Some Applications of Homotopy Perturbation Method

In this thesis paper, I review the basic idea of Homotopy perturbation method (HPM), Modified Homotopy perturbation method (MHPM) and Homotopy perturbation transform method (HPTM). Then apply these on some higher order non-linear problems.Further, I tried to compare the results obtained from Modified homotopy perturbation method with HPM using the Sine-Gordon and fractional Klein-Gordon equation respectively. Homotopy perturbation transform method is the coupling of homotopy perturbation and Laplace transform method. Lastly, I applied the homotopy perturbation and homotopy perturbation transform method for solving linear and non-linear Schrödinger equation

Insights into the low energy incomplete fusion

In the present work, channel-by-channel excitation functions of different evaporation residues populated via complete and/or incomplete fusion in C12+169Tm system have been measured for an energy range Elab?53–90MeV, using recoil-catcher activation technique followed by off-line ?-spectroscopy. Experimentally measured excitation functions have been analysed in the framework of statistical model code PACE. To probe the effect of entrance-channel parameters on the onset and strength of incomplete fusion, relative contributions of complete and incomplete fusion have been deduced from the analysis of experimentally measured excitation functions. The percentage fraction of incomplete fusion deduced from the analysis of excitation functions has been studied in terms of incident energy, entrance-channel mass-asymmetry, ground state alpha-Q-value, neutron skin thickness of target nuclei, and nuclear potential parameters. It has been found that incomplete fusion start competing with complete fusion even at slightly above barrier energies where complete fusion is assumed to the sole contributor. The probability of incomplete fusion increases with incident energy, entrance channel mass-asymmetry, large negative ground state alpha-Q-value, neutron skin thickness, and nuclear potential parameters for individual projectiles.Indian Institute of Technology Bombay Science and Engineering Research Board Central Mechanical Engineering Research Institute, Council of Scientific and Industrial ResearchWe thank the Director of IUAC New Delhi for extending necessary facilities to perform these experiments, target laboratory for helping in the target preparations, and the Pelletron crew for smooth operation during the experiments. Authors are thankful to Prof. R. K. Bhowmik, Prof. P. K. Raina, Dr. S. Muralithar, Dr. R. P. Singh for scientific discussions during the experiments and data analysis. One of the authors P.P.S. acknowledges startup grant from the Indian Institute of Technology Ropar, the Council of Scientific and Industrial Research for a research grant ref.no. CSIR/03(1353)/16/EMR-II , and the Science and Engineering Research Board for a young scientist award ref.no. YSS/2014/000250

Entrance channel effect on incomplete fusion

In the present work, the onset and strength of incomplete fusion were studied in terms of various entrance channel parameters. Excitation functions for individual evaporation residues were measured in the 12C+169Tm system at energies from 5 to 7.5AMeV, and analysed in the framework of the statistical model code PACE-IV to deduce the fraction of incomplete fusion. It was found that the probability of incomplete fusion increases with the incident energy as well as with the mass asymmetry of interacting partners for individual projectiles. Moreover, the critical value of the input angular momentum (lcrit) obtained from the experimental cross sections was compared with that calculated using the Wilczynski formula and a slight difference has been found. © 2018 Jagellonian University. All rights reserved.Science and Engineering Research BoardOne of the authors, P.P.S., acknowledges the Science and Engineering Research Board (SERB), India, for a Young Scientist research award, reference No. YSS/2014/000250

Deciphering the Diversity of Somatic Alterations and Salmonella Infection in Gallbladder Cancer by Whole Exome Sequencing

Introduction: Gallbladder cancer is relatively a rare lethal malignancy with dismal prognosis.  While in India there is high incidence (3.9-8.6/1, 00,000) with majority of patients having advanced disease. Recent developments in next generation sequencing technologies have enabled the discovery of new molecular therapeutic targets in many human cancers. Objectives: Interrogate the landscape of somatic alterations in Indian gall bladder cancer using whole exome sequencing technology. Material and Methods: We interrogated the coding region of 27(10 paired and 7 unpaired) Indian gall bladder cancer samples using whole exome sequencing at an average coverage of 100X and above. We further validated the findings using an additional set of 27 FFPE samples. Results: Using a bioinformatics filtering approach, we identify a total of 5060 somatic variants found across 17 tumors consisted of 3239 missense, 1449 silent, 131 nonsense, 135 indels and 106 splice site mutations The average mutation rate considering the paired tumors is about 7.7 mutations/mb. We found TP53 (35.2%), ERBB2 (17.6%), SF3B1 (17.6%), ATM (17.6%) and AKAP11 (17.6%) mutations in more than two samples by exome sequencing analysis. Furthermore, we examined our exome sequencing data for identifying Salmonella sequences as well as presence of 143 HPV types using computation subtraction based on HPVDetector. Based on our evaluation we found association of typhoidal Salmonella strains in 11 of 26 gall bladder cancer samples and non-typhoidal Salmonella species in 12 of 26 samples, 6 samples were co-infected with both. Conclusions: The profiling of somatic alterations and identification of non typhoidal Salmonella traces may aid in changing the current treatment paradigm of gall bladder cancer