• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.939-962
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• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Proceedings of the KIPE Conference
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• 2001.07a
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• pp.479-482
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• 2001

This paper proposes a modified $\alpha$ conduction mode for controlling the output voltage magnitude of three-phase square-wave VSIs with an R-L load. From the viewpoint of both power capacity and switching losses, three-phase square-wave inverters are now used in most high power systems. When the square-wave VSI is driven with $\alpha$ conduction mode to control the magnitude of output voltages, interval over than half period is operated with $180^{\circ}$ conduction mode and the other interval with $120^{\circ}$ conduction mode. In $120^{\circ}$ conduction mode operation, two output terminals are connected to DC supply and the third one remains open. The potential of this open terminal will depend on the load characteristics and is unpredictable except the case of pure resistive loads. To cope this problem, we propose the modified α conduction mode.

• Journal of the korean academy of Pediatric Dentistry
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• v.46 no.2
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• pp.190-199
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• 2019

$Carbopol^{(R)}$ 907 used as surface protecting agent in White's method is the one of the artificial caries lesion producing solution was discontinuing of production. New surface protecting material to substitute of $Carbopol^{(R)}$ 907 was required. The author prepared an artificial caries lesion producing solution as follows White's method with $Carbopol^{(R)}$ 907 and also another artificial caries lesion producing solution with $Carbopol^{(R)}$ $2050^{(R)}$. 96 flattened and polished enamel samples were immersed in a demineralizing solution of 0.1 mol/L lactic acid, 0.2% carboxyvinylpolymer and 50% saturated hydroxyapatite for 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 18 and 20 days. All samples from each group were subjected to polarized microscopy observed and image analysis for measuring the lesion depth. From the review of polarized images, the artificial caries lesion producing solution using $Carbopol^{(R)}$ 907 and $Carbopol^{(R)}$ 2050 can produced an artificial caries that was very similar to natural caries characters. From the regression analysis of the lesion depth produced by the artificial caries lesion producing solution using $Carbopol^{(R)}$ 907 and $Carbopol^{(R)}$ 2050, $Carbopol^{(R)}$ 2050 estimate as Y = 9.8X + 8.0 and $Carbopol^{(R)}$ 907 was Y = 8.4X - 0.4. R square value of $Carbopol^{(R)}$ 2050 and $Carbopol^{(R)}$ 907 was 0.965 and 0.945 respectively. The rate of demineralization by the artificial caries lesion producing solution using $Carbopol^{(R)}$ 2050 was faster than that of $Carbopol^{(R)}$ 907. And R square value of $Carbopol^{(R)}$ 2050 and $Carbopol^{(R)}$ 907 were very high and it means that the lesion depth was very high coefficient to demineralization period.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.661-668
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• 2006

There have been some controversies on the use of the coefficient of determination for linear no-intercept model. One definition of the coefficient of determination, $R^2={\sum}\;{\widehat{y^2}}\;/\;{\sum}\;y^2$, is being widely accepted only for linear no-intercept models though Kvalseth (1985) demonstrated some possible pitfalls in using such $R^2$. Main objective of this note is to report that $R^2$ is not a desirable measure of fit for the no-intercept linear model. In fact it is found that mean square error(MSE) could replace $R^2$ efficiently in most cases where selection of no-intercept model is at issue.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1093-1101
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• 2018

Let (RDTF, M) be a Milnor square. In this paper, it is proved that R is a ${\mathcal{C}}$-hereditary domain if and only if both D and T are ${\mathcal{C}}$-hereditary domains; R is an almost perfect domain if and only if D is a field and T is an almost perfect domain; R is a Matlis domain if and only if T is a Matlis domain. Furthermore, to give a negative answer to Lee, s question, we construct a counter example which is a C-hereditary domain R with $w.gl.dim(R)={\infty}$.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Proceedings of the Acoustical Society of Korea Conference
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• 1991.06a
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• pp.151-156
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• 1991

In this paper, we propose a new algorithm for designing the R-G filter that has optimum performance in terms of mean square sidelobe level(MSSL) for the Barker code. The advantage of the conventional R-G filter lies in its simple structure so that it can be easily implemented. However, the conventional R-G filter dose not have optimum performances in terms of peak sidelobe level(PSL), mean sidelobe level(MSL), and MSSL. Recently, a(R-G)LP filter of which filter coefficients are obtained by the linear programming algorithm was proposed and known to have optimum performance in PSL. The proposed (R-G)LS filter keeps the simple structure of the conventional R-G filter and has the filter coefficients that minimizes the sidelobe in the least square sense. The analytic results show that the proposed (R-G)LS filter has better performances than the conventional R-G filter in terms of PSL, MSL, and MSSL. Compared with (R-G)LP filter, the proposed (R-G)LS filter has better performances in terms of MSL and MSSL. The proposed filter design algorithm can be applied to the other binary codes such as truncated pseudonoise(PN) codes and concatenated codes.

• ETRI Journal
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• v.31 no.1
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• pp.68-70
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• 2009

In this letter, a parametric analysis of the Fresnel-field antenna measurement method is performed for a square aperture. As a result, the optimum number of Fresnel fields for one far-field point is guided as $M_{opt}=N_{opt}=D^2/{\lambda}R+5$, where D is the antenna diameter, ${\lambda}$ is the wavelength, and R is the distance between the source antenna and the antenna under test. For the aperture size 5 ${\leq}$ $L_x/{\lambda}$ ${\leq}$ 20, the tolerable distances for gain errors of 0.5 dB and 0.2 dB can be guided as $R_{0.5\;dB}$ ${\approx}$ $1.2Lx/{\lambda}$ and $R_{0.2\;dB}$ ${\approx}$ $2.0L_x/{\lambda}$, where $L_x$ is the lateral length of the square aperture. The tolerable distances for 20 ${\leq}$ $L_x/{\lambda}$ ${\leq}$ 200 are also proposed. This measurement guideline can be fully utilized when performing the Fresnel-field antenna measurement method.

• Korean Journal of Metals and Materials
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• v.47 no.10
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• pp.613-620
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• 2009

The Kachanov-Rabotnov (K-R) creep model was proposed to accurately model the long-term creep curves above $10^5$ hours of Alloy 617. To this end, a series of creep data was obtained from creep tests conducted under different stress levels at $950^{\circ}C$. Using these data, the creep constants used in the K-R model and the modified K-R model were determined by a nonlinear least square fitting (NLSF) method, respectively. The K-R model yielded poor correspondence with the experimental curves, but the modified K-R model provided good agreement with the curves. Log-log plots of ${\varepsilon}^{\ast}$-stress and ${\varepsilon}^{\ast}$-time to rupture showed good linear relationships. Constants in the modified K-R model were obtained as ${\lambda}$=2.78, and $k=1.24$, and they showed behavior close to stress independency. Using these constants, long-term creep curves above $10^5$ hours obtained from short-term creep data can be modeled by implementing the modified K-R model.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.285-293
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• 2006

Let X be a n-set and let A = [aij] be a $n {\times} n$ matrix for which $aij {\subseteq} X$, for $1 {\le} i,\;j {\le} n$. A is called a generalized Latin square on X, if the following conditions is satisfied: $U^n_{i=1}\;aij = X = U^n_{j=1}\;aij$. In this paper, we prove that every generalized Latin square has an orthogonal mate and introduce a Hv-structure on a set of generalized Latin squares. Finally, we prove that every generalized Latin square of order n, has a transversal set.