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Elementary Algebra for Origami: The Trisection Problem Revisited
Issue:
Volume 1, Issue 4, October 2013
Pages:
39-43
Received:
8 September 2013
Published:
20 October 2013
Abstract: This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving the trisection problem, one of the three famous problems of ancient Greek mathematics. Emphasis in this article is put on the way how the origami-based construction of the trisection corresponds to obtaining a solution for a cubic equation.
Abstract: This article presents an algebraic background in solving the angle trisection problem using origami-folding. Origami has been originally the art of paper folding, and recently aroused strong interest in a wide discipline of science and technology owing to its deep mathematical implication. Origami is also known to be an efficient tool for solving t...
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Fixed Point Theorem in 2 – Metric Spaces of Implicit Relations
Rajesh Shrivastava,
Neha Jain,
K. Qureshi
Issue:
Volume 1, Issue 4, October 2013
Pages:
44-48
Received:
4 September 2013
Published:
30 October 2013
Abstract: In this paper present on Fixed point Theorem in 2-metric spaces .A concept which has been in focus recent times. The result is supported with an example.
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Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties
Sashka Petkova,
Andrey Antonov,
Rumyana Chukleva
Issue:
Volume 1, Issue 4, October 2013
Pages:
49-54
Received:
9 September 2013
Published:
30 October 2013
Abstract: The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.
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Determination of One Dimensional Temperature Distribution in Metallic Bar Using Green’S Function Method
Virginia Mwelu Kitetu,
Thomas Onyango,
Jackson Kioko Kwanza,
Nicholas Muthama Mutua
Issue:
Volume 1, Issue 4, October 2013
Pages:
55-70
Received:
7 September 2013
Published:
30 October 2013
Abstract: The present study focuses on determination of temperature distribution in one dimensional bar using Green’s function method. The Green’s Function is obtained using separation of variables, variation formulation principles and Heaviside functions. The Boundary Integral Equation is obtained using the fundamental solution, Divergence theorem, Green Identities, Dirac delta properties and integration by parts. The solution of heat equation given by the Green’s Function and the boundary integral equation has satisfied the uniqueness, regularity and stability of heat equation. The uniqueness, regularity and stability have been proved using smooth properties of class k function, Lyapunov function and Norm. The BEM implementation is performed using FORTRAN 95 software. Solutions to the test problems are presented and time dependence results are in agreement with computed analytical solutions.
Abstract: The present study focuses on determination of temperature distribution in one dimensional bar using Green’s function method. The Green’s Function is obtained using separation of variables, variation formulation principles and Heaviside functions. The Boundary Integral Equation is obtained using the fundamental solution, Divergence theorem, Green Id...
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Derivation of Turbulent Energy in Presence of Dust Particles
Issue:
Volume 1, Issue 4, October 2013
Pages:
71-77
Received:
14 October 2013
Published:
10 November 2013
Abstract: Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.
Abstract: Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order. In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors ar...
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Effect of an Adiabatic Fin on Natural Convection Heat Transfer in a Triangular Enclosure
Sreebash C Paul,
Suvash C. Saha,
Y. T. Gu
Issue:
Volume 1, Issue 4, October 2013
Pages:
78-83
Received:
20 October 2013
Published:
10 November 2013
Abstract: Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.
Abstract: Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the bound...
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Mathematical Model for Determining the Effect of Government Policies on Nigerians’ Standard of Living and the Achievement of Economic Comfort in Nigeria
Ogwumu,
David. O,
James Friday. E
Issue:
Volume 1, Issue 4, October 2013
Pages:
84-91
Received:
4 October 2013
Published:
20 November 2013
Abstract: The research is concerned with the development of a mathematical model for determining the Effect of Government Policies on Nigerians’ Standard of Living which when not properly handled in turn could hamper the economic comfort of the country at large. The model was validated and observations about the model’s results and the questionnaire data (before and after the introduction of government financial policies, gp) were compared. Thereafter, the results of the comparison were analyzed using suitable statistical tools. The findings from the comparisons showed that government sudden financial policies take/reduce up to approximately 10% of the citizen’s standard of living and income. Likewise, the results from our model and the questionnaire data have a higher degree of correlation which thus recommending the model as a standard measure for estimating the effect of Government Financial Policies on Nigerians’ Standard of Living.
Abstract: The research is concerned with the development of a mathematical model for determining the Effect of Government Policies on Nigerians’ Standard of Living which when not properly handled in turn could hamper the economic comfort of the country at large. The model was validated and observations about the model’s results and the questionnaire data (be...
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