Rajabova Lutfiya Nusratovna – Head of the Department of Mathematical Analysis and Theory of Functions of the Faculty of Mechanics and Mathematics of the Tajik National University, Doctor of Physical and Mathematical Sciences, Professor.

*About the activities
of the department*

The department was established in 1953, during the years of its existence, it was led by experienced teachers and experienced scientists who made their valuable contribution to the development of mathematical science in the country and the world. Until 1973, Professor M.A. Subkhankulov, associate Professor G.B. Boboev, S.N. M.M. Izrailova took over the leadership of the department. From 1977 to January 2013, the department was headed by Academician of the National Academy of Sciences of the Republic of Tajikistan, Doctor of Physical and Mathematical Sciences, Professor Nusrat Rajabov. From 2013 to 2018 , Associate Professor Kadyrov, from 2018 to 2020, headed the department of Doctor of Physical and Mathematical Sciences, Professor Yusupov G. Since December 2020, Doctor of Physical and Mathematical Sciences, Professor Rajabova L.N. holds the position of head of the department.

The department mainly at the faculties of Mechanics, Mathematics and physics provides the educational process in the subjects of mathematical analysis, the theory of complex variable functions, additional chapters of modern analysis, special courses, etc. Over the past 45 years, more than 65 candidates and 7 doctors of sciences (M.Shabozov, A.Sattorov, R.Mustafakulov, Rajabova L.N. Shrumova V.F. Yusupov G. Shamsiddinov F.) have grown through postgraduate studies, sending teachers to scientific centers in Novosibirsk, Moscow, St. Petersburg, Voronezh, Samara and other cities, working and functioning in various spheres in the republic and abroad.

The main topic of the research works of the department is Academician AMIT, Professor N.R.Rajabov, who has been in charge since 1977, is “The Theory of Elliptic, Hyperbolic and Parabolic Equations”. Research work was conducted at the department until 1977 on the topic “Tauber’s theorems and their application”, which was headed by Professor M.A.Subkhankulov, and later M.M.Izrailova. During the lifetime of T.Ya.Barinova, research work was carried out on the topic “Mathematical Methods for Solving Problems of the Theory of Elasticity and Hydrodynamics”. In addition, until 1997, Professor M.Shabozov worked at the department on the topic “Theory of Splines” and Professor R. Mustafakulov conducted research on the topic “Differential Equations on aGeometric Graph” until 2007. Teachers of the department gave significant results on the topic “Differential equations with singular and super- singular coefficients”, “One-dimensional equations, Volterra-type integral equations with singular and super-singular marked boundary and inner kernels”. The results obtained on this topic have been published in world-famous publications: the Russian Academy of Sciences, Longman, World Scientfic, Kluwer, Academic Publishers, Springer (USA), the Academy of Sciences of the Republic of Tajikistan, the National University of Tajikistan, the University of Tehran, etc.

During the work of the department, its teachers have published more than 800 scientific articles, 18 monographs and several teaching aids. One of the monographs published in 1992 by the National State University of Tajikistan publishing house was translated into Persian in 1996 and into English in 1997. Three young teachers of the department vol G. Kadyrov, O. Melikov, B. Sohimkulov deserves a small grant from the World Federation of Germany (Switzerland), L.N. Rajabova is a laureate of the World Federation of Scientists Award (2011). In addition, the lecturer of the department, Professor N.Rajabov, received a scholarship from the German Academy of Sciences (DAAD, 1995), a scholarship from the scientific part of NATO (Hungarian Department of Science and Technology, 2003), a Fulbright scholarship (USA 2006), an international award “Stars of the Commonwealth”. According to the obtained scientific results, the season took place at three international congresses of mathematicians of the world (Warsaw 1983, Zurich 1994, Berlin 1998), at the first conferences of mathematicians of Asian countries (Hong Kong), at the Second ISSAC Congress (Japan 1999), the Third Congress of Mathematicians of European countries (Barcelona 2003), at the sixth ISSAC Congress(Ankara 2007), at the Seventh ISSAC Congress (London College), in London, 2009). Amata International Conference – 12 (Ankara, Turkey, 2012), many conferences, symposiums and international scientific schools located in Germany, Spain, Sweden, Belgium, France, China, Iran, Yugoslavia, Uzbekistan, Kazakhstan and other countries of the near and far abroad.

On the basis of the department, the International conference “Differential Equations and Their Application” (Dushanbe, October 25-28, 1998), in cooperation with other departments, the International conference “Differential and integral equations with unit coefficients” (Dushanbe, 2003), the International Scientific and Theoretical conference “Modern mathematical puzzles and their implementation”, dedicated to the 80-ththe anniversary of academician National Academy of Sciences of Tajikistan N. Rajabov (September 25-26, 2018), as well as the International Scientific and Practical conference “Modern Problems of Mathematics and its Applications” dedicated to the 20th anniversary of the development of exact, natural and mathematical sciences in cooperation with the Women’s Committee of the World Mathematical Union on October 20-21, 2022. Republican scientific conferences “Differential and integral equations” dedicated to the 60th anniversary of the foundation and the 70th anniversary of Academician of the Academy of Sciences of the Republic of Tajikistan Nusrat Rajabov (Dushanbe, September 25-26, 2008) and “Theory of differential and integral equations and their applications” dedicated to the 20th anniversary of Independence of the Republic of Tajikistan (Dushanbe, June 23-24, 2011).

On the initiative of the Department of Mathematical Analysis and Theory of Functions published “Collection of articles of higher educational institutions of the Ministry of Higher and Secondary Special Education of the Republic of Tajikistan”, “Differential and Integral Equations”, issue 1, Dushanbe 1977, issue 2, Dushanbe 1978, issue 3, Dushanbe 1980. The articles published in this collection in scientific journals in Russia, Germany, and the USA have received a well-deserved assessment by industry scientists. Several young scientists defended their PhD thesis on the basis of articles published in this collection. In different years, recognized Russian scientists, Doctor of Physical and Mathematical Sciences, Professor of St. Petersburg State University, have been teaching special courses and encouraging students to research – Petersburg M. M. Smirnov (1977), Head of the Department of Higher Mathematics of the Faculty of Applied Mathematics and Cybernetics of Lomonosov State University in Moscow (Russia) V.A.Iliin (1978), Doctor of Physical and Mathematical Sciences, Professor of the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences A. I. Yanushauskas (1980), Director of the Institute of Mathematics at the Free University Of West Berlin, Professor G. Beger (1982), Dean of the Faculty of Mathematics of Ganzhou State University (People’s Republic of China), Professor Lin Wei (1988) and other scientists were invited.

Now the department has 2 doctors of physical and mathematical sciences, Professor, academician AMIT N.Rajabov, Doctor of Physical and Mathematical Sciences, Professor L.N. Rajabova, 4 candidates of physical and mathematical sciences, associate professors-K.Boltaev, A.Mirzoev, Mirkalonova M., B.Shoimkulov, 2 candidates of sciences, senior lecturer –M. Khushvaqtzoda M.Senior teacher O.Melikov, associate professor Kadyrov D.A. works.

The Department of Mathematical Analysis and Theory of Functions makes a worthy contribution to the training of highly qualified personnel for faculties and mathematical departments of universities of Tajikistan and foreign countries. In the Government of the Republic of Tajikistan, Majlisi Namoyandagon Majlisi Oli of the Republic of Tajikistan, Faculty of Mathematics of Academician Bobojon Gafurov Khujand State University, M.Osimi Tajik Technical University, Nasiri Khusrav Kurgan-Tyubin State University, Department of Mathematics of Gasoline Faculty and Mining Engineering Faculty of Suez Canal University in Egypt, Syrian University, Kazakhstan Technical University The University of Shymkent, the Military College of Moscow and other educational and government institutions, teachers of the department, including Academician AMIT, Doctor of Physical and Mathematical Sciences, Professor M.Shabozov, A.Q.Jabirov, Doctor of Physical and Mathematical Sciences, Professor A.Rasulov, F.Shamsiddinov, A.Juraev, Candidate of Physical and Mathematical Sciences, Associate Professor A.Olimov, N.Dehkanbayev, K.Fozilov, A.Adib, A.Dzhelo, Or.Shishkina, V.Shevchuk, M.Akhmedov, Izzatulloev D. and others are working. Of these, A.Adib in Egypt, Mohamed Elzaid Abdel-Aab in Syria, or E. Shishkina is in Germany, V. Shevchuk works and works in Moscow.

Teachers of the Department of Mathematical Analysis and Theory of Functions are working on the development of textbooks and teaching aids for applicants and higher educational institutions of the republic. In particular, Associate Professor of the department A.Mirzoev, together with employees of other departments, conducts a test manual in mathematics “A Set of Test Problems in Mathematics” (Sino, DDMT, 2002, 2003, Dushanbe, 2005, 2006, 2008, 2010, 2012) developed and published for applicants. Students and postgraduates of the Faculty of Mechanics and Mathematics from N.Rajabov’s academic resources “Integral images and peripheral problems of some differential equations with single lines and unit levels”, parts 1-4 (Monday 1980, 1981, 1982, 1985) are used to study special courses. Students of the higher courses of the Faculty of Mechanics and Mathematics of the National State University of Tajikistan and students of the University of Tehran from the book of academician N.Rajabov uses “Introduction and Theory of Partial Differential Equations With Redundant Unit Coefficients” (Dushanbe, DDMT, 1992), translated into Persian in 1996 and into English in 1997.

Teachers of the department professors

A.S.Sattorov, R.M.Mustafakulov, associate professor H.M.Malikov, S.H.Mulloev, Dr.M.Kadyrov, G.A.Yusupov, B.Shoymkulov, F.S.Shrumova, associate professor S.Q.Zaripov wrote the following textbooks ” Analysis of a one–dimensional function ” (an educational tool for mathematical analysis), Parts 1, 2 – Dushanbe, 1990, Sinai Publishing House;

“True Numbers and the Limit of the Numerical Sequence”, – Dushanbe, 1991.-65 p. (SH.Mulloev, H.M.Malikov);

“Laboratory work of mathematical analysis” – Dushanbe, 1982, 68 p. (SH.Mulloev, H.M.Malikov);

“Practical mathematical analysis on the use of derivatives and integrals” – Dushanbe, 1982, 93 p. (A.S.Sattorov, H.S.Mulloev);

“Derivatives and Differentials of Vector Functions of a Vector Argument” – methodological guide for students of the mechanics and mathematics sector – Dushanbe, Sino 2003, 32 P. (R.M.Mustafakulov);

“Textbook on the course of the theory of complex variable functions” for students of the mechanics, mathematics and mechanical physics section. – Dushanbe, 2004, 104 P. (R.M.Mustafakulov);

“Textbook on basic elementary functions for students of the mechanics and mathematics sector” – Dushanbe, 2006, 88 p. (R.M.Mustafakulov);

“Methodical instructions for solving examples and problems from the theory of complex variable function” – typography DSRT, 2011, 245 P. (D.Yusupov, Abdulofizov G.);

“Manual to solve the problem of mathematical analysis”, textbooks, part 4, Dushanbe – 2013, LLC “Er – graf”, 83 p. (F.S.Shrumova, B.M.Shoymkulov, etc.);

“Mathematical analysis with the solution of examples and problems”, textbooks, part 1, typography DMT, 2013, 273 p.; part 2, “Sarmad-company”, 320 p.

Also in 2007, the monograph of Professor N.Rajabov “Volterra–type integral equations with single boundary and inner nuclei and their application”, – Dushanbe, 2007, publishing house”Devashtich”. – 222 p. it is published that on the basis of this monograph, a special course will be conducted for students of the 4th and 5th courses, starting from the 2008-2009 academic year.

In 2011, the English edition of this monograph “Volterra Type Integra Equations with boundary and interior fixed singularity and super – singularity rernels and their application” was published, LAPBERT Academic Publishing, Germany in the tag 282 pages, in which an additional chapter of 100 pages on integrated equations of type I.N.Vekua is connected with cores located on the border, a feature and a feature of oversupply.

Significant results have also been achieved on two-dimensional, three-dimensional and, in some cases, multidimensional Volterra-type integral equations with single and supersingular lines and regions. The results obtained in the monograph of Rajabov N. Rajabova L. “Introduction to the theory of multidimensional Volterra integral equations with marked singular and multidimensional kernels and their application” was published in the volume of 502 pages in 2012 in the edition of LAP LAMBERT Academic Publishing, Germany in Russian. In connection with the presented study, it became possible to study integral equations of the two-dimensional Volterra type with nuclei of various special properties, and a number of studies were conducted in this area, and significant results were published. Including in the monograph of Rajabova L.N. A. M.B. “Integral equations. A number of classes of special Volterra-type integral equations for unbounded spheres.”LAP LAMBERT Academic Publishing. 90 pages .. 2022, the scientific results of the study of Volterra-type double integral equations with weakness and specialization on the band are presented. In the monograph of Rajabov N. Rajabova L.N. Zaripov S.B. “Integral symmetric double Volterra type equations with singular and supernatural lines” – Saarbiicken : LAP LAMBERT, Academic Publishing 2019. – 108 p. integral symmetric two-dimensional Volterra type equations are studied.

An overridden system of three second-order equations consisting of an unknown function associated with singular and supersingular lines is also studied for the first time. The results obtained in the monograph of N. Rajabov, Mohamed Elzaid Abdel–Aab “redundant linear system of order two with singular and supersingular lines” was published in Russian in the size of 233 pages in 2011 in the edition of LAP LAMBERT Academic Publishing, Germany.

Monograph of Rajabov N. Rajabova L.N. Zaripov S. “Differential equations with unit coefficients”. LAP LAMBERT, Academic Publishing 2017, Saarbiicken 2017, 116 P. devoted to the still unexplored study of differential equations with unit coefficients. In the monograph of N. Rajabov “A top-secret system of linear integral singular equations, Voltaire-type super-signalizations of the third kind with logarithmic and supernatural kernels and their application” Dushanbe 2021c., 317p. for the first time, a redefined system of integral equations with special kernels is being studied.

Also, teachers of the department Yusupov G.A. and Langarshoev M.R. in 2010-2020, scientific research was conducted on the topic “The theory of better convergence”. Significant results have been obtained on this topic. The results obtained have been published in prestigious mathematical journals, scientific publications of the Russian Academy of Sciences, Siberian Mathematical Journal, Proceedings of the Institute of Mathematics and Mechanics of the Russian Academy of Sciences, Approximation Theory journal, News about the Long State University, Analysis Mathematica, reports of the Academy of Sciences of the Republic of Tajikistan, News of the Academy of Sciences of the Republic of Tajikistan in Tajik, Russian and English.

The curricula for the specialties are also periodically improved by the teachers of the department. The first programs from the disciplines of specialization “theory of complex variable functions” back in 1977 on special courses “peripheral problems of analytical functions”,”theory of generalized analytical functions”,”Tauber’s Theorem” were compiled by teachers N.Rajabov S.H.Mulloev M.A.Subkhonkulov, M.M.Israilova. Later curricula for reading special courses “theory of potentials for elliptic equations with single coefficients”, “simple differential equations on graphs”, “integral equations for Euler – Poisson – Darboux equations with one and two single lines”,”theory of splines”, “Volterra double-type integral equations with special lines” instructors N.Rajabov, R.Mustafakulov, A.S.Sattorov, M.Shakhbozov, L.N. Rajabova and others were compiled.

In recent years, teachers of the department have compiled special course programs on the topics “general hyperbolic equations with two single lines”, “integral one-dimensional Voltaire-type equations with single nuclei marked with an inscription”, “differential equations in geometric graphics”. Weekly scientific and theoretical seminar of the department “complex analysis and its application to differential equations”, since 1977, under the guidance of Professor N.Rajabov, has been working regularly. The share of this seminar is very large for the education and development of highly qualified personnel, candidates and doctors of sciences for higher educational institutions of the Republic of Tajikistan and beyond. Today, teachers of the department are making every effort to improve the quality of education and upbringing, scientific research and training of highly qualified specialists in the field of mathematics for the needs of the country and beyond