• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.

• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

• Cross-Cultural Studies
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• v.49
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• pp.95-126
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• 2017

The purpose of this paper is to compare learners' academic texts with academic texts of native speakers and to examine the usage patterns of learners' objectification strategies in detail. In order to achieve objectivity as a discourse mechanism applied to describe the results of academic inquiry in a scientific way with universality and validity, we analyzed concepts and signs such as related intentionality, accuracy, and mitigation of the linguistic markers of objectification strategies. As a result of the comparison, it was analyzed that there are intersectional overlaps with the signs that reveal objectivity, signs indicating related mechanisms, and there is a different set that is differentiated. Objective markers can be broadly classified as emphasizing stativity of research results, separating research subjects from research results, and generalizing research contents. Sustainable expressions and noun phrases emphasize statehood, and non-inhabited expressions, passive expressions, and self-quotations are maintained in the distance between the claimant and the writer, and the pluralization through first-person pronouns and suffixes contributes to generalization. In the case of the learner, the non-inhuman expression of the quotation type appears to be very less compared to the maw speaker, which could be due to the lack of recognition of the citation method of the Korean academic text. Next, in the generalization of the research contents, the expression of 'we' was very less compared to the maw speakers.

• Water for future
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• v.37 no.2
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• pp.82-89
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• 2004

과학적인 유역관리를 위한 모형개발 환경의 구현은 구체적인 방법론의 제시와 더불어 중요한 연구과제이다. 모형개발자들은 개발과정이나 표현과정, 모형의 보정 혹은 구동과정에서 빈번히 반복적이고 시간 소모적인 소프트웨어의 작업을 수행해왔다. 이 과정에서 상당한 시간과 자원의 낭비가 발생되었고, 많은 경우 개발된 모형이 일반화되는데 상당한 장애요인이 되었다. 또한 개발자들 상호간의 상이한 개발환경은 모형의 통합이나 상호검증에 긍정적으로 작용하지 못했다.(중략)

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.31-36
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• 2005

EDF에 근거한 Cramer-von Mises 형태의 통계량을 합교원리를 이용하여 다변량으로 일반화한다. 그리고 제안된 통계량의 귀무가설에서의 극한분포를 적절한 공분산함수를 가진 가우스 과정의 적분의 형태로 표현하고 통계량의 근사적인 계산방법을 고려한다.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.1
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• pp.1-6
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• 2001

In this paper we reanalyze Kohonen‘s learning vector quantizing (LVQ) Learning rule which is based on Hcbb’s learning rule with a view to a gradient descent method. Kohonen's LVQ can be classified into two algorithms according to 6learning mode: unsupervised LVQ(ULVQ) and supervised LVQ(SLVQ). These two algorithms can be represented as gradient descent methods, if target values of output neurons are generated properly. As a result, we see that the LVQ learning method is a special case of a gradient descent method and also that LVQ is represented by a generalized percetron-like LVQ(PLVQ).

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.4
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• pp.389-405
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• 1999

본 논문에서는 상호 연결망의 노드를 행렬로 표현하고 행렬연산을 이용하여 에지를 정의한 새로운 상호 연결망으로 행렬-스타 그래프를 제안한다. 행렬-스타 그래프는 널리 알려진 스타 그래프를 일반화한 그래프이다. 먼저, 행렬-스타 그래프의 노드를 2 $\times$ n 행렬로 표현한 행렬-스타 그래프 MS2,n 에 대하여 주요 망 척도인 분지수, 연결도, 확장성, 대칭성, 리우팅 ,지름 방송등을 분석한다. 다음으로, 행렬-스타 그래프 MS2,n의 노드를 2차원과 3차원으로 일반화한 행렬-스타 그래크 MSk,n과 MS k,n,p를 정의하고 행렬-스타그래프 MSk,n,p 의 라우팅 알고리즘과 지름을 분석한다. 상호연결망의 중요 망 척도중 하나는 망 비용이고 상호연결망의 망 비용은 그 연결망의 분지수와 지름의 곱으로 정의된다. star 그래프는 다른 상호 연결망보다 작은 망 비용을 갖는다. 최근에 제안된 Macro-Star 그래픈 star 그래프에 비해 상대적으로 망 비용이 작은 값을 갖는 연결망이다. (n2)!개의 노드를 갖는 행렬-스타 그래프 MSk,k,k(k={{{{ `^{ 3} SQRT { n$^2$} }}}} )와 ((n-1)2 + 1)!개의 노드를 갖는 Macro-Star 그래프 MS(n-1, n-1)의 망 비용은 행렬-스타그래프 MSk,k,k(k={{{{ `^{ 3} SQRT { n$^2$} }}}})는 O(n2,7)이고, Macro-Star 그래프 MS(n-1 , n-1)은 O(n3) 이다. 이는 행렬-스타 그래프가 스타 그래프와 Macro-Star 그래프보다 망비용이 우수함을 의미한다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.3C
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• pp.237-244
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• 2006

I/Q phase unbalance caused by non-ideal circuit components is inevitable physical phenomenons and leads to performance degradation when we implement a practical coherent M-ary phase shift keying(M-PSK) demodulator. In this paper, we present an exact and general expression involving two-dimensional Gaussian Q-functions for the bit error rate(BER) of uniform M-PSK with I/Q phase unbalance over an additive white Gaussian noise(AWGN) channel. First we derive a BER expression for the k-th bit of 8, 16-PSK signal constellations when Gray code bit mapping is employed. Then, from the derived k-th bit BER expression, we present the exact and general average BER expression for M-PSK with I/Q phase unbalance. This result can readily be applied to numerical evaluation for various cases of practical interest in an I/Q unbalanced M-PSK system, because the one- and two-dimensional Gaussian Q-functions can be easily and directly computed using commonly available mathematical software tools.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.1
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• pp.30-36
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• 2016

In this paper, an Rx-ordering aided sphere decoding algorithm for generalized spatial modulation (GSM) systems is proposed. In the proposed sphere decoding algorithm, to efficiently reduce the search region, the received signals are optimally ordered, which results in the reduction of computational complexity. To evaluate the performance and the computational complexity of the proposed Rx-ordered sphere decoding algorithm, the simulations are performed. In the simulation results, it is observed that in GSM systems, the proposed decoding algorithm achieves the same error performance with the conventional SD, whereas it efficiently decreases the computational complexity for symbol detection.

• School Mathematics
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• v.11 no.2
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• pp.243-260
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• 2009

In this paper, we have designed a teaching unit for the learning mathematising of secondary pre-service teachers by exploring generalized fibonacci sequences. First, we have found useful formulas for general terms of generalized fibonacci sequences which are expressed as combinatoric notations. Second, by using these formulas and CAS graphing calculator, we can help secondary pre-service teachers to conjecture and discuss the limit of the sequence given by the rations of two adjacent terms of an m-step fibonacci sequence. These processes can remind secondary pre-service teachers of a series of some mathematical principles.