• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• East Asian mathematical journal
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• v.31 no.2
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• pp.145-165
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• 2015

The purpose of this study is to suggest how to go about teaching and learning secondary school algebra by analyzing problem-solving ability and problem-solving process through algebraic reasoning. In doing this, 393 students' data were thoroughly analyzed after setting up the exam questions and analytic standards. As with the test conducted with technical school students, the students scored low achievement in the algebraic reasoning test and even worse the majority tried to answer the questions by substituting arbitrary numbers. The students with high problem-solving abilities tended to utilize conceptual strategies as well as procedural strategies, whereas those with low problem-solving abilities were more keen on utilizing procedural strategies. All the subject groups mentioned above frequently utilized equations in solving the questions, and when that utilization failed they were left with the unanswered questions. When solving algebraic reasoning questions, students need to be guided to utilize both strategies based on the questions.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.259-272
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• 2017

In this paper we study the mapping properties of the finite field restricted averaging operators to various algebraic varieties. We derive necessary conditions for the boundedness of the generalized restricted averaging operator related to arbitrary algebraic varieties. It is shown that the necessary conditions are in fact sufficient in the specific case when the Fourier transform on varieties has enough decay estimates. Our work extends the known optimal result on regular varieties such as paraboloids and spheres to certain lower dimensional varieties.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.469-479
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• 1996

Toric variety is a normal algebraic variety containing algebraic torus $T_N$ as an open dense subset with an algebraic action of $T_N$ which is an extension of the group law of $T_N$. A toric variety can be described in terms of a certain collection, which is called a fan, of cones. From this fact, the properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. That is, we can translate the diffcult algebrogeometric properties of toric varieties into very simple properties about the combinatorics of cones in affine spaces over the reals.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.6
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• pp.259-265
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• 2001

In the last two decades, many researchers proposed various usages of the orthogonal functions such as Walsh, Haar and BPF to solve the system analysis, optimal control, and identification problems from and algebraic form. In this paper, a simple procedure to design and algerbraic observer for the descriptor system is presented by using block pulse function expansions. The main characteristic of this technique is that it converts differential observer equation into an algerbraic equation. And furthermore, a simple recursive algorithm is proposed to obtain BPFs coefficients of the observer equation.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.77-89
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• 2002

In this paper, we define for a component $X_{0}$ of a nonsingular compact real algebraic surface X the complex genus of $X_{0}$, denoted by gc($X_{0}$), and use this to prove the nonexistence of nonzero degree entire rational maps f : $X_{0}$ Y provided that gc(Y) > gc($X_{0}$), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.449-473
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• 2012

In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.