Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

We construct Lagrangian translating solitons by desingularizing the intersection points between Grim Reaper cylinders with same phase using special Lawlor necks. The resulting could have arbitrarily many ends and non-contractible loops.

Here we construct a fake smooth structure on a compact contractible 4-manifold W , where W is a well-known Mazur manifold obtained by attaching in two-handle to S x B along its boundary as in Figure 1. * Here we use the conventions of [2]. The results of this paper imply: Theorem 1. There is a smooth contractible 4-manifold V with dV = d W, such that V is homeomorphic but not diffeomorphic to W...

This paper analyzes contactual situations between many principals and many agents. Agents have private information and principals take actions. Principals can contract not only on the reports of the agents but also on the contracts offered by the other principals. Contracts are required to be representable in a formal language. The main result of the paper is a full characterization of the allo...

A triangulation of a surface is called q-equivelar if each of its vertices is incident with exactly q triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in equivelar triangulation of a surface. AMS classification : 57Q15, 57M20, 57N05.

The geodesic flow of any Riemannian metric on a geodesically convex surface of negative Euler characteristic is shown to be semi-equivalent to that of any hyperbolic metric on a homeomorphic surface for which the boundary (if any) is geodesic. This has interesting corollaries. For example, it implies chaotic dynamics for geodesic flows on a torus with a simple contractible closed geodesic, and ...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

Lickorish has constructed large families of contractible 4–manifolds that have knotted embeddings in the 4–sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of the complement of a knotted contractible manifold. Here we make a few observations regarding Lickorish’s construction, showing how to extend it to construct c...