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29 results on '"Dimiev, Stancho"'

1. Hyperbolic hypercomplex D-bar operators, hyperbolic CR-equations and harmonicity

Author

Apostolova, Lilia N., Dimiev, Stancho, and Stoev, Peter

Subjects
Mathematics - Complex Variables, 30G35
Abstract

This paper is partially a review of the development of the Investigation Program announced by Stancho Dimiev at the Bedlevo Conference on Hypercomplex Analysis (2006). A new aspect related with hyperbolic complex numbers, their generalizations and applications on hyperbolic harmonicity is included in some Appendix of S. Dimiev. The recent results on the hyperbolic complex structures are exposed. We describe systematically the $\partial$-bar trik which led to Cauchy-Riemann type systems for different generalized hypercomplex algebras. This is in fact an elementary $\partial$-bar type theory of the PDE on the mentioned algebras. Microlocal treatment (distributions and Fourier transform) of the solutions is included too, with one result of P. Popivanov., Comment: 22 pages

Published
2010

2. On hypercomplex pseudo-Hermitian manifolds

Author

Gribachev, Kostadin, Manev, Mancho, and Dimiev, Stancho

Subjects
Mathematics - Differential Geometry, 53C15, 53C50 (Primary) 32Q60, 32Q15 (Secondary)
Abstract

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal invariance and the conformal equivalence of the basic types manifolds are studied. A known example is characterized in relation to the obtained results., Comment: 12 pages, presented on The Sixth International Workshop on Complex Structures and Vector Fields, St Konstantin, Bulgaria, 3-6 September 2002

Published
2008
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3. Gauss Integers and Diophantine Figures

Author

Dimiev, Stancho and Markov, Krassimir

Subjects
Mathematics - Number Theory, Mathematics - Metric Geometry, 11A99, 11D04, 11D09
Abstract

In this paper Gauss integers are used for to develop some geometry of full Erdoes graphs which vertics are points with integer coordinates. These graphs are called Diophantine figures., Comment: 15 LaTeX pages. This paper is an enlarged exposition of short 6 page communication with the same title, which will appear in the Proceedings of the 31 Spring Conference of the Union of Bulgarian's mathematicians (Borovetz, Bulgaria, April 3-6, 2002)

Published
2002

8. Hyperbolic Fibrations and PDE

Author

Dimiev, Stancho

Subjects
PDO, hyperbolic fibration, Minkowski metrics, Euclidean fibration, Mathematics::Symplectic Geometry
Abstract

In this note we try to distinguish the hyperbolic fibrations from the Euclidean one with the help of the invariant action of partial differential operators on the fibration. Two examples are given., 2010 Mathematics Subject Classification: 35L10, 35L90.

Published
2012

16. Matrix 2[sup n]-holomorphy

Author

Apostolova, Lilia N., primary, Dimiev, Stancho, additional, Marinov, Marin S., additional, Stoev, Peter, additional, Venkov, George, additional, Pasheva, Vesela, additional, and Kovacheva, Ralitza, additional

Published
2010
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19. Matrix Fourth-Complex Variables

Author

Dimiev, Stancho, primary, Marinov, Marin S., additional, Stoev, Peter, additional, Venkov, George, additional, Kovacheva, Ralitza, additional, and Pasheva, Vesela, additional

Published
2009
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22. Cyclic hypercomplex number systems.

Author

Dimiev, Stancho, Stoev, Peter, and Todorov, Vladimir

Subjects
*HYPERCOMPLEX numbers, *POLYNOMIALS, *MATRICES (Mathematics), *PROBLEM solving, *DIVISION algebras, *DIMENSION theory (Algebra), *MATHEMATICAL functions
Abstract

We consider formal hypercomplex number systems of special type, namelly the introduced here polynomial type number systems. The corresponding matrix algebras of polynomial type are always associative of real dimension 2k, k ∈ N. Our problem is related with the question of the extention of function theory over the mentioned algebras, like the classical case of real dimension 2, i.e. k = 1. The difference is in the fact that the classical case we have division algebras, but in the considered here algebras we have non-divisions ones. [ABSTRACT FROM AUTHOR]

Published
2012
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23. Matrix 2n-holomorphy.

Author

Apostolova, Lilia N., Dimiev, Stancho, Marinov, Marin S., and Stoev, Peter

Subjects
*HOLOMORPHIC functions, *MATRICES (Mathematics), *FUNCTIONS of several complex variables, *REAL variables, *MATHEMATICAL programming, *MATHEMATICAL analysis, *REAL numbers
Abstract

The 4-real holomorphy is the matrix holomorphy of 4-real variables x0+jx1+j2x2+j3x3, xk∈R. Its CR system is expressed in real partial derivatives ∂/∂x and ∂/∂y as a pair of CR(x0,x2) and CR(x1,x3). It is explained here that the double-complex holomorphy, introduced in [2], arises parallely with 2n-real holomorphy. For instance, 4-real holomorphy implies double-complex one, and 8-real holomorphy implies fourth-complex one. Moreover, except the matrix representation of the 2n-holomorphy we develop and hyperbolic matrix 2n-holomorphy. A correction for a wrong proposition in [1] is given. Let us remark that a formal symbolic treatment of the algebra of the 2n-real numbers was announced in Kazan geometric school [6], developed especially in the inadmissible for us paper [7]. [ABSTRACT FROM AUTHOR]

Published
2010
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