41 research outputs found
Differential game with many pursuers when controls are subjected to coordinate-wise Integral constraints
No full textIn this paper, we study a differential game of many pursuers and one
evader in R2.The motions of all players are simple. An integral constraint
is imposed on each coordinate of the control functions of players. We say
that pursuit is completed if the state of a pursuer coincides with that
of the evader at some time. The pursuers try to complete the pursuit,
and the evader tries to avoid this. Sufficient conditions for completion
of the differential game were obtained. The strategies of the pursuers
are constructed based on the current values of control parameter of the
evader. Also an illustrative example is provided
A description of an automorphism of a split metacyclic p-group
No full textA map on a group is not necessarily an automorphism on the group. In this paper we determined the necessary and sufficient conditions of a map on a split metacyclic p-group to be an automorphism, where we only considered p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We considered the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then used the relations and the regularity of the split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism
A description of an automorphism of a non-split metacyclic p-group
Get PDFA map on a group is not necessarily an automorphism on the group. In this paper we study the necessary and sufficient conditions for a map on a non-split metacyclic p-group to be an automorphism, where we only consider p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We consider the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then use the relations and the regularity of the non-split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism
A description of an automorphism of a split metacyclic p-group
Get PDFA map on a group is not necessarily an automorphism on the group. In this paper we determined the necessary and sufficient conditions of a map on a split metacyclic p-group to be an automorphism, where we only considered p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We considered the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then used the relations and the regularity of the split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism
Approximately cubic funtional equations and cubic multipliers.
Get PDFIn this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions
Evasion differential game of two evaders and one pursuer with integral constraints
Get PDFA simple motion evasion differential game of two evaders and one pursuer was studied. Control functions of all players are subjected to integral constraints. We say that evasion is possible if the state of at least one of the evaders does not coincide with that of the pursuer. We proved that if the total energy of the evaders is greater than or equal to the energy of the pursuer, then evasion is possible. Though the game is considered in a plane, the results of the paper can be easily extended to ℝn
Construction of strategies of pursuers in a differential game of many players with state and integral constraints
Get PDFThe approach of a group of controlled objects, the pursuers, to another one, the evaders, is considered. The motions of all the objects are described by simple differential equations. The control functions of players are subjected to integral constraints. The amount of control resources such as fuel, energy etc. are described by such constraints. Given a non-empty convex subset of Rn all objects move in this set. If the position of each evader yj , j ∈ {1, 2, ..., k}, coincides with the position of a pursuer xi, i ∈ {1, ..., m}, at some time tj , i.e. xi(tj ) = yj (tj ), then we say that pursuit can be completed. The total resource of the pursuers is assumed to be greater than that of the evaders. We show that pursuit can be completed in this differential game
Pursuit differential game of two pursuers and one evader in ℝ2 with coordinate-wise integral constraints
Get PDFA pursuit differential game of two pursuers and one evader in ℝ2 is studied. All players' controls are subjected to coordinate-wise integral constraints. By definition, pursuit is completed if the state of a pursuer coincides with that of the evader at some time. The problem is to find conditions of completion of pursuit. We show that if the energy vector of the evader belongs to a polygon, then pursuit can be completed
Random stability and hyperstability of multi-quadratic mappings
Get PDFIn this paper, we introduce a new quadratic functional equation. In light of this equation, we define the multi-quadratic mappings and reduce the system of n equations defining the
multi-quadratic mappings to a single equation. We also obtain some stability and hyperstability results concerning multi-quadratic mappings in the setting of random normed spaces
