volume 154 number 1 Jule-August
On Some Analogies of Riemann-Lebesgue Theorem for Functions of Multiple Variables -1
Presented by Academician L.Zhizhiashvili,
Abstract. In the present paper the limits in Pringsheim's sense of the type
(u,v)a (l 1u, l 2v)dudv
for functions f and a from various classes are investigated.
Signature Method for Counting Point in Semi-Algebraic Subsets
Presented by Corr. Member of the Academy
ABSTRACT. The theorems on counting root numbers of real polynomial endomorphism in an arbitrary semi-algebraical set are given and several cases are considered. The estimate of the computational complexity of counting root numbers is obtained. The mentioned facts generalize early results obtained by the author. Particularly the numbers of variables and equations are unrestricted.
On the Correctness of the Multipoint Boundary Value Problem for the System of Generalized Ordinary Differential Equations
Presented by Academician I.Kiguradze, April 10, 1995
Abstract. The sufficient conditions are given to guarantee the correctness of the problem
dx(t)=dA(t) × f(t,x(t)),
xi(ti)=j i(x) (i=1,...,n),
where t1,...,tn Î [a,b], A:[a,b]® Rn´ n is a matrix-function with bounded variation components, f:[a,b]´ Rn® Rn is a vector-function belonging to the Caratheodory class corresponding of A, and j i(i=1,...,n) are the continuous functionals from the space of vector-functions of bounded variation into R.
Corr. Member of the Academy N.Berikashvili
On the Criterion of the Secondary Cross Section
Presented June 13, 1996
ABSTRACT. New formula for the secondary obstruction to Serre fibration is given.
Some Properties of Fourier Trigonometric Series of Even and Odd Functions
Presented by Academician L.Zhizhiashvili, June 20, 1995
ABSTRACT. Problems of continuity of sums of definite type "cosine" and "sine" series are considered. The criterion of the sum of "sine" series from the class Hw is established.
Non-Abelian Tensor Products of Finite Groups with Non-Compatible Actions
Presented by Corr. Member of the Academy H.Inasaridze, February 20, 1996.
ABSTRACT. Some sufficient conditions for finiteness of a generalized non-abelian tensor product of groups are established.
Problems of Convergence Multiple Expansions in Complex Sphere for Polynomial Differential Bundle with Constant Coefficients
Presented by Academician L.Zhizhiashvili, December 20, 1995
Abstract. In case of constant coefficiental operator of the third order the problem of convergence spectral expansion has been studied in complex domain. The analogue of Abeli's well-known theorem about convergence power series has been obtained.
On Possible Meanings of Upper and Lower Derivatives
Presented by Academician L.Zhizhiashvili, November 27, 1995
ABSTRACT. In the paper there is investigated the behaviour of upper and lower derivatives of the integrals with respect to the differentiation bases formed of intervals. The main result consists in that the analogy of the famous theorem of Besicovich generally is not true for translation invariant Busemann-Feller differentiation bases formed of intervals.
Lusternik-Schnirelmann Category of a Weak Formal Space
Presented by Corr. Member of the Academy N.Berikashvili, December 26, 1994
ABSTRACT. The paper presents the Lusternik-Schnirelmann category computed for a class of spaces by the integral cohomology ring.
Some Properties of Belman's and Loo's Transformations
Presented by Academician L.Zhizhiashvili, May 23, 1996
ABSTRACT. Some properties of Belman's and Loo's trasformations and invariant classes for this transformations are studied.
About Matrices of Singular and Fundamental Solutions for Equations of the Generalised Couple - Stress Thermoelasticity Plane Theory
Presented by Academician T.Burchuladze, March 26, 1996
ABSTRACT. The matrices of fundamental and other singular solutions are constructed explicit for the system of stationary equations of two - dimensional generalised couple - stress thermoelasticity theory and some of their properties are indicated.
Summability of the Fourier Series over Generalized Spherical Functions by the Abel and (C, a ) Methods
Presented by Academician L.Zhizhiashvili, May 2, 1996.
ABSTRACT. Some theorems on Abel and (C, a ) summability of Fourier series over generalized spherical functions are proved.
Conjugation Problem for a Second Order Hyperbolic System with Discontinuous Coefficients
Presented by Academician I.Kiguradze, July 8, 1996
ABSTRACT. The conjugation problem is considered for a second order degenerated hyperbolic system with discontinuous coefficients. The uniqueness and existence theorems are proved.
On the Extension of Kotelnikoff-Shannon Formula
Presented by Academician V.Chavchanidze, June 10,1996.
ABSTRACT. The extension of Kotelnikoff-Shannon formula which gives the possibility to increase interpolation step on the discreet points together with process value up to some order considering derivative value is given in the paper.
Continuous Oscillations in Compensated Semiconductor under Impure Electric Breakdown
Presented by Corr. Member of the Academy N.Tzintzadze, June 1, 1996
ABSTRACT. On the basis of mathematical model describing generation - recombination processes from impurity levels, dielectric relaxation of electric field and delay of electron temperature Te relatively to the change of electric field necessary and sufficient condition of appearing persistant oscillations in compensated semiconductor under impure electric breakdown is established. This condition is reduced to rather simple form after a number of transformations. It contains the delay time of electron temperature t D as an important parameter characterizing the behavior of the system. The dependence of t D from Te is studied. It is shown that while regarding the dynamics of the system t D with good accuracy can be considered constant.
E.Khutsishvili, M.Paghava, A.Kuchashvili
Thermal Expansion Coefficient of Gallium Arsenide at High Temperatures
Presented by Corr. Member of the Academy G. Tsagareishvili, June 22, 1996
Abstract. Thermal exspansion coefficient of single and polycrystals gallium arsenide has been investigated at the temperature range from 300 to 900 K.
Good agreement of gallium arsenide thermal expansion coefficient temperature dependence with that of heat capacity of semiconductors was found.
The effect of annealing at 823 and at 873 K of gallium arsenide is expected to be connected with the process of arsenic impoverishment of the material.
N.Kekelidze, R.Charmakadze, R.Alania, D.Kakushadze, A.Berdzenishvili, Z.Tkeshelashvili
Investigation of the Electroluminescent Properties of Gallium Nitride Structures Implanted with Zn and Mg Ions
Presented by Corr. Member of the Academy T.Sanadze, August 6, 1996
ABSTRACT. Epitaxial GaN layers which always contain a great number of donor type defects were strongly compensated by doping in the growth process with further Zn and Mg ion implantation.
Electroluminescent structures with new and important properties were obtained. Intensive light emission was produced in practically entire range of visible and near-ultraviolet light spectrum. The emission colour changes with variation in the degree of doping and the voltage applied to the structure. "Oscillation" of the current-voltage characteristic not observed in other structures was identified. Strong polarization of the short-wave band with a maximum at 3.29eV was found.
A.Rukhadze, M.Chogovadze, L.Chachkhiani
Radiative Instability in Ideal Liquid with the Tangential Discontinuity
Presented by Corr. Member of the Academy N. Tsintsadze, June 27, 1996
ABSTRACT. The nature of the tangential discontinuity in the ideal liquid has been investigated. New type of instability - radiative instability stipulated by motion of a light liquid above the surface of heavy one has been discovered. This radiative instability should be considered as stimulated Cherenkov sound wave radiation from discontinuity surface.
Application of Theory of Graphs in Systemic-Structural Analysis of Educational Material
Presented by Academician G.Tsintsadze, June 17, 1996
ABSTRACT. The method of systemic analysis is considered. The mathematical criterion of efficiency of this method, relative information, is devised in terms of graphs theory.
Algebraic Investigation of Fisher’s Reaction
Presented by Corr. Member of the Academy L.M.Khananashvili, June 29, 1995
Abstract. The algebraic method of recording of organic molecules and reactions in terms of ANB - matrices is presented. Their diagonal elements are the atomic numbers of chemical elements, whereas nondiagonal ones - the multipli-cities of chemical bonds. Algebraic investigation of Fisher’s reaction is given in terms of this method.
M.Kezherashvili, N.Lekishvili, L.Asatiani, B.Butskhrikidze, L.Kipiani
The Silicon-Containing New Bisazodyes
Presented by Corr. Member of the Academy L.Khananashvili, May 20, 1996
ABSTRACT. The silicon-containing new bisazodyes were synthesized and studied. Some of the synthesized dyes were investigated for dyeing natural silk fibres. It was established that the colours of obtained dyes on natural silk is characterized by brightness and high fastness to different treatment.
N.Kobakhidze, Z.Machaidze, M.Gverdtsiteli
Algebraic Investigation of Thioethers
Presented by Corr. Member of the Academy L.Khananashvili, June 12, 1996
ABSTRACT. Algebraic investigation of thioethers was carried out in terms of ANB - matrices method. Their diagonal elements represent atomic numbers of chemical elements, whereas nondiagonal ones - the multiplicities of chemical bonds.
M.Sturua, T.Vephkhvadze, R.Ziaev, D.Tsakadze, Sh.Samsonia, A.Abdusamatov
Alkaloids of Magnolia (Magnolia obovata Thunb)
Presented by Corr. Member of the Academy D.Ugrekhelidze, July 21, 1996
ABSTRACT. From magnolia (Magnolia obovata Thunb) gathered in Batumi Georgia) well-known alkaloids remerin, anonain, liriodenin and lanuginozin were isolated and identified. By modern methods the structure of fifth alkaloid was ascertained - N-oxide of isolaurelin, which is isolated from plants for the first time.
K.Amirkhanashvili, L.Rapoport, Academician T.Andronikashvili
Studies of Sorbent-Sorbate Adsorption Interaction
on Capillary Chromatography
Presented September 2, 1996
ABSTRACT. A review is made on the capillary columns used in gas-liquid chromatographic investigation. The preference utilization of quartz capillary columns is shown.
Academician I.Gamkrelidze, D.Shengelia, G.Chichinadze
Macera Nappe in the Crystalline Core of the Greater Caucasus and its Geological Significance
Presented August 14, 1996
ABSTRACT. It is indicated that in the Elbrus subzone of the Main Range zone of the Greater Caucasus are preserved separate fragments of once indivisible Macera nappe which was overthrusted from south (from the Pass subzone) during the sudetic phase. Due to this conclusion division of metamorphic complexes of the Greater Caucasus into series, their interrelations and questions of its age succession is considered in a new light.
Method of Compact Limestones Treatment for Micropaleontological Investigation
Presented by Academician I.Gamkrelidze, June 06, 1996
ABSTRACT. A new method is applied for separation of microforaminifers from the Upper Cretaceous compact limestones, glauconitic sandstones and clay and marlaceous limestones of the Gagra-Djava zone.
New Data on the Formation of Microcline Granites of Dzirula Salient
Presented by Corr. Member of the Academy G.Zaridze July 8, 1996
ABSTRACT. Considering structure of Dzirula salient characteristics of binary granites formation of inner Massif of the Caucasus it is assumed that during Tournasion-early-middle Visean period the rocks of sialic profile (the substratum of microcline granitoids) were overthrust by allochthons of femic profile. The thickening of the crust caused the change in PT gradient which stimulated the process of selective melting in sialic rocks and formation of S-type granites. The trace of tectonic transport of allochton was closed and thus erased by granitoid magma activity (late Visean-Bashkirian) in major areas.
The Way of Boundary Effect Detection at Conductor Setting
Presented by Academician T.Loladze, June 27, 1996
ABSTRACT. An original way of detection of thermoelectromotive force originated on the border of solid and liquid phases of current conducting material is proposed. A simple and accessible scheme is worked out for registration of the mentioned effect.
Practical application of the method opens possibilities of quantitative estimation of boundary effect of conductors, fixing their place in thermoelectric metal series and of consecutive control of thermal processes in the zone of unipolar current pulse resistance welding and of crystallization process control.
Nonstationary Process Control in Supply Pipelines by the Finite Control Method
Presented by Academician G.Chogovadze, June 22, 1996.
ABSTRACT. In the paper problem of pressure control at the beginning and at the end of supply pipeline is considered. The method of finite control is used. On the basis of differential equations describing the nonstationary operation regime in the pipeline and using optimal control theory, the control functions are obtained. They allow to reduce pressure oscillations to a minimum in the pipeline at transfer from one stationary regime to another.
To the Applied Programmes Packet of DC Traction Machines Automation Design
Presented by Corr. Member of the Academy I.Jebashvili, July 4, 1996
ABSTRACT. We report on the necessity of d.c traction electric machines automation design complex approach. The work suggests a packet of applied programmes and determines the application of each programme.
Automatic System for Watching Movement of Stormclouds
Presented by Academician M.Salukvadze, June 21, 1996
ABSTRACT. Proposed system for watching movement of stormclouds together with the other methods of meteorological researches enable us to be prepared long before the storm and increase considerably the efficiency of hailprevention system.
R.Akhalkatsi, T.Bolotashvili, R.Solomonia, Corr. Member of the Academy N.Aleksidze
Identification of Concanavalin A Binding Proteins of Rat Brain Cellular Nuclei By Gel Electrophoresis and Blotting
Presented March 5, 1996
Abstract. The existence of concanavalin A-binding proteins has been discovered in rat brain cellular nuclei PBS soluble (180, 150, 125 and 63 kD) and triton X-100 extractable fractions (180, 175, 150, 125, 120, 107, 95, 70, 63, 57 kD) by the method of gel electrophoresis and blotting. A hypothesis is presented, that rat brain nuclear membrane pores modulator is concanavalin A lectin like protein.
Purification and Partial Characterization of Invertase from Fungal Fusant
Presented by Academician G.Kvesitadze, July 21, 1996
ABSTRACT. Invertase from fungal fusant was purified by ammonium sulfate fractionation, DEAE-cellulose chromatography and Sephadex G-100 gel filtration. The purified enzyme appeared homogeneous on disc electrophoresis. Its molecular weight was estimated to be 76000 by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and 75000 - by gel filtration. The carbohydrate content of the enzyme equals to 25%. The optimum activity of enzyme was observed at about 50° C and it was stable up to 55° C. Although the enzyme was stable between the pH 4.0 and 5.5 the optimum pH for its activity was about 4.6.
I.Chkhikvishvili, A.Shalashvili, G.Papunidze, I.Targamadze, T.Meladze
Polymethoxylated Flavones and Flavanones of Citrus Flowers
Presented by Corr. Member of the Academy N.Nutsubidze, June 13, 1996
Abstract. Polymethoxylated flavones and flavanones have been investigated in Citrus flowers. It was revealed that the flowers of orange, mandarin, lemon and grapefruit contain polymethoxylated flavones: 5-OH-6, 7, 8, 3', 4' - pentamethoxyflavone, tangeretin, tetra-O-methylscutelarein, 3, 5, 6, 7, 8, 3', 4' - heptamethoxyflavone, nobiletin, sinensetin and flavanones: didimin, poncirin, hesperedin, neohesperedin, narirutin, naringin, eriocitrin and neoeriocitrin.
Academician K.Nadareishvili, H.Grebenchuk
Questions of Linear Forecasting in Ecology and their Decision by Methods of Decomposition on Double Orthogonal Systems of Functions
Presented October 1, 1996
ABSTRACT. The paper furnishes for linear forecasting and retrospective analysis of the state of technogenic fields at the decision of problems of ecodynamics.
Shown, that, an unsoluble situation, as it were, when the forecast of parameters of technogenic fields cannot give reliable results, the opportunity of construction of the mathematical theory, allowing at certain restrictions of the character of temporary series to build the correct forecasts and to make retrospective analysis. This opportunity is associated with the methods of decomposition of finite functions on double orthogonal basis. Thus, if the basis is orthogonal simultaneously on a final piece and on the whole axis, it is possible to build estimations in past and in future with any beforehand given error.
G.Gogichadze, T.Dolidze, T.Gogichadze
Possible Reason for Tumour Cells Appearance in Hemolytic Anemias of Different Origin
Presented by Academician N.Javakhishvili, June 10, 1996
ABSTRACT. At hemolytic anemias of different genesis side by side with hemolysis process of somatic cells fusion may take place with formation of tumour cell. Some agents may induce both fusion process and destructive effects in somatic cells by induction on plasma membranes pores of different size.
Clinical Significance of Ictal EEG Patterns in Patients with Mesial Temporal Lobe Epilepsy
Presented by Corr. Member of the Academy V.Mosidse, August 22, 1996
Abstract. We analyzed lateralization accuracy and reliability of EEG seizure patterns in 118 seizures in 24 patients with mesial temporal lobe epilepsy as documented by hippocampal atrophy on MRI and unitemporal spikes on interictal EEG. Two blinded electroencephalographers independently determined morphology, location and time course of ictal EEG changes. A lateralization was possible in 88.4 to 92.0% of seizures. Lateralization always corresponded to the side of the interictal spike focus and of hippocampal atrophy on MRL. Lateralization was never incorrect. Lateralization at seizure onset was possible in only 30.4 to 33.9% of seizures. A later significant pattern which allowed lateralization occured in 83.8 to 93.6% of seizures with a non-lateralized onset and started 12.8 to 13.2 seconds after EEG seizure onset. Interobserver reliability for lateralization was excellent with a kappa value of 0.85. Concerning the individual patients, in 19-20 patients all seizures were lateralized, in 4 patients a mixture of lateralized and non-lateralized seizures occured and in one patient no seizure was lateralized.
N.Okujava,V.Bakhutashvili (Corr.Member of Academy), B.Korsantia
THE PHAGOCYTOSIS SYSTEM IN PATIENTS WITH DESTRUCTIVE ULMONARY TURERCULOSIS AND THE EFFECTIVENESS OF PLAFERON IN STIMULATING OF PHACOGYTIG ACTIVITY
ABSTRACT. In patiente with destructive pulmonary tuberculosis the phogocytosis system was studied.Significant depression of activity of phagocytosis system in those patients was determined. The most pronounced shifts of phagocytie indices was noted in patients with fibro-cavitary tuberculosis. The rise of absorption and intracellular digestion capacity of neutrophils correlated with the severity of tuberculous process. The absente of dynamics of phagocytic indices was a significant practical value and pointed to the necessity of the use of immunomodulators along with antituberculous chemotherapy.
Plaferon caused the positive dynamics of phagocytic indices.
HLA - Markers During Glaucoma and Cataract Diseases in Georgian Population
Presented by Corr. Member of the Academy N.Tatishvili, April 11, 1996
Abstract. Persons of Georgian nationality were examined: 69 patients having glaucoma disease and 73 patients with cataract.
It was determined that the genetic markers of predisposition to the glaucoma disease are antigenes A1; A10; B12; gaplotipes A1-B35; A1-B5; A10-B35; B5-B12. Antigenes of cataract are HLA A3; B15; B40 and gaplotipes A11-B15; A2-B40.
Spore-Pollen Complexes of Chaudian Deposits Bearing the Decidua of Colchis Redwood Forest
Presented by Academecian L.Gabunia 19.03.1996
ABSTRACT. Recent spectra of layers bearing the decidua of redwood forest of Colchida are presented. Data of palynological analysis as well as paleocarpological testify Colchida's antiquity as a refugium, its connection with tropical and subtropical regions in geological past and ultimate delayed rate of its organic world transformation through anthropogene.
history of science
L.Razmadze, Corr. Member of the Academy D.Jokhadze
Darwin's Evolutionary Theory and "Kvali"
Presented August 29, 1996
ABSTRACT. The Georgian weakly political, scientific and literary newspaper "Kvali" (1893 - 1904) was one of the printed organs in Georgia publishing the most complete scientific articles on Darvin's evolutionary theory. The material described in this paper gives chance to the wide sections of population of Georgia to know about new achievements in different sciences as well as those of biology through newspapers.
History of Science
Treatment of Wounds in Georgian Traditional Medicine and New Aspects of Research in History of Medicine
Presented by Corr. Member of the Academy V.Mosidze, October 10, 1996
ABSTRACT. Treatment of wounds in Georgian traditional medicine are discussed in the work. The material of about 500 manuscripts and more than 40 expeditions was analysed.
The material is processed by computer. A special computer program was created and criteria and coefficient of reliability were determined. The latter is the basis for utilization/prohibition of traditional remedies. Strategy and policy of utilization of traditional remedies have been determined.
History of Science
Corr. Member of the Academy T.Sanadze
To the 30th Anniversary of Discrete Saturation Pulsed EPR Spectroscopy
Presented August 6, 1996
ABSTRACT. History of discovery and development of the discrete saturation pulsed spectroscopy and examples of its application are presented. Invited lecture on the XXVII Anniversary Congress AMPERE, Kazan, 1994 is offered.