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Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H 0 , we employ Continuous Unitary Transformations (CUT) to obtain a "classical" effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed , as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U , first transition occurs at U = U c 1 , where spin and charge gaps both vanish and remain zero up to U = U c 2 . A gap-less state in charge and spin sectors characterizes a metal. For U > U c 2 spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.

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A static, asymptotically flat, spherically symmetric solutions is investigated in f(R) theories of gravity for a charged black hole. We have studied the weak field limit of f(R) gravity for the some f(R) model such as f(R) = R + epsilon h(R). In particular, weconsider the case lim_{R =0} {h(R)/ dh(R)/dR}=0 and find the space time metric for f(R) = R + {mu}^{4} /R and f(R) = R^{1-epsilon} theories of gravity far away a charged mass point

In this paper, using f (R) theory of gravity we explicitly calculate cosmological evolution in the presence of a perfect fluid source in four-and fivedimensional, spacetime in which this cosmological evolution in self-creation is presented by Reddy et al 2009 Int. J. Theor. Phys. 48 10. An exact cosmological model is presented using a relation between Einsteins gravity field equation components due to a metric with the same component from f (R) theory of gravity. Some physics and kinematical properties of the model are also discussed.

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