 |
 |
[7] viXra:2412.0153 [pdf] submitted on 2024-12-24 21:04:33
Authors: Miloš Čojanović
Comments: 11 Pages. This work is licensed under a Creative Commons Attribution 4.0 International License.
In this paper, we will prove that with the use of Vieta's formulas, it is possible to apply a unified method in solving equations of the third and fourth degree.
Category: Algebra
[6] viXra:2412.0151 [pdf] submitted on 2024-12-24 01:38:23
Authors: Harry Willow
Comments: 25 Pages. (Note by viXra Admin: Please cite and list scientific references)
There is nothing new about group theory in this paper. It presents group theory problems at undergraduate level and their solutions. In presenting the solutions, we avoid using advanced theorems from group theory but we try to discuss the solutions using elementary facts in group theory.
Category: Algebra
[5] viXra:2412.0127 [pdf] submitted on 2024-12-22 03:18:50
Authors: Joseph Musonda
Comments: 11 Pages. (Note by viXra Admin: Please Do NOT use author's name to name the title, formula, equations etc.)
The purpose of this paper is simply to present to the mathematics community a novel approach of solving systems of linear equations in two and three variables. This method uses products of coefficients with determinants and constants with determinants. The method is derived through the cross multiplication of equations which results in finding the critical values (Dx, Dy and Dz). These critical values are later substituted in any initial given equation for the purpose of finding scale factor K. It is this scale factor that is multiplied with critical values to find real solutions. The analysis of this formula shows that it is certainly accurate for all problems it is invented for. Unlike the Crammer’s rule, substitution method, elimination method that requires three and four determinants to solve a two and three variable problems of linear systems of equations, for this method the two and three variable problems only two and three determinants respectively. In two variables In three variables x= (c1Dx)/M x=(d2Dx)/M y=(c1Dy)/M y=(d2Dy)/M z=(d2Dz)/MCoefficients an,bn,cn and constants is obtained from any of the single equation. The ratio method is formally derived and proven in the methodology section and Denominator (M) =a1Dx+ b1Dy for a two variable equations and M=a1Dx+ b1Dy+ c1Dz for 3 variable equations.Keywords: Linear systems of equations, Ratios, Critical Values, Scale factor K, Crammer’s rule, elimination method, substitution method.
Category: Algebra
[4] viXra:2412.0120 [pdf] submitted on 2024-12-19 03:51:41
Authors: Harry Willow
Comments: 18 Pages.
There is nothing new about group theory in this paper. It presents group theory problems at undergraduate level and their solutions. In presenting the solutions, we avoid using advanced theorems from group theory but we tried to discuss the solutions using elementary facts in group theory.
Category: Algebra
[3] viXra:2412.0072 [pdf] submitted on 2024-12-12 11:12:13
Authors: Tai-Choon Yoon
Comments: 5 Pages.
Int(f(x)^2+g(x)^2)^(1/2)dx and Int((dx/dt)^2+(dy/dt)^2)^(1/2)dt are integral equations that appear in the process of calculating the length of an ellipse. They do not provide an exact solution, and already known solutions are somewhat complicated. The solutions both the two elliptic integral equations above can be obtained by the method of eliminating the square root. The arc length of an ellipse is given by l = aθE(k), and E(k) is expressed as a power series regarding the eccentricity of the ellipse.
Category: Algebra
[2] viXra:2412.0034 [pdf] submitted on 2024-12-06 06:49:22
Authors: Michael Reed
Comments: 4 Pages.
Presents multilinear Lie bracket optimized by Lie bracket recursion formula.
Category: Algebra
[1] viXra:2412.0010 [pdf] submitted on 2024-12-02 21:40:02
Authors: Subrat Verma
Comments: 6 Pages.
These are some notes on category theory that might be useful to a first-year graduate student in mathematics. This is the first of a three-part series including references to literature, on the theme of identity, examples of objects defined using the universal property and a section on monomorphisms and epimorphisms.
Category: Algebra
| Third-Party Links: |
|