Ultra Linear Continuous Functionals and Ultra Generalized Complex Numbers in the Ultra Generalized Function Spaces

2012 ◽  
Vol 5 (4) ◽  
pp. 156-162
Author(s):  
Sabra Ramadan
Keyword(s):  
Function Spaces ◽  
Generalized Function ◽  
Complex Numbers ◽  
Generalized Complex ◽  
Generalized Complex Numbers ◽  
Continuous Functionals

Geometry of Generalized Complex Numbers

2004 ◽  
Vol 77 (2) ◽  
pp. 118-129 ◽  
Author(s):  
Anthony A. Harkin ◽  
Joseph B. Harkin
Keyword(s):  
Complex Numbers ◽  
Generalized Complex ◽  
Generalized Complex Numbers

scholarly journals And Where are Fluctuations In Quantum-Mechanical Wave Function?

2020 ◽  
Vol 1 (1) ◽  
Keyword(s):  
Wave Functions ◽  
Quantum Mechanical ◽  
Complex Numbers ◽  
Potential Well ◽  
Bohr Radius ◽  
Mechanical Wave ◽  
Generalized Complex ◽  
Different Types ◽  
Generalized Complex Numbers ◽  
Weight Coefficients

The generalized complex numbers containing weight coefficients for a paraxial case are described. An evident analogy between the wavy systems of trajectories, the module and an argument of complex numbers and the module and an argument of wave functions is drawn.Their geometrical interpretation is given on the plane and on the sphere. The symmetric and asymmetrical systems of wavy trajectories are considered. The examination of different types of wavy and zigzag trajectories of our systems of rays is presented. An evident analogy of these systems and wave functions describing finding of an electron in a potential well and near an atomic nucleus is drawn. The possible arrangement of a wave of de Broglie of an electron on the sphere of Bohr radius is shown. In the offered work great mathematicians whose works are connected with researches of complex numbers are marked out in {braces}: {Cardano, Hamilton, Gauss, Cauchy and Euler}.

scholarly journals New Insight into Quaternions and Their Matrices

2021 ◽  
Author(s):  
Gülsüm Yeliz Şentürk ◽  
Nurten Gürses ◽  
Salim Yüce
Keyword(s):  
Complex Numbers ◽  
Computational Results ◽  
Quaternion Matrix ◽  
Matrix Representations ◽  
Alternative Approach ◽  
Generalized Complex ◽  
Generalized Complex Numbers ◽  
Generalized Quaternion ◽  
Crucial Part ◽  
Insight Into

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

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