in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

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.

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...

We prove that any complete hyperbolic 3–manifold with finitely generated fundamental group, with a single topological end, and which embeds into S is the geometric limit of a sequence of hyperbolic knot complements in S. In particular, we derive the existence of hyperbolic knot complements which contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3–manifold with t...

Let Γ be a torsion-free cocompact lattice in Aut(T1) × Aut(T2), where T1, T2 are trees whose vertices all have degree at least three. The group H2(Γ,Z) is determined explicitly in terms of an associated 2-dimensional tiling system. It follows that under appropriate conditions the crossed product C∗algebra A associated with the action of Γ on the boundary of T1 ×T2 satisfies rankK0(A) = 2 · rank...

We extend the techniques developed by Millson and Raghunathan in [MR] to prove nonvanishing results for the cohomology of compact arithmetic quotients M of hyperbolic n-space H with values in the local coefficient systems associated to finite dimensional irreducible representations of the group SO(n, 1). We prove that all possible nonvanishing results compatible with the vanishing theorems of [...

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...

We generalize a result of Sury [Sur92] and prove that uniform discreteness cocompact lattices in higher rank semisimple Lie groups (first conjectured by Margulis [Mar91]) is equivalent to weak form Lehmer’s conjecture. include short survey related results conjectures.

In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated with even integer weight vector-valued automorphic forms non-cocompact Fuchsian groups first kind. end, their L-functions and exponential sums have been discussed.