• 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 $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.43 no.11 s.353
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• pp.83-89
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• 2006

This paper describes the design of I/Q channel 12bit Digital-to-Analog Converter(DAC) which shows the conversion rate of 120MHz and the power supply of 3.3V with 0.35um CMOS n-well 1-poly 4-metal process for advanced wireless transceiver. The proposed DAC utilizes 4-bit thermometer decoder with 3 stages for minimum glitch energy and linearity error. Also, using a optimized 4bit thermometer decoder for the decrement of the chip area. Integral nonlinearity(INL) of ${\pm}1.6LSB$ and differential nonlinearity(DNL) of ${\pm}1.3LSB$ have been measured. In single tone test, the ENOB of the proposed 12bit DAC is 10.5bit and SFDR of 73dB(@ Fs=120MHz, Fin=1MHz) is measured, respectively. Dual-tone test SFDR is 61 dB (@ Fs=100MHz, Fin=1.5MHz, 2MHz). Glitch energy of 31 pV.s is measured. The converter consumes a total of 105mW from 3.3-V power supply.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.435-453
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• 2008

In this paper, by using q-deformed bosonic p-adic integral, we give $\lambda$-Bernoulli numbers and polynomials, we prove Witt's type formula of $\lambda$-Bernoulli polynomials and Gauss multiplicative formula for $\lambda$-Bernoulli polynomials. By using derivative operator to the generating functions of $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, we give Hurwitz type $\lambda$-zeta functions and Dirichlet's type $\lambda$-L-functions; which are interpolated $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, respectively. We give generating function of $\lambda$-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and $\lambda$-Bernoulli polynomials and ordinary Bernoulli numbers of order r and $\lambda$-Bernoulli numbers, respectively. We also study on $\lambda$-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define $\lambda$-partial zeta function and interpolation function.

• Asian-Australasian Journal of Animal Sciences
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• v.28 no.9
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• pp.1335-1344
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• 2015

A set of prediction equations to estimate the nitrogen-corrected apparent metabolizable energy (AMEn) of individual ingredients and diets used in the poultry feed industry was evaluated. The AMEn values of three energy ingredients (maize, sorghum and defatted maize germ meal), four protein ingredients (soybean meal, maize gluten meal 60% crude protein, integral micronized soy and roasted whole soybean) and four diets (three containing four feedstuffs, complex diets, and one containing only corn-soybean meal, basal diet) were determined using a metabolism assay with male broilers from 1 to 7, 8 to 21, 22 to 35, and 36 to 42 days old. These values were compared to the AMEn values presented in the tables of energy composition or estimated by equation predictions based on chemical composition data of feedstuffs. In general, the equation predictions more precisely estimated the AMEn of feedstuffs when compared to the tables of energy composition. The equation AMEn (dry matter [DM] basis) = 4,164.187+51.006 ether extract (% in DM basis)-197.663 ash-35.689 crude fiber (% in DM basis)-20.593 neutral detergent fiber (% in DM basis) ($R^2=0.75$) was the most applicable for the prediction of the energy values of feedstuffs and diets used in the poultry feed industry.

• The Journal of the Acoustical Society of Korea
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• v.39 no.5
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• pp.379-389
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• 2020

In this study, the flow and noise performances of high-speed fan motor unit for cordless vacuum cleaner is improved by optimizing the impeller which drives the suction air through flow passage of the cordless vacuum cleaner. Firstly, the unsteady incompressible Reynolds averaged Navier-Stokes (RANS) equations are solved to investigate the flow through the fan motor unit using the computational fluid dynamics techniques. Based on flow field results, the Ffowcs-Williams and Hawkings (FW-H) integral equation is used to predict flow noise radiated from the impeller. Predicted results are compared to the measured ones, which confirms the validity of the numerical method used. It is found that the strong vortex is formed around the mid-chord region of the main blades where the blade curvature change rapidly. Given that vortex acts as a loss for flow and a noise source for noise, impeller blade is redesigned to suppress the identified vortex. The response surface method using two factors is employed to determine the optimum inlet and outlet sweep angles for maximum flow rate and minimum noise. Further analysis of finally selected design confirms the improved flow and noise performance.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.21 no.2
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• pp.131-136
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• 1985

The calculation of the resulting fluid motion is an important problem of ship hydrodynamics. For a partially immersed body the condition of constant pressure at the free surface can be linearized. The resulting linear boundary-value problem for the velocity potential is the Neumann-Kelvin problem. The two-dimensional Neumann-Kelvin problem is studied for the half-immersed circular cylinder by Ursell. Maruo introduced a slender body approach to simplify the Neumann-Kelvin problem in such a way that the integral equation which determines the singularity distribution over the hull surface can be solved by a marching procedure of step by step integration starting at bow. In the present pater for the two-dimensional Neumann-Kelvin problem, it has been suggested that any solution of the problem must have singularities in the corners between the body surface and free surface. There can be infinitely many solutions depending on the singularities in the coroners.