• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• Asian-Australasian Journal of Animal Sciences
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• 제19권11호
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• pp.1603-1609
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• 2006

To estimate undegraded intake protein (UIP) fraction in feeds and fodders, on the basis of their neutral detergent insoluble N content was studied. Samples of six feeds and forages were incubated in situ for a time equivalent to their mean retention time, estimated on the basis of their digestibility plus 10 h (to account for a lag in passage of particles from the rumen). The samples were incubated for 0, 25, 50, 75 and 100% of the estimated total mean retention time. UIP value of leguminous forages, obtained from the fractional rates of degradation and passage, were highly correlated with those estimated from samples incubated for 75% of total mean retention time, while incubating the non-leguminous forages and groundnut cake for this point over estimate the UIP fraction.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.631-636
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• 2015

Let D be an integral domain and w be the so-called w-operation on D. In this note, we introduce the notion of *(w)-domains: D is a *(w)-domain if $(({\cap}(x_i))({\cap}(y_j)))_w={\cap}(x_iy_j)$ for all nonzero elements $x_1,{\ldots},x_m$; $y_1,{\ldots},y_n$ of D. We then show that D is a $Pr{\ddot{u}}fer$ v-multiplication domain if and only if D is a *(w)-domain and $A^{-1}$ is of finite type for all nonzero finitely generated fractional ideals A of D.

• 대한기계학회논문집
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• 제17권10호
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• pp.2509-2517
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• 1993

Lapping is a very complicated and random process resulting from the variation of abrasive grains in its sizes and shapes and from the numerous factors having an effect on the process quality. Thus it needs to be analyzed by experimental method rather than by theoretical method to obtain the relative effects of factors quantitatively. In this study, cylindrical lapping experiment designed by Taguchi's L8 orthogonal array was performed and analyzed by Yates' ANOVA table. As a result, effective factors and interaction effects were identified and discussed. Also the optimal factor combination to obtain the largest improvement of surface roughness was selected and confirmatory experiments were peformed.

• 대한수학회보
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• 제43권3호
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

• 대한안전경영과학회지
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• 제10권3호
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• pp.237-243
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• 2008

The present study proposes two normality tests using nonparametric rank measures for small sample such as modified normal probability paper(NPP) tests and modified Ryan-Joiner Test. This research also reviews various normality tests such as $X^2$ test, and Kullback-Leibler test. The proposed normality tests can be efficiently applied to the sparsity tests of factor effect or contrast using saturated design in $k^n$ factorial and fractional factorial design.

• 천문학회지
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• 제40권3호
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• pp.61-65
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• 2007

The 2-1 and 5-4 transitions of SiO have been observed toward the Sgr B2 region, including the Principal Cloud(the GMC containing Sgr B2(M)) and its surroundings. The morphology and velocity structure of the SiO emission show a close resemblance with the HNCO Ring feature, identified by Minh & Irvine(2006), of about 10 pc in diameter, which may be expanding and colliding with the Principal Cloud. Three SiO clumps have been found around the Ring, with total column densities $N_{SiO}{\sim}1{\times}10^{14}cm^{-2}$ at the peak positions of these clumps. The fractional SiO abundance relative to $H_2$ has been estimated to be ${\sim}(0.5-1){\times}10^{-9}$, which is about two orders of magnitude larger than the quiet dense cloud values. Our SiO observational result supports the existence of an expanding ring, which may be triggering active star formations in the Principal Cloud.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.108-110
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• 2006

A prediction model of charge concentration of silicon nitride (SiN) thin films was constructed by using neural network and genetic algorithm. SIN films were deposited by plasma enhanced chemical vapor deposition and the deposition process was characterized by means of $2^{6-1}$ fractional factorial experiment. Effect of five training factors on the model prediction performance was optimized by using genetic algorithm. This was examined as a function of the learring rate. The root mean squared error of optimized model was 0.975, which is much smaller than statistical regression model by about 45%. The constructed model can facilitate a Qualitative analysis of parameter effects on the charge concentration.

• 대한수학회지
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• 제57권4호
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• pp.845-871
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• 2020

We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in ℝ/ℤ.

• Journal of Welding and Joining
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• 제6권2호
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• pp.47-55
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• 1988

This paper reports on a study of the influence of welding variables on the weld shape of Al-7020 in pulse-GMA welding. Five variables, i.e., wire feed rate, peak pulse current, welding speed, welding votage, and pulse frequency were investigated for their effects on the weld shape. From the results of the 2$^{n-1}$ fractional factorial design, quantitative effects of each variable and the interaction of two variables were obtained, and consequently wire feed rate, welding voltage, and welding speed were determined as the main welding variables. Supplementary experiment was performed for ivestigating the detailed relationship between the main variables nd the seld shape. In this experiment, the penetation of the seldment increased when the wire feed rate was raised, nad the bead width increased when the welding voltage was raised or the welding speed was reduced.d.