• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.321-336
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• 2012

Cognitive subject imposes structures on an object to shape it into a structured thing. Structures that the subject imposes on an object in a given problem context can be diverse horizontally and vertically. In view of the horizontal diversity of structure, problem-solving activities focusing on various structures may enrich the present problem-solving education which emphasizes applying and comparing a couple of problem-solving strategies. Finding an algebraic formula for a figural pattern should be regarded as a new starting point of searching for more various structures. In view of the vertical diversity of structure, it should be aware that students may see different structures from the structure that their teacher expect them to see. The vertical diversity of structure enables us to provide students with experience of progress.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.529-537
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• 2014

The paper introduces a new product of polynomials defined over a field. It is a generalization of the ordinary product with inner polynomial getting non-overlapping segments obtained by multiplying with coefficients and variable with expanding powers. It has been called 'Ordered Power Product' (OPP). Considering two rings of polynomials $R_m[x]=F[x]modulox^m-1$ and $R_n[x]=F[x]modulox^n-1$, over a field F, the paper then considers the newly introduced product of the two polynomial rings. Properties and algebraic structure of the product of two rings of polynomials are studied and it is shown to be a ring. Using the new type of product of polynomials, we define a new product of two cyclic codes and devise a method of getting a cyclic code from the 'ordered power product' of two cyclic codes. Conditions for the OPP of the generators polynomials of component codes, giving a cyclic code are examined. It is shown that OPP cyclic code so obtained is more efficient than the one that can be obtained by Kronecker type of product of the same component codes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Proceedings of the Korea Database Society Conference
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• 1997.10a
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• pp.483-503
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• 1997

One important question that arises when dealing with temporal databases in context of object-oriented systems is the method that associates time with attributes relationship semantics. Results of previous work about attribute versioning, particularity extending flat(First Normal Form: FNF) or nested(Non-First Normal Form: NFNF) relational models. are not applicable to temporal object-oriented databases. This is because object-oriented models provide more powerful constructs than traditional models for structuring complex objects. Therefore, this paper presents an formal approach for incorporating temporal extension to object-oriented databases. Our goal in this paper is to study temporal object-oriented database representation according to generalization, aggregation and association among objects. We define tile concepts of attribute versioning in temporal object-oriented model, and we concentrate on the representation of temporal relationship among objects. Another contribution of this paper is to specify time constraints on relationship semantics and analyze our model based on representation criteria. By means of formalizing tile temporal object oriented model, this paper can not only provide tile robust operating functions that design algebraic operators, but also entrance the reuse of modules.

• Journal of Digital Convergence
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• v.13 no.6
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• pp.157-164
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• 2015

An efficient retrieval of useful information is a prerequisite of an optimal decision making system. Hence, A research of data mining techniques finding useful patterns from the various forms of data has been progressed with the increase of the application of Big Data for convergence and integration with other industries. Each technique is more likely to have its drawback so that the generalization of retrieving useful information is weak. Another integrated technique is essential for retrieving useful information. In this paper, a uncertainty measure of information is calculated such that algebraic probability is measured by Bayesian theory and then information entropy of the probability is measured. The proposed measure generates the effective reduct set (i.e., reduced set of necessary attributes) and formulating the core of the attribute set. Hence, the optimal decision rules are induced. Through simulation deciding contact lenses, the proposed approach is compared with the equivalence and value-reduct theories. As the result, the proposed is more general than the previous theories in useful decision-making.

• School Mathematics
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• v.16 no.4
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• pp.803-825
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• 2014

From the early stages of learning algebra, literal symbols are used to represent algebraic objects such as variables and parameters. The concept of parameters contains both indeterminacy and fixity resulting in confusion and errors in understanding. The purpose of this research is to compare the beginners of algebra and pre-service teachers who completed secondary mathematics education in terms of understanding this paradoxical nature of parameters. We recruited 35 middle school students in eight grade and 73 pre-service teachers enrolled in a undergraduate course at one university. Using them we conducted a survey on the perception of the nature of parameters asking if one considers parameters suggested in a problem as variables or constants. We analyzed the collected data using the mixed method of qualitative and quantitative approaches. From the analysis results, we identified several difficulties in understanding of parameters from both groups. Especially, our statistical analysis revealed that the proportions of subjects with limited understanding of the concept of parameters do not differ much in two groups. This suggests that learning algebra in secondary mathematics education does not improve the understanding of the nature of parameters significantly.