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Singularity Induced Interior Stokes Flows
N. Akhtar,
G. A. H. Chowdhury
Issue:
Volume 3, Issue 1, February 2017
Pages:
1-10
Received:
18 September 2016
Accepted:
10 November 2016
Published:
9 December 2016
Abstract: Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.
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A Method of the Best Approximation by Fractal Function
Yong-Suk Kang,
Myong-Gil Rim
Issue:
Volume 3, Issue 1, February 2017
Pages:
11-18
Received:
7 September 2016
Accepted:
5 November 2016
Published:
9 December 2016
Abstract: We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.
Abstract: We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an e...
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Analysis on the Properties of a Permutation Group
Xiao-Yan Gu,
Jian-Qiang Sun
Issue:
Volume 3, Issue 1, February 2017
Pages:
19-24
Received:
17 October 2016
Accepted:
21 November 2016
Published:
27 December 2016
Abstract: The structures of the subgroups play an important role in the study of the nature of symmetric groups. We calculate the 11300 subgroups of the permutation group S7 by group-theoretical approach. The analytic expressions for the numbers of subgroups are obtained. The subgroups of the permutation group S7 are all represented in an alternative way for further analysis and applications.
Abstract: The structures of the subgroups play an important role in the study of the nature of symmetric groups. We calculate the 11300 subgroups of the permutation group S7 by group-theoretical approach. The analytic expressions for the numbers of subgroups are obtained. The subgroups of the permutation group S7 are all represented in an alternative way for...
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Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change
Philip Ajibola Bankole,
Adeniyi Adewopo
Issue:
Volume 3, Issue 1, February 2017
Pages:
25-29
Received:
31 October 2016
Accepted:
10 December 2016
Published:
7 January 2017
Abstract: This paper focuses on Numéraire change technique for pricing financial assets with stochastic interest rate. It makes sense to introduce the notion of stochastic interest rate when dealing with long term option pricing problems rather than constant interest rate addressed in the past by most papers. We consider the application of Numéraire Change technique to pricing of Investor’s Savings Plan (ISP) with swaption between two interest rates, inflation and exchange rates of two different countries. The result shows that it is better to incorporate stochastic interest rate into long term option pricing problems and Numéraire technique is better applied if faced with several risks factors.
Abstract: This paper focuses on Numéraire change technique for pricing financial assets with stochastic interest rate. It makes sense to introduce the notion of stochastic interest rate when dealing with long term option pricing problems rather than constant interest rate addressed in the past by most papers. We consider the application of Numéraire Change t...
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Application of a Two-Step Third-Derivative Block Method for Starting Numerov Method
Oluwaseun Adeyeye,
Zurni Omar
Issue:
Volume 3, Issue 1, February 2017
Pages:
30-35
Received:
26 September 2016
Accepted:
10 December 2016
Published:
12 January 2017
Abstract: Numerov method is one of the most widely used algorithms in physics and engineering for solving second order ordinary differential equations. The numerical solution of this method has been improved by different authors by using different starting formulas but in recent years, there has been a dearth in that trend which informed the introduction of a two-step third-derivative block method in this paper to start Numerov method with the aim of getting better results than previous approaches. The selection of the steplength as two is to have a uniform basis for comparison with other existing two-step starting formula in literature. Although, the accuracy of the two-step method adopted in this article was enhanced by the introduction of higher derivative. Hence, this paper presents a two-step third-derivative block method which displayed better accuracy when adopted for starting Numerov method as shown in the numerical results. Thus, the third-derivative block method, as a starting formula, is seen to be quite suitable for starting Numerov method when applied to physical models.
Abstract: Numerov method is one of the most widely used algorithms in physics and engineering for solving second order ordinary differential equations. The numerical solution of this method has been improved by different authors by using different starting formulas but in recent years, there has been a dearth in that trend which informed the introduction of ...
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Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method
Maysoon M. Aziz,
Saad Fawzi Al-Azzawi
Issue:
Volume 3, Issue 1, February 2017
Pages:
36-42
Received:
13 October 2016
Accepted:
3 November 2016
Published:
12 January 2017
Abstract: This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti- synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.
Abstract: This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti- synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu ...
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A Limiting Transition in a Singularly Perturbed Equation with the Loss of Stability
Dilmurat Abdillajanovich Tursunov
Issue:
Volume 3, Issue 1, February 2017
Pages:
43-48
Received:
24 November 2016
Accepted:
3 January 2017
Published:
16 January 2017
Abstract: A limiting transition is performed in some systems of singularly perturbed differential equations in the case of change of stability. This phenomenon is found in laser physics, chemical kinetics, plastic deformation, biophysics, in the modified Zieglers system, and in the simulation of upland forest fires, safe combustion with maximum temperature, etc. Cases when such equations have explicit solutions are extremely rare. For sufficiently small values of the parameter to determine the behavior of the solution a daunting task even for super computers, but it is possible with the asymptotic series. Therefore, studies of singularly perturbed problems when the condition of asymptotic stability is relevant.
Abstract: A limiting transition is performed in some systems of singularly perturbed differential equations in the case of change of stability. This phenomenon is found in laser physics, chemical kinetics, plastic deformation, biophysics, in the modified Zieglers system, and in the simulation of upland forest fires, safe combustion with maximum temperature, ...
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Eigenvalue Intervals for Fractional Boundary Value Problems with Nonlinear Boundary Conditions
Issue:
Volume 3, Issue 1, February 2017
Pages:
49-53
Received:
29 October 2016
Accepted:
6 January 2017
Published:
18 January 2017
Abstract: In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion obtained results with others.
Abstract: In presented paper, we study eigenvalue intervals for fractional boundary value problems with nonlinear boundary conditions. In this case, for the existence of at least one positive solution of the boundary value problem the new sufficient conditions are established. By means of example, the main results is illustrated. Finally, given comparsion ob...
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