• Honam Mathematical Journal
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• v.8 no.1
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• pp.51-74
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• 1986

The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.49-63
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• 2023

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-R², a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed R² interestingly proves quite invariant to an increasing number of response categories of an ordinal model.

• Journal of Technology Innovation
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• v.13 no.2
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• pp.207-222
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• 2005

A prerequisite for making R&D more productive is to able to measure its productivity. Most of the previous studies on this topic have attempted to measure R&D productivity at the firm or industry levels. In this study, however, R&D productivity is measured at the national level to provide R&D policy implications, particularly for Asian countries. Contrary to the previous studies where total factor productivity was adopted, this study employs the data envelopment analysis (DEA) approach to measure R&D productivity. DEA is a multi-factor productivity analysis model for measuring the relative efficiency of each Decision Making Unit (DMU). In addition to the basic DEA model that includes all inputs and outputs, five additional models are constructed by combining single input with all outputs and single output with all inputs in order to measure specialized R&D efficiency. In this study, the twenty-seven countries are classified into four clusters based on the output-specialized R&D efficiency: inventors, merchandisers, academicians, and duds. Then, the characteristics of the Asian countries with respect to R&D efficiency are identified. It is found that Singapore ranks high in total efficiency, and Japan in patent-oriented efficiency. Meanwhile, China, Korea, and Taiwan are found to be relatively inefficient in R&D. We expect that the findings from this study will be able to provide directions for R&D policy-making of the Asian countries.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.781-789
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• 1998

Let K be a loosely self-similar set. Then a-dimensional packing measure of K is the same as that of a Borel subset K( $r_1^{\alpha}$ㆍㆍㆍ$r_{m}$ $^{\alpha}$/) of K. And packing dimension of K is equal to that of K\K( $r_1^{\alpha}$ㆍㆍㆍ $r_{m}$ $^{\alpha}$/) and K( $r_1^{\alpha}$ㆍㆍㆍ $r_{m}$ $^{\alpha}$/).X> $^{\alpha}$/)).

• Proceedings of the Technology Innovation Conference
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• 2006.02a
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• pp.5-20
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• 2006

An efficient and productive R&D operation is a major source of competitive advantage in today's economy, and a lot of efforts are made to raise R&D productivity. A prerequisite for making R&D more efficient and productive is to be able to measure it. Hence, a number of studies have attempted to measure R&D productivity. R&D productivity, in the previous studies, was measured with patents at the firm or industry level. However, most previous studies considered only a quantitative aspect, not a quantitative aspect of patents. In this study, various dimensions of patent quality as well as patent quantity were considered for the measurement of R&D performance. The differences in R&D performance across sectors were examined, and it was found that electrical/electronic industry shows higher R&D performance than mechanic and chemical industries. Discriminant analysis based on inputs and outputs for R&D shows' that there exist a strong discriminatory power across industries. The results of this research can provide the directions 'for the firm's R&D policy.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.293-307
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• 2024

In this paper, we give a general method to compute the linear independence measure of 1, log(1 - 1/r), log(1 + 1/s) for infinitely many integers r and s. We also give improvements for the special cases when r = s, for example, ν(1, log 3/4, log 5/4) ≤ 9.197.

• The Journal of Korean Academy of Orthopedic Manual Physical Therapy
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• v.16 no.2
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• pp.82-87
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• 2010

Purpose : This study was investigate The correlations between the Balance and the knee muscle power and the ankle muscle power. Methods : This studied selected 9cases of the healthy persons. Each measure of muscle power used Bio-dex pro-3. Balance measure was used balance-meter the ability to measure Ant-post, lateral, overall balance. Result : 1. Knee flexor and extensor causes ankles that plantar flexion strength and high correlation r= .745, r= .825 have, Ankle dorsi flexor strength and a bit of correlation r= .249, r= .221) have. 2. Ankle plantar flexor strength and overall balance and correlation was the r= .204, Ankle dorsi flexor strength and lat. balance and correlation was the r= .314. 3. Knee extensor strength and overall balance and correlation was the r=.212.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.707-717
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• 1997

The square of Brownian density process $Q^\lambda$ is defined where $\lambda$ is a parameter. Applying limit theorems of stochastic integrals w.r.t. martingale measure, we prove a weak limit theorem for $Q^\lambda$ in $D_{S'(R^d)}[0,1]$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.