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Irrational Outputs from Rational Inputs in Theta-3 Functions Using Dirichlet’s Theorem
Theta Functions are not an easy subject of mathematics because new researches about this wide topic are still being published regularly. The findings about Theta Functions lead directly to many applications in different fields of applied mathematics and help also to develop old interesting mathematical ...
A new Approach to Hyper Dual Split Quaternions with Different Polar Representation
Hamilton first introduced quaternions in 1843 as a way to represent rotations in three dimensional space, and since then, they have become the important tool in many fields. One advantage of quaternions over other methods of representing rotations is their ability to avoid the problem of gimbal lock, ...
Solving first-order systems of linear hyperbolic partial differential equations using fast Fourier transform
In this paper, we address the exact solution of the general first-order systems of linear hyperbolic partial differential equations using the Fourier transformation technique. This transformation converts the system from the physical domain into a system of first-order ordinary differential equations ...
A mathematical letter about a condition that makes a Diophantine equation have no natural numbers as a solution
In this short mathematical letter, we introduce an interesting result about the powers of a general form of Diophantine equations. This work gives a condition that makes this Diophantine equation have no possible natural numbers as a solution or have specific prime numbers as a solution. The ...