• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.83-91
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• 2023

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring M_n(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

• Journal of Korean Society for Geospatial Information Science
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• v.5 no.1 s.9
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• pp.93-101
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• 1997

The purpose of this paper is to study the using method of the satellite image processing and GIS(Geographic Information System) map-algebra for the sustainable (land-use) plan. The research has been made by the two kinds of approaching steps. The first one is to allocate the sustainable zoning which is applicable to the environmental and the legal restriction elements base on space structure. The second one is to make a more sustainable plan through the extension of analysis range and the inclusion of analyzed environmental impacts within the plan making processes.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.105-126
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• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2680-2700
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• 2017

Finite field arithmetic over GF($2^m$) is used in a variety of applications such as cryptography, coding theory, computer algebra. It is mainly used in various cryptographic algorithms such as the Elliptic Curve Cryptography (ECC), Advanced Encryption Standard (AES), Twofish etc. The multiplication in a finite field is considered as highly complex and resource consuming operation in such applications. Many algorithms and architectures are proposed in the literature to obtain efficient multiplication operation in both hardware and software. In this paper, a modified serial multiplication algorithm with interleaved modular reduction is proposed, which allows for an efficient realization of a sequential polynomial basis multiplier. The proposed sequential multiplier supports multiplication of any two arbitrary finite field elements over GF($2^m$) for generic irreducible polynomials, therefore made versatile. Estimation of area and time complexities of the proposed sequential multiplier is performed and comparison with existing sequential multipliers is presented. The proposed sequential multiplier achieves 50% reduction in area-delay product over the best of existing sequential multipliers for m = 163, indicating an efficient design in terms of both area and delay. The Application Specific Integrated Circuit (ASIC) and the Field Programmable Gate Array (FPGA) implementation results indicate a significantly less power-delay and area-delay products of the proposed sequential multiplier over existing multipliers.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.10 no.1
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• pp.7-13
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• 2011

Matrix multiplication is a fundamental operation of linear algebra and arises in many areas of science and engineering. This paper introduces an efficient parallel matrix multiplication scheme on N ${\times}$ N mesh-connected SIMD array processor, called multiple hierarchical SIMD architecture (HMSA). The architectural characteristic of HMSA is the hierarchically structured control units which consist of a global control unit, N local control units configured diagonally, and $N^2$ processing elements (PEs) arranged in an N ${\times}$ N array. PEs are communicating through local buses connecting four adjacent neighbor PEs in mesh-torus networks and global buses running across the rows and columns called horizontal buses and vertical buses, respectively. This architecture enables HMSA to have the features of diagonally indexed concurrent broadcast and the accessibility to either rows (row control mode) or columns (column control mode) of 2D array PEs alternately. An algorithmic mapping method is used for performance evaluation by mapping matrix multiplication on the proposed architecture. The asymptotic time complexities of them are evaluated and the result shows that paralle matrix multiplication on HMSA can provide significant performance improvement.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.479-484
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction $Q=(a_1,a_2,...,a_d)$ generated by d elements in A and $G(I)=\bigoplus_{n\geq0}I^n/I^{n+1}$ of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a$_1$] and P = mS. In this paper, we show that the following conditions are equivalent. (1) $I^2$ = QI and I = Q:I. (2) $I^2S$ = $a_1$IS and IS = $a_1$S：sIS. (3) $I^2$Sp = $a_1$ISp and ISp = $a_1$Sp ：sp ISp. We denote by $X_A(Q)$ the set of good ideals I in $X_A(Q)$ such that I contains Q as a reduction. As a Corollary of this result, we show that $I\inX_A(Q)\Leftrightarrow\IS_P\inX_{SP}(Qp)$.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.4
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• pp.437-446
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• 2018

This paper describes the real-time logic implementation of orthogonal matching pursuit(OMP) algorithm for compressive sensing digital receiver. OMP contains various complex-valued linear algebra operations, such as matrix multiplication and matrix inversion, in an iterative manner. Xilinx Vivado high-level synthesis(HLS) is introduced to design the digital logic more efficiently. The real-time signal processing is realized by applying dataflow architecture allowing functions and loops to execute concurrently. Compared with the prior works, the proposed design requires 2.5 times more DSP resources, but 10 times less signal reconstruction time of $1.024{\mu}s$ with a vector of length 48 with 2 non-zero elements.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.937-957
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• 2010

The purpose of this study is to discover the features of symbol sense. This study tries to sum up the meaning and elements of symbol sense and the measures to improve them through documents. Also based on this, it analyzes the learning conditions about symbol sense for 6th grade mathematically able students and suggests the method that activates symbol sense in the math of elementary schools. Considering various studies on symbol sense, symbol sense means the exact knowledge and essential understanding in a comprehensive way. Symbol sense is an intuition about symbols that grasps the meaning of symbols, understands the situation of question, and realizes the usefulness of symbols in resolving a process. Considering all other scholars' opinions, this study sums up 5 elements of the symbol sense. (The recognition of needs to introduce symbol, ability to read the meaning of symbols, choice of suitable symbols according to the context, pattern guess through visualization, recognize the role of symbols in other context) This study draws the following conclusions after applying the symbol questionnaires targeting 6th grade mathematically able students : First, although they are math talents, there are some differences in terms of the symbol sense level. Second, 5 elements of the symbol sense are not completely separated. They are rather closely related in terms of mainly the symbol understanding, thereby several elements are combined.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.155-178
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• 2014

This study starts from the problem that although the solution premise the generality in algebra, a lot of students don't understand the generality of algebraic solution. We investigated this problem to understand cognitive characteristic of students. Moreover, we tried to find the elements which helping students understand the generality of algebraic solution. The purpose is to get the didactical implications. To do this, we had investigated the cognition of twenty middle school students for generality of solution. As result, 70 % of them didn't cognize the generality of solution. We had a personal interview with four students who showed a lack of sense of generality of algebraic solution. Putting into three action which we designed to help the change of their recognition, we observed and analyzed students cognizance change. Three action is the check of accordance for individual results, the check of solution accordance for different variables and the check of arbitrary variables. Based on the analysis, we discussed on the cognitive characteristic of students and the effect of three action. We finally discussed on the didactical implications to help students understand the generality of algebraic solution.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.359-374
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• 2014

Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.