Hypernumbers applied or how they interface with the physical world. (English) Zbl 1024.01501
Summary: This paper presents a summary review of current hypernumber research and applications, including essential historical background.
MSC:
01A65 | Development of contemporary mathematics |
00A05 | Mathematics in general |
00A69 | General applied mathematics |
44A40 | Calculus of Mikusiński and other operational calculi |
83A05 | Special relativity |
01A60 | History of mathematics in the 20th century |
References:
[1] | Cartan, Eli, Lecons sur la Théorie des Spineurs (1938), Hermann: Hermann Paris · Zbl 0019.36301 |
[2] | Jacobson, N., Lectures in Abstract Algebra I (1975), Springer: Springer New York · Zbl 0314.15001 |
[3] | MacLane, Saunders, Mathematics: Form and Function (1986), Springer: Springer New York · Zbl 0628.01019 |
[4] | Musès, C., Applied hypernumbers, Appl. Math. Comput., 3, 111-126 (1977) · Zbl 0359.10050 |
[5] | Musès, C., Hypernumbers and quantum field theory, with a summary of physically applicable hypernumber arithmetics and their geometries, Appl. Math. Comput., 12, 139-169 (1983) · Zbl 0439.17011 |
[6] | Musès, C., Computing in the bio-sciences with \(hypernumbers^*\), International Journal of Bio-Medical Computing, 10, 519-525 (1979) |
[7] | Musès, C., Hypernumbers and quantum field theory, with a summary of physically applicable hypernumber arithmetics and their geometries, Appl. Math. Comput., 6, 63-94 (1980) · Zbl 0439.17011 |
[8] | Musès, C., Hypernumbers and quantum field theory, with a summary of physically applicable hypernumber arithmetics and their geometries, Appl. Math. Comput., 12, 139-167 (1983) · Zbl 0565.44004 |
[9] | Pezzo, P.del, Sulle superficie dell’\(n^{ mo }\) ordine immerse nello spazio di \(n\) dimensioni, Rendiconti della Reale Accademia delle scienze fisiche e matematiche di Napoli, 1, 241-255 (1887) · JFM 19.0841.02 |
[10] | Price, F. B., An Introduction to Multicomplex Spaces and Functions (1991), Marcel Dekker: Marcel Dekker New York · Zbl 0729.30040 |
[11] | Riley, J. D., Contributions to the theory of functions of a bicomplex variable, Tôhoku Math. J., 5, 2, 132-165 (1953) · Zbl 0052.31102 |
[12] | Segre, C., Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann., 40, 413-467 (1892) · JFM 24.0640.01 |
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