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A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values
Khapaeva Tatiana Mikhailovna
Issue:
Volume 3, Issue 4, August 2014
Pages:
117-120
Received:
4 June 2014
Accepted:
4 July 2014
Published:
20 July 2014
Abstract: A variational method for calculation of the eigenfunctions and eigenvalues in the Sturm-Liouville problem with the Neumann boundary values is offered. The method is based on a functional, which is introduced in this work. An appropriate numerical algorithm is developed. Calculations for the three potentials are produced: sin((x-π)2/π), cos(4x) and the high not isosceles triangle. The method is applied to the Sturm-Liouville problem with the Dirichlet boundary values. Some suppositions about the inverse Sturm-Liouville problem are made.
Abstract: A variational method for calculation of the eigenfunctions and eigenvalues in the Sturm-Liouville problem with the Neumann boundary values is offered. The method is based on a functional, which is introduced in this work. An appropriate numerical algorithm is developed. Calculations for the three potentials are produced: sin((x-π)2/π), cos(4x) and ...
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The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems
Aref Shahmansoorian,
Sahar Jamebozorg
Issue:
Volume 3, Issue 4, August 2014
Pages:
121-124
Received:
17 June 2014
Accepted:
8 July 2014
Published:
20 July 2014
Abstract: One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.
Abstract: One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smalle...
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Modelling the Migratory Population Dynamics of the Serengeti Ecosystem
Janeth James Ngana,
Livingstone Serwadda Luboobi,
Dmitry Kuznetsov
Issue:
Volume 3, Issue 4, August 2014
Pages:
125-129
Received:
7 July 2014
Accepted:
15 July 2014
Published:
30 July 2014
Abstract: Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.
Abstract: Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, He...
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Generalized Difference Formula for a Nonlinear Equation
Issue:
Volume 3, Issue 4, August 2014
Pages:
130-136
Received:
12 July 2014
Accepted:
22 July 2014
Published:
30 July 2014
Abstract: In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas.
Abstract: In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied deriva...
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Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem
Issue:
Volume 3, Issue 4, August 2014
Pages:
137-149
Received:
9 July 2014
Accepted:
29 July 2014
Published:
10 August 2014
Abstract: The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory.
Abstract: The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the presen...
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Modeling and Stability Analysis for a Varicella Zoster Virus Model with Vaccination
Stephen Edward,
Dmitry Kuznetsov,
Silas Mirau
Issue:
Volume 3, Issue 4, August 2014
Pages:
150-162
Received:
30 July 2014
Accepted:
8 August 2014
Published:
20 August 2014
Abstract: In this paper, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. The effective reproductive number, R_e is defined as the number of secondary cases that one infected individual will cause through the duration of the infectious period. The disease-free equilibrium is computed and proved to be locally asymptotically stable when R_e<1 and unstable when R_e>1 .It is proved that there exists at least one endemic equilibrium point for all R_e>1. In the absence of disease-induced death, it is proved that the transcritical bifurcation at R_0=1 is supercritical (forward). Sensitivity analysis is performed on the basic reproduction number and it is noted that the most sensitive parameters are the probability of transmission of the disease from an infectious individual to a susceptible individual per contact, β, per capita contact rate ,c, per capita birth rate, π and the progression rate from latent to infectious stage, δ. Numerical simulations of the model show that, the combination of vaccination and treatment is the most effective way to combat the epidemiology of VZV in the community.
Abstract: In this paper, a deterministic mathematical model for transmission dynamics of Varicella Zoster Virus (VZV) with vaccination is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. The effective reproductive number, R_e is defined as ...
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Regularized Minimum Length Method in Scattered Data Interpolation
Issue:
Volume 3, Issue 4, August 2014
Pages:
163-170
Received:
3 August 2014
Accepted:
15 August 2014
Published:
20 August 2014
Abstract: In an attempt of accumulating more experiences of interpolating scattered data using the minimum length method, this study chooses new kernel functions from the machine learning technique to implementing this minimum length method. But, consulting with the regularization theory, a regularized minimum length method is created by solving coefficient of it in a penalized least squares approximation problem. The purpose of creating this regularized minimum length method is responding to a pilot observation finding the instability of original minimum length method under dense interpolation points. Testing the regularized minimum length method finds that applying it is time-saving but its performance is comparable to the radial point interpolation with polynomial reproduction. Inverse multiquadric and rational quadric kernel functions are two preferred kernel function to perform the regularized minimum length method. In conclusion, the proposed regularized minimum length method can be a useful scattered data interpolation method.
Abstract: In an attempt of accumulating more experiences of interpolating scattered data using the minimum length method, this study chooses new kernel functions from the machine learning technique to implementing this minimum length method. But, consulting with the regularization theory, a regularized minimum length method is created by solving coefficient ...
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Mathematical Model for the Population Dynamics of the Serengeti Ecosystem
Janeth James Ngana,
Livingstone Serwadda Luboobi,
Dmitry Kuznetsov
Issue:
Volume 3, Issue 4, August 2014
Pages:
171-176
Received:
11 August 2014
Accepted:
23 August 2014
Published:
30 August 2014
Abstract: Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased.
Abstract: Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data did...
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Analysis of the Irrigation Water Price in Rice Production Tanzania
Amos Michael,
Dmitry Kuznetsov,
Silas Mirau
Issue:
Volume 3, Issue 4, August 2014
Pages:
177-185
Received:
12 August 2014
Accepted:
23 August 2014
Published:
30 August 2014
Abstract: Over the past 50 years, cross-sectoral water utilization in Tanzania has grown considerably due to the increase of human populations which increasing food demands and growing of economic activities that require water in production. The agriculture sector is one of the major users of water resource for irrigation activities. The purpose of this paper was to analyse the irrigation water price in rice production in Tanzania. The secondary data were collected from the Ministry of Agriculture, Food Security and Cooperatives in Statistics Unit and zonal irrigation units. Elasticities were estimated using ordinary least squares technique with the help of STATA 11. Factor analysis technique was also applied. The estimated water price coefficient was found to be -0.03 and the average water price was estimated to be 5.50 Tshs/m3. However the water productivity was 0.3kg/m3, whereas the production was estimated to be 2.5ton/ha.
Abstract: Over the past 50 years, cross-sectoral water utilization in Tanzania has grown considerably due to the increase of human populations which increasing food demands and growing of economic activities that require water in production. The agriculture sector is one of the major users of water resource for irrigation activities. The purpose of this pape...
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Construction of Generalized Coordinates’ Basis Functions in Lagrangian Dynamics of Flat Manipulators
Bagautdinov Ildar Nyrgaiazovich,
Pavlov Alexander Ivanovich,
Zhuravlev Evgeny Alekseevich,
Bogdanov Evgeny Nikolaevich
Issue:
Volume 3, Issue 4, August 2014
Pages:
186-190
Received:
13 August 2014
Accepted:
29 August 2014
Published:
20 September 2014
Abstract: Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trigonometric functions of generalized coordinates, i.e. basis functions. A number of these functions are connected to number of links by quadratic dependence. Constant coefficients in expansions in basic functions are determined from linear equation systems, representing kinetic energy of the mechanism in its several nonrecurring configurations with non-zero values for one or two generalized velocities. The resulting system of dynamics differential equations is integrated numerically with Runge-Kutta method in software environment Mathcad. Efficiency of the proposed method of creating and solving dynamic equations is demonstrated by example of numerical solution the direct dynamic problem of three-link mechanism.
Abstract: Second order Lagrange equations are used for describing dynamics of planar mechanism with rotation joints. For calculating kinetic energy of the links local coordinates of velocity vectors are used as well as recursive matrix transformations. Kinetic energy quadratic form coefficients are represented by linear combinations of seven independent trig...
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