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Hydromagnetic Stagnation Point Flow over a Porous Stretching Surface in the Presence of Radiation and Viscous Dissipation
Emmanuel Maurice Arthur,
Ibrahim Yakubu Seini
Issue:
Volume 3, Issue 5, October 2014
Pages:
191-196
Received:
17 August 2014
Accepted:
2 September 2014
Published:
20 September 2014
Abstract: This paper investigates the hydromagnetic stagnation point flow of an incompressible viscous electrically conducting fluid towards a stretching sheet in the presence of radiation and viscous dissipation. The Newton-Raphson shooting method along with the fourth-order Runge-Kutta integration algorithm has been employed to tackle the third order, nonlinear boundary layer problem governing the flow. Numerical results for dimensionless local skin friction coefficient and the local Nusselt numbers are presented in tables while graphical results are presented for velocity and temperature profiles for various values of the controlling parameters. The results show that the heat transfer of a hydromagnetic fluid over a porous stretching surface subject to radiation and viscous dissipation can be controlled and a final product with desired characteristics can be achieved.
Abstract: This paper investigates the hydromagnetic stagnation point flow of an incompressible viscous electrically conducting fluid towards a stretching sheet in the presence of radiation and viscous dissipation. The Newton-Raphson shooting method along with the fourth-order Runge-Kutta integration algorithm has been employed to tackle the third order, nonl...
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Realization of Inhomogeneous Boundary Conditions as Virtual Sources in Parabolic and Hyperbolic Dynamics
Issue:
Volume 3, Issue 5, October 2014
Pages:
197-204
Received:
13 August 2014
Accepted:
11 September 2014
Published:
20 September 2014
Abstract: Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper systematically deals with this situation via the conversion of the boundary inhomogeneity to a virtual source in conjunction with boundary homogeneity. For such a purpose, the 2D transfer-function is developed based on the Laplace-Galerkin integral transform as the main tool of this conversion. A section of numerical visualization is included to explore the topology of the virtual-source solution. Some interesting findings therein will be addressed.
Abstract: Scientists and engineers encounter many kinds of parabolic or hyperbolic distributed dynamics, which are often with inhomogeneous boundary conditions in practice. Boundary inhomogeneity makes the dynamics essentially nonlinear, which prevents the Hilbert space from being applied for modal decomposition and intelligent computation. Thus, this paper ...
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Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio
Phares Kaboneka,
Wilson Mahera Charles,
Silas Mirau
Issue:
Volume 3, Issue 5, October 2014
Pages:
205-216
Received:
19 August 2014
Accepted:
30 August 2014
Published:
20 September 2014
Abstract: Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier. Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.
Abstract: Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision espec...
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Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics
Issue:
Volume 3, Issue 5, October 2014
Pages:
217-224
Received:
20 August 2014
Accepted:
10 September 2014
Published:
20 September 2014
Abstract: This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function and geometrical isomorphism between the space-time domain and the mode-frequency domain are developed, whereof the H∞-norm is extended to be 2D-H∞ norm in mode-frequency domain. On grounds of this small-gain theorem, robust performance of any Sturm-Liouville plant can be formulated as robust stability of a feedback connection, whereupon feedback syntheses can be performed via modal-spectral μ-loopshaping.
Abstract: This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function ...
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Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges
Issue:
Volume 3, Issue 5, October 2014
Pages:
225-230
Received:
10 September 2014
Accepted:
19 September 2014
Published:
30 September 2014
Abstract: An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking.
Abstract: An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are seve...
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A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean
Rini Yanti,
M Imran,
Syamsudhuha
Issue:
Volume 3, Issue 5, October 2014
Pages:
231-234
Received:
11 July 2014
Accepted:
12 September 2014
Published:
30 September 2014
Abstract: We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.
Abstract: We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, g...
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The Time-Dependent Similarity Solutions of Boundary Layer Equations of Power-Law Fluids with Non-Isothermal Surface
Issue:
Volume 3, Issue 5, October 2014
Pages:
235-239
Received:
16 September 2014
Accepted:
23 September 2014
Published:
30 September 2014
Abstract: Unsteady, two dimensional boundary layer flows over a heated surface of power-law fluids are investigated. Surface temperature is assumed to have o power-law variation with the time and the distance. Similarity transformation is applied to the partial differential equation system with three independent variables is reduced into an ordinary differential equations systems. Numerical solutions of non-linear differential equations are found by using a finite difference scheme. Solutions are obtained for boundary layer flow velocity and thermal boundary layer profile. Effects of flow behavior index, Prandtl number, suction-injection parameter and surface temperature exponent with the time and the distance are outlined in the figures.
Abstract: Unsteady, two dimensional boundary layer flows over a heated surface of power-law fluids are investigated. Surface temperature is assumed to have o power-law variation with the time and the distance. Similarity transformation is applied to the partial differential equation system with three independent variables is reduced into an ordinary differen...
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Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
Issue:
Volume 3, Issue 5, October 2014
Pages:
240-246
Received:
14 September 2014
Accepted:
29 September 2014
Published:
10 October 2014
Abstract: An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given.
Abstract: An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation,...
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Transient MHD Boundary-Layer Slip-Flow of Heat and Mass Transfer Over a Stretching Surface Embedded in Porous Medium with Waste Discharge Concentration and Convective Boundary Conditions
Adetunji Adeniyan,
Joshua Aanuoluwapo Adigun
Issue:
Volume 3, Issue 5, October 2014
Pages:
247-255
Received:
11 September 2014
Accepted:
22 September 2014
Published:
20 October 2014
Abstract: The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous incompressible and electrically conducting fluid encompassing a convectively heated stationary permeable sheet is assumed to be described in terms of Darcian law. The nonlinear governing partial differential equations obtained are converted into ordinary differential equations by means of appropriate similarity transformations and consequently solved numerically using the forth order Runge-Kutta method with a shooting technique and depicted graphically for some pertinent values of the physical parameters embedded in the flow model. In addition, the skin-friction coefficient, the heat and pollution mass concentration rates are sorted out in tabular form, analyzed and discussed. We opine that findings of this present study will be found useful for environmental systems in pollution control and ventilation, and serve as complementary reference for researchers.
Abstract: The transient two-dimensional MHD boundary-layer stagnation point flow with heat and mass transfer in a saturated porous medium is presented here by taking into account the transient dispersion of a pollutant spewed by an external source in the presence of a uniform transverse magnetic field and stress (pressure) work. The laminar flow of viscous i...
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Electricity Market and Its Risk Management in Nigeria
Achudume Celestine,
Chukwuma Raphael Nwozo
Issue:
Volume 3, Issue 5, October 2014
Pages:
256-261
Received:
19 September 2014
Accepted:
29 September 2014
Published:
30 October 2014
Abstract: This paper is on the development of adequate mathematical model of electricity price via Fourier series. Fourier series is the representation of a function f(x) as an infinite series in sine and cosine terms. Our choice of Fourier series model for electricity price is as result of its volatility, fluctuation trends of hydro flow and poor market designs and we use actively-traded natural gas to hedge against electricity price in Nigeria. The natural gas prices are volatile but do not have a clear seasonal pattern, thus eliminating natural gas price volatility through hedging substantially reduce the electricity price, this development of logical mathematical frame work in the form of hedging tools assures an investor of his or her safety in the power sector.
Abstract: This paper is on the development of adequate mathematical model of electricity price via Fourier series. Fourier series is the representation of a function f(x) as an infinite series in sine and cosine terms. Our choice of Fourier series model for electricity price is as result of its volatility, fluctuation trends of hydro flow and poor market de...
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Exact, Polynomial, Determination Solution Method of the Subset Sum Problem
Issue:
Volume 3, Issue 5, October 2014
Pages:
262-267
Received:
13 October 2014
Accepted:
28 October 2014
Published:
10 November 2014
Abstract: In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation to the solution on the hyperarches was constructed. Calculation experiments were conducted, and the obtained polynomial algorithm, practically and theoretically solved exactly the (SSP) problem.
Abstract: In this paper we give original geometrical interpretation to the domain of definition of integer and combinatorial problems. The solution of the problems concerning NP class has been carried out on the hyperarches. The existence criterion of the solution on the hyperarches has been defined. The method for establishing the sequence of approximation ...
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The Equivalence of the Maximum Likelihood and a Modified Least Squares for a Case of Generalized Linear Model
Issue:
Volume 3, Issue 5, October 2014
Pages:
268-272
Received:
11 October 2014
Accepted:
3 November 2014
Published:
10 November 2014
Abstract: During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. However, if the data are not Gaussian, this equivalence is no longer valid. Also, if the normal equations are not linear, we make use of iterative methods (Newton-Raphson algorithm, Fisher, etc ...). In this work, we consider a particular case where the data are not normal and solving equations are not linear and that it leads to the equivalence of the maximum likelihood method at least squares but modified. At the end of the work, we concluded by referring to the application of this modified method for solving the equations of Liang and Zeger.
Abstract: During the analysis of statistical data, one of the most important steps is the estimation of the considered parameters model. The most common estimation methods are the maximum likelihood and the least squares. When the data are considered normal, there is equivalence between the two methods, so there is no privilege for one or the other method. H...
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Finite Iterative Algorithm for Solving a Class of Complex Matrix Equation with Two Unknowns of General Form
Mohamed A. Ramadan,
Mokhtar A. Abdel Naby,
Talaat S. El-Danaf,
Ahmed M. E. Bayoumi
Issue:
Volume 3, Issue 5, October 2014
Pages:
273-284
Received:
24 October 2014
Accepted:
6 November 2014
Published:
20 November 2014
Abstract: This paper is concerned with an efficient iterative algorithm to solve general the Sylvester-conjugate matrix equation of the form ∑_(i= 1)^s▒〖A_i V B_i 〗+ ∑_(j=1)^t▒〖C_j W D_j 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C The proposed algorithm is an extension to our proposed general Sylvester-conjugate equation of the form ∑_(i= 1)^s▒〖A_i V 〗+ ∑_(j=1)^t▒〖B_j W 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C When a solution exists for this matrix equation, for any initial matrices, the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.
Abstract: This paper is concerned with an efficient iterative algorithm to solve general the Sylvester-conjugate matrix equation of the form ∑_(i= 1)^s▒〖A_i V B_i 〗+ ∑_(j=1)^t▒〖C_j W D_j 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C The proposed algorithm is an extension to our proposed general Sylvester-conjugate equation of the form ∑_(i= 1)^s▒〖A_i V 〗+ ∑_(j=1)^t▒〖...
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