Foreword

Abstract

The present volume of the Journal of Physics: Conference Series represents contributions from participants of the International Conference ’’Algebra, Analysis and Quantum Probability” (Tashkent, 10-12 September 2015) organized by the Institute of Mathematics and the Faculty of Mechanics and Mathematics of the National University of Uzbekistan (NUUz) in collaboration with University Putra Malaysia (UPM) and International Islamic University Malaysia (IIUM).The Conference is dedicated to the 100th anniversary of one of the outstanding scientists of Uzbekistan, the founder of the Tashkent scientific school of functional analysis, who has initiated the investigations on operator algebras and quantum probability theory in Uzbekistan - Professor Tashmukhamed Alievich Sarymsakov (10 Sept. 1915 - 19 Dec. 1995). Among the mathematical community Professor T. A. Sarymsakov is widely known for his research in the fields of probability theory, functional analysis, general topology and their applications. A gifted teacher and skilful organizer he had a beneficial effect on the development of many new mathematicians in Uzbekistan. Professor T.A. Sarymsakov, an outstanding organizer of science in Uzbekistan, was one of the founders of the Uzbekistan Academy of Sciences, where from 1943 he was a member and Vice President, and from 1946 to 1952 president of the Academy of Sciences. Professor Sarymsakov successfully combined his fruitful scientific research with teaching and social work. During 1943-1944, 1952-1958 and 1971-1983 he was the rector of Tashkent State University (now the National University of Uzbekistan). He has made a significant contribution to the development of higher education in Uzbekistan, serving from 1959 to 1960 as the Chairman of the State Committee, and from 1960 to 1971 as the Minister of Higher and Secondary Special Education of Uzbekistan.The main objective of the scientific conference was to facilitate communication and collaboration between mathematicians from different countries and it was focused on contemporary issues in the theory of operator algebras and non-commutative integration, structure theory of non-associative algebras and their applications in the theory of dynamical systems and quantum probability.The Conference venue was the Mechanics and Mathematics Faculty of the National University of Uzbekistan and Institute of Mathematics.The program of conference included plenary and invited lectures (40 minutes), short communications (15 minutes) given by more than 100 participants, including invited speakers from Australia, Brazil, France, Germany, Italy, Malaysia, Russia, Spain, USA and Uzbekistan in the following main sections of the conference:Operator algebras and non-commutative integration;Structure theory of non-associative algebras;Quadratic operators and quantum probability;Theory of dynamical systems and statistical physics.We would like to thank the Invited Speakers for their significant contributions to the conference. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to our sponsors for their financial support.Guest Editors:Shavkat Ayupov, Vladimir Chilin, Nasir Ganikhodjaev, Farrukh Mukhamedov, Isamiddin Rakhimov