Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...

The notions of quasi-prime submodules and developed  Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...

is a vector space isomorphism of V" onto T(m). The tangent bundle 3(Af) of the manifold M consists of the ordered pairs (m, v) where mEM and vE T(m). Therefore, as a point set only, 3(Af) is M X V". We shall assume that the reader is familiar with the fibre space topology which is customarily assigned to 3(M). (For a description of this topology and the facts concerning fibre bundles which we s...

We study topology change in M theory compactifications on Calabi-Yau three-folds in the presence of G flux (the four form field strength). In particular, we discuss vacuum solutions in strongly coupled heterotic string theory in which the topology change is inevitable within a single spacetime background. For rather generic choices of initial conditions, the field equations drive the Kähler mod...