• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.11a
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• pp.248-251
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• 1999

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at i(oration n upon the arrival of new data. The RLS algorithm may be viewed as a special case of the Kalman filter. Indeed this special relationship between the RLS algorithm and the Kalman filter is considered. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. The resulting rate of convergence is therefore typically an order of magnitude faster than the simple LMS algorithm. This improvement in performance, however, Is achieved at the expensive of a large increase in computational complexity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• The Mathematical Education
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• v.50 no.2
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.9
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• pp.3458-3481
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• 2021

Existing methods for blind identification of linear block codes without a candidate set are mainly built on the Gauss elimination process. However, the fault tolerance will fall short when the intercepted bit error rate (BER) is too high. To address this issue, we apply the reverse algebra approach and propose a novel "two-step-screening" algorithm by solving the linear error equations on the binary Galois field, or GF(2). In the first step, a recursive matrix partition is implemented to solve the system linear error equations where the coefficient matrix is constructed by the full codewords which come from the intercepted noisy bitstream. This process is repeated to derive all those possible parity-checks. In the second step, a check matrix constructed by the intercepted codewords is applied to find the correct parity-checks out of all possible parity-checks solutions. This novel "two-step-screening" algorithm can be used in different codes like Hamming codes, BCH codes, LDPC codes, and quasi-cyclic LDPC codes. The simulation results have shown that it can highly improve the fault tolerance ability compared to the existing Gauss elimination process-based algorithms.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.403-430
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• 2011

The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.123-143
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• 2010

The Skeleton Tower problem is an example of a curriculum that integrates algebra and geometry. Finding the number of the cubes in the tower can be approached in more than one way, such as counting arithmetically, drawing geometric diagrams, enumerating various possibilities or rules, or using algebraic equations, which makes the tasks accessible to students with varied prior knowledge and experience. So, it will be a good topic which can be used in the elementary grades if we exclude the method of using algebraic equations. The purpose of this paper is to propose some points which can be considered with attention by gifted children education teachers by analyzing the 4th Skeleton Tower problem solutions made by 3rd and 4th graders in their selection test who applied for the education of gifted children in math at J University for the year of 2010.

• Journal of KIISE:Databases
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• v.32 no.4
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• pp.383-393
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• 2005

Retrieval of images from image databases by spatial relationship can be effectively performed through visual interface systems. In these systems, the representation of image with 2D strings, which are derived from symbolic projections, provides an efficient and natural way to construct image index and is also an ideal representation for the visual query. With this approach, retrieval is reduced to matching two symbolic strings. However, using 2D-string representations, spatial relationships between the objects in the image might not be exactly specified. Ambiguities arise for the retrieval of images of 3D scenes. In order to remove ambiguous description of object spatial relationships, in this paper, images are referred by considering spatial relationships using the spatial location algebra for the 3D image scene. Also, we remove the repetitive spatial relationships using the several reduction rules. A reduction mechanism using these rules can be used in query processing systems that retrieve images by content. This could give better precision and flexibility in image retrieval.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1015-1027
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• 2009

Many problems of confounding and identifiability for polynomial models in an experimental design can be solved using methods of algebraic geometry. The theory of $Gr\ddot{o}bner$ basis is used to characterize the design. In addition, a fractional factorial design can be uniquely represented by a polynomial indicator function. $Gr\ddot{o}bner$ bases and indicator functions are powerful computational tools to deal with ideals of fractions based on each different theoretical aspects. The problem posed here is to give how to move from one representation to the other. For a given fractional factorial design, the indicator function can be computed from the generating equations in the $Gr\ddot{o}bner$ basis. The theory is tested using some fractional factorial designs aided by a modern computational algebra package CoCoA.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.