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Application of Partial Differential Equations to Drum Head Vibration, Signal Transmission and Chemical Communication in Insects
Issue:
Volume 4, Issue 4, August 2016
Pages:
169-174
Received:
10 May 2016
Accepted:
28 May 2016
Published:
17 June 2016
Abstract: The application of partial differential equations to drumhead vibration, signal transmission and chemical communication in insects has been investigated. This study looked at three cases in communication namely: a single drumbeat on an idealized circular drumhead being struck at the centre of the circular membrane; signal transmission in a Coaxial cable and finally concentration of pheromone in still air within a tunnel. The governing equation of Case I was solved using separation of variables method whereas Laplace transform was used to solve Cases II and III. MATLAB software was then used to obtain simulations on the solutions obtained from the three cases. It was concluded that vibrations of a circular drumhead as a result of a single drumbeat mainly concentrates around the centre of the membrane and tends to flatten out further away from the centre. Signal propagation decreases with increasing distance and so the shorter the cable the less signal strength is lost. Finally, concentration of pheromone can only last for a given time and distance.
Abstract: The application of partial differential equations to drumhead vibration, signal transmission and chemical communication in insects has been investigated. This study looked at three cases in communication namely: a single drumbeat on an idealized circular drumhead being struck at the centre of the circular membrane; signal transmission in a Coaxial ...
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New Predictor-Corrector Iterative Methods with Twelfth-Order Convergence for Solving Nonlinear Equations
Issue:
Volume 4, Issue 4, August 2016
Pages:
175-180
Received:
16 May 2016
Accepted:
31 May 2016
Published:
17 June 2016
Abstract: In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-order convergence. Several numerical examples are given to illustrate the efficiency and robustness of the proposed methods. Comparison with other well-known iterative methods is made.
Abstract: In this paper, we propose and analyze new two efficient iterative methods for finding the simple roots of nonlinear equations. These methods based on a Jarratt's method, Householder's method and Chun&Kim's method by using a predictor-corrector technique. The error equations are given theoretically to show that the proposed methods have twelfth-orde...
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Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method
Michael Chimezie Anyanwu,
Roseline Ngozi Okereke
Issue:
Volume 4, Issue 4, August 2016
Pages:
181-185
Received:
6 May 2016
Accepted:
20 May 2016
Published:
13 July 2016
Abstract: The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price and the stochastic interest rate, we obtain a pricing of pure discount bond available in the market. Our method of valuation is to apply eigenfunction expansion to the variable that describes the evolution of the interest rate, and Fourier transform to the variable that describes the log asset price.
Abstract: The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price...
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Solutions of Ordinary Differential System by Using Symmetry Group
Sameer Qasim Hasan,
Wissam Salman Abd
Issue:
Volume 4, Issue 4, August 2016
Pages:
186-191
Received:
19 June 2016
Accepted:
28 June 2016
Published:
28 July 2016
Abstract: In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these transformations are interest in lie groups theory.
Abstract: In this paper the idea is to use a coordinate transformation that takes a system of ordinary differential equations with no obvious solution to system of integrables. The techniques that which introduced presented the cases of symmetry transformations also the particular case that involving an integrating factory homogeneous coordinates all these t...
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The Time Window Model and Shortest Path Model Design for Travel All 5A Scenic Spot in China
Yawei Li,
Yandong Li,
Xiaorong Li
Issue:
Volume 4, Issue 4, August 2016
Pages:
192-196
Received:
28 June 2016
Accepted:
8 July 2016
Published:
2 August 2016
Abstract: Travel has became one of the most popular ways of modern lifestyle. This paper mainly discusses the route planning of travel all 5A scenic spots in the China. Firstly, We establish a mathematical model and transform the limited conditions include the scenic tour time, driving time, accommodation and other aspects to the mathematical formulas. Then, we introduce the relevant variables from the basic formula and draw the flow chart of the algorithm. In some places that densely-scenic spot, we use the "postman problem" to give the solution and specific analysis some places according to the specific conditions. Specifically, according to the seven regions of the country, we find the best path. In the same area, according to the specific circumstances such as the time and route of the integration, while considering the requirements of the subject like visit time and proportion of driving time, we plan to visit scenic spots one provine by province In order to improve the utilization rate of the time, we arrange the tour attractions in different regions in one year, let the vistor feel the difference between different areas of the landscape, fully enjoy the great rivers and mountains of the motherland, enhance the overall quality of tour.
Abstract: Travel has became one of the most popular ways of modern lifestyle. This paper mainly discusses the route planning of travel all 5A scenic spots in the China. Firstly, We establish a mathematical model and transform the limited conditions include the scenic tour time, driving time, accommodation and other aspects to the mathematical formulas. Then,...
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