Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Fundamental Related Abstracts

2 Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian

Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

Abstract:

In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using StirlingĀ“s formula.

Keywords: Fundamental, discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations

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1 The Difference in Basic Skills among Different Positional Players in Football

Authors: Habib Sk, Ashoke Kumar Biswas

Abstract:

Football is a team game. Eleven players of each team are arranged in different positions of play to serve the specific task during a game situation. Some such basic positions in a soccer game are (i) goal keepers (ii) defenders (iii) midfielders and (iv) forwards. Irrespective of the position, it is required for all football players to learn and get skilled in basic soccer skills like passing, receiving, heading, throwing, dribbling, etc. The purpose of the study was to find out the difference in these basic soccer skills among positional players in football if any. A total of thirty-nine (39) teen aged football players between 13 to 19 years were selected from Hooghly district in West Bengal, India, as subjects. Out of them, there were seven (7) goal keepers, twelve (12) defenders, thirteen (13) midfielders, and seven (7) forwards. Passing, dribbling, tackling, heading, and receiving were the selected basic soccer skills. The performance of the subjects of different positional groups in different selected soccer skills was tested using a standard test for each. On the basis of results obtained through statistical analysis of data, following results were obtained: i) there was significant difference among the groups in passing, dribbling and heading but not in receiving; ii) the goal keepers and defenders were the weakest in all selected soccer skills; iii) midfielders were found better in receiving than other three skills of passing, dribbling and heading; and iv) the forward group of players was found to be the better in passing, dribbling and heading but weakest in receiving than other groups.

Keywords: Performance, Fundamental, difference, Position, soccer, skill

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