arXiv subjects
Publications and source records attributed to Gheorghe Ivan.
The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and corresponding examples are presented.
The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector space-groupoid.
We determine the fractional almost Poisson realizations for fractional Euler top system with one control. These realizations allow us to introduce a fractional Leibniz algebroid structure on R3 and also to define the q-fractional Euler top system with one control on a fractional Leibniz algebroid. Finally, the numerical integration of them are discussed.
The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the fractional stability of the fractional 2-dimensional fractional Toda lattice with one linear control.
The purpose of this paper is to study the transitive group-groupoids.
The main purpose of this paper is to propose six programs in C++ for matrix computations and solving recurrent equations systems with entries in min plus algebra.
The main purpose of this paper is to propose five programs in C++ for matrix computations and solving recurrent equations systems with entries in max plus algebra.
We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.
The aim of this paper is to present the stochastic Poisson equations associated to Lie algebroids. The stochastic Poisson equations associated to a refinement of a concrete principal bundle are determined.
We give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid.
The theory of derivative of noninteger order goes back to Leibniz, Liouville and Riemann. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics. In this paper we define the fractional tangent bundle on a manifold, using a method of Radu Miron. The fractional Leibniz algebroids are investigated. The associated objects have an geometric character. Some fractional dynamical systems on a fractional Leibniz algebroid are disscussed.
In this paper we introduce the $ε$ - revised system associated to a Hamilton - Poisson system. The $ε$ - revised system of the rigid body with three linear controls is defined and some of its geometrical and dynamical properties are investigated.
The main aim of this paper is to present a program on computer for decide if an universal algebra is a groupoid. Using the theory of groupoids and the program BGroidAP1 we prove a theorem of classification for the groupoids of type (4;2).