SELF TRANSACTIONS, VOLUME 1 (ELECTRONIC VERSION) The printed version was published in 1994 in Eney Publishing, Kharkov, Ukraine ISBN 5  7700  0403  7 CONTENTS 

S.B. Karavashkin. THE MATTER AS PHYSICAL REALITY 

First published in SELF Transactions, vol.1 (1994), pp.514 

The author considers the problem of ether being a subject of discussions for many generations of scientists. He proves it to be the physical reality of more thin order transmitting the interactions that cannot be associated with the concept of an abstract field of forces possessing an action but not possessing the physical properties, because of the excessive geometrisation of this concept. Keywords: Philosophy of science; Physical ether; Field theory Classification by PASC 2001: 01.70.+w; 02.30.Em; 03.50.z; 03.50.De 

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S.B. Karavashkin. ON LONGITUDINAL ELECTROMAGNETIC WAVES. CHAPTER 1. LIFTING THE BANS 

First published in SELF Transactions, vol.1 (1994), pp.1547 

This is the initial version of an introduction chapter of a monograph devoted to the theoretical and experimental proof of the longitudinal electromagnetic waves existence. This chapter proves that the known Maxwell divergence equation works correct only in stationary fields. Its form for dynamical fields is derived. Some typical inexactitudes having led the scientists to the conclusion that the energy does not propagate in the near field are shown, and the contradictions between the Ampere law and Lorenz equation for dynamical magnetic fields acting on a charge are considered as well. As the supplement to this paper, the author published the Review to the primary experiment on radiation and reception the longitudinal EM wave demonstrated by S. B. Karavashkin Keywords: theoretical physics, mathematical physics, wave physics, vector algebra, electromagnetic theory, dynamical potential fields. Classification by MSC 2000: 76A02, 78A02, 78A25, 78A40 Classification by PASC 2001: 03.50.z; 03.50.De; 41.20.Jb; 43.20.+g; 43.90.+v; 46.25.Cc; 46.40.Cd 

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S. B. Karavashkin. SOME PECULIARITIES OF DERIVATIVE OF COMPLEX FUNCTION WITH RESPECT TO COMPLEX VARIABLE 

First
published in SELF Transactions, vol.1 (1994), pp.7794 

This paper is the introducing for a monograph devoted to the new branch of theory of complex variable – nonconformal mapping. This new original method enables to connect the mathematical models to which the linear modelling is applicable with nonlinear mathematical models, i.e. with the cases when the mapping function is not analytical in a conventional Caushy – Riemann meaning but is analytical in general sense and has all the necessary criterions of the analyticity, except of the direct satisfying to the Caushy – Riemann equations. As an example, the exact analytical solution of the Besseltype equation in the continuous range of an independent variable has been obtained. 

Keywords: Theory of complex variable, Nonconformal mapping, Quasiconformal mapping, Bessel functions Classnames by MSC 2000: 30C62; 30C99; 30G30; 32A30. 

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PUBLICATIONS IN OTHER EDITIONS CONTENTS


S.B. Karavashkin. EXACT ANALYTICAL SOLUTION FOR 1D ELASTIC HOMOGENEOUS FINITE LUMPED LINE VIBRATION 

First published in Materials. Technologies. Tools (National Academy of Sciences of Belarus), 4 (1999), 4, pp.513 

We will analyse in this paper the principal demerits of conventional approaches to the problem of vibrant 1D homogeneous finite lumped line and present the exact analytical solutions for forced and free vibrations in finite lines with free ends and with the free end and fixed start. We will analyse these solutions and their distinctions from the conventional concept on the vibration pattern in such lines. We will give the check of presented solutions proving them to be complete and exact 

Keywords: Mathematical physics, Wave physics, Dynamics, Finite elastic lumped lines, ODE systems, Microwave vibrations in elastic lines Classification by MSC 2000: 30E25; 70E55; 70J35; 70J60; 70K40; 70F40 Classification by PASC 2001: 02.60.Lj; 05.10.a; 05.45.a; 45.30.+s; 46.15.x; 46.25.Cc; 46.40.f; 46.40.Fr 

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S. B. Karavashkin. THE FEATURES OF INCLINED FORCE ACTION ON 1D HOMOGENEOUS ELASTIC LUMPED LINE AND CORRESPONDIG MODERNISATION OF THE WAVE EQUATION 

First published in Materials. Technologies. Tools (National Academy of Sciences of Belarus), 6 (2001), 4, pp.1319 

We analyse the exact analytical solutions for 1D elastic lumped lines under action of an external force inclined to the line axis. We show that in this case an inclined wave being described by an implicit function propagates along the line. We extend this conclusion both to free vibrations and to distributed lines. We prove that the presented solution in the form of implicit function is a generalizing for the wave equation. When taken into consideration exactly, the dynamical processes pattern leads to the conclusion that the divergence of a vector in dynamical fields is not zero but proportional to the scalar product of the partial derivative of the given vector with respect to time into the wave propagation direction vector. 

Keywords: Mathematical physics, Wave physics, Dynamics, Elastic lumped lines, Inclined force action, General solution of the wave equation, Vector flgebra, Divergence of vector in dynamical fields, ODE systems Classification by MSC 2000: 30E25; 70E55; 70J35; 70J60; 70K40; 70F40 Classification by PASC 2001: 02.60.Lj; 05.10.a; 05.45.a; 45.30.+s; 46.15.x; 46.25.Cc; 46.40.f; 46.40.Fr 

S. B. Karavashkin. TRANSFORMATION OF DIVERGENCE THEOREM IN DYNAMICAL FIELDS 

First published in Archivum mathematicum (BRNO), 37(2001) No 3, pp. 233  243 

In this paper we will study the flux and the divergence of vector in dynamical fields, on the basis of conventional divergence definition and using the conventional method to find the vector flux. We will reveal that in dynamical fields the vector flux and divergence of vector do not vanish. In the terms of conventional EM field formalism, we will show the changes appearing in dynamical fields.  
Keywords: Theoretical physics, Mathematical physics, Wave physics, Vector algebra. Classification by MSC 2000: 76A02, 78A02, 78A25, 78A40 

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Supplement: New Year question from Leo 
