Formulae of extrapolations and filtration of partially observed solutions to quasi-linear functional differential equations with random disturbances.

part IV

Sokhadze G.A.

Akaki Tsereteli State University, Kutaisi

The explicit formulae of prediction of the solutions to nonlinear functional differential equations with random terms are presented. The evolutionary case and the case of so-called generalized solutions in the Sobolev space are considered individually.

Keywords: functional differential equations, extrapolation, filtration, prediction, Sobolev space.




A note about the absolute continuity of measures at cylindrical-type transformations

Sokhadze G.A.

Akaki Tsereteli State University, Kutaisi

The cylindrical-type transformation of the functional space is discussed. The absolute continuity of measures at such transformations is justified. The Radon-Nikodim equation is given.

Keywords: measure density, functional space, absolute continuity, cylindrical-type transformation.



The relation between the inflation rate and the exchange rate

Bidjuk P.I., Gogoladze N.G. and Sokhadze G.A.

Kiev Technical University, Ukraine

Akaki Tsereteli State University, Kutaisi

The relation between the price level index and the currency exchange rate was established. This relation  allows us to assess theoretically the unknown parameter of the price index or the exchange rate.

Keywords: price level, exchange rate, mathematical model.




The System approach to econometric forecast based on using time series models

Bidjuk P.I. and  Kordzadze T.Z.

Kiev Technical University, Ukraine

Akaki Tsereteli State University, Kutaisi

The construction of forecasting functions is considered for the following classes of  processes: stationary autoregression processes and autoregression with the moving average. There are given forecasting functions, derived without and with solving the model equations. The basic types of equations for describing the heteroscedastic and cointegrated processes are discussed.

Keywords: econometric forecast, time series model, autoregression, system approach. 




On the problem of surface wave damping in the conducting medium being inhomogeneous by the frequency of electron collisions

Chogovadze M.E., Bzhalava T.L. and Kalandadze I.G.

Georgian Technical University

The impact of inhomogeneity of the conducting medium (plasma) on surface wave damping was studied for the case when, at constant concentration of particles (electrons), the inhomogeneity of the medium is caused by the inhomogeneity of the frequency of electron collisions. A correction to the decrement of surface wave damping caused by this type of inhomogeneity was determined. It is demonstrated that, if the absorption in homogeneous plasma is the same both in the area of normal skin effect and in the area of inertial skin effect, the additional absorption emerging at inhomogeneous frequency of electron collisions has different values in those areas.

Keywords: plasma, surface waves, damping, inhomogeneous conducting medium, frequency of electron collisions.



The effect of energy localization on the emergence of quantum-mechanical interaction

Kutubidze B.V. and Janelidze O.M.

Shota Rustaveli State University, Batumi

There are presented the models of activation of interactions in InP and GaAs by formation of the electric dipole moment of quantum transitions by means of their excitation with deep centers. The London interaction is determined by the ability of deep center electrons of changing their quantum state under excitation. The great amount of energy of the London interaction is determined by its strong dependence on the distance.

Keywords: quantum-mechanical interaction, energy localization, dipole moment.




relationship between the magnitude of mobility and the concentration of electrons

Kutubidze B.V. and Janelidze O.M.

Shota Rustaveli State University, Batumi

There is presented a model explaining the abnormal decrease in the mobility of electrons in the case of reduction of their concentration.

The quantum interaction between electrons and dipole moments of quantum transitions, occurring in the excited deep centers, initiated by the localization of longitudinal acoustic oscillations of lattice atoms (LL AOLA) is the source of efficient electron scattering and promotes the resonance and London scattering of cold and warm electrons at increasing tension of electric field or increasing temperature.

Keywords: mobility of electrons, concentration of electrons, quantum interaction, relationship.




Kutelia E.R., Eristavi B.G., Okrosashvili M.N. and Okrosashvili I.M.

Republic Center of Structural Investigations, Georgian Technical University

The composition, the character of chemical bonding with the metal atoms and the thickness of the adsorbed layers on the surface of nanoparticles were studied. The analyses of separate layers were carried out by sputtering of the investigated surface of the sample using the accelerated argon ions with energy of 1keV. It was revealed that,­ after long-term keeping in the air, the  adsorbed layer mainly consists of oxygen in the state of the physical adsorption on the surface of the particles of the nanosized powders of nickel and cobalt,  and that it does not take part in the oxidation of the metal atoms. Oxygen is in chemical bonding with the titanium atoms on the surface layers of nanoparticles, though the carbon atoms are not in the state of physical adsorption. In the following sublayers, the tendency of carbide formation is initially observed, but at the  depth of 300Å from the physical surface, along with titanium oxide, titanium carbide is present.    

Keywords: nickel, cobalt, titanium, nanopowders, adsorbed layers, vapor phase, assessment, composition, thickness.




On ONE realization of sufficient conditions of optimality by krotov for the neural-network dynamic system

Beradze M.S.

Akaki Tsereteli State University, Kutaisi

In this paper the problem of optimal control for the continuous analog of discrete neural model is stated and resolved. The analytical expressions of optimal processes on the basis of Krotov’s sufficient conditions of optimality are given .There is offered an example of realization of  Krotov’s method for the four-dimensional system.

Keywords: neural network, optimal processes, Krotov’s method..





Kotetishvili K.V., Chilindrishvili D.R. and Chikhladze G.G.

Georgian Technical University

A new theory of short dipole antenna placed into the material environment is proposed. It is based on the solution of Hallen’s integral equation for the short vibrator (dipole antenna). The solution of this equation presenting the distribution of axial current through the dipole antenna and the radiation characteristic of the short dipole antenna were found.

Keywords: probe, dipole antenna, vibrator, Hallen’s integral equation.





Kevanishvili G.Sh., Sikmashvili Z.I., Kevanishvili I.G., 

Kotetishvili K.V., Asanidze A.V. and Chikhladze G.G.


Georgian Technical University


Abstract: A new technique of estimation and improvement of electromagnetic compatibility (emc) of antenna systems is suggested. So-called compatibility function  is introduced;  being some dimensionless (relative) geometric parameter of the antenna. The analysis of this function allows us to determine numerical values of  providing the eligible emc of the antenna within the given sector of space. The effectiveness of the policy is illustrated by a particular example.

Keywords: antenna vibrator, electromagnetic compatibility, directivity diagram.




Dekanosidze Sh.V., Kvatadze Z.A., Kekelia G.V. and Chikhladze G.G.


Georgian Technical University


Abstract: Electrodynamic properties of the system of dielectric rods placed in different cross-sections of rectangular waveguide were investigated. It is shown, particularly, that the system under study exhibits the resonance properties of total reflection and transmission.

Keywords: waveguide, reflection, transmission, resistance.


Space Time Codes with Outer Warp and CPM


Shavgulidze S. A.,  Asanidze A.V.  and Dzagnidze T.I.


Georgian Tecnnical University


Abstract. This paper deals with the space time code design of concatenated codes, where the outer code consists of lo parallel concatenated convolutional codes, and the inner code is continuous phase modulation (CPM). The possibility of constructing the full-diversity space time codes is discussed. A linear modulation approximation to CPM  is given. Using the Gram-Schmidt orthogonalization transform, the CPM signal is generated as a vector with finite energy in a different Euclidean space. A woven coded CPM construction is considered in searching channel codes which are able to exploit maximum diversity. The investigations  have been performed for a quasi-static Rayleigh fading channel.

Keywords: space time codes, code constructions, continuous phase modulator, outer warp.


Negation and THE Negation of Negation in Power Engineering


Aburjania A.N., Begiashvili V.I.,  Nachkebia Sh.Sh.,

Rezan Turan, Museliani T.G. and Aburjania L.A.


Georgian Technical University

 Macroenergy Holding Company, Ltd., Tbilisi, Georgia

Sarda Corporation, Vienna, Austria


Abstract. It has been established that, at the analysis of multicircuit systems, Maxwell’s mathematical form of expression of electromagnetic inertia of mutual induction results in the equilibrium equations making no physical sense and may lead to emergency situations. Induced current is the negation of inducing current alteration. Mutual induction between the inducing and the induced currents is negative. The mutual induction emf resulted from a change in the induced current in the circuit of inducing current is the negation of negation. Negation and the negation of negation serve as physical bases of field propagation and energy transfer. In the case of positive magnetic coupling, the mutual induction emf is negative and it inhibits the alteration of electric current force in the circuit, and vice versa, in the cases of negative magnetic coupling, the mutual induction emf is positive, and it contributes to the alteration of electric current force in the circuit. The magnetic field energy of inductively coupled circuits is defined as an algebraic sum of energy of separate circuits with an allowance for the sign of mutual induction. Practical tasks of mathematical modeling have been solved.

Keywords: inertia, induction, energy, emf, momentum.


Inertial Reference Frame of Electrodynamics


(Abstract of the Articles Published in 2000-2007)


Aburjania А.N., Begiashvili V.I. and Rezan Turan

Georgian Technical University,

 Macroenergy Holding Company, Ltd, Tbilisi, Georgia

 Sarda Corporation, Vienna, Austria



Determination of the reliability function of nonredundant element of power object

Namgaladze D.P. and Kiziria T.I.

Georgian Technical University

At considering the reliability indices of the system element with recovery, the time of operation and recovery is usually accounted for. But, in practice, there often occur the situations when, after the failure of the system (or its element), it takes considerable time to begin  repairing (time for revealing the damages, time for organization of repairing work, delivery of spare parts etc.).

The total dead time is called the waiting time.  In the present work, the reliability indices of the element of power object with account for the waiting time are determined analytically by using Markovian processes.

Keywords: power object, reliability, redundancy.



On the availability factor of power objects at recovery time distribution by the erlang law

Namgaladze D.P. and Gurgenidze D.R.

Georgian Technical University

When considering the indices of maintenance of designed or operating power objects, much attention is given to the availability factor, which is defined as the probability that the power object operates satisfactorily at any moment of operation, and that it is a determinate value. In the work, a stochastic quantity, the availability index, is introduced. Its density of probability distribution is analyzed for the case when the operating time is distributed by the exponential law, and the recovery time obeys the Erlang law.

Keywords: power object, reliability, availability, availability index.





determination of the residual operating time of unrestorable  element of power object with normal probability distribution

Gurgenidze D.R.

Georgian Technical University

In practice, it is often necessary to determine the functions representing the expected residual operating time for the power object element which has operated without failure for some time. The density of probability distribution of operating time could be determined from the initial probability distribution of operating time. In this work, analytical relations are derived for determination of the function of residual operating time in the period of the first preventive inspection when the mean-time-between-failures of the unrestorable element of the power object has exponential and normal distribution.

Keywords: power object, reliability, operating time, residual operating time, probability distribution.




Surguladze G.G., Topuria N.Sh. and Vacharadze I.V.

Georgian Technical University

The issues of designing and development of program technology of the unified office-work of the distributed organizational systems on the basis of modern object-oriented methods are discussed. A conceptual model of problem area was constructed on the basis of Objective-Role Modelling. The structure of relational database was designed in the automated mode. For simulation and analysis of business processes of the distributed system, the graph of Petri network was constructed.

Keywords: automation of business processes, database, Objective-Role Modelling, Petri networks.





Basaria F.P., Bokuchava G.V., Barbakadze K.G. and Biliseishvili M. J.

I. Vekua Institute of Physics and Technology, Sukhumi

Glass/enamel coatings based on SiO2-B2O3-PbO-Na2O for the surface of the arms of thermal elements (made from  PbTe) do not worsen the electric and mechanical properties. Besides, the high level of antisublimation protection is conditioned by the “soft” state of the glass/enamel coating (viscosity 106-1011Pa) at working temperature 350-5000C of the thermal element arms.

Key words: thermal element arms, glass/enamel coatings, antisublimation properties.




On The Impact of weak Magnetic Fields on Biological Systems

Kandelaki A.Sh., Kvavadze M.G. and Kandelaki M.A.

Akaki Tsereteli State University, Kutaisi

The impact of weak magnetic field on the water solution of albumin was studied. It was revealed that slight impacts of magnetic field on the products of thermodissociation of water and their spins could cause macroscopic changes in the structure of water and albumin dissolved in it.

Keywords: biological systems, albumin, water solution, weak magnetic field, structural changes.



The unity of symmetry and asymmetry – the basis of life. Part I

Tsivtsivadze T.I., Chigogidze N.Sh., Skhiladze R.A. , Kldiashvili R.Sh. and Sulakvelidze G.A.

Georgian Technical University

Problem Laboratory of Synthesis and Research of Physiologically Active Substances No. 393

The dialectical unity of symmetry and asymmetry is considered as the basic of life. The development of the notion of symmetry from the ancient times to the present day is demonstrated. It is noted that the principles of symmetry play a dominating role in the perception of the world around us and in the existence of limitations in the diversity of structures and the number of possible versions imposed by these principles. Diverse manifestations of symmetry in animate and inanimate nature are analyzed.

Keywords: basis of life, symmetry , asymmetry, unity of symmetry and asymmetry.






Sepiashvili D.P.

Georgian Engineering Academy

The information which reaches us from the outer environment is descrete. We can watch the real world only in particular time intervals. Quanta permanently disappear and emerge again in the real world. The time (Dt) it takes the quantum to disappear from watcher’s field of vision determined by Heisenberg law: Dt ×DE ~. The lower is the frequency, i.e. the quantum energy, the longer is the time (Dt) it takes the particle to disappear from or to emerge in the real space. As the Universe expands, the frequency, i.e. the energy of quanta, decreases. As this takes place, if the number of quanta existing in the real space-time decreases, the mass of the matter actually existing in the Universe will decrease, which, in its turn, will make weaker the gravitational field. As the frequency of fluctuations decreasesб the length of quanta, v=C/l, increases, i.e they “stretch”. Probably just this phenomenon manifests itself in the form of accelerated expansion of the Universe.

Keywords : matter, the Universe, expansion, quantum, hypothesis.



On the probable results of joint operation of

the man-quantum computer system

Khvedelidze M.A.

International Informatization Academy

Georgian Engineering Academy

The author considers the issue of probable results of joint operation of the man-quantum computer system  from the standpoint of the global law of duality of energoinformation work of the matter allowing to extend significantly the knowledge about the Universe. This law was justified in previous works.

Keywords: matter, duality of energoinformation work, man-quantum computer system, joint operation, probable results.



Specific features of plastic deformation of  reinforced sintered materials

Sharashenidze D.А. and Ramishvili V.N.

F. Tavadze Institute of Metallurgy and Materials Science

A method of reinforcement of the powder matrix with wire has been developed. The method allows producing the noncompact reinforced blanks for their  subsequent plastic deformation. The investigation of deformation and sintering of the granular matrix-reinforcing material system was performed for composition Ni-W and Ni-Mo.

Keywords: powder metallurgy, sintered materials, reinforcement plastic, deformation.



The prospects of development of electric power network in Georgia

Mshvidobadze T..J.

Georgian Technical University

The possibility of application of one of the versions of development of the electric power network in Georgia is discussed. The algorithm of grouping of the versions of power network development, which allows choosing the optimal network configuration under indefinite conditions, is offered. The experiments have demonstrated that the same optimal decision can be found by considerable reduction in the number of versions.

Keywords:  electric power network, development, prospects, grouping algorithm.



Cryptographic data protection in the local network

Adamia V.B., Arabuli N.V., Machavariani N.V. and Eliauri L.Sh.

Georgian Technical University

The cryptographic method of data protection in the local network is discussed. The method involves real-time coding. This is the simplest and the most efficient way of protecting the transmitted data against unauthorized access. The proposed version of the method is considered. for specific conditions with a lot of constraints. There is given the mathematics of applicability of the method, which justifies its high reliability.

Keywords: cryptography, data protection, local network, real-time coding.






Taktakishvili G.N., Partskhaladze R.I., Kvezereli T.I. and Jashi D.R.

COLOR Company

There is proposed a method of color-printing quality control by means of the equipment for generation of electronic image-forming device, which consists of an optoelectronic system and an A4 scanner emitter. The design of the equipment and the original software described in the article allow us to calculate accurately and efficiently the densitometric parameters of multicolor imprint and to find the error in the alignment of the register marks. The adjustment of the device, retaining of the reference color parameters and the register correction are performed automatically.

Keywords:  polychromatic print, color, optical compactness, scanner.



New ENVIRONMENT FRIENDLY Resource-Saving Technology for Processing of Arsenic- Containing Ores


Iashvili T.S.


Georgian Technical University


Abstract.New technology of processing of arsenic-containing ores is proposed. This technology allows improving some parameters of processing, namely, decreasing the process temperature from 800-10000C to 615-6500C, decreasing the processing time form 8-19h to 1.5-2h, increasing the yield of arsenic etc. The proposed technology fulfils the ecological requirements. This technology can also be used for extraction of accompanying arsenic from the ores of nonferrous metals. The technology allows processing the arsenic-containing residue and reducing the concentration of arsenic in the residue to the permissible limit.

Keywords: arsenic, arsenic-containing ores, processing, residue.




Miminoshvili E.B., Vardosanidze T.O. and Miminoshvili K.E.

Georgian Technical University

Georgian University of Social Sciences

There are presented the results of X-ray analysis  of the structure of hexamethylenetetramine monohydrochloride (C6H13N4)Cl at temperature 153(2)K (а=8.860(1); b=8.860(1); c=8.929(1)Å, γ=120º, V=607.02(10)Å3; R3m, Z=3; R= 0.0202).

Keywords: molecular structure, hexamethylenetetramine monohydrochloride, Urotropin, X-ray analysis.



Kinetic method of determination of nanogram amounts of iodine in natural objects

Supatashvili G.D., Karsanidze N.K., Loria N.V., Liparishvili S.N., Shedania Z.V. and Janashvili N.E.

Iv. Javakhishvili Tbilisi State University

A kinetic method has been used for determination of nanogram amounts of iodine in natural water and foodstuffs of vegetable and animal origin. The method is based on the indicator reaction between nitrite and thiocyanate ions.  The sensitivity of the method is 5 ng, and the mean error is less than 5%.

Keywords: natural objects, iodine, nanogram amount, kinetic method.





Determination of the dependence of the amount of precipitated agent on the concentration of the reagent-solution and the time

Dondoladze N.G., Megrelishvili Z.N.  and Mekvabishvili N.I.

Shota Rustaveli State University, Batumi

For the development of the technology for water softening with the use of the reagent-solution, the nature of changes in the precipitation rate at different concentrations of the reagent-solution was investigated. The approximation of dependence of the amount of  precipitated agent on the reagent –solution concentration and the time of precipitation is discussed. The agreement between the data obtained experimentally and the data calculated according to the obtained dependence was evaluated by criterion.  For this purpose, the obtained results were checked for homogeneity, random character  and stability in time. The tables for calculating the  criterion are given. For the number of degrees of freedom and for the probability level , the  criterion was determined, 

Keywords: water softening, reagent-solution, natural water, precipitation, approximation, criterion.






EXPERIMENTAL design and optimization of the processes of extraction of tea lipids

Tsutskiridze N.R., gvinianidze T.N. and Buchukhishvili M.L.

Akaki Tsereteli State University, Kutaisi

Optimal economic parameters of the processes of extraction of tea lipids (the product yield and the cost per unit of production) and the factors affecting these parameters are discussed. The experimental design of those processes was performed. The realization of the matrix of second-order central composition rotatable design allowed deriving the adequate regression equations describing the processes. By using the method of indefinite Lagrange factors, the optimal conditions of the production process of extraction of tea lipids were established.

Keywords: lipids, tea, extraction, process optimization, experimental design.



Investigation of the kinetics of the process of withering of tea mass in the vibroaeropseudocondensed layer

Megrelidze T.J., Shubladze Z.L., Dolidze B.Z. and Galogre L.J.

Georgian technical University

Scientific – Production Association of Subtropical Cultures and Tea Production

The process of tea mass withering in the vibroaeropseudocondenced (VAPC) layer is discussed. There are given the experimental results at harmonic mode of vibration of the working body with variable parameters: air temperature                T=320-330k; amplitude of vibrations A=0-7mm; relative humidity of tea mass W=60-75%. It was established that, when the air temperature at the installation inlet increased from 320k to 330k, the time of withering decreased by a factor of 4 to 12. The vibrations with the amplitude of 3mm hardly affected the withering rate. When the amplitude was increased from 3mm to 7mm, the rate of withering changed significantly.  The empirical formula for calculation of the rate of tea mass withering in the VAPC layer was derived, and the optimum parameters were established.

Keywords: tea leaves, withering, vibroaeropseudocondensed layer, kinetics.



Investigation of the motion of green tea leaves In the vibroaeropseudocondensed layer

Megrelidze T.J. , Shubladze Z.L. and Dolidze B.Z.

Georgian Technical University

Scientific-Production Association of subtropical cultures and tea production

The belt conveyer unit with convection heat feeding, which is commonly used for withering of tea leaves, is discussed. It is mentioned that this unit has significant drawbacks, the main of which is the nonuniformity of the withering process, which adversely affects the product quality. For intensification of the process of tea mass withering by achieving the uniform withering, a rational method of simultaneous treatment of tea leaves with vibrations and the products with hot air from bottom upwards was chosen. By theory, there were derived differential equations of the motion of tea leaves on the vibrating surface and the equation determining the critical frequency of roller rotation under the condition of removal of the tea leaf from the vibrating surface. The obtained theoretical data were justified experimentally.

Keywords: green tea leaves, vibroaeropseudocondensed layer, motion , withering.




Investigation of the velocity of soaring of green tea leaves

Megrelidze T.J., Shubladze Z.L. , Dolidze B.Z.  and Galogre L.J.

Georgian Technical University

Scientific-Production Association of Subtropical cultures and Tea Production

The necessity in performing the experiments for determination of the velocity of soaring of green tea leaves with the aim of designing a unit for tea leaf withering is demonstrated. There is given a circuit diagram of the experimental device for determination of the velocity of soaring of tea leaves with consideration for simultaneous action of vibrations and the air stream. It was determined that the velocity of tea leaf soaring increased from                                    2.67 m/s to 4.65 m/s when the tea mass thickness was increased from 80mm to 240mm at relative humidity             W1 =70-75%. At increasing the tea mass thickness from 60 mm to 180 mm and at relative humidity W2 = 60-62%, the velocity of tea leaf soaring increased from 3.17 m/s to 6.13 m/s.

Keywords: green tea leaves , vibroaeropseudocondensed layer, withering unit, soaring velocity 




Khetsuriani G.S., Tavdidishvili D.R. and Minadze N.M.

Akaki Tsereteli State University, Kutaisi

The chemistry of cherry-laurel fruit growing in Western Georgia was studied. It was established that  this fruit is characterized by high content of pectin substances. Their qualitative indices were studied. It is shown that they are characterized by good complexing ability. The cherry-laurel fruit without stones may be used in the production of preventive foodstuff.

Keywords: cherry-laurel, pectin substances, preventive foodstuff.