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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D.P.Borycenko  Karavashkina. ON THE CAUSE OF LIKE CHARGES BEAM SQUEEZE 

First
published in SELF Transactions, vol.1 (1994), pp.5256 

The dynamical instability of the beam of samecharged particles is considered. This instability is shown to be caused by the Lorentz force turning the beam inside out due to the different speeds of central and peripheral particles of a beam. It is supposed that such instability is one of the main causes, why it is impossible to squeeze the plasma flow in tokamaks. Classification by PASC 2001: 52.30.q; 52.35.g; 52.35.Mw; 52.35.Py; 52.55.Fa; 52.55.Hc Keywords: plasma physics, plasma instability, ponderomotive forces, Lorentz force, stellarators, tokamaks Full text: / 5256 /


S.B. Karavashkin ON THE NEW CLASS OF FUNCTIONS BEING THE SOLUTION OF THE WAVE EQUATION 

First published in SELF Transactions, vol.1 (1994), pp.5766 

We will prove that not only the commonly known explicit timedelay functions but implicit functions also are the solutions of secondorder wave equation. This class of implicit functions is the covering solution of the wave equation. This considerably broadens the area of wave equation application onto the modelling of wave processes in nonlinear media


Keywords: mathematical physics, wave physics, wave equation, implicit functions, modelling of nonlinear wave equations Classification by MSC 2000: 35G20, 35J05, 35L05, 35L10 Classification by PASC 2001: 03.65.Ge, 41.20.Cv 

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S.B. Karavashkin TRANSFORMATION OF CONTINUITY EQUATION IN NONLINEAR MODELS OF POTENTIAL FLOWS OF CONTINUA 

First
published in SELF Transactions, vol.1 (1994), pp.6776 

We will prove the theorem of divergence of vector for deformed continua


Keywords: mathematical physics, wave physics, vector algebra, mechanics of deformed continua Classification by MCS 2000: 76A02, 76A10, 76D33 Classification by PASC 2001: 47.10.+g, 47.15.x, 47.20.Ky, 47.35.+i 

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S. B. Karavashkin and O.N. Karavashkina. SOME FEATURES OF DERIVATIVE OF COMPLEX FUNCTION WITH RESPECT TO COMPLEX VARIABLE 

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

This paper, with all its outward simplicity and obvious statements, is an effort to take a look at the complex plane and operations in it from some unexpected point of view. Or rather, not so much the approach will be unexpected as the concept of complex function will be broadened up to the limits related to most general definitions. 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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Dyna P. BorycenkoKaravashkina. ON CLOUDS FORMATION 
First
published in SELF Transactions, vol.1 (1994), pp.95 112 
TThis paper studies charge formation in the clouds due to the motion of clouds in the magnetic field of Earth and explains some important points related to formation of cyclones and anticyclones, trade winds and typhoons.

Keywords: meteorology, cloud formation, Earth’s magnetic field, cyclones, anticyclones, trade winds, typhoons. Classnames by PASC 2001: 91.40.Dr, 92.60.Ek, 92.60.Gn, 92.60.Jq, 92.60.Mt, 92.60.Nv, 92.60.Pw 
PUBLICATIONS IN OTHER EDITIONS CONTENTS

S.B. Karavashkin EXACT ANALYTIC SOLUTION FOR 1D INFINITE VIBRANT ELASTIC LUMPED LINE 
First published in Materials. Technologies. Tools (National Academy of Sciences of Belarus), 4 (1999), 3, pp.1523 
We will analyse the most important drawbacks of conventional solutions for the problem of vibrant infinite 1D elastic lines with lumped parameters. We will present the exact analytic solutions for forced and free vibrations of semifinite and infinite homogeneous elastic lines. We will analyse these solutions, examine their physical meaning and verify them, to perform their exactness and completeness.

Keywords: mathematical physics, wave physics, dynamics, infinite elastic lumped lines, ODE 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. 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 the main shortcomings 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 the 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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Full text in Postscript 
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 will analyse the exact analytical solutions for 1D elastic lumped lines affected by external force inclined to the line axis. We will show that in this case an inclined wave described by an implicit function propagates along the line. We will extend this conclusion both to free vibrations and to distributed lines. We will prove that the presented solution in the form of implicit function is a generalising for the wave equation. When taken into consideration exactly, the pattern of dynamical processes 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 vector of wave propagation direction.

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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