## Chair of Computational Algebra and Discrete Mathematics

# The computing algebra and discrete mathematics chair

**The head-professor, Doctor of phys.-maths Science – Varbanets Pavel Dmytrievytch**

## Professors staff:

- Balandina N.M – senior teacher
- Prosyanuk N.S. – senior teacher, candidate of phys.-maths science
- Gurova T.V. – senior teacher
- Savastru O.V. – assistent
- Gunyaviy O.A. – senior teacher, candidate of phys.-maths science
- Simonova I.G. – associated professor, candidate of phys.-maths science
- Belozerov G.S. – associated professor, candidate of phys.-maths science
- Fedorovskiy S.V. – associated professor, candidate of phys.-maths science
- Belyayev V.M. –assistent
- Yakimova N.A. – asossiated profesor, the candidate of tech.science
- Kovaltchyk F.B. – associated professor, candidate of phys.-maths science

## The opening date of the chair:

After separation of algebra and geometry chairs (1964), the chair of “Algebra and Numbers Theory” appeared, which is now renamed in “Computing Algebra and Descrete Maths” chair from 2002.

The chair-head: Doctor of phys.-maths science, professor, Varbanets Pavel Dmitrievytch,1978.

## The number of professors:

Regular lecturers – 10, including doctors of phys.-maths science, professor – 1 person, candidates of science, associated professors – 7. Besides, the elementary process is provided by 1 teacher-pluralize.

## Scientific Work:

### The following subjects are introduced for 1991-2004 period of time:

- Information and encoding theory;
- Cryptology;
- Linear algebra end analytic geometry (for economists);
- Linear algebra and theory of numbers (for information technology faculty);
- Theory of graphs (for the students of physical faculty);
- Field theory (for masters of mathematics faculty );
- Economical statistics (for the speciality “Mathematical economics”)
- Algorithms end formal tramsformations;
- Theory of algorithms;
- Algebraical algorithmic;
- Asymptotic problems of numbers theory;
- Arithmetic codes;
- Arithmetic and algebraical cryptology elements;
- Factor analysis;
- Mathematical methods of prediction in economics;
- Proceedings (cryptological authentication methods;
- New summability methods of weighted trigonometric sums;
- Economical models
- Diophantine equations with quadratic forms;

## The following courses of lectures and methodical investigations:

- Varbanets P.D., Kovaltchik F.B., Theory of numbers (1996)
- Dementiyeva V.U., Algebra (course of lectures) (1999)
- Varbanets P.D., Kovaltchik F.B., Theory of groups (course of lectures)
- Bulitko V.K., Discrete mathematics (1999)
- Kovaltchik F.B., Theory of numbers (course of lectures) (2001)
- Yakimova N.A., Activity analysis (Kharkiv, 2003)
- Yakimova N.A., Course of lectures on logistics (2004)

Instructional guidelines on algebra courses, algebra and discrete mathematics teaching methodology, etc. (5 units in all)

## Personnel training:

### Doctoral thesises have been defended by (2):

- Bulitko V.K. Subturing revises of limited complication (1993)
- Varbanets P.D., Asymptotic problems of numbers theory (1995).

### Candidate dissertations (7):

- Zarzhitskiy P.A., (Poland), About one of multiplicative function classes. (01.01.06), (1991).
- Belozerov K.S., Asymptotic formulas for quantity of some diophantine equations solutions (01.01.06), (1992).
- Zhanbyrbayeva U.B., (Kazakhstan), Asymptotic problems of numbers theory in the sectorial zones (01.01.06), (1993).
- Fedorovskiy S.V., Division of numbers, which are presented by special forms (01.01.01 , 01.01.06), (1994).
- Yakimova N.A., Predicative models of logical spaces in the knowledge represantation system (01.05.02), (1999).
- Gunyaviy O.A., Triginometric sums end their utilisation, (01.01..06), (2004).
- Prosyanuk N.S., Statistic problems of numbers, (01.01.06), (2004).

## Scientific work:

### Concepts of scientific researches:

- Recursive function theory
- Asymptotic problems of numbers theory

### Among them:

- Classification of subturing revises.
- Criterions of plentitude for different types of revises.
- Criterions of plentitude for maximal plurals in terms of complication plentitude.
- m-composity with delimitation on a raised function.
- Multilevel delimitations complexity of m-composity.
- Extended problem of divisors Z by Z[ i ].
- Devision of natural numbers with divisors in the classes of excesses.
- Division without quadratic gaussian numbers.
- Asymptotic formulas for integrated functions of natural numbers figuring quantity with quadratic formulas in arithmetic progression.
- Valuations of trigonometric sums on multitypes over the high
- Valuations of trigonometric sums using method of exponential couples.
- Utilisation of functional equations method in asymptotic problems of numbers theory.
- Crude functional equation for zeta-functions of quadratic forms.

There have been pursued 3 departmental and 1 high-budgetary schemes during 1991-2004. - Division of multiplicative and additive functions values.
- Functional equations method in theory of numbers.
- Recursive function theory
- Asymptotic problems of numbers theory research.

## Published in 2004:

- G. Belozorov, P. Varbanets, Diophantine equations with quadratic forms, Ann.. Univ. Sci. Budapest, Sect. Comp., 23(2004), 107-121.
- P. Varbanets, Integer primitive points on elliptic conus in arithmetic progression/ Ann. Univ. Sci. Budapest, Sect. Comp., 24(2004), 93-108.
- P. Varbanets, Diophantine equations with quadratic forms. Scientific notes of International university for the humanities, 1(2004), 132-147.
- N. Prossyanuk Solutions congruence division in the ring of the whole gaussian numbers, Mercury of KNU named after T. Shevtchenko, 1(2004), 48-56.
- N. Balamdina, About squared arithmetic function in the sense of Dirichlet over Z[i], X international scientific conference named after acad. M. Kravtchuka, Kyiv 2004, pages 304.
- U. Yershova, F. Kovaltchik, One asymptotic formula, X international scientific conference named after acad. M. Kravtchuka, Kyiv 2004, p. 377.
- P. Varbanets, About average square of a remainded term, Reports thesises VI International algebra and theoty of numbers conference, dedicated to 100-years anniversary of N.G. Tchudakov, Saratov, 2004
- F. Kovaltchik, About one additive problem, at the same place.
- O. Savastru, Divisors extended problem, at the same place.
- O. Savastru, Values functions distribution of gaussian numbers simple divisors, Thesises of International conference in memoriam of V.Y. Bunyakovskogo, Kyiv, 2004, 116-117.
- P. Varbanets, F. Kovaltchik, Diophantine equation with five squares on k and l – free numbers, at the same place, p.42
- P. Varbanets, Some problems of the Epstein zeta-function average value at the same place.
- A. Gvozdinskiy, V. Gubin, N. Yakimova, Predicative models of the knowledge representation, X International scientific conference “Theory and techniques of information emission, reception and processing” anniversary, Kharkov – Tuapse, 2004, 38-39.
- A. Gvozdinskiy, V. Gubin, N. Yakimova, О природе слабоструктурированных источников информации, там же, 94-95.

### 11 reports were presented during scientific conferences.

The basic results of the fundamental researches: new asymptotic values of quantity solutions of diophantine equations with quadratic formulas are set up, crude functional equation for Epstein zeta-function is found.

## Research scientific students’ work:

38 students took part in this research scientific work in 2004.

9 works have been published with students’ participation, among them – 4 articles and 5 thesises.

16 students reports took part at the scientific conferences ( Odessa, Kyiv, Novaya Kakhovka, Simpheropol).

2 rewards have been received during RSW competitions, one student (E. Berkovytch) became a student of the year, Odessa, 2004 (in nomination – young talants), one student (E. Berkovytch) received “Computer Systems Odessa” grant.

2 chair students circles are in work: cryptology circle, and theory of numbers circle; one seminar of discrete mathematics.