• The Pure and Applied Mathematics
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• v.31 no.4
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• pp.439-451
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• 2024

Motivated by an algorithm to generate all Pythagorean triples, Romik introduced a dynamical system on the unit circle, which corresponds the continued fraction algorithm on the index-2 sublattice. Cha et al. extended Romik's work to other ellipses and spheres and developed a dynamical system generating all Eisenstein triples. In this article, we review the dynamical systems by Romik and by Cha et al. and find connections to the continued fraction algorithms.

• Korean Journal of Soil Science and Fertilizer
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• v.30 no.3
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• pp.209-225
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• 1997

Daily rainfalls and evaporations from copper pan measured in Suweon from 1964 to 1996 were figured respectively so that past soil moisture deficits can be understood clearly at a glance in relation to the characteristics of weather. Past drought intensities in Suweon were computed on the basis of Oh's 50mm pan model estimating drought in terms of daily, monthly shortage of evapotranspiration and growthless time fraction. Yearly differences in drought seem to result mainly from yearly differences in rainfall distribution and intensity, because there is the periodical similarity in evaporation from year to year. The most intense drought continued from December, 1964 to June, 1965 for 190 days and the most frequent rainfalls were observed from June, 1989 to August, 1990 for 15 months. The applied Oh's drought estimation model was reinforced with figuring programs with a view to later application for other districts. Present economic value index of irrigation were distributed in the range of 120% to 210% of one season yield for spring chinese cabbage, calculated on the basis of 10 year's accumulation of its expectable future yield increase. Therefore, the same value can be invested for the installation of new irrigation system even only for spring chinese cabbage, if its depreciation period is 10 years.

• Korean Journal of Plant Tissue Culture
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• v.27 no.6
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• pp.423-428
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• 2000

In 1997 when cloned sheep Dolly and soon after Polly were born, it had become head-line news because in the former the nucleus that gave rise to the lamb came from cells of six-year-old adult sheep and in the latter case a foreign gene was inserted into the donor nucleus to make the cloned sheep produce human protein, factor IX, in e milk. In the last few years, once the realm of science fiction, cloned mammals especially in livestock have become almost commonplace. What the press accounts often fail to convey, however, is that behind every success lie hundreds of failures. Many of the nuclear-transferred egg cells fail to undergo normal cell divisions. Even when an embryo does successfully implant in the womb, pregnancy often ends in miscarriage. A significant fraction of the animals that are born die shortly after birth and some of those that survived have serious developmental abnormalities. Efficiency remains at less than one % out of some hundred attempts to clone an animal. These facts show that something is fundamentally wrong and enormous hurdles must be overcome before cloning becomes practical. Cloning researchers now tent to put aside their effort to create live animals in order to probe the fundamental questions on cell biology including stem cells, the questions of whether the hereditary material in the nucleus of each cell remains intact throughout development, and how transferred nucleus is reprogrammed exactly like the zygotic nucleus. Stem cells are defined as those cells which can divide to produce a daughter cell like themselves (self-renewal) as well as a daughter cell that will give rise to specific differentiated cells (cell-differentiation). Multicellular organisms are formed from a single totipotent stem cell commonly called fertilized egg or zygote. As this cell and its progeny undergo cell divisions the potency of the stem cells in each tissue and organ become gradually restricted in the order of totipotent, pluripotent, and multipotent. The differentiation potential of multipotent stem cells in each tissue has been thought to be limited to cell lineages present in the organ from which they were derived. Recent studies, however, revealed that multipotent stem cells derived from adult tissues have much wider differentiation potential than was previously thought. These cells can differentiate into developmentally unrelated cell types, such as nerve stem cell into blood cells or muscle stem cell into brain cells. Neural stem cells isolated from the adult forebrain were recently shown to be capable of repopulating the hematopoietic system and produce blood cells in irradiated condition. In plants although the term$\boxDr$ stem cell$\boxUl$is not used, some cells in the second layer of tunica at the apical meristem of shoot, some nucellar cells surrounding the embryo sac, and initial cells of adventive buds are considered to be equivalent to the totipotent stem cells of mammals. The telomere ends of linear eukaryotic chromosomes cannot be replicated because the RNA primer at the end of a completed lagging strand cannot be replaced with DNA, causing 5' end gap. A chromosome would be shortened by the length of RNA primer with every cycle of DNA replication and cell division. Essential genes located near the ends of chromosomes would inevitably be deleted by end-shortening, thereby killing the descendants of the original cells. Telomeric DNA has an unusual sequence consisting of up to 1,000 or more tandem repeat of a simple sequence. For example, chromosome of mammal including human has the repeating telomeric sequence of TTAGGG and that of higher plant is TTTAGGG. This non-genic tandem repeat prevents the death of cell despite the continued shortening of chromosome length. In contrast with the somatic cells germ line cells have the mechanism to fill-up the 5' end gap of telomere, thus maintaining the original length of chromosome. Cem line cells exhibit active enzyme telomerase which functions to maintain the stable length of telomere. Some of the cloned animals are reported prematurely getting old. It has to be ascertained whether the multipotent stem cells in the tissues of adult mammals have the original telomeres or shortened telomeres.