• 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.

• 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.