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CERTAIN GENERALIZED THORN GRAPHS AND THEIR WIENER INDICES
Kathiresan, KM.,Parameswaran, C. The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.5
If G is any connected graph of order p; then the thorn graph $G_p^*$ with code ($n_1$, $n_2$, ${\cdots}$, $n_p$) is obtained by adding $n_i$ pendent vertices to each $i^{th}$ vertex of G. By treating the pendent edge of a thorn graph as $P_2$, $K_2$, $K_{1,1}$, $K_1{\circ}K_1$ or $P_1{\circ}K_1$, we generalize a thorn graph by replacing $P_2$ by $P_m$, $K_2$ by $K_m$, $K_{1,1}$ by $K_{m,n}$, $K_1{\circ}K_1$ by $K_m{\circ}K_1$ and $P_1{\circ}K_1$ by $P_m{\circ}K_1$ and their respective generalized thorn graphs are denoted by $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ respectively. Many chemical compounds can be treated as $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ of some graphs in graph theory. In this paper, we obtain the bounds of the wiener index for these generalization of thorn graphs.
CERTAIN GENERALIZED THORN GRAPHS AND THEIR WIENER INDICES
KM. Kathiresan,C. Parameswaran 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.5
If G is any connected graph of order p; then the thorn graph G∗p with code (n1, n2, ... , np) is obtained by adding ni pendent vertices to each ith vertex of G: By treating the pendent edge of a thorn graph as P2, K2, K1, 1, K1 ◦K1 or P1 ◦K1, we generalize a thorn graph by replacing P2 by Pm, K2 by Km, K1, 1 by Km, n, K1 ◦ K1 by Km ◦ K1 and P1 ◦ K1by Pm ◦ K1 and their respective generalized thorn graphs are denoted by GP ;GK;GB;GKK and GPK respectively. Many chemical compounds can be treated as GP, GK, GB, GKK and GPK of some graphs in graph theory. In this paper, we obtain the bounds of the wiener index for these generalization of thorn graphs.
Manju Chandran,John P.Bilezikian,Nurshazwani Mat Salleh,Hao Ying,Joel Lau,James Lee,Mechteld C. deJong,Aye Chan Maung,Rajeev Parameswaran 대한골다공증학회 2022 Osteoporosis and Sarcopenia Vol.8 No.1
Objectives: We sought to assess the incidence of hungry bone syndrome (HBS) following parathyroidectomy (PTX) for primary hyperparathyroidism (PHPT) in a cohort of multi-ethnic patients from a developed country in the Asia Pacific. Methods: One hundred and sixty-four patients who underwent PTX for PHPT between 2012 and 2019 at the 2 largest public hospitals in Singapore were identified. HBS was defined as serum albumin-adjusted calcium ≤ 2.1 mmol/L with normal or raised serum intact parathyroid hormone (iPTH) levels, manifesting on or after the 3rd day, or persisting for more than 3 days post-operatively. Results: Chinese constituted 73.8%, Malays 12.2%, Indians 9.8%, and other races 4.3%. HBS developed in 4 patients (2.4%) (95% CI, 0.8%-6.5%). HBS patients had significantly longer in-hospital stays; 20 days [IQR:15-22] vs 2 days [IQR:1-3]; P < 0.001in those who did not develop HBS. There was no difference in the incidence of HBS stratifying for age, sex, vitamin D status, or use of preoperative anti-resorptive medication use. For every 10 unit increase in iPTH and alkaline phosphatase (ALP) levels, the risk of HBS increased by 14% and 11%; RR (95% CI), 1.14 (1.05-1.21) and 1.11 (1.03-1.18), respectively. Conclusions: The low incidence of HBS in multi-ethnic patients undergoing PTX by multiple surgeons for PHPT at the 2 largest public hospitals that see the most such patients in Singapore, a developed country, is consistent with the asymptomatic/milder form of presentation of PHPT in the developed world.
Bhuyan Sudhansu Sekhar,Barik Durga Prasad,Dash Byomkesh,Rout Prachitara,Pattnaik Snigdha Samir,Verma Ramlakhan,Katara Jawahar Lal,Parameswaran C.,Devanna B. N.,Sahoo Raj Kishore,Mishra Anindita,Sabari 한국작물학회 2024 Journal of crop science and biotechnology Vol.27 No.2
Hybrid rice has a considerable yield advantage over inbred lines, but the adoption rate in India is quite slow. In a three-line hybrid rice breeding programme, the development of fertility restorer lines that have enhanced grain quality is crucial. Employment of doubled haploid (DH) technology will accelerate the development of improved R lines in a short period of time, thus hastening the pace of hybrid rice breeding. This investigation was carried out for the evaluation of genetic diversity and assessment of population differentiation in 113 DHs derived from BC1F1s of IMP. IR 42266-29-3R and Nagina 22. A total of 46 SSR (Simple Sequence Repeat) markers resulted in an average of 2.00 alleles per locus. Polymorphism information content (PIC) value ranged from 0.31 to 0.37 with an average of 0.36. RM496, RM25520, RM483 and RM553 were found to be the best markers for the identification of genetic diversity. Structure analysis classified 113 DHs into four groups, which matched the Neighbour-Joining method using UPGMA cluster analysis. The AMOVA results demonstrated substantial genetic variations within subpopulation than among sub-population. The SSR marker-based molecular fingerprinting could serve as a sound basis in the identification of genetically distant as well as in the duplicate sorting of the morphologically close population in future breeding programmes