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2009 - 200912010 - 20131
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Subject: Mathematics × Author: Gangwar, Sukhdev Singh × Start date: 2004 ×
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    ThesisItemOpen Access
    A study of thermo-magnetic effects on static state of cholesteric liquid crystal between two hot co-axial circular cylinders
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2009-06) Gangwar, Sukhdev Singh; Sharma, A.K.
    Liquid crystal the fourth state of matter is observed between the crystalline solid and amorphous liquid states. It exihibits the properties of liquids as well as that of crystalline solid state. In the present study we have considered an infinite static layer of cholesteric liquid crystal lying between two infinite hot co-axial circular cylinders in the presence of azimuthal magnetic field when both the cylinders are held at different temperatures and are lying at rest. We have examined the thermo-magnetic effects in this problem. After obtaining the system of governing differential equations we have solved it numerically by Newton Raphson method. The results are then graphically plotted. It has been observed that orientation of molecules varies with the variation of magnetic field and temperature gradient parameters.
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    ThesisItemOpen Access
    Study of some probabilistic and computational methods for fuzzy and intuitionistic fuzzy time series forecasting
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2013-08) Gangwar, Sukhdev Singh; Sanjay Kumar
    Time series forecasting in the environment of fuzzy and intuitionistic finds its scope in various branches of sciences and engineering. The present research work mainly focus on development and implementation of fuzzy and intuitionistic fuzzy time series forecasting models. In this study, 6 different models of fuzzy and intuitionistic fuzzy time series forecasting were developed. Model 1, model 2 and model 3 were computational algorithm based higher order fuzzy time series forecasting models. These models were based on multiple partitions which were created using a ratio formula that uses maximum and minimum of time series data. Model 4, model 5 and model 6 used the concept of IFS to include degree of hesitation in time series forecasting. In model 4, the concept of IFS was used in fuzzification process. In model 5, fuzzy sets induced from IFS were used to establish fuzzy logical relations. Model 6 is purely intuitionistic fuzzy time series forecasting model. Both model 4 and model 5 used max-min composition of fuzzy logical relations and model 6 used max-min composition of intuitionistic fuzzy logical relations. All developed models (model 1 to model 6) were implemented on the time series data of enrollments of University of Alabama and share prices of SBI. Results of all forecasting models have been presented graphically to show their trend with actual time series data. Performance analysis of all models has been discussed in terms of MSE and AFE. Time series data of enrollments of University of Alabama were used to show robustness of all models to show their sensitivity towards the unexpected fluctuation in time series data. In forecasting enrollments of University of Alabama, the performance of model 3 in terms of both MSE and AFE is found better than model 1 and model 2. In forecasting share prices of SBI, the performance of model 1 in terms of both MSE and AFE is found better than model 2 and model 3. In forecasting enrollments of University of Alabama, the performance of model 5 in terms of both MSE and AFE is better than other IFS based forecasting models (model 4 and model 6). In forecasting share prices of SBI, the performance of model 6 in terms of MSE is found better than model 4 and model 5 but the performance of model 5 in terms of AFE is found better other model 4 and model 6. Overall, in the case of forecasting the enrollments of University of Alabama, model 3 outperforms than the model 1, model 2, model 4, model 5 and model 6 in terms of MSE and AFE. In terms of MSE and AFE, model 1 outperforms than the model 2, model 3, model 4, model 5 and model 6 in forecasting share prices of SBI. Model 6, intuitionistic fuzzy time series forecasting model and also gives the good performance with respect to other models. The present study may be helpful in research of many forecasting branches as well as in the fields of fuzzy and intuitionistic fuzzy time series forecasting.