Proverbs of Arittapatti and its Reflection on the Society

Oral traditions are the historical and geographical shadow of a country. They are the messages that are transmitted orally from one generation to another. The messages may be passed down through speech, song, folktales, mythological stories and narrations, proverbs and sayings. They are the gems of the ancient wisdom and knowledge of a society. They provide information about the daily life of the people of the region. Especially, proverbs help to understand the customs and traditions, religious practices and the heritage of the society. They play the pivotal role in the anthropological, historical and cultural study. India is the land of villages is famous for its diverse culture embedded with oral tradiitons. Especially, Tamil Nadu is the treasure house of oral traditions. Though there are reports describing the significance of the oral traditions focusing Tamil Nadu, this study aims to highight the association of proverbs in the day to day life of the village community, Arittaptti, even today

Experimental study to determine angle of fire on selected solid targets by 9mm semi-automatic pistol

Crimes involving the use of firearms represent a significant area of forensic investigation. In legal proceedings of criminal events that involve the use of firearms and ammunitions, the expert forensic officer should be able to produce crucial information to the court. The existence of bullet holes is a significant aspect in crime scene reconstruction. It is a terminal ballistics study using various solid targets. The study is aimed to conduct an experimental firing study by using 9 mm pistol fired on selected solid targets viz. plywood, ceramic tiles, glass plate, aluminium metal sheet and PVC sheet and examined the damaged characteristics. The range of firing was fixed as 10m in all shooting exercises. The shooting exercise was conducted at Sungai Buloh shooting range by trained firearms experts, Polis Di Raja Malaysia, Bukit Aman. Kuala Lumpur. The result of the investigation showed that the angle of impact is below 90 degree in all the targets

Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation

We consider the nonlinear Helmholtz (NLH) equation describing the beam propagation in a planar waveguide with Kerr-like nonlinearity under non-paraxial approximation. By applying the Lie symmetry analysis, we determine the Lie point symmetries and the corresponding symmetry reductions in the form of ordinary differential equations (ODEs) with the help of the optimal systems of one-dimensional subalgebras. Our investigation reveals an important fact that in spite of the original NLH equation being non-integrable, its symmetry reductions are of Painlev\'e integrable. We study the resulting sets of nonlinear ODEs analytically either by constructing the integrals of motion using the modified Prelle-Singer method or by obtaining explicit travelling wave-like solutions including solitary and symbiotic solitary wave solutions. Also, we carry out a detailed numerical analysis of the reduced equations and obtain multi-peak nonlinear wave trains. As a special case of the NLH equation, we also make a comparison between the symmetries of the present NLH system and that of the standard nonlinear Schr\"odinger equation for which symmetries are long available in the literature.Comment: Accepted for publication in "Applied Mathematics and Computation". 18 pages, 15 figure