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We present a simple construction of the instantonic type equation over octonions where its similarities and differences with the quaternionic case are very clear. We use the unified language of Clifford Algebra. We argue that our approach is the pure algebraic formulation of the geometric based soft Lie algebra. The topological criteria for the stability of… (More)

In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and 8 × 8 real matrices (a translation is also given for 4 × 4 complex matrices). The use of a complex geometry allows us to overcome the hermiticity… (More)

We discuss how to represent the non-associative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and Super Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace… (More)

We give a one dimensional octonionic representation of the different Clif-which can be given by 8 × 8 real matrices taking into account some suitable manipulation rules.

- M FAYEZ, K ABDEL-KHALEK
- The Journal of the Egyptian Medical Association
- 1962

Taking into account the recent dualities we rederive the super p-brane scan. Our main results are the importance of the metric's signature and the existence of an S self-dual super 5-brane at D=14 with signature (7,7) or (11,3).

We study the compatiblity between the higher dimension dualities and the Yang-Mills equation of motion. Taking a 't Hooft solution as a starting point, we come to the conclusion that for only 4 dimensions the self duality implies the equation of motion for generic instanton size. Whereas in higher dimensions, the self duality is compatable with the equation… (More)

- M F El-Hawary, F A El-Shobaki, +4 authors A Khashaba
- The Gazette of the Egyptian Paediatric…
- 1975

The study deals with investigations on anaemia due to iron or protein calorie deficiency and that associating acute glomerulonephritis, nephrosis and schistosoma haematobium. The rate of intestinal iron absorption using an oral dose of ferrous sulphate equivalent to 4 mg clemental iron/kg body weight was studied. The supplementing action of ascorbic acid in… (More)

- QUATERNION ANALYSIS, Khaled ABDEL-KHALEK
- 2008

Quaternion analysis is considered in full details where a new an-alyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.

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