### Scientific projects

**Scientific projects:**

**Chiziqsiz tizimlarni matematik modellashtirish**

**The title of the scientific project:** OT-F4-85 « Development of nonlinear mathematical models and effective computational algorithms for the study of modern problems of biology and ecology»

**Project participants (full name, academic degree, position):**

Takhirov J., DSc, professor, head of department

Turaev R., Ph.D., associate professor, senior researcher

Rasulov M. S., senior researcher

**Brief description of the project: **

The aim of the project is to build new non-linear mathematical models and search for the most effective numerical methods for the study of structure formation processes.

**Dynamical systems and its applications**

**OT-F4-84** Discrete-numerical method for polynomial systems and its application to the modeling of cyclic and controlled processes (2017-2020 yy.)

**Head of the Project: academician А.Azamov**

(Goal: Development of new research methods for dynamic systems, including modeling cyclic processes.)

**ЁФА-Атех-2018-182** Study of mathematical models of cyclic chemical reactions of the Brusselator type using the methods of the theory of dynamic systems (2018-2019 yy.)

**Head of the Project: PhD, О.S.Аkhmedov**

(Goal: To prove the existence of a closed trajectory in the three-dimensional model of the Brusselator by DN-tracking; develop an updated model of the Brusselator in dimension 4 and, if possible, in dimension 5; creating a software package for the study of mathematical models of the Brusselator in dimensions 3-5)

**Ehtimollar nazariyasi Grantlar**

1. **Ф****4-****ФА****-****Ф009** “Approximation problems of probability distribution and their applications in mathematical statistics”

**Project manager O.Sh. Sharipov**

2. **ОТ****-****Ф****4-83** "Limit theorems for probability distributions and statistical analysis of functional data."

**Project Manager O.Sh. Sharipov**

__Medical and Biological Informatics__

**Scientific projects**: FA-Atech-2018-4 "Development of virtual methods of molecular optimization in the creation of new drugs: deep machine learning and the interpretability of predictive models of biological activity"

**Project manager:** Professor Adilova F.T.

**The main goal** of this project is to develop algorithms, and software for solving the two above problems, to increase the accuracy of the model and its interpretability.

**Дифференциальные уравнения**

**Scientific projects: **OT-F4-88 “Investigation of direct and inverse problems for the second and higher order mixed type equations”

**Head of the project:** Professor Ashurov.R

(Studying of unique solvability of direct and inverse problems for mixed type and fractional differential equations).

**Хисоблаш математикаси, grantlar**

1. FA-F1-F004 + F014 “Theories of cubature formulas, splines and numerical modeling of the processes of forecasting the real state and ensuring the safety of critical structures" (2007-2011). (Project manager: Prof. H.M. Shadimetov)

2. F4-FA-F013 “Nonassociative and operator algebras, dynamical systems and their applications in statistical physics and population biology" (2012-2016). (Project Leader: academician Sh.A. Ayupov)

3. OT-F4-86 "Development of optimal methods for the approximate solution of differential and integral equations in Hilbert spaces" (2017-2020). (Project Leader: Dr. of Physics and Mathematics A.A.R. Hayotov)

The purpose of this project is to conduct research on the following topical problems of computational mathematics, which are closely related to each other, the directions: development of optimal difference schemes for the approximate solution of linear ordinary differential equations or their systems; development of methods for optimal quadrature formulas for the approximate solution of linear integral equations; to construct optimal quadrature and cubature formulas for the approximate solution of the Fourier coefficients in different Hilbert spaces; in spaces of differentiable functions, construct optimal interpolation formulas and extremal splines; in Hilbert spaces, construct optimal formulas for the numerical integration of various types of singular integrals.