• 대한수학회논문집
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• 제11권2호
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• pp.503-514
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• 1996

We consider non-constant coefficient elliptic equations of the type -div(a \bigtriangledown u) = f$, and employ the P-version of the finite element method as a numerical method for the approximate solutions. To compute the integrals in the variational form of the discrete problem we need the numerical quadrature rule scheme. In practice the integrations are seldom computed exactly. In this paper, we give an $L_2(\Omega)$-error estimate of $\Vert u = \tilde{u}_p \Vert_{0,omega}$ in comparison with $\Vert u = \tilde{u}_p \Vert_{1,omega}$, under numerical quadrature rules which are used for calculating the integrations in each of the stiffness matrix and the load vector.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 12th Asian Congress of Fluid Mechanics
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• pp.64.1-64.1
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• 2008

• 대한수학회지
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• 제57권6호
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• 대한수학회지
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• 제55권2호
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• pp.373-390
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• 2018

In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.

• 한국토양비료학회지
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• 제49권1호
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• pp.87-92
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• 2016

With the population growth and industrialization, the characteristics of discharged waste water and sewage have become more diverse. The removal of phosphorus (P) in the wastewater is essential for the prevention of eutrophication in the river and stream. This study was performed in order to estimate the field application of the Bacillus sp. 3434 BRRJ. Bacillus sp. 3434 BRRJ was cultured in the raw wastewater and synthetic medium at the 5 L reactor. The best optimum conditions for P removal by Bacillus sp. 3434BRRJ in the synthetic medium at the 5 L reactor were as follows: temperature, $30^{\circ}C$; P concentration, 20 mg/L; carbon sources, glucose + acetate (1:1); oxygen concentration, alternatively anaerobic and aerobic conditions. P removal efficiency under the optimum condition was 89.4%. In case of wastewater, P removal efficiency was 95.5% under controlled at $30^{\circ}C$. Through this study we confirmed that P removal by Bacillus sp. 3434BRRJ in case of wastewater was as effective as the synthetic medium. It is considered that Bacillus sp. 3434 BRRJ can be applied to the treatment of wastewater in order to biologically remove P from the wastewater on a large scale.

• 대한수학회지
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• 제57권1호
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• pp.89-111
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• 2020

In the present paper, we give some characterization of the L₂ maximal estimate for the operator P^t_a,γf(Γ(x, t)) along curve with complex time, which is defined by $$P^t_{a,{\gamma}}f({\Gamma}(x,t))={\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}}}}\;e^{i{\Gamma}(x,t){\xi}}e^{it{\mid}{\xi}{\mid}^a}e^{-t^{\gamma}{\mid}{\xi}{\mid}^a}{\hat{f}}({\xi})d{\xi}$$, where t, γ > 0 and a ≥ 2, curve Γ is a function such that Γ : ℝ×[0, 1] → ℝ, and satisfies Hölder's condition of order σ and bilipschitz conditions. The authors extend the results of the Schrödinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schrödinger operators along the curves.

• 한국물환경학회지
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• 제25권5호
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• pp.689-696
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• 2009

Unit load approach has been used to estimate the non-point pollutant load in Total Water Pollution Load Management System (TWPLMS). In this study, locally applicable unit loads for road and parking lot were developed based on the measurements of 9 rainfall events from 2007 to 2008 in Yongin city of Gyeongan stream watershed. Observations showed that stormwater runoff began at low precipitation (>1 mm) and peak pollutant concentration occurred at the beginning of the runoff because of impervious nature of the sites. Averaged event mean concentrations (EMCs) of road (parking lot) were estimated as COD 105.36(62.69) mg/L, BOD 15.94(13.20) mg/L, TSS 183.45(66.52) mg/L, T-N 4.63(3.28) mg/L, T-P 0.45(0.39) mg/L. Higher EMCs at the road than parking lot may reflect heavier traffic. Unit loads Estimated from the EMCs and 10 year average rainfall data were COD $331.17kg/km^2{\cdot}day$, BOD $50.20kg/km^2{\cdot}day$, TSS $580.13kg/km^2{\cdot}day$, T-N $14.68kg/km^2{\cdot}day$, T-P $1.43kg/km^2{\cdot}day$ in the road and COD $186.59kg/km^2{\cdot}day$, BOD $39.22kg/km^2{\cdot}day$, TSS $199.15kg/km^2{\cdot}day$, T-N $9.70kg/km^2{\cdot}day$, T-P $1.16kg/km^2{\cdot}day$ in the parking lot. The estimated unit loads are not so comparable to the ones listed in TWPLMS technical guideline and published data that locally developed unit loads should be used to estimate non-point pollutant loads.

• 대한수학회지
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• 제58권2호
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• 한국농공학회논문집
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• 제54권6호
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• pp.29-37
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• 2012

This study was carried out to runoff characteristics in an upland livestock manure compost. Irrigation, runoff and water quality data in the upland were analyzed periodically from May to November in 2011. The observed amount of rainfall, irrigation, runoff for the experimental upland during the investigation period were 1,299.7 mm, 32.0 mm, and 340.7 mm, respectively. The concentrations of T-N in compost and non-compost upland during study period were ranged from 2.09 mg/L to 6.66 mg/L and from 1.99 mg/L to 6.01 mg/L, respectively. which was generally higher than the quality standard of agricultural water (1.0 mg/L). The concentrations of T-P in compost and non-compost upland during study period were ranged from 0.069 mg/L to 0.525 mg/L and from 0.018 mg/L to 0.152 mg/L, respectively. The runoff pollutants loadings of T-N and T-P in compost upland were 10.05 kg/ha and 0.56 kg/ha, respectively. The runoff pollutants loadings of T-N and T-P in non-compost upland were 9.09 kg/ha and 0.26 kg/ha, respectively. The runoff pollutants loadings in T-N and T-P from this study were much lower values than the pollutant loadings of T-N and T-P from the upland published by the others studies. Runoff pollution loadings due to the upland field in order to identify the characteristics of various crops, farming methods and a variety of targets taking into account regional characteristics by conducting continuous monitoring runoff load estimate will be required.

• Asian-Australasian Journal of Animal Sciences
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• 제16권4호
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• pp.489-493
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• 2003

Reproductive traits of sows are determined chiefly by the genetic background of the dam herself. Whether the breed of the serviced boars also contributes is not yet clear. A total of 8,946 litters of Landrace (L) sows from 68 farms were examined. Of these, 876, 1,260, and 6,810 litters were produced from natural mating with L, Yorkshire (Y), and Duroc (D) breeds, respectively. The birth litter size (BLS), weaning litter size (WLS), live born piglets (LBP), and survival rate % (SR), of every litter were recorded. A general linear-model procedure was followed to estimate the effects of boars' breed (B), parity (P) and B${\times}$P interaction on the reproductive traits of the sows. Results show that BLS, WLS, and LBP were all significantly (p<0.001) affected by B and P. SR% was significantly influenced by B but not by P. L sows crossbred with Y or purebred with L produced litters with higher BLS, WLS, and LBP values than those bred with D. Pure L breeding yielded litters with lower SR% than did crossbreeding with D, while the difference between SR% due to LY and that due to LD crossbreeding was not significant. The interaction of B with P was significant with respect to BLS, WLS, and LBP (p<0.001), but not SR%. No significant B effect on reproductive traits was measured in sows at their first parity; but at latter parities, LL or LY produced litters with similarly high BLS, WLS and LBP, which values were all significantly greater than those of LD litters. The breed of boar evidently affected the subsequent reproductive performance of L sows and this effect may be further manipulated by the parity effect. Breed differences in semen quality and the success of fetus development with different interactions of the genetic background with the uterus function of the sow that may contribute to these effects are discussed.