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IMCS/

About IMCS

The Institute of Mathematics was formed in 1964 on basis of Mathematical Department of the Institute of Physics and Mathematics, founded in 1961.

The main objectives in the work of the Institute are the following: to maintain existing research domains, to develop new directions in line with the Republic of Moldova needs, to integrate into the world science, to train highly qualified specialists.

In mathematical logic the functional completeness problems for intuitionistic propositional logic and for first-order predicate logic have been solved. It has been demonstrated that there does not exist algorithm for solving the problem of functional expressibility in the modal logic S4 and in Gödel-Löb logic.

In domain of algebra, keeping on the investigations of Academician V. Andrunachievici, new results in the structural theory of algebras without nilpotent elements, in the theory of varieties and strongly regular algebras have been obtained. The properties of quasiregularity and primitivity relative to right ideals have been studied. In the theory of rings and modules there have been studied radicals, torsions and localizations. In the case of some special constructions (adjunct situations, Morita contexts) the behavior of torsions, localizations and lattices of submodules at the transition from one category to another has been studied by means of principal functors.

In theory of binary and n-ary quasigroups various problems of algebra, geometry and combinatorics have been studied. Various applications of quasigroups in encryption and coding of information have been studied. Topological aspects of algebraic systems have been represented by constructing of the general theory of radicals of rings and topological modules, as well as by investigation of possibilities of topologizing and continuation of the ring topology and by studying of the structure of local compact rings. The properties of maximal series in lattice of all group topologies in abelian groups have been studied.

The existence of an infinite set of Fiodorov groups in Lobacevski spaces has been demonstrated for the first time using a constructive approach, this leading to changes in arythmicity hypothesis. New geometric methods for obtaining of discrete groups and decompositions of Lobacevski space have been developed, as well as methods for construction and studying of hyperbolic varieties. In normal linear spaces and in graphs the elements of the convexity theory have been developed.

The algebraic invariants method has been developed, in recent years being completed by the Lie algebras methods. Geometric properties of invariants for various nonlinear differential equations have been studied. Normal finite smooth forms of local families of vector fields in a neighborhood of an invariant variety have been described.

Solvability of mixed problems for non-stationary partial differential equations have been demonstrated; large-time asymptotics of solutions have been obtained.

Methods and algorithms for minimizing of concave linear piecewise functions on the polyhedral set of solutions of the system of linear inequalities have been studied. Algorithms for minimizing of such kind of functions on the set of solutions of polyhedral of linear inequalities when the objective function has a form of the sum of minimums of sets of linear functions have been proposed. Polynomial and strongly polynomial algorithms for solving of combinatorial problems related to finding of the optimal configuration in oriented graphs and optimal road in networks have been developed. A game variant of the discrete optimal control problem has been investigated; the existence theorems of Nash equilibrium situation for discrete dynamic games has been demonstrated.

Macroeconomic and interindustry models have been developed,as well as the corresponding programs for prognosis of the national economic development.

In domain of computational mathematics and numerical methods there have been developed, theoretical grounded and applied methods for solving of some problems of gravitational gas dynamics in conditions of thermal conductivity with equations of state well approximating the real conditions. Methods for numerical modeling of non-stationary processes in deformable bodies on their interaction have been proposed.

Effective methods based on formal grammars and languages for development of application and system software have been implemented. A computational noncommutative algebra system for calculation of Gröbner basis, Anick resolution, Hilbert series and for prediction of the infinite obstructions behavior based on their finite component have been developed. Formal models of computation based on universal Turing machines and molecular calculations have been constructed. A toolkit for building and managing of computational lexicons has been developed, being used in development of RomSP package – a spellchecker for Romanian language.

A conceptual structure of the decision support systems (DSS) has been proposed and founded, constituting a base for DSS development for specific domains addressing poorly structured problems.

A concept of Information Society creation in the Republic of Moldova has been proposed.

Methods for implementation of discrete simulation languages, algorithms for visualization and analysis of the experiments results, for automatization of design and implementation of problem-oriented simulation systems have been developed.

Information-analytical system "Scientific potential of the Republic of Moldova" containing information about research institutions and persons with scientific degrees in the country, as well as toolkit for analysis of such information has been developed.