• Research in Mathematical Education
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• v.16 no.4
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• East Asian mathematical journal
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• v.29 no.4
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• pp.355-392
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• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.205-211
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• 2002

Unknown inputs observer(UIO) which is achieved by the coordinate transformation method has the differential of system outputs in the observer and the equation for unknown inputs estimation. Generally, the differential of system outputs in the observer can be eliminated by defining a new variable. But it brings about the partition of the observer into two subsystems and need of an additional differential of system outputs still remained to estimate the unknown inputs. Therefore, the block pulse function expansions and its differential operation which is a newly derived in this paper are presented to alleviate such problems from an algebraic form.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.595-597
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• 1998

This paper deals with an algebraic compensator design for dynamic systems using a novel BPF transformation method. To obtain an algebraic compensator for the system, block pulse function's differential operation is used. Compare to unalgebraic compensator, proposed algebraic compensator is less sensitive to the measurement noise.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.379-386
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• 2018

We generalized the quadratic fuzzy numbers on ${\mathbb{R}}$ to ${\mathbb{R}}_2$. By defining parametric operations between two regions valued ${\alpha}-cuts$, we got the parametric operations for two triangular fuzzy numbers defined on ${\mathbb{R}}_2$. The results for the parametric operations are the generalization of Zadeh's extended algebraic operations. We generalize the 2-dimensional quadratic fuzzy numbers on ${\mathbb{R}}_2$ that may have maximum value h < 1. We calculate the algebraic operations for two generalized 2-dimensional quadratic fuzzy sets.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2543-2545
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• 2005

It is well known that the orthogonal function is a very useful to estimate an unknown inputs in the linear dynamic systems for its recursive algebraic algorithm. At this aspects, derivative operation(matrix) of orthogonal functions(walsh, block pulse and haar) are introduced and shown how it can useful to design an UIO(unknown inputs observer) design.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.2
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• pp.139-158
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• 1995

A temporal database systems provides timing information and maintains history of data compared to the conventional database system. In this paper, we present a temporal relational database which use an interval-stamping method for instant-based events and for interval-based states. A set of temporal algebraic operators are developed on an instance of time and interval of time so that we can manipulate events and states at a same time. The set of operation is the basis for creating a relational algebra that is closed for temporal relations. And temporal SQL is also suggested as a temporal query relational language for our algebraic operations on temporal relations.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.1
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• pp.1-7
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• 2002

This paper proposes a algebraic parameter determination of MRA(Model Reference Adaptive Control) controller using block Pulse functions and block Pulse function's differential operation. Generally, adaption is performed by solving differential equations which describe adaptive low for updating controller parameter. The proposes algorithm transforms differential equations into algebraic equation, which can be solved much more easily inn a recursive manner. We believe that proposes methods are very attractive and proper for parameter estimation of MRAC controller on account of its simplicity and computational convergence.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.209-216
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• 2002

In this paper, we introduce a concept of (H)-property which generalize that of increasing(decreasing) property of binary operation. We also treat some works related to operations on fuzzy numbers and generalize earlier results of Kawaguchi and Da-te(1994).