• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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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 ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• Journal of Drive and Control
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• v.7 no.3
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• pp.20-28
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• 2010

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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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.

• Journal of The Korean Society of Agricultural Engineers
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• v.51 no.5
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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.

• Journal of the Korean Society of Food Science and Nutrition
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• v.42 no.12
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• pp.2012-2018
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• 2013

The objective of this research was to investigate the quality characteristics of the spirits by different distillation and filtrations. The contents of alcohol, total acids, and amino acids in rice mash were 15%, 0.25 g/100 mL, and 0.15 g/100 mL, respectively. The soluble content was $10^{\circ}Brix$, and pH was 4.6 in the rice mash. Lactic acid was the most prominent organic acid found in rice mash. The rice spirit distilled by a multi stage distiller showed the highest amounts of aroma compounds, such as fusel oil and esters. However, the filtration did not affect the amounts of total aroma compounds. It is suggested that a multi stage distiller may influence taste and flavor positively by enhancing the aroma and removing the impurities in rice spirits.

• Proceedings of the Korean Society for Applied Microbiology Conference
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• 1986.12a
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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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.

• Journal of Korean Society of Water and Wastewater
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• v.13 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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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).