Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization
Abdelilah Kamal H. Sedeeg,
Shawgy H. Abd Alla
Issue:
Volume 5, Issue 3, June 2017
Pages:
57-67
Received:
13 October 2016
Accepted:
8 November 2016
Published:
12 June 2017
Abstract: The Fractional Poincare’ inequalities in Rn are endowed with a fairly general sequence measure. We show a control of L2 norm by a non–Local quantity. The assumption on the sequence measure is that it satisfies the classical Poincare’ inequality, with general results. We also verify quantity of the tightness at infinity provided by the control on the fractional derivative in terms of a sequence of a weight growing at infinity. The illustration goes to the generator of the Ornstein-Uhlenbeck semi group and some estimates of its powers.
Abstract: The Fractional Poincare’ inequalities in Rn are endowed with a fairly general sequence measure. We show a control of L2 norm by a non–Local quantity. The assumption on the sequence measure is that it satisfies the classical Poincare’ inequality, with general results. We also verify quantity of the tightness at infinity provided by the control on th...
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The Impact of Infective Immigrants on the Spread of Dog Rabies
Aberu Mengistu Tulu,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 3, June 2017
Pages:
68-77
Received:
11 April 2017
Accepted:
2 May 2017
Published:
23 June 2017
Abstract: In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using ode 45 of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text.
Abstract: In this paper, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Di...
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The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid
Binyam Zigta,
Purnachandra Rao Koya
Issue:
Volume 5, Issue 3, June 2017
Pages:
78-90
Received:
14 April 2017
Accepted:
27 April 2017
Published:
23 June 2017
Abstract: In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.
Abstract: In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving...
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Population Harvesting on both Prey and Predator
Aynalem Berhanie Emru,
Purnachandra Rao Koya,
Mohammed Yiha Dawed
Issue:
Volume 5, Issue 3, June 2017
Pages:
91-98
Received:
29 April 2017
Accepted:
8 May 2017
Published:
29 June 2017
Abstract: In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.
Abstract: In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: a...
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