complete partitions of n and the number of double-complete partitions of n.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.431-437
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• 2002

Representing a positive integer in terms of a sum of smaller numbers with certain conditions has been studied since MacMahon [5] pioneered perfect partitions. The complete partitions is in this category and studied by the second author[6]. In this paper, we study complete partitions with more specified completeness, which we call the double-complete partitions.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.367-382
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• 2011

We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.

• Kyungpook Mathematical Journal
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• v.1 no.1
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• pp.41-44
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• 1958

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1997.10a
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• pp.166-169
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• 1997

For parallel processing, the compiler partitions a loaded program into a set of tasks and makes a schedule for the tasks that will minimize parallel processing time for the loaded program. Building an optimal schedule for a given set of partitioned tasks of a program has known to be NP-complete. In this paper we introduce a GA(Genetic Algorithm)-based scheduling method in which a chromosome consists of two parts of a string which decide the number and order of tasks on each processor. An additional computation is used for feasibility constraint in the chromosome. By granularity theory, a partitioned program is categorized into coarse-grain or fine-grain types. There exist good heuristic algorithms for coarse-grain type partitioning. We suggested another GA adaptive to the coarse-grain type partitioning. The infeasibility of chromosome is overcome by the encoding and operators. The number of processors are decided while the GA find the minimum parallel processing time.

• Annals of Laboratory Medicine
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• v.38 no.6
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• pp.503-511
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• 2018

Background: Sampling a healthy reference population to generate reference intervals (RIs) for complete blood count (CBC) parameters is not common for pediatric and geriatric ages. We established age- and sex-specific RIs for CBC parameters across pediatric, adult, and geriatric ages using secondary data, evaluating patterns of changes in CBC parameters. Methods: The reference population comprised 804,623 health examinees (66,611 aged 3-17 years; 564,280 aged 18-59 years; 173,732 aged 60-99 years), and, we excluded 22,766 examinees after outlier testing. The CBC parameters (red blood cell [RBC], white blood cell [WBC], and platelet parameters) from 781,857 examinees were studied. We determined statistically significant partitions of age and sex, and calculated RIs according to the CLSI C28-A3 guidelines. Results: RBC parameters increased with age until adulthood and decreased with age in males, but increased before puberty and then decreased with age in females. WBC and platelet counts were the highest in early childhood and decreased with age. Sex differences in each age group were noted: WBC count was higher in males than in females during adulthood, but platelet count was higher in females than in males from puberty onwards (P <0.001). Neutrophil count was the lowest in early childhood and increased with age. Lymphocyte count decreased with age after peaking in early childhood. Eosinophil count was the highest in childhood and higher in males than in females. Monocyte count was higher in males than in females (P <0.001). Conclusions: We provide comprehensive age- and sex-specific RIs for CBC parameters, which show dynamic changes with both age and sex.

• Journal of the Korea Society of Computer and Information
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• v.27 no.2
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• pp.43-51
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• 2022

In this paper, we suggest the method to improve the existing method leaning context-free grammar(CFG) using tabular representation(TBL) as a chromosome of genetic algorithm in grammatical inference and show the more efficient experimental result. We have two improvements. The first is to improve the formula to reflect the learning evaluation of positive and negative examples at the same time for the fitness function. The second is to classify partitions corresponding to TBLs generated from positive learning examples according to the size of the learning string, proceed with the evolution process by class, and adjust the composition ratio according to the success rate to apply the learning method linked to survival in the next generation. These improvements provide better efficiency than the existing method by solving the complexity and difficulty in the crossover and generalization steps between several individuals according to the size of the learning examples. We experiment with the languages proposed in the existing method, and the results show a rather fast generation rate that takes fewer generations to complete learning with the same success rate than the existing method. In the future, this method can be tried for extended CYK, and furthermore, it suggests the possibility of being applied to more complex parsing tables.