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Congruences modulo 7 and 11 for (s,t)-regular bipartitions
Ranganatha D. 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2
Let Bs,t(n) denote the number of (s, t)-regular bipartitions of n. In this paper, we prove several infinite families of congruences modulo s for Bs,t(n), where (s, t)∈{(7, 5), (7, 25) (7, 125), (11, 5)}.
S. R. Ranganatha,C. V. Kavitha,K. Vinaya,D. S. Prasanna,S. Chandrappa,Sathees C. Raghavan,K. S. Rangappa 대한약학회 2009 Archives of Pharmacal Research Vol.32 No.10
The present work deals with the anticancer effect of benzimidazole derivatives associated with the pyridine framework. By varying the functional group at N-terminal of the benzimidazole by different L-amino acids, several 2-(4-(2,2,2-trifluoroethoxy)-3-methylpyridin-2-ylthio)-1Hbenzo[d]imidazole derivatives 9(a-j) were synthesized. Their chemical structures were confirmed by 1H NMR, IR and mass spectroscopic techniques. The synthesized compounds were examined for their antiproliferative effects against human leukemia cell lines, K562 and CEM. The preliminary results showed most of the derivatives had moderate antitumor activity. Compound 9j containing cysteine residue exhibited good inhibition compared to other amino acid resides. In addition DNA fragmentation results suggest that 9j is more cytotoxic and able to induce apoptosis.
Arithmetic properties of partition four tuples with 3-cores
Chandrashekar Adiga,Ranganatha D 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.3
Let A<sup>k<sub>3 (n) denote the number of partition k-tuples of n where each partition is 3- core. In this paper, employing elementary generating function dissection techniques, we establish several innite families of congruences for A<sup>4<sub>3 (n). For example, we proved that for all integers α ≥ 0, k ≥ 0 and n ≥ 0, A<sup>4<sub>3(4<sup>(k+1)n + 5.2<sup>(2k+1) - 4/ 3)≡ 0 mod (4<sup>4k+5 -4)/63), A<sup>4<sub>3(16<sup(k+1)α n + 4<sup>(2k+2)α+1 -4) / 3 ≡ A<sup>4<sub>3(n) mod (64<sup>k+1 -1/63).