• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.331-336
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• 2007

We consider infinite nested radicals in which the arguments are positive polynomial sequences. It is shown that the evaluation of such a nesting is always finite, and we prove necessary and sufficient conditions for the evaluation to be a finite polynomial.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.1-15
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• 2022

In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

• Parasites, Hosts and Diseases
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• v.54 no.6
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• pp.733-742
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• 2016

Acquaintance is scanty on primaquine (PQ) efficacy and Plasmodium vivax recurrence in Udupi district, Karnataka, India. We assessed the efficacy of 14 days PQ regimen (0.25 mg/kg/day) to prevent P. vivax recurrence. Microscopically, aparasitemic adults (${\geq}18years$) after acute vivax malaria on day 28 were re-enrolled into 15 months' long follow-up study. A peripheral blood smear examination was performed with participants at every 1-2 month interval. A nested PCR test was performed to confirm the mono-infection with P. vivax. Of 114 participants, 28 (24.6%) recurred subsequently. The median (IQR) duration of the first recurrence was 3.1 (2.2-5.8) months which ranged from 1.2 to 15.1 months, including initial 28 days. Participants with history of vivax malaria had significantly higher risk of recurrence, with hazard ratio (HR) (95% CI) of 2.62 (1.24-5.54) (P=0.012). Severity of disease (11.4%, 13/114) was not associated (P=1.00) with recurrence. Of 28 recurrence cases, the nPCR proved that P. vivax mono-infection recurrence rate was at least 72.7% (16/22) at first recurrence. In Udupi district, PQ dose of 0.25 mg/kg/day over 14 days seems inadequate to prevent recurrence in substantial proportion of vivax malaria. Patients with a history of vivax malaria are at high risk of recurrences.