• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.277-294
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• 2021

In this paper, we introduce the notions of Wijsman regularly invariant convergence types, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$)-convergence, Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-convergence, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$) -Cauchy double sequence and Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-Cauchy double sequence of sets. Also, we investigate the relationships among this new notions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.47-52
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• 1999

In this note we give a characterization on weak convergence of bounded linear functionals in $\sigma$-complete abstract M spaces.

• Asia-Pacific Journal of Business
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• v.10 no.1
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• pp.1-11
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• 2019

Asian countries have been striving for economic integration for decades. This effort may lead to the convergence of income level through externalities across countries. This paper investigates whether the convergence phenomenon holds for income levels in Asian countries for the periods between 1975-2015 applying the traditional methodology of ${\sigma}-$ and ${\beta}-convergence$. Although the absolute ${\beta}-convergence$ of income levels in Asian and ASEAN+3 countries do hold, ${\sigma}-convergence$ and conditional ${\beta}-convergence$ of income level generally do not exist. This suggests that the benefits of economic integration in Asian countries were not yet realized to be significant. A plausible explanation is that the economies of Asian countries are largely based on low trade openness and a high level of informal economy.

• ETRI Journal
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• v.29 no.6
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• pp.835-837
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• 2007

A multi-bit sigma-delta modulator architecture is described for low-distortion performance and a high-speed operation. The proposed architecture uses both a delayed code and a delayed differential code of analog-to-digital converter in the feedback path, thereby suppressing signal components in the integrators and relaxing the timing requirement of the analog-to-digital converter and the scrambler logic. Implemented by a 0.13 ${\mu}m$ CMOS process, the sigma-delta modulator achieves high linearity. The measured spurious-free dynamic range is 89.1 dB for -6 dBFS input signal.

• ETRI Journal
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• v.33 no.6
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• pp.897-903
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• 2011

A hybrid ${\Delta}{\Sigma}$ modulator for audio applications is presented in this paper. The pulse generator for digital-to-analog converter alleviates the requirement of the external clock jitter and calibrates the coefficient variation due to a process shift and temperature changes. The input resistor network in the first integrator offers a gain control function in a dB-linear fashion. Also, careful chopper stabilization implementation using return-to-zero scheme in the first continuous-time integrator minimizes both the influence of flicker noise and inflow noise due to chopping. The chip is implemented in a 0.13 ${\mu}m$ CMOS technology (I/O devices) and occupies an active area of 0.37 $mm^2$. The ${\Delta}{\Sigma}$ modulator achieves a dynamic range (A-weighted) of 97.8 dB and a peak signal-to-noise-plus-distortion ratio of 90.0 dB over an audio bandwidth of 20 kHz with a 4.4 mW power consumption from 3.3 V. Also, the gain of the modulator is controlled from -9.5 dB to 8.5 dB, and the performance of the modulator is maintained up to 5 nsRMS external clock jitter.

• Journal of the Korean Society of Industry Convergence
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• v.13 no.1
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• pp.49-54
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• 2010

Lean 6 sigma has recently been used to describe a management system which combines lean management and 6 sigma. The marriage between Lean manufacturing and 6 sigma has proven to be a powerful tool for cutting waste and improving the organization operations. Time and quality are the most important metrics in improving any company's production and profit performance. lean 6 sigma is a management innovation for improving production efficiency, process quality, cost reduction, investment efficiency and customer's satisfaction. in this paper, Advanced cell line is builded the home appliance goods of the LCD TV final assembly line of domestic company line, training the multi-skilled man and controlling the production information system based on Lean 6 sigma.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Journal of the Korean Society of Industry Convergence
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• v.13 no.2
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• pp.107-112
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• 2010

The automation and Cell-Line of manufacturing process are going to be new trend in the industry spot. But workers bodily burden by manual labour is still doing repeatedly at many processes. It is appearing to workers bodily burden (Shoulder, waist, hand, wrist, leg) with repeating works at assembly line which is from the static working space. The analysis with 6 Sigma Tool at specific standard assembly line improve the point at issue for unsuitable items and analyzed objects. Physical pain of worker is solved by the improvement action for the factor of 7 items with the result of analysis. It was known to be improved by solving of workers burden related to the change of 6 Sigma level from 2.16 to 4.1 at assembly line.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.