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[4] viXra:2501.0085 [pdf] submitted on 2025-01-13 21:45:46
Authors: Ahcene Ait Saadi
Comments: 17 Pages.
In this paper, I introduce a new concept (new Frame), which allows me to have functions that have another definition. That is to say, in this frame: a function is an application that associates with each element of the starting set E, zero or several images of the arrival set F.I study in this frame, the derivability of functions, therefore the equation of a tangent to a curve. The integral calculation, I leave it to the young checkers who, surely, will develop this new and original mathematical tool, this in the interest of science and knowledge.
Category: Algebra
[3] viXra:2501.0023 [pdf] submitted on 2025-01-06 20:58:45
Authors: Ahcene Ait Saadi
Comments: 15 Pages.
This paper introduces a new concept concerning periodic functions. These functions entitled: pseudo- trigonometric functions, allow us to draw curves and periodic straight line segments.I defined the functions : pseudo-sine denoted( spx) and pseudo-cosine denoted (cpx), as well as their reciprocal functions. I defined the hyperbolic pseudo-sine and hyperbolic pseudo-cosine functions. This new mathematical tool allows me to calculate differential equations and integrals of a new kind.
Category: Algebra
[2] viXra:2501.0020 [pdf] submitted on 2025-01-05 22:20:18
Authors: Muhammad Talha
Comments: 11 Pages.
This paper presents a comprehensive derivation of a calculatorfriendly expression for computing the power of one complex number raised to another, specifically z1 = a + bi raised to z2 = c + di. By leveraging the fundamental properties and formulae intrinsic to complex numbers, we develop an explicit, practical method that can be implemented on modern scientific and graphical calculators, such as the Casio FX-991ES or newer models. The derivation emphasizes the mathematical rigor required to handle the inherent complexities of exponentiation in the complex plane, while also providing a user-friendly format that simplifies direct calculation. This work not only bridgesthe gap between theoretical mathematics and practical computation but also offers a valuable tool for students, educators, and professionals who frequently engage in complex number arithmetic. With this approach, the need for advanced computational tools like Mapleor Mathematica for complex exponentiation is significantly reduced. The derived formula is capable of calculating complex exponents withprecision up to six decimal places, closely matching the accuracy of these sophisticated tools. Thus, it enhances the efficiency of problemsolving in various mathematical and engineering applications.
Category: Algebra
[1] viXra:2501.0019 [pdf] submitted on 2025-01-05 05:19:40
Authors: Anatolii V. Tushev
Comments: 11 Pages.
The paper is a survey where we discuss various methods for obtaining results oninduced modules over group rings of soluble groups of finite rank. These methodsallow us to obtain results on the structure of solvable groups admitting primitiveand semiprimitive faithful irreducible representations. In particular, it allows usto study the structure of irreducible representations of some classes of nilpotentgroups.
Category: Algebra
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