• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.137-145
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

• Korean Journal of Child Studies
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• v.27 no.4
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• pp.65-80
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• 2006

Data were collected from 110 preschoolers, 59 boys, 51 girls (ages 4-5) and their mothers. Peer competence was assessed by the Child Behavior Scale (Birsh & Ladd, 1998) and the Peer Rating Scale (Asher et al., 1979). Children's internal representations were measured by the MacArthur Story-Stem Battery (2004) and coded by the MacArthur Narrative Coding Manual (2004). Maternal parenting behaviors were observed during mother-child interaction at home and analyzed with the Teaching Strategies Rating Scale (Erickson, Sroufe, & Egeland, 1985). Data were analyzed by structural equation modeling analysis. Results confirmed the pathway from maternal parenting behaviors via children's internal representations to peer competence showing a significantly good model fit.

• Communications of Mathematical Education
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• v.15
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• pp.281-286
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• 2003

The primary purpose of this study was to investigate how and to what extent 'representations' affect the students' understanding and the growth of understanding in a technology [GSP]-based collegiate mathematics classroom. There are three themes related as frames of the study along with this purpose, which are mentioned in the first chapter and extended in the second chapter: technology in mathematics education; images on computer screen - visualization and representation; understanding and growth of understanding. Three research questions guided this study: 1) How do students present each component of representations when they study 'transformations' in a technology [GSP]-based classroom? If there is any difference between the first and second presentation for each component, how are they different?; 2) How and to what extent do representations affect the students' understanding and the growth of understanding in a technology [GSP]-based classroom?; What types of benefits and obstacles are there when students study 'transformations' in a technology [GSP]-based classroom?

• Speech Sciences
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• v.8 no.4
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• pp.243-257
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• 2001

In English textbooks, there are three kinds of English intonation representations: Trager & Smith's, Weak-strong, Audio-lingual way. Each representation has its merits and demerits. Therefore, just one of them is insufficient to represent English intonation properly. Trager & Smith's representation is relevant to show holistic intonation itself. In contrast to this merit, it is not appropriate to represent downstep, declination, etc. With Weak-strong, it is good to show weak and strong point in the sentence. It is not, however, consistent with intonation. Instead of these representations, some textbooks accept Audio-lingual method. Audio-lingual method gives students more chances to hear native speakers' intonations. But it doesn't give ways to understand English intonation itself. In English textbooks, they don't have any hierarchies dependent upon students' proficiency. In spite of various intonations, they just accept a few limited intonation models. Thus, it is necessary to review all kinds of intonation representations and to develop more advanced and relevant English intonation representation.

• Korean Journal of Child Studies
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• v.27 no.3
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• pp.81-100
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• 2006

This study explored the relationship of behavioral inhibition to narrative representations. Narratives of 96 four-year-old children were recorded and analyzed by the scoring system of Robinson, Holmberg and Klute(in press). Six clusters were found : Constrained(47.9%), Anxious/Restricted(23.9%), Emotional Integrated/Empathic(12.5%), Empathic/Avoidant(6.3%), Dysregulated(5.2%) and Anxious/Avoidant(4.2%) clusters. Behavioral inhibition was determined by observations using "Play with Unfamiliar Peers(Rubin et al., 2002)". Behavioral inhibition differences corresponded to the children's narrative representation clusters; The Anxious/Restricted Cluster was related to more and the Emotional Integrated/Empathic Cluster to less inhibited behavior. In context-specific differences, more inhibited behavior was related to Anxious/Avoidant Clusters during show-and-tess and to Empathic/Avoidant Clusters during card-sorting activities, respectively.

• Journal of Families and Better Life
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• v.17 no.3
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• pp.33-46
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• 1999

The purpose of this stud was to investigate how the children's perceptions of interpersonal relations(parent, family and peers) and self are related to social preference. The subjects of this study were 625 children of 5th and 6th grade in 4 primary schools in Tajon. Social preference was highly correlated with perceptions of peer and of father. The direct path between boy's perceptions of parent/family and peer ratings of social preference was no longer significant whereas there was a significant path mediated by their perception of self. This suggests that boys and girls' peer representations were established for the role as mediators between parents/ family representations and peer ratings of social preference. In addition negative representations of self and others were found to be associated with increased social impairment and less positive status in the peer groups.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1556-1562
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• 2003

In this paper, a new representations of extended threshold Boolean filter(ETBF), called SA filter, is introduced. The structure of this representations is a one of multistage filters. The first stage is subfilters of nonlinear filters such as maximum, minimum, or exclusive-OR operators. The second stage is linear combination of Int stage outputs. Although the structure of this representations is very similar to SAM filters, SA filters encampass all ETBF not subset of ETBF.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.745-758
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• 2011

Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.