Mathematics

The Department of Mathematics

One of the goals of the Department of Mathematics is to benefit from the faculty members’ fields of study in line with the needs of the scientific community of the country with the purpose of meeting these needs. Moreover, the Department of Mathematics takes strides towards carrying out scientific projects commissioned by different institutions and organizations as an economic source of income for the university. The ultimate goal of this group can be defined as to operationalizing mathematics and to carry out projects to solve the gaps of the scientific community.

The Algebra working group works in the specialized fields of Semigroup theory, Module theory, Language and Automata theory, Cryptography and Logic, Combinations and Graphs.

In addition to proposing and studying Pure Mathematics topics in Algebra (particularly the theory of semigroups and their representations) and its relationship with other branches of mathematics, a number of operational plans are pursued in the 10-year horizon of the group:

The Application of Algebra in oil and agriculture industries

The Application of Algebra in this area aims at finding suitable models for groups of oil wells or oil fields so that their production behavior can be assessed over time. This is carried out using Algebraic polynomials, Grubner bases and modeling for finite sets. The method can also be used for other industrial and agricultural products.

Modeling Persian grammar using Machine and Language theory in algebra

The formal language and machine theory is a branch of Mathematics that studies languages and their algorithms. Although works have been done in modeling other languages, Persian has remained underexplored. Therefore, Modeling Persian grammar is one of the goals pursued by the group of Algebra.

Application of Algebraic Automata in describing natural selection phenomena in genetics and biology

Biological natural selection phenomena can be modeled using language and machine theory. The aim of this plan is the investigation and modelling of the development of such biological phenomena as cancer cells or other pathogens using. To achieve this goal, two-dimensional Automata is applied as an effective method in finding treatments for such diseases.

Capabilities and personal programs to empower the community in specialized fields

Considering the obvious importance of pure science, particularly mathematics, in the development of other sciences and technologies, its application will undeniably lead to the rapid and comprehensive growth of society. Therefore, in addition to carrying out scientific research and expanding the boarders of knowledge, Pure Mathematics can also be used as an important tool in applied sciences as well as in improving the society’s level of mathematical knowledge. Thus, regarding the historical, cultural, social and economic situation of the southern region of Fars and the city of Jahrom, the following areas can be prioritized by the Department of Mathematics:

Economic and military

- The application of mathematics as a major tool in data encryption and decryption in military and telecommunications sciences;

- Modeling agricultural, industrial and service products in the form of algebraic polynomials and finding methods of further development and elimination of errors to compare other regions and increasing productivity (these methods are frequently used in other countries in such areas as agriculture and industries as oil and gas extraction, power plants, etc.).

cultural and educational

- Training talented human resources for transferring mathematical science to the future generations of the region;

- Fulfilling the scientific needs of other disciplines through offering service courses and mathematical related subjects in the universities of the region as well as providing the mathematical foundations required in their research;

- Training, correcting, strengthening and updating the school teachers’ scientific information and educational skills in the region;

- Offering special and high level training, such as national and international math Olympiads related subjects, to the elite students of the city.

- Training preschool children in order to develop their creativity and to establish the foundations of mathematical thinking for elevating human resources for future generations.

Promoting the elimination of the society's fear from mathematics, reconciling with it and strengthening the scientific spirit of the society.

Considering the establishment of the Master degree of Mathematical Analysis at Jahrom University, and regarding the recruitment of two faculty members specialized in the areas of Harmonic Analysis, Banach Algebras, Operator Theory and particularly in frame theory, as a recent interdisciplinary branch in Mathematics, there is the possibility of further research in this field of study in the working group of Mathematical Analysis. Thus far, a number of postgraduate students have also carried out their research in this new area.

In line with the needs of the society, the working group of Optimization intend to accomplish the following issues:

Proposing a mathematical model for the prevention of the progression of bone metastasis using optimal control;
Investigating certain methods of optimal control in angiogenesis of tumors;
Optimizing certain parameters with the aim of reducing latency of pedestrians and vehicles in traffic networks;
Offering strategies for optimal control of HIV infection by considering drug resistance;
Carrying out a study on the economic applications of the theory of optimal control;
Optimal controlling of tumor cell growth in the treatment of cancer with drugs;
Exerting optimal energy control by minimizing fatigue in vertical axis wind turbines;
Locating main mobile stations with the purpose of strengthening them against threats using two-level models;
Navigating and routing based on service quality in smart power networks equipped with software-driven network infrastructure;
Developing methods for solving a range of optimal control problems and applying it in tumor chemotherapy.

Considering the faculty members’ areas of interest, knowledge and capabilities, the long-term goals and issues to be achieved by the faculty members of the Department of Mathematics of Jahrom University can be summarized as below:

Proposing a mathematical model for the prevention of the progression of bone metastasis using optimal control;
Investigating certain methods of optimal control in angiogenesis of tumors;
Optimizing certain parameters with the aim of reducing latency of pedestrians and vehicles in traffic networks;
Offering strategies for optimal control of HIV infection by considering drug resistance;
Carrying out a study on the economic applications of the theory of optimal control;
Optimal controlling of tumor cell growth in the treatment of cancer with drugs;
Exerting optimal energy control by minimizing fatigue in vertical axis wind turbines;
Locating main mobile stations with the purpose of strengthening them against threats using two-level models;
Navigating and routing based on service quality in smart power networks equipped with software-driven network infrastructure;
Developing methods for solving a range of optimal control problems and applying it in tumor chemotherapy;
Creating a database of digital and printed specialized books and articles in the area of mathematics, with a particular focus on the faculty members’ areas of interest;
Establishing different working groups with the purpose of carrying out joint studies between the specialized fields;
Establishing a working group with the purpose of identifying and carrying out joint scientific and research activities with the other majors and disciplines at the university;
Establishing a working group with the purpose of identifying and carrying out research and executive plans related to the industry and services sectors (projects in optimization and operations research, cryptography, telecommunications, network security, etc.);
Conducting fundamental mathematical research in the areas of new technologies (e.g. dynamic systems, fuzzy and new logics, cryptography and decoding, chaotic and fractal systems, etc.);
Establishing an educational and research institution of mathematics under the supervision of the university with the purpose of identifying and raising talented students interested in mathematics as well as reinforcing the educational and research basics of other students;
Organizing regular seminars in the department to both familiarize and share various research topics and projects carried out by the faculty members as well as regularly inviting experts from other universities;
Setting up a specialized laboratory of mathematics for the purpose of teaching and performing computational tasks, as well as performing complex calculations in research projects of other disciplines;
Recruiting new members with the required specialties related to areas of the current members with the purpose of reinforcing and completing the educational and research activities of the group;
Rewriting physical and engineering models more accurately with the help of the two sciences of fuzzy numbers and derivation of fractional order with the aim of making them more compatible with the real world as well as solving the problems;
Proposing a mathematical model, designing CT scan as well as radiography devices and optimizing them through the application of inverse problems in partial differential equations;
Proposing models for the movement and behavior of air currents through differential equations and chaotic systems.