• 대한수학회보
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• 제57권5호
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• pp.1231-1240
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• 2020

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to ℤ-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

• 대한수학회보
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• 제37권1호
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• pp.191-207
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• 2000

Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• 드라이브 ㆍ 컨트롤
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• 제7권3호
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• pp.20-28
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• 2010

• 충청수학회지
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• 제7권1호
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• pp.75-86
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• 1994

Let L be a Lie algebra over an algebraically closed field F of chracteristic p > 0 which has an $\underline{1}$-filtration. We prove that W(1;$\underline{1}$) is the only restricted simple Lie algebra having an $\underline{1}$-filtration. And we show that the even dimensional Lie algebra can not have an $\underline{1}$-filtration.

• 한국농공학회논문집
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• 제51권5호
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• pp.95-100
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• 2009

The water purification systems have been hardly used for agricultural purpose due to their complicated compositions and high costs for farmers, while only simple filtrations have been applied to irrigation systems in order to prevent the system from clogging problems. This study therefore developed a clean water supplying system, the Filter-Disinfection-Adsorption (FDA) system, especially for greenhouse cultivation of where low quality of water is available. This system has also been produced for providing convenience water to farmers in the areas of no water supply service systems for the purpose of washing their bodies or agricultural machineries after farm work. The FDA system consists of three stages of purification processes with an integral module, including disk and teflon filtrations and Ultraviolet (UV) sterilization processes. Indoor experiments were undertaken with a trial product of the FDA system to test its performance. The operation test of the process was performed as well as the condition check of each item including UV module, filters, control panel, pump, valves, etc. The results shows good performance of each test with no critical problems. The initial and maintenance costs were also analysed with other purification systems. From the comparisons, the FDA system found to be very economical and easy to use.

• 한국식품영양과학회지
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• 제42권12호
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• pp.2012-2018
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• 2013

쌀을 이용하여 제조한 술덧을 이용하여 상압다단식증류기, 상압단식증류기와 감압단식증류기를 이용하여 증류한 증류식소주의 주요 향기성분 및 증류 수율에 미치는 영향과 숙성된 증류주의 여과방법에 따른 주요 향기성분 변화를 조사하였다. 증류에 사용된 술덧의 알코올 함량, 비중 및 가용성 고형분 함량은 각각 15%, 0.997, $10^{\circ}Brix$이었으며, 총산 함량 및 아미노산 함량은 각각 0.25 및 0.15 g/100 mL로 증류주 제조에 적합하였다. 증류주의 향기성분 중 퓨젤오일은 i-amyl alcohol> i-butanol> n-propanol> n-butanol 순으로 검출되었다. 또한 전체 퓨젤오일 함량은 상압다단식증류기를 이용하여 증류하였을 때 가장 많았으며(6,676 mg/L), 증류기 종류에 관계없이 증류과정 중의 초류(4,884~4,931 mg/L)에 가장 많이 함유되어 있었다. 에스테르 화합물은 ethyl acetate가 주된 에스테르 화합물이었으며 초류에서 1,727~2,203 ${\mu}L/L$, 본류에서 68~97 ${\mu}L/L$가 검출되었다. 전체 에스테르 화합물 함량은 상압다단식증류기를 이용하여 증류하였을 때 가장 많이 검출되었으며, 증류기의 종류에 관계없이 초류에 가장 많이 함유되어 있었다. 각 증류기 별로 증류한 증류주를 숙성시킨 후 활성탄 여과 및 냉동 여과를 시킨 다음 향기성분은 여과방법에 따른 변화가 미비하였다.

• 한국미생물생명공학회:학술대회논문집
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• 한국미생물생명공학회 1986년도 추계학술대회
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• pp.521.3-522
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• 1986

A gene encoding alcohol dehydrogenase (ADH) in Zymomonas mobilis was cloned into E. coli JM 83 with plasmid pUC 9. The ADH produced by the E. coli transformant was purified bysonication, (NH$^4$)2SO4 fractionation, Affi-Gel blue and hydroxylapatite chromatography. The ADH produced by Z. mobilis was also purified by the same procedures. The two enzyme preparations were characterized and compared. It was found that the E. coli ADH was identical to one of two ADH isozymes of Z. mobilis. Analytical gel filtrations led to the conclusion that the molecule of E. coli ADH was composedv of four subunits having molecular weight of 40,000 (+1,000) dalton each The effect of metal ions on ADH activity and optimum pH were investigated.

• 대한수학회보
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• 제55권2호
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• pp.561-572
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• 2018

In this paper we consider the concept of statistical causality in continuous time between flows of information, represented by filtrations. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical finance. We give necessary and sufficient conditions, in terms of statistical causality, for extremality of measure in the set of martingale measures. Also, we have considered the extremality of measure which involves the stopping time and the stopped processes, and obtained similar results. Finally, we show that the concept of unique equivalent martingale measure is strongly connected to the given concept of causality and apply this result to the continuous market model.

• 상하수도학회지
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• 제13권2호
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• pp.41-46
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• 1999

Backwashing is an important process for the efficient operation of granular filters, and the efficiency of the surface washing among the backwashing processes can affect the filtrations rate and filter run-time. In this study, the efficiency of surface washing is evaluated using real filters for three cases: with surface washing (with and without drainage of water to the surface of filter bed) and without surface washing. As a result, in the case of adopting both the drainage and surface washing, the filter of which condition is initially worse than those of the other filters shows improvement in head-loss development, filtration velocity, filter run-time, and total filtration volume. On the other hand, the conventional method of surface washing rarely has an effect on the filter washing.

• 대한수학회보
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• 제40권1호
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• pp.29-51
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• 2003

In this paper we construct a natural filtration associated to the plethysm $S_{r}(\wedge^2 \varphi)$ over arbitrary commutative ring R. Let $\phi$ : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of $S_{r}(\wedge^2 \varphi)$ as a $GL(F){\times}GL(G)$- complex such that its associated graded complex is ${\Sigma}_{{\lambda}{\in}{\Omega}_{\gamma}}=L_{2{\lambda}{\varphi}$, where ${{\Omega}_{\gamma}}^{-}$ is a set of partitions such that $│\wedge│\;=;{\gamma}\;and\;2{\wedge}$ is a partition of which i-th term is $2{\wedge}_{i}$. Specializing our result, we obtain the filtrations of $S_{r}(\wedge^2 F)\;and\;D_{r}(D_2G).