• School Mathematics
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• v.13 no.4
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• pp.563-580
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• 2011

This study is centered on the application of metaphor theory to math education from the cognitive-linguistic view. This study, at first, introduced what metaphor is, and looked into it from the math-educational view. Furthermore, on the basis of that, this study examined the significance of metaphor to math education, and dealt with its relevance to math education, focusing on the functions that metaphor has. This study says that metaphor has the function of explanation, elaboration and representation. In addition, this study examplifies that using metaphor can be an effective math learning strategy for mathematical concept explanation, mathematical connection and mathematical representation learning.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.243-246
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• 1988

Let M(z)=exp (-1+z/1-z) be the unit singular inner function. See [1] or [2] for the basic facts about inner functions. We define the iterations of M9z) as (Fig.) Since the composition M$_{2}$(z)=M.M(z) is known (see [5] for example) to be singular inner function it has the "cannonical" representation (Fig.) where .mu. is a finite, positive singular Borel measure on the unit circle T. In section 2, we have explicit cannonical representation of M$_{2}$(z) by determining the singular measure .mu. In section 3 we show that (Fig.) These facts might have been known but could not be found in the literature.iterature.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.999-1008
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• 2017

By mainly using certain properties arising from the semisimple Lie group SO(2, 1), we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1409-1418
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• 2023

The Hurwitz-type Euler zeta function ζ_E(z, q) is defined by the series ${\zeta}_E(z,\,q)\,=\,\sum\limits_{n=0}^{\infty}{\frac{(-1)^n}{(n\,+\,q)^z}},$ for Re(z) > 0 and q ≠ 0, -1, -2, . . . , and it can be analytic continued to the whole complex plane. An asymptotic expansion for ζ^'_E(-m, q) has been proved based on the calculation of Hermite's integral representation for ζ_E(z, q).

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.571-591
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• 2012

To the best of our knowledge, there is no method, in the literature, to find the fuzzy optimal solution of fully fuzzy shortest path (FFSP) problems i.e., shortest path (SP) problems in which all the parameters are represented by fuzzy numbers. In this paper, a new method is proposed to find the fuzzy optimal solution of FFSP problems. Kumar and Kaur [Methods for solving unbalanced fuzzy transportation problems, Operational Research-An International Journal, 2010 (DOI 10.1007/s 12351-010-0101-3)] proposed a new method with new representation, named as JMD representation, of trapezoidal fuzzy numbers for solving fully fuzzy transportation problems and shown that it is better to solve fully fuzzy transportation problems by using proposed method with JMD representation as compare to proposed method with the existing representation. On the same direction in this paper a new method is proposed to find the solution of FFSP problems and it is shown that it is also better to solve FFSP problems with JMD representation as compare to existing representation. To show the advantages of proposed method with this representation over proposed method with other existing representations. A FFSP problem solved by using proposed method with JMD representation as well as proposed method with other existing representations and the obtained results are compared.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.741-753
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• 1998

Let G(*) be a Borel function applied to a stationary long memory sequence {X$_{i}$} of standard Gaussian random variables. Focusing on the process {G(X$_{i}$)}, the present paper establishes the almost sure representation for the empirical quantile process, that is, Bahadur's representation, and for the empirical process with respect to sample mean. Statistical applications of the representations are also addressed.sed.

• Journal of Mechanical Science and Technology
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• v.16 no.11
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• pp.1522-1539
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• 2002

In the present study, an explicit algebraic stress model is shown to be the exact tensor representation of algebraic stress model by directly solving a set of algebraic equations without resort to tensor representation theory. This repeals the constraints on the Reynolds stress, which are based on the principle of material frame indifference and positive semi-definiteness. An a priori test of the explicit algebraic stress model is carried out by using the DNS database for a fully developed channel flow at Rer = 135. It is confirmed that two-point correlation function between the velocity fluctuation and the Laplacians of the pressure-gradient i s anisotropic and asymmetric in the wall-normal direction. Thus, a novel composite algebraic Reynolds stress model is proposed and applied to the channel flow calculation, which incorporates non-local effect in the algebraic framework to predict near-wall behavior correctly.

• East Asian mathematical journal
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• v.38 no.2
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• pp.165-185
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• 2022

The six core competencies have been emphasized in the mathematics curriculum revised in 2015. In particular, the communication is very important for students' representing their own thinking and enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of the communication such as the understanding of mathematical representation, development and transition of mathematical representation, the representation of his own thinking, the understanding of the others' thinking. And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the communication competency were shown in each textbook.