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| viXra.org > Functions and Analysis > 2102 |
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[5] viXra:2102.0153 [pdf] submitted on 2021-02-24 18:08:33
Authors: Bertrand Wong
Comments: 4 Pages.
The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. Although they are relatively simple-looking, the three-dimensional Navier-Stokes equations misbehave very badly. Even with nice, smooth, reasonably harmless initial conditions, the solutions could wind up being extremely unstable. The field of fluid mechanics would be dramatically altered through a mathematical understanding of the outrageous behaviour of these equations. An explanation why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence or chaos (which is a three-dimensional phenomenon), would be provided. [Published in an international journal.]
Category: Functions and Analysis
[4] viXra:2102.0136 [pdf] submitted on 2021-02-22 19:21:15
Authors: Saburou Saitoh, Keitaroh Uchida
Comments: 11 Pages.
In this paper, we will consider the basic relations of the normal solutions (hyper exponential functions by K. Uchida) of ordinary differential equations and the division by zero calculus. In particular, by the concept of division by zero calculus, we extend the concept of Uchida's hyper exponential functions by considering the equations and solutions admitting singularities. Surprisingly enough, by this extension, any analytic functions with any singularities may be considered as Uchida's hyper exponential functions. Here, we will consider very concrete examples as prototype examples.
Category: Functions and Analysis
[3] viXra:2102.0129 [pdf] submitted on 2021-02-21 16:36:02
Authors: Joseph Bakhos
Comments: 6 Pages.
Algebraic equations are derived to approximate the relationship
between the rectangular coordinates and the polar coordinates of a vector.
These equations can then be used without recourse to imaginary numbers,
transcendental functions, or innite sums. This submission incorporates changes to previous work so that the functions presented involving quaterns are now valid from -infinity to +infinity, using a new type of step function
Category: Functions and Analysis
[2] viXra:2102.0114 [pdf] replaced on 2023-03-15 13:06:24
Authors: Joseph Bakhos
Comments: Published in: Journal of Advances in Mathematics and Computer Science, Volume 38, Issue 6, Pages 33-38. DOI: 10.9734/jamcs/2023/v38i61766 Published: 27 March 2023. May be viewed at this site: https://journaljamcs.com/index.php/JAMCS/article/view/1766
Abstract. Quaterns are introduced as a new measure of rotation. Rotation in quaterns has an advantage in that only simple algebra is required to convert back and forth between rectangular and polar coordinates that use quaterns as the angle measure. All analogue trigonometric functions also become algebraic when angles are expressed in quaterns. This paper will show how quatern measure can be easily used to approximate trigonometric functions in the first quadrant without recourse to technology, innite sums, imaginary numbers, or transcendental functions. Using technology, these approximations can be applied to all four quadrants to any degree of accuracy. This will also be shown by approximating u to any degree of accuracy desired without reference to any traditional angle measure at all.
Category: Functions and Analysis
[1] viXra:2102.0071 [pdf] replaced on 2021-03-29 05:29:42
Authors: Kouider Mohammed Ridha
Comments: 4 Pages.
Josephus function is a new numerical function which presented by Kouider (2019,[1]) by studying Joseph's problem . In this paper we interesting in study of its derived function and some of its related properties for Josephus function. From this point of view we saw that we can define a more comprehensive function than the Josephus function. And we called it the Kouider function with basis ض. We have also studied some of its related properties with proof as well.
Category: Functions and Analysis
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