Minimum Time Problem for Co-operative Parabolic System with Control-State Constraints
Issue:
Volume 1, Issue 1, October 2016
Pages:
1-7
Received:
6 September 2015
Accepted:
17 September 2015
Published:
12 October 2016
DOI:
10.11648/j.mma.20160101.11
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Abstract: In this paper, the minimum time problem for differential systems of parabolic type with distributed control and control - state constraints are considered. The minimum time problem is replaced by an equivalent one with fixed time and the necessary optimality conditions of time-optimal control are obtained by using the generalized Dubovitskii-Milyutin Theorem (see [1]).
Abstract: In this paper, the minimum time problem for differential systems of parabolic type with distributed control and control - state constraints are considered. The minimum time problem is replaced by an equivalent one with fixed time and the necessary optimality conditions of time-optimal control are obtained by using the generalized Dubovitskii-Milyut...
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On the Hausdorff Distance Between the Heaviside Function and Some Transmuted Activation Functions
Nikolay Kyurkchiev,
Anton Iliev
Issue:
Volume 1, Issue 1, October 2016
Pages:
8-12
Received:
18 August 2016
Accepted:
12 October 2016
Published:
14 October 2016
DOI:
10.11648/j.mma.20160101.12
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Abstract: In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.
Abstract: In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in th...
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Analysis of a Generalized Formulation of MHD Isothermal Flow over Exponentially Stretching Sheet Under Variable Magnetic Effect
Bahaa Saleh,
Yousef Abdel-Rahim
Issue:
Volume 1, Issue 1, October 2016
Pages:
13-19
Received:
3 September 2016
Accepted:
8 October 2016
Published:
17 October 2016
DOI:
10.11648/j.mma.20160101.13
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Abstract: The paper has presented and discussed a single generalized algebraic formulation for magneto-hydrodynamic (MHD) flow over an isothermal exponentially stretching sheet under an exponential magnetic field over a range of a magnetic parameter (M), 0≤M≤1.0 and has analyzed relative weights of different terms in the governing equation. Solution methodology is based on minimization of the residual of the governing equation and results are in perfect agreement with other previously published works. Wall shear stress has been formulated as single algebraic equation of M. Inside flow region, shear stress is maximum at the wall and suffers an exponential decrease in vicinity of sheet at similarity variable (η), η≤4.0, where 1st and 3rd terms in the governing equation are the most dominant terms. Within the vicinity of the sheet, the velocity has suffered an exponential decrease that became steeper with the increase of M, signifying a retardation effect of the magnetic field. Beyond η=4.0 the flow region is almost stagnant. The analysis shows that high nonlinearity of the governing equation has led to an oscillatory nature especially in the vicinity of the sheet, which becomes more damped at higher values of M. In the range, 0≤η≤0.25, the 2nd nonlinear term in the equation can be neglected, while in the range, 0.25≤η≤0.75, the 4th term can be neglected. In the range, 0.75≤η≤1.0 both the 3rd and 4th terms of the equation can be neglected. Although neglecting any term of the governing equation will be at the sacrifice of the accuracy of the solution, yet the 2nd term, which is nonlinear, can be totally deleted from the equation at a sacrifice of about 10% of the accuracy of the solution.
Abstract: The paper has presented and discussed a single generalized algebraic formulation for magneto-hydrodynamic (MHD) flow over an isothermal exponentially stretching sheet under an exponential magnetic field over a range of a magnetic parameter (M), 0≤M≤1.0 and has analyzed relative weights of different terms in the governing equation. Solution me...
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An Improved Model for Predicting Fluid Temperature in Deep Wells
Issue:
Volume 1, Issue 1, October 2016
Pages:
20-25
Received:
17 July 2016
Accepted:
14 October 2016
Published:
21 October 2016
DOI:
10.11648/j.mma.20160101.14
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Abstract: The objective of this study was to develop an improved method to predict fluid temperature profiles in high-temperature wells for designing production string in deep-water development. The method was developed on the basis of heat transfer involves heat convection and conduction inside the production string and in the annular space. The governing equations were solved using the method of characteristics, resulting in two simple closed-form equations. The method was coded in a spreadsheet for easy applications. Data from three wells were employed to check the accuracy of the new method. Comparisons of results from Hasan's method, Gilbertson et al.'s method, and the new method with temperature data measured in two gas-lift wells show that the new method best predicts well temperatures in trend. A comparison of results given by Mao's method and the new method with temperatures observed in a deep-water gas well testing indicates that the new method better predicts well temperatures with errors less than 4%. This work provides petroleum engineers a simple and accurate method for predicting temperature profiles in oil and gas production operations, especially deep-water operations. It eliminates the need for sophisticated analytical and numerical models in fluid temperature analysis.
Abstract: The objective of this study was to develop an improved method to predict fluid temperature profiles in high-temperature wells for designing production string in deep-water development. The method was developed on the basis of heat transfer involves heat convection and conduction inside the production string and in the annular space. The governing e...
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