• East Asian mathematical journal
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• v.33 no.4
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• pp.333-351
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• 2017

Schools are expected to ultimately moderate the difference of inequality issues among social groups and reduce the achievement gaps. This study investigates this expectation, in particular, how students' mathematics achievements are influenced by their parents' education at the individual level and by collective responsibility for teaching at the school level as well as the interaction of the two. Using a two-level hierarchical linear model, this study indicates that a school collective responsibility has a larger positive effect on students' mathematics achievement when their parents' education level is high. This means that school's collective responsibility accelerates inequity in students' mathematics achievement. Knowing that collective responsibility has less of an effect on students whose parents' education is not high, researchers, schools, and school districts should continue to search for school effects that have more of a positive impact on the relationship between mathematics achievement for students whose parents' education is not high in order to have more equitable results for all students.

• Proceedings of the KIEE Conference
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• 1993.07b
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• pp.569-571
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• 1993

This paper describes a life expectation of electrical insulating materials using a mathematical model. The mathod simultaneously uses the maximum likelihood estimation and the Newton-Raphson method. By using these method, we will reduce time and costs in voltage-life aging test.

• Research in Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2021

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.99-106
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• 1984

J. Yeh has recently introduced the concept of conditional Wiener integrals which are meant specifically the conditional expectation E$^{w}$ (Z vertical bar X) of a real or complex valued Wiener integrable functional Z conditioned by the Wiener measurable functional X on the Wiener measure space (A precise definition of the conditional Wiener integral and a brief discussion of the Wiener measure space are given in Section 2). In [3] and [4] he derived some inversion formulae for conditional Wiener integrals and evaluated some conditional Wiener integrals E$^{w}$ (Z vertical bar X) conditioned by X(x)=x(t) for a fixed t>0 and x in Wiener space. Thus E$^{w}$ (Z vertical bar X) is a real or complex valued function on R$^{1}$. In this paper we shall be concerned with the random vector X given by X(x) = (x(s$_{1}$),..,x(s$_{n}$ )) for every x in Wiener space where 0=s$_{0}$ $_{1}$<..$_{n}$ =t. In Section 3 we will evaluate some conditional Wiener integrals E$^{w}$ (Z vertical bar X) which are real or complex valued functions on the n-dimensional Euclidean space R$^{n}$ . Thus we extend Yeh's results [4] for the random variable X given by X(x)=x(t) to the random vector X given by X(x)=(x(s$_{1}$).., x(s$_{n}$ )).

• Honam Mathematical Journal
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• v.26 no.4
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• pp.463-469
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(pdf) f(x). Let $Y_n=max\{X_1,\;X_2,\;{\cdots},\;X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of $\{X_n,\;n{\geq}1\}$, if $Y_j>Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, $n{\geq}1$, where u(n)=min\{j{\mid}j>u(n-1),\;X_j>X_{u(n-1)},\;n{\geq}2\} and u(1) = 1. Suppose $X{\in}Exp(1)$. Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.451-470
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• 2020

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition 0 = t₀ < t₁ < ⋯ < t_n < t_n+1 = T of [0, T], define X_n : C[0, T] → ℝⁿ⁺¹ by X_n(x) = (x(t₀), x(t₁), …, x(t_n)). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X_n which has a drift and does not contain the present position of paths. As applications of the formula with X_n, we evaluate the Radon-Nikodym derivatives of the functions ∫₀^T[x(t)]^mdλ(t)(m∈ℕ) and [∫₀^Tx(t)dλ(t)]² on C[0, T], where λ is a complex-valued Borel measure on [0, T]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C[0, T].

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• The Mathematical Education
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• v.50 no.4
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• pp.489-505
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• 2011

This study is an analysis on the focus of textbooks regarding the statistical chapters of "measures of representative(central tendency) and of the spread". Applying the summary-concept criteria of Juhyeon Nam(2007), 4 kinds of aspect of the chapter; (1) definition and its teleological validity of the measures of representative, (2) definition and practical value of the measures of spread (3) distributional form on the measures of representative and of spread (4) location and scale preservation or invariance of the measures of representative and of spread were observed. On the measures of representative, some definitions were insufficient to check the teleological validity of the measure. Most definitions of the measure of spread were based on the practical view points but no preparation for the future statistical inferences were found even by implication. Some books mention about the measures of representative and of spread for distributions, but we could not find any comments on the correspondence between the sample mean and the expectation of a distribution or population mean. However it is stimulant that some books check the validity of corresponding measures with the location and scale preservation or invariant property, that were not found in the previous curriculum.

• Communications of Mathematical Education
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• v.32 no.1
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• pp.23-36
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• 2018

Recently, we are working to utilize it in various fields with the expectation of the potential of artificial intelligence. There is also interest in applying to the field of education. In the field of education, machine learning and deep learning, which are used in artificial intelligence technology, are deeply interested in how to learn on their own. We are interested in how artificial intelligence and artificial intelligence technologies can be used in education and we have an interest in how artificial intelligence can be applied to mathematics education. The purpose of this study is to investigate the direction of mathematics education as the change of education paradigm and the development of artificial intelligence according to the development of information and communication technology. Furthermore, we examined how artificial intelligence can be applied to mathematics education.