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A Classic New Method to Solve Quartic Equations
Amir Fathi,
Nastaran Sharifan
Issue:
Volume 2, Issue 2, April 2013
Pages:
24-27
Abstract: Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.
Abstract: Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the pre...
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Using Maple to Study the Double Integral Problems
Issue:
Volume 2, Issue 2, April 2013
Pages:
28-31
Abstract: This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.
Abstract: This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adop...
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Solving Boussinesq Equation by Bilinear Bӓcklund Transformation
Issue:
Volume 2, Issue 2, April 2013
Pages:
32-35
Abstract: In this paper Hirota bilinear method is applied to constructing Backlund transformation of the Boussinesq equation. The bilimear Backlund form are used to obtain the soliton solution of the Boussinesq equation. Also as an application for the bilinear Bӓcklund transformation, new classes of wave solutions to the Boussinesq Equation are computed.
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Theorem on a Matrix of Right-Angled Triangles
Issue:
Volume 2, Issue 2, April 2013
Pages:
36-41
Abstract: The following theorem is proved: All primitive right-angled triangles (primitive Pythagorean triples) may be defined by a pair of positive integer indices (i,j), where i is an uneven number and j is an even number and have no com-mon factor. The sides of every positive integer right angled triangle are then defined by the indices as follows: For hy-potenuse h, uneven leg u and even leg e, h = i2 + ij + j2/2, e = ij + j2/2, u = i2 + ij. This defines an infinite by infinite matrix of right angled triangles with positive integer sides.
Abstract: The following theorem is proved: All primitive right-angled triangles (primitive Pythagorean triples) may be defined by a pair of positive integer indices (i,j), where i is an uneven number and j is an even number and have no com-mon factor. The sides of every positive integer right angled triangle are then defined by the indices as follows: For...
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Series of Primitive Right-Angled Triangles
Issue:
Volume 2, Issue 2, April 2013
Pages:
42-53
Abstract: From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle. This allows for the creation of a series of fractions that have as their limit an irrational number. Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed. Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.
Abstract: From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle. This allows for the creation of a series of fractions that have as their limit an irrational number. Formulae for finding the next triangle in the triangle series, and thus ...
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The Effect of Radiation on Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate in Presence of Heat Generation
Amena Ferdousi,
M. Mostafizur Rahman,
Mohammad Salek Parvez,
M. A. Alim
Issue:
Volume 2, Issue 2, April 2013
Pages:
54-63
Received:
16 May 2013
Published:
30 May 2013
Abstract: This paper presents a new extension for the effect of radiation on natural convection flow with variable viscosity from a porous vertical plate in presence of heat generation. The governing boundary layer equations are first transformed into a non dimensional form and the resulting non linear system of partial differential equations are then solved numerically using finite difference method together with Keller-Box scheme. The numerical results show that the variable viscosity affects the surface shear stress and the rate of heat transfer, which are here in terms of skin friction coefficient and local Nusselt number. It affects velocity as well as temperature profiles also. These are shown graphically and tabular form for a selection of parameters set of consisting of viscosity variation parameter, heat generation parameter Q, radiation effect Rd , Prandtl number Pr
Abstract: This paper presents a new extension for the effect of radiation on natural convection flow with variable viscosity from a porous vertical plate in presence of heat generation. The governing boundary layer equations are first transformed into a non dimensional form and the resulting non linear system of partial differential equations are then solved...
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