• The Mathematical Education
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• v.56 no.1
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• pp.81-100
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• 2017

The concept of variable is a big idea to develop algebraic thinking. Variable has multiple meanings such as the unknown, a tool for generalization, and the relationship between varying quantities. In this study we analyzed in what ways the meanings of variable were presented in the current elementary mathematics textbooks and workbooks. The results showed that the most frequent meaning of variable was 'the unknown', 'a tool for generalization', and 'the relationship between varying quantities' in order. A close look at the results revealed that the same symbol was often used in representing different values of variable as the unknown. In taking variable as a tool for generalization, questions to provoke generalization were sometimes included not in the textbooks but in the teachers' manuals. The main focus in dealing with variable as the relationship between varying quantities was on finding out the dependent values compared to the independent ones. Building on these results, this study is expected to suggest implications for how to deal with variable concept in elementary mathematics instructional materials.

• Speech Sciences
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• v.15 no.2
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• pp.145-156
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• 2008

The purpose of this study was to investigate the reason why puberphonia patients revisit hospitals after completion of its treatment and the effect of visual voice therapy on voice improvement. The subject the study included are two puberphonia patients who had been diagnosed by laryngologists. The patients who were diagnosed as puberphonia by the laryngologist and treated by the a speech pathologist, completed their treatment and revisited hospital. The study used laryngoscopy, acoustic and aerodynamic analysis before and after voice treatment to investigate what change happens and why generalization of treatment effect did not occur naturally in the daily life. Their voices of pre-therapy and post-therapy were analyzed on the aspects of acoustics, aerodynamics and laryngeal endoscopy. As a result, it was found that fundamental frequency(Fo) was significantly lowered in respect of acoustic change and maximum phonation time(MPT) was increased to some extent in respect of aerodynamic change. In addition, there was a laryngoscopic change and commissure glottic chink disappeared generally in the phonation. The reason why the generalization did not occur naturally in one’s daily routine was mainly due to the fact that high-pitched voicing was used for a long time. Other than that reason, negative reaction or attitude of surrounding people and lack of confidence were to blame for failure of generalization.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.537-542
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• 2004

Multi-Layer Perceptron network has been mainly applied to many practical problems because of its nonlinear mapping ability. However the generalization ability of MLP networks may be affected by the number of hidden nodes, the initial values of weights and the training errors. These factors, if improperly chosen, may result in poor generalization ability of MLP networks. It is important to identify these factors and their interaction in order to control effectively the generalization ability of MLP networks. In this paper, we have empirically identified the factors that affect the generalization ability of MLP networks, and compared their relative effects on the generalization performance for the conventional and visualized weight selecting methods using the controller box.

• School Mathematics
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• v.5 no.3
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• pp.343-360
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• 2003

In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

• Journal of Korea Multimedia Society
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• v.24 no.12
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• pp.1624-1631
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• 2021

With the continued development of image processing technology, we live in a time when it is difficult to visually discriminate processed (or tampered) images from real images. However, as the risk of fake images being misused for crime increases, the importance of image forensic science for identifying fake images is emerging. Currently, various deep learning-based identifiers have been studied, but there are still many problems to be used in real situations. Due to the inherent characteristics of deep learning that strongly relies on given training data, it is very vulnerable to evaluating data that has never been viewed. Therefore, we try to find a way to improve generalization ability of deep learning-based fake image identifiers. First, images with various contents were added to the training dataset to resolve the over-fitting problem that the identifier can only classify real and fake images with specific contents but fails for those with other contents. Next, color spaces other than RGB were exploited. That is, fake image identification was attempted on color spaces not considered when creating fake images, such as HSV and YCbCr. Finally, dropout, which is commonly used for generalization of neural networks, was used. Through experimental results, it has been confirmed that the color space conversion to HSV is the best solution and its combination with the approach of increasing the training dataset significantly can greatly improve the accuracy and generalization ability of deep learning-based identifiers in identifying fake images that have never been seen before.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.429-437
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• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.563-572
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• 2008

In this paper, we discuss about a generalization of the Key Distribution Pattern which was proposed by C. Mitchell and F. Piper[6]. It is allowing secure communication between every n-pair of users($n\leq2$) in a large network for reducing storage requirements. We further suggest a generalization of K. Quinn's bounds in [9] for the number of subkeys in such general Key Distribution Patterns.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.881-898
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• 2002

Our aim in this paper is to introduce a generalization of some notions in homological algebra. We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and $\mu$-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.