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Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block
Md. Raihanul Haque,
Md. Abdul Alim,
Md. Mahmud Alam,
Md. Shahidul Alam
Issue:
Volume 5, Issue 6, December 2019
Pages:
74-82
Received:
14 October 2019
Accepted:
9 November 2019
Published:
21 November 2019
Abstract: In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.
Abstract: In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along...
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Empirical Analysis of Long-run and Short-run Dynamic Effects of Deposit Rate, Inflation Rate and GDP on Bank Deposit: Vector Error Correction Model Approach
Issue:
Volume 5, Issue 6, December 2019
Pages:
83-93
Received:
19 August 2019
Accepted:
26 September 2019
Published:
27 November 2019
Abstract: This paper empirically examines the long-run and short run dynamic effects of deposit rate (r), inflation rate (π) and GDP on bank deposit. The study targeted commercial bank of Ethiopia (CBE) because it has been taking a lion’s share in terms of deposit amount which in turn plays a vital role in deposit refunding for investors. To show the long-run and short run dynamic effects of r, π and GDP on the deposit amount of CBE we took 30 years data from the year 1988 to 2017 from MOFED, CSA, National bank of Ethiopia and CBE data sets. To achieve the objectives vector error correction model (VECM) was used after checking the possible assumptions of our economic series. The results of ADF test statistics confirms our economic series are stationary at their first difference. This indicates that the variables are integrated of order one, I (1). Johansen’s co-integration test suggests one co-integrating relationship between the variables. According to our findings, the coefficient of the error correction term for CBE deposit is statistically significant, and the speed of convergence to equilibrium of approximately 16 percent. Hence, in the short run, deposits are adjusted by 16 percent of the past year’s deviation from equilibrium. The joint effect result indicates that except deposit rate all included variables have no significant short-run effect on deposit amount. More specifically, the result of Johansen normalization restriction shows in the long-run on average inflation rate and GDP have a negative effect on deposit, while deposit rate has a positive effect on the total amount of deposit held by CBE, among other findings. Finally, the government and other concerned bodies should take necessary steps to mobilize deposit in CBE.
Abstract: This paper empirically examines the long-run and short run dynamic effects of deposit rate (r), inflation rate (π) and GDP on bank deposit. The study targeted commercial bank of Ethiopia (CBE) because it has been taking a lion’s share in terms of deposit amount which in turn plays a vital role in deposit refunding for investors. To show the long-ru...
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Global Stability of Critical Points for Type SIS Epidemiological Model
Edgar Ali Medina,
Manuel Vicente Centeno-Romero,
Fernando José Marval López
Issue:
Volume 5, Issue 6, December 2019
Pages:
94-99
Received:
20 July 2019
Accepted:
19 August 2019
Published:
2 December 2019
Abstract: The construction of mathematical models is one of the tools used today for the study of problems in Medicine, Biology, Physiology, Biochemistry, Epidemiology, and Pharmacokinetics, among other areas of knowledge; its primary objectives are to describe, explain and predict phenomena and processes in these areas. The simulation, through mathematical models, allows exploring the impact of the application of one or several control measures on the dynamics of the transmission of infectious diseases, providing valuable information for decision-making with the objective of controlling or eradicating them. The mathematical models in Epidemiology are not only descriptive but also predictive, helping to prevent pandemics (epidemics that spread through large areas and populations) or by intervening in vaccination and drug acquisition policies. In this article we study the existence of periodic orbits and the general stability of the equilibrium points for a susceptible-infected-susceptible model (SIS), with a non-linear incidence rate. This type of model has been studied in many articles with a very particular incidence rate, here the novelty of the problem is that the aforementioned incidence rate is very general, in this sense this research provides a solution to an open problem. The methodology used is the Dulac technique, proceeding by reduction to the absurdity of the statement to the main test. It shows that the only point of equilibrium is asymptotically stable global. It can be noted that this problem may be subject to discretion or for equations in timescales. This can generate other research.
Abstract: The construction of mathematical models is one of the tools used today for the study of problems in Medicine, Biology, Physiology, Biochemistry, Epidemiology, and Pharmacokinetics, among other areas of knowledge; its primary objectives are to describe, explain and predict phenomena and processes in these areas. The simulation, through mathematical ...
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Optimum Solutions of Fredholm and Volterra Integro-differential Equations
Muhammad Akbar,
Rashid Nawaz,
Sumbal Ahsan
Issue:
Volume 5, Issue 6, December 2019
Pages:
100-112
Received:
5 April 2019
Accepted:
29 November 2019
Published:
6 December 2019
Abstract: Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed for solving integro-differential equations. In this paper, a powerful semi analytical technique known as Optimal Homotopy Asymptotic Method (OHAM) has been used for finding the approximate solutions of Fredholm type integro-differential equations and Volterra type integro-differential equations. The proposed method does not required discretization like other numerical and approximate method, and it is also free from any small/large parameters. The presented technique provides better accuracy at lower order of approximation, the accuracy of the method can further be increases with higher order of approximation. Moreover, we can easily adjust and control the convergence region. The ability of the method is checked with different problems in literature. The results obtained through OHAM are compared with solutions of Adomian Decomposition Method. It is observed that solutions obtained through the proposed method is more accurate than existing techniques, which proves the validity and stability of the proposed method for solving integro-differential equations. The presented technique is more consistent, effective, suitable and rapidly convergent. The use of Optimal Homotopy Asymptotic Method is simple and straight forward. For the computation of problems, we have used Mathematica 9.0.
Abstract: Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed for solving integro-differential equations. In this paper, a powerful semi analytical technique known as Optimal Homotopy Asymptotic Method (OHAM) has been used for finding the approximate solution...
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Simple and Effective Theory of Movement Steadiness
Smol’yakov Eduard Rimovich
Issue:
Volume 5, Issue 6, December 2019
Pages:
113-117
Received:
10 November 2019
Accepted:
2 December 2019
Published:
11 December 2019
Abstract: It is proposed the very simple and quick method for estimation of the asymptotic stability of any nonlinear dynamic systems, in particular, of the high-dimensional systems for which Tailor series of the right-hand sides of the differential equations converge very slowly. In such problems, the sum of terms of the order of smallness higher than two can substantially exceed the value of any term of second order. In this case, Lyapunov’s methods cannot guarantee correct stability estimate at all. The new method does not use the notion of Liapunov function and, therefore, one has no numerous shortcomings of all Liapunov methods. In this paper, it is proposed to replace the very complex problem of the searching for Liapunov function with a very simple problem of the searching maximum of the function of n coordinates (that is of the velocity of variation in metrics of the perturbed state space). However, one is not intended for the linear systems.
Abstract: It is proposed the very simple and quick method for estimation of the asymptotic stability of any nonlinear dynamic systems, in particular, of the high-dimensional systems for which Tailor series of the right-hand sides of the differential equations converge very slowly. In such problems, the sum of terms of the order of smallness higher than two c...
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Strongly Ƥ-projective Modules and Ƥ-projective Complexes
Issue:
Volume 5, Issue 6, December 2019
Pages:
118-124
Received:
30 October 2019
Accepted:
26 November 2019
Published:
19 December 2019
Abstract: In this paper we first study the properties of Strongly Ƥ-projective modules, and obtain some equivalent conclusions about Strongly Ƥ-projective modules, it is proved that a finitely generated right R-module N is strongly Ƥ-projective if and only if Exti (N, R) = 0 for all i ≥ 1 over left noetherian and right perfect ring, a Ƥ-projective right R-module N is strongly Ƥ-projective if and only if the first syzygy of N is strongly Ƥ-projective. Then we extend the notion of Ƥ-projective modules to that of Ƥ-projective complexes. We study the relationships between Ƥ-projective complexes and Ƥ-projective modules, it is proved that a complex C is Ƥ-projective if and only if every Ci is Ƥ-projective for every integer i if and only if Ext1 (C, P) = 0 for every projective complex Ƥ if and only if for every exact sequence 0→A→Ƥ→C→0 with Ƥ projective, A→Ƥ is a projective preenvelope of A. Some characterizations of Ƥ-projective complexes also obtained.
Abstract: In this paper we first study the properties of Strongly Ƥ-projective modules, and obtain some equivalent conclusions about Strongly Ƥ-projective modules, it is proved that a finitely generated right R-module N is strongly Ƥ-projective if and only if Exti (N, R) = 0 for all i ≥ 1 over left noetherian and right perfect ring, a Ƥ-projective right R-mo...
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