Doctor of Physics (Ph.d), 1995, Georgian Technical University, Tbilisi Georgia. Dissertation: The Crystallographic Theory of Twinning and Computer Simulation. Candidate of Sciences, 1977, GTU.Thesis: Structural Transformations During Ordering in Cu-Pd and Fe-Pd Alloys Institution: GIXI ingenierie informatique, Paris, France. Software course.06.1981 – 07 1981, Certificate (Attestation de stage). Institution: Institute of Improvement of Skill of Information Workers (Specialty: International Systems of Scientific Information), Moscow, Russia.09.1979-10 1979, Certificate. Institution: Graduate student at the Institute of Physics of Metals and Materials Science, (CNII Ch.M.), Moscow, Russia.09.1971 – 06.1972. Institution: Georgian Technical University, Tbilisi 09 1967 – 07 1972, Diploma of Engineer Physicist. 1996 (current): Professor of Physics at the Georgian Technical University. Research: structural phase transformations in solid state, crystallography and computer simulation of diffraction processes, Lecturer 1980-1982: Senior research fellow at the Radiochemical Laboratory of the GTU. 1974-1980: Junior research fellow at the Radiochemical Laboratory of the GTU. 1972-1974: Assistant at the Department of General Physics, GTU. Summer 1977: Sabbatical at the Institute of Physics and Materials Science (CNII Ch.M.), Moscow, Russia. Publications: 99, in Russian and in English. (incl. 2 guide books for students on X-ray characterizations and electron diffraction, in Georgian). Professional societies: Georgian Physical Society, Georgian Academy of Ecology, Member of British Computer Society, Incorporated in the World Directory of Crystallographers For practical application of the developed approach one may simply follow a hypothesis that in compound twins the shear plane P corresponding to the plane of twinning K1 contains not only the normal m to K1, as it follows from the definition of the plane P, but also one of the conventional basis vectors n = ,  or  of the lattice, as a consequence of the proposed approach. Generally, one of the three calculated values of 1 (with rational indices) coincides with the experimentally determined one, with the accuracy of sign. Sure, for cubic crystals all the three values are operative because of symmetry. Here are some calculated examples in the table below. Notes: —- experimental data not available to the author * morphological system 1) exact value, (1 0.06 0). 2) exact value, (1 -3.991 0) The crystallographic data are taken from: N.V. Klassen-Neklyudova: Mechanical Twinning of Crystals. Plenum Press, NY 1964. Kelly, A., Groves. G.W.: Crystallography and Crystal Defects. Longman, London 1970. Christian, J.W.: The Theory of Transformations in Metals and Alloys. Pergamon Press, Oxford 2002. Source.