"Hypercomplex Numbers in geometry and Physics" 1 (19), Vol 10, 2013
j019

Content of Issue

Sir Roger Penrose visit in Russia at April, 2013
2013jaz | Pavlov D.G.

Editor's note

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Sir Roger Penrose press conference (RIA NEWS, Moscow, April 5, 2013)
2013jbz

Editor's note

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POWER AND BEAUTY OF COMPLEX NUMBERS AND ITS ROLE IN TWISTOR THEORY DEVELOPMENT
2013jcz | Penrose Roger

Russian translation of public lecture of Professor Roger Penrose organized by Bauman Moscow State Technical University and the Research Institute of Hypercomplex Systems in Geometry and Physics. The lecture presents some aspects of complex numbers, its physical applications and fundamentals of twistor theory.

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SEEING THROUGH BIG BANG INTO ANOTHER WORLD. CONFORMAL CYCLIC COSMOLOGY. BASIC INTRODUCTION
2013jdz | Penrose Roger

Russian translation of public lecture of Professor Roger Penrose organized by Bauman Moscow State Technical University and the Research Institute of Hypercomplex Systems in Geometry and Physics. The lecture presents basic introduction to Conformal Cyclic Cosmology

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ALGEBRA, GEOMETRY AND PHYSICS OF DOUBLE NUMBERS
2013jfz | Pavlov D.G., Kokarev S.S.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia; RSEC Logos, Yaroslavl, Russia, geom2004@mail.ru, logos-center@mail.ru

The paper presents developed version of talk, given at the seminar, which took place 04.04.2013 in PFUR (Moscow) with sir R. Penrose. Some important analogies of complex algebra and analysis based on double numbers algebra are considered (polar and exponential forms of double numbers, elementary functions over double numbers, linearfractional transformations and hyperbolic spinors, h-holomorphic functions and their properties, h-holomorphic extensions). The second part of the paper is devoted to some physical applications of double numbers algebra (SR and its conformal generalization, the «theory of everything» in Hyperland, extravariational principle). The theory of Hyperland can be treated as low-dimensional version of future more realistic «theory of everything», based on polynumbers algebra Pn.

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ON THE FOUNDATIONS OF THE GENERALIZED EQUIVALENCE THEORY (ANISOTROPIC GEOMETRODYNAMICS)
2013jiz | Siparov S.V.  // Civil Aviation State University, Saint-Petersburg, Russia, sergey.siparov@gmail.com

The principal features of the generalized equivalence theory (anisotropic geometrodynamics) are discussed. The motivation that led to this approach on the base of the analysis of some inconsistencies present in the foundations of the classical mechanics is given. The results of the use of this approach for the interpretation of some observations on the galactic scale that had no explanations before and for the interpretation of observations without the use of the notion of dark matter are presented.

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