The aim of this paper is to give some basic properties of the symmetric groupoid of an arbitrary ... more The aim of this paper is to give some basic properties of the symmetric groupoid of an arbitrary or finite set. The determination of subgroupoids and related topics on the symmetric groupoid of a finite set is discussed.
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure w... more 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 new concept of vector groupoid has applications in geometry and other areas. 1
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure w... more 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 new concept of vector groupoid has applications in geometry and other areas. 1
In this paper we introduce the concept of generalized vector groupoid. Several properties of them... more In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established. 1
Abstract. In this paper we study the differential systems on Leibniz algebroids. We introduce a c... more Abstract. In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These types of algebroids are used in the presentation of associated differential systems. We give some interesting examples of differential systems on algebroids and the orbits of the solutions of corresponding systems are established. 1 1
In this paper we introduce the ε -revised system associated to a Hamilton -Poisson system. The ε ... more 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. 1
In this paper we construct the inductive limit of an inductive system of Lie groupoids. Also, som... more In this paper we construct the inductive limit of an inductive system of Lie groupoids. Also, some properties of inductive limits of Lie groupoids are established.
The aim of this paper is to present the stochastic Poisson equations associated to Lie algebroids... more 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.
In this paper we give three programs on computer for finding the subgroupoids, wide subgroupoids ... more In this paper we give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid. Applying these programs for groups, we can determine all subgroups and normal
We refer to the anchored vector bundles and Lie algebroids. The main purpose of this paper is to ... more We refer to the anchored vector bundles and Lie algebroids. The main purpose of this paper is to establish several remarkable properties of linear connections on Lie algebroids.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also... more The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
Numerous Mircea Puta's papers were dedicated to the study of Maxwell - Bloch equations. The m... more Numerous Mircea Puta's papers were dedicated to the study of Maxwell - Bloch equations. The main purpose of this paper is to present several types of fractional Maxwell - Bloch equations.
In this paper we introduce the " - revised system associated to a Hamil- ton - Poisson syste... more In this paper we introduce the " - revised system associated to a Hamil- ton - Poisson system. The " - revised system of the rigid body with three linear controls is defined and some of its geometrical and dynamical properties are investigated. 1
In this paper we present an algorithm for finding of group-subgroupoids of a finite group-groupoi... more In this paper we present an algorithm for finding of group-subgroupoids of a finite group-groupoid. Acknowledgments. The authors are very grateful to the reviewers for their comments and suggestions. References [1] R. Brown, Topology and Groupoids, BookSurge LLC, U.K., 2006. [2] R. Brown and C.B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Kon. Nederl. Akad. Wet., 79 (1976), 296-302. [3] M. Degeratu, Gh. Ivan and M. Ivan, On the cyclic subgroupoids of a Brandt groupoid, Proceed. Int. Conf. Comp., Commun. Control (ICCCC 2006), Baile Felix-Oradea. Vol. I, Suppl. Issue (2006), 181 -186. [4] Gh. Ivan, Algebraic constructions of Brandt groupoids, Proceedings of the Algebra Symposium, ”BabeşBolyai” University, Cluj-Napoca, (2002), 69-90. [5] Gh. Ivan and G. Stoianov, The program BGroidAP2 for determination of all subgroupoids of a Brandt groupoid, Analele Univ. de Vest, Timişoara, Seria Mat.-Inf., 42, No 1 (2004), 93-118. [6] M. Ivan, A...
The main purpose of this paper is to describe the fractional Euler Lagrange equations on Lie alge... more The main purpose of this paper is to describe the fractional Euler Lagrange equations on Lie algebroids. In the case when the Lie algebroid is the direct product of the tangent bundle over a manifold with a Lie algebra, then the fractional Euler-Lagrange equations are exactly the fractional Wong equations. M.S.C. 2000: 17B66, 53C05.
In this paper we investigate the dynamical behavior of fractional differential system associated ... more In this paper we investigate the dynamical behavior of fractional differential system associated to 5D Maxwell-Bloch model in terms of fractional Caputo derivatives.
We define the notion of vector space-groupoid. The main purpose of this paper is to give the basi... more We define the notion of vector space-groupoid. The main purpose of this paper is to give the basic properties of vector space-groupoids.
The aim of this paper is to give some basic properties of the symmetric groupoid of an arbitrary ... more The aim of this paper is to give some basic properties of the symmetric groupoid of an arbitrary or finite set. The determination of subgroupoids and related topics on the symmetric groupoid of a finite set is discussed.
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure w... more 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 new concept of vector groupoid has applications in geometry and other areas. 1
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure w... more 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 new concept of vector groupoid has applications in geometry and other areas. 1
In this paper we introduce the concept of generalized vector groupoid. Several properties of them... more In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established. 1
Abstract. In this paper we study the differential systems on Leibniz algebroids. We introduce a c... more Abstract. In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These types of algebroids are used in the presentation of associated differential systems. We give some interesting examples of differential systems on algebroids and the orbits of the solutions of corresponding systems are established. 1 1
In this paper we introduce the ε -revised system associated to a Hamilton -Poisson system. The ε ... more 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. 1
In this paper we construct the inductive limit of an inductive system of Lie groupoids. Also, som... more In this paper we construct the inductive limit of an inductive system of Lie groupoids. Also, some properties of inductive limits of Lie groupoids are established.
The aim of this paper is to present the stochastic Poisson equations associated to Lie algebroids... more 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.
In this paper we give three programs on computer for finding the subgroupoids, wide subgroupoids ... more In this paper we give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid. Applying these programs for groups, we can determine all subgroups and normal
We refer to the anchored vector bundles and Lie algebroids. The main purpose of this paper is to ... more We refer to the anchored vector bundles and Lie algebroids. The main purpose of this paper is to establish several remarkable properties of linear connections on Lie algebroids.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also... more The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
Numerous Mircea Puta's papers were dedicated to the study of Maxwell - Bloch equations. The m... more Numerous Mircea Puta's papers were dedicated to the study of Maxwell - Bloch equations. The main purpose of this paper is to present several types of fractional Maxwell - Bloch equations.
In this paper we introduce the " - revised system associated to a Hamil- ton - Poisson syste... more In this paper we introduce the " - revised system associated to a Hamil- ton - Poisson system. The " - revised system of the rigid body with three linear controls is defined and some of its geometrical and dynamical properties are investigated. 1
In this paper we present an algorithm for finding of group-subgroupoids of a finite group-groupoi... more In this paper we present an algorithm for finding of group-subgroupoids of a finite group-groupoid. Acknowledgments. The authors are very grateful to the reviewers for their comments and suggestions. References [1] R. Brown, Topology and Groupoids, BookSurge LLC, U.K., 2006. [2] R. Brown and C.B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Kon. Nederl. Akad. Wet., 79 (1976), 296-302. [3] M. Degeratu, Gh. Ivan and M. Ivan, On the cyclic subgroupoids of a Brandt groupoid, Proceed. Int. Conf. Comp., Commun. Control (ICCCC 2006), Baile Felix-Oradea. Vol. I, Suppl. Issue (2006), 181 -186. [4] Gh. Ivan, Algebraic constructions of Brandt groupoids, Proceedings of the Algebra Symposium, ”BabeşBolyai” University, Cluj-Napoca, (2002), 69-90. [5] Gh. Ivan and G. Stoianov, The program BGroidAP2 for determination of all subgroupoids of a Brandt groupoid, Analele Univ. de Vest, Timişoara, Seria Mat.-Inf., 42, No 1 (2004), 93-118. [6] M. Ivan, A...
The main purpose of this paper is to describe the fractional Euler Lagrange equations on Lie alge... more The main purpose of this paper is to describe the fractional Euler Lagrange equations on Lie algebroids. In the case when the Lie algebroid is the direct product of the tangent bundle over a manifold with a Lie algebra, then the fractional Euler-Lagrange equations are exactly the fractional Wong equations. M.S.C. 2000: 17B66, 53C05.
In this paper we investigate the dynamical behavior of fractional differential system associated ... more In this paper we investigate the dynamical behavior of fractional differential system associated to 5D Maxwell-Bloch model in terms of fractional Caputo derivatives.
We define the notion of vector space-groupoid. The main purpose of this paper is to give the basi... more We define the notion of vector space-groupoid. The main purpose of this paper is to give the basic properties of vector space-groupoids.
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