Browsing by Author "Anuruddhika, M. L. P."

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    Consistency of mixed number algebra in some applications
    (Research Symposium on Pure and Applied Sciences, 2018 Faculty of Science, University of Kelaniya, Sri Lanka, 2018) Anuruddhika, M. L. P.; Doe, M.; Senanayake, N. P. W. B. V. K.
    Mixed number is the sum of a scalar and a vector. The operations of addition, multiplication, inverse and etc. are defined in mixed number algebra. Mixed number algebra is consistent with different laws of Physics such as Pauli matrix algebra and Dirac equation but not consistent with quaternion and geometric products. Even though the quaternion and geometric products are not dealing well with differential operators, mixed product is successfully dealing with them. We have derived the displacement operator, the vector differential operator, the angular momentum operator and Klein-Gorden equation in quantum mechanics in terms of mixed numbers. The Maxwell’s equation and the Lorentz force clearly expressed using mixed numbers. Length contraction and time dilation of special Lorentz transformation, most general Lorentz transformation and mixed number Lorentz transformation are clearly explained. Formulas of the relativistic aberration, Doppler’s effect and the reflection of light ray by a moving mirror are obtained using special Lorenzt transformation, most General Lorenzt transformation, mixed numbers, quaternion and geometric products Lorenzt transformation. Among them, formulas that we derived using mixed numbers are simpler. In our work it has been shown that the calculations using mixed numbers in quantum mechanics and electrodynamics are easier than calculations using quaternion and geometric products. As a conclusion mixed number algebra can be used in different fields of physics and mathematics.
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    The Holt-Winters’ method for forecasting water discharge in Attanagalu Oya
    (Faculty of Science, University of Kelaniya, Sri Lanka., 2021) Anuruddhika, M. L. P.; Premarathna, L. P. N. D; Perera, K. K. K. R.; Hansameenu, W. P. T.; Weerasinghe, V. P. A.
    Forecasting river water discharge is significant in developing flood and agriculture management plans. Annual flood events damage properties, agricultural field, and infrastructures, etc. can be observed in Attanagalu Oya catchment area in Sri Lanka. Therefore, the aim of this study is to forecast water discharge rates (m3/s) at the Dunamale gauging station of Attanagalu Oya using Holt-Winter's method. Holt-Winter's method was chosen because of its’ ability to model trend and seasonal fluctuations, less data requirements and simplicity. Time series models were fitted using the Holt-Winter's method to daily water discharge rates for the period of 2015 –2019 and water discharge was forecasted for the year 2020. The accuracy of the fitted time series models was tested using root mean squares error (RMSE) and mean absolute error (MAE) values. Results showed that the additive Holt-Winters’ method is more appropriate for future forecasting which gave the minimum RMSE and MAE values. Forecasted results will be useful to identify future flood events in advanced to take necessary actions to mitigate damages.