• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.391-397
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• 2019

In this paper, we give a simple proof of the improved Johnson bound for A(n, d), the maximum number of codewords in a binary code of length n and minimum distance d, given by Mounits, Etzion and Litsyn.

• Korean Journal of Food Science and Technology
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• v.24 no.1
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• pp.74-81
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• 1992

To develop the beverage from Schizandra chinensis Baillon, extraction condition was optimized, using the fractional factorial design with 3 variables and 3 levels, by a RSM computer program. The optimum extraction time, extraction temperature and alcohol concentration levels were 3 hrs, $80{\sim}85^{\circ}C$ and 0%(water) for a desired yield, color and non-volatile organic acid. And to obtain the optimum recipe, amounts of extract, sugar and citric acid were optimized, using the fractional factorial design with 3 variables and 3 levels, by a RSM program. The optimum extract, sugar and citric acid levels were 4%, 9.6%n and 0.06%, respectively, for a disired flavor and overall acceptance.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.1312-1315
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• 2002

This research describes the design of a fully integrated fractional-N frequency synthesizer intended for the local oscillator in IMT-2000 system using 0.18-$\mu\textrm{m}$ CMOS technology and 1.8-V single power supply. The designed fractional-N synthesizer contains following components. Modified charge pump uses active cascode transistors to achieve the high output impedance. A multi-modulus prescaler has modified ECL-like D flip-flop with additional diode-connected transistors for short transient time and high frequency operation. And phase-frequency detector, integrated passive loop filter, LC-tuned VCO having a tuning range from 1.584 to 2.4 ㎓ at 1.8-V power supply, and higher-order sigma-delta modulator are contained. Finally, designed frequency synthesizer provides 5 ㎒ channel spacing with -122.6 dBc/Hz at 1 ㎒ in the WCDMA band and total output power is 28 mW.

• International Journal of Korean Welding Society
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• v.1 no.2
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• pp.36-44
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• 2001

To get the appropriate welding process variables, mathematical modeling in conjunction with many experiments is necessary to predict the magnitude of weld bead shape. Even though the experimental results are reliable, it has a difficulty in accurately predicting welding process variables for the desired weld bead shape because of nonlinear and complex characteristics of welding processes. The welding condition determined for the desired weld bead shape may cause the weld defect if the welding current/voltage/speed combination is improperly selected. In this study, the $2^{n-1}$ fractional factorial design method and correlation parameter were used to investigate the effect of the welding process variables on the fillet joint shape, and the multiple non-linear regression analysis was used for modeling the gas metal arc welding(GMAW）parameters of the fillet joint. Finally, a fuzzy rule-based method and a neural network method were proposed so that the complexity and non-linearity of arc welding phenomena could be effectively overcome. The performance of the proposed neuro-fuzzy system was evaluated through various experiments. The experimental results showed that the proposed neuro-fuzzy system could effectively check the welding conditions as to whether or not weld defects would occur, and also adjust the welding conditions to avoid these weld defects.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.483-495
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• 2007

In a general fractional factorial design, the n-levels of a factor are coded by the $n^{th}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $2^p$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $2^p$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• Journal of the military operations research society of Korea
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• v.27 no.1
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• pp.73-88
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• 2001

Designing high quality products and processes at a low cost is central technological and economic challenge to the engineer. The combination of engineering concepts and statistical implementations offered by Taguchi\`s off-line design technique has proven t be invaluable. By examining some deficiencies in designs from the Taguchi\`s highly fractional, orthogonal main effect plan based on orthogonal arrays, alternative method is proposed. The maximum resolution or the minimum aberration criterion is commonly used for selecting 2$^{n-m}$ fractional designs. We present new high resolution (low aberration) linear graphs to simplify the complexity of selecting designs with desirable statistical properties. The new linear graphs approach shows a substantial improvement over Taguchi\`s linear graphs and other related graphical methods for planning experiment. The new set of linear graphs will allow the experimenter to maintain the simple approach suggested by Taguchi while obtaining the best statistical properties of the resulting design such as minimum aberration as a by-product without dependency on complicated computational algorithm or additional statistical training.g.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.473-495
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• 2023

The use of mathematical modelling in the study of epidemiological disorders continues to grow substantially. In order to better support global policy initiatives and explain the possible consequence of an outbreak, mathematical models were constructed to forecast how epidemic illnesses spread. In this paper, fractional derivatives and (${\varpi}$ - F_𝓒)-contractions are used to explore the existence and uniqueness solutions of the novel coronavirus-19 model.

• Mass Spectrometry Letters
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• v.14 no.4
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• pp.173-177
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• 2023

Kendrick plots offer an alternative visualization of mass spectral data which reveals ion series and patterning by turning a mass spectrum into a map, plotting the fractional mass (wrongly called mass defect) as a function of mass-to-charge ratios and ion abundances. Although routinely used for polymer mass spectrometry, two unreported applications of these Kendrick plots are proposed using the program "kendo2": the graphical recalibration of a mass spectrum via the simulation of a theoretical fractional mass and a multi-segment fit; and the rapid evaluation of scan-to-scan variation of accurate mass measurements used as tolerances for the blank subtraction of UPLC-MS data files. Both applications are compatible with any type of high-resolution MS data including LC/GC-MS(/MS).